Semiconductor Manufacturing

Run-to-Run Control in
SEMICONDUCTOR
MANUFACTURING
Edited by
James Moyne
Enrique del Castillo
Arnon Max Hurwitz
CRC Press
Boca Raton London New York Washington, D.C.
Library of Congress Cataloging-in-Publication Data
Moyne, James.
Run-to-run control in semiconductor manufacturing / by James Moyne, Enrique Del
Castillo, and Arnon Max Hurwitz.
p. cm.
Includes bibliographical references and index.
ISBN 0-8493-1178-0 (alk. paper)
1. Semiconductors—Design and construction. 2. Semiconductor industry—Production
control. 3. Electronic packaging 4. Production management. I. Del Castillo, Enrique. II.
Hurwitz, Arnon Max. III. Title.
621.3815′2—dc21 00-059910
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Preface
The goal of this book is to provide a practical guide to the understanding, imple-
mentation, and use of run-to-run (R2R) control in semiconductor manufacturing as
well as manufacturing in general. The target audience is intentionally wide and
includes technology directors and strategists, technical managers, control engineers,
process engineers, systems designers, integrators, and users. The aim of the authors
is to provide insight into the development, integration, application, enhancement,
and operation of R2R control. In addition, the book points to new directions in R2R
process control, some of which have only recently been discussed in the literature.
These directions point to avenues of opportunity for developing even more effective
R2R control strategies for the fabricator of the future.
WHO SHOULD USE THIS BOOK

The benefits of R2R control implementation are wide-ranging and affect the many
levels of the manufacturing hierarchy. As such, this book is structured to provide
benefit to readers at each of these levels. For example, the following is a sample of
who might utilize this book as a guide and aid in implementing an effective R2R
control initiative either on a single tool, or facility-wide in a fabrication facility:
• A corporate-level technical strategist would utilize the book as a resource

to:
1. Collect convincing evidence indicating that R2R control will provide
significant competitive advantage.
2. See that proven R2R control solutions are available.
3. Read that benefits, such as Cpk and yield, have been proven and quan-
tified.
4. Plan a strategy for integration.
• A facility director would utilize the book for directing facility-wide R2R
control development and deployment. Specifically, the facility director
would utilize the book to define plans for:
1. Identifying target applications for R2R control.
2. Performing the necessary requirements analysis and identifying equip-
ment, metrology, control, and integration deficiencies.
3. Identifying the “control problem” for each candidate process, including
process quality metrics.
4. Determining the controllability of each candidate process.
5. Developing stand-alone control solutions for each candidate process.
6. Integrating these control solutions for a fab-wide R2R control solution.

• The process engineer for each process would utilize the book to develop
an effective control solution for his/her process. The book would aid the
process engineer in:
1. Process input and output parameter selection and refinement.
2. Process identification for control.
3. Development of an industrial-quality solution that addresses require-
ments of parameter bounds, discretization, parameter weighting, pro-
cess and metrology noise rejection, etc.
4. Development, integration, and testing of the control software solution.
HOW TO READ THIS BOOK

We have put this book together with the intent that it be of use to the beginning
reader in R2R control as well as the specialist seeking detailed information on R2R
control methods and/or recent directions and developments. In order to achieve this
we have divided the text into six parts plus a conclusion. The Introduction and first
chapter of each part* should be read first by the reader new to the subject. These
first chapters have been chosen because they are, on the whole, more introductory
and less burdened with technicalities than later chapters in the same part. Specialist
readers may, of course, pick and choose as they wish.
* Excerpt for Part 6: Advanced Topics.

Editors
James Moyne, Ph.D., is an Associate Research Scientist in the Electrical Engi-
neering and Computer Science Department at the University of Michigan, and is
President and co-founder of MiTeX Solutions, Inc., Canton, Michigan. (MiTeX
Solutions was acquired by Brooks Automation, Inc. in June 2000.) James received
his B.S.E.E. and B.S.E. in math, and his M.S.E.E. and Ph.D. in electrical engineering
from the University of Michigan. He has over 30 refereed publications in the areas
of discrete control, advanced process control, databases, sensor bus technology, and
communications, and is the author of the patent on the Generic Cell Controller run-
to-run control enabling technology. He is also the author of a number of SEMI
(semiconductor manufacturing) international standards in the areas of sensor bus
systems and communications, and has received four SEMI outstanding achievement
awards and a technology transfer award.
James lives in Canton, Michigan, where his hobbies include writing music and
playing the keyboard and sax. He is a published poet, has released a solo album of
New Age music, and is a member of Cornerstone, which is currently working on
its second Rock/Pop album.
Enrique del Castillo, Ph.D., is an Associate Professor in the Harold and Inge
Marcus Department of Industrial and Manufacturing Engineering at the Pennsylvania
State University. He holds a Ph.D. in industrial engineering from Arizona State
University, and a Master of Engineering in operations research and industrial engi-
neering from Cornell University. Dr. Castillo’s research interests include quality
engineering and applied statistics, with particular emphasis on response surface
methodology and time series control. He has over 35 papers in journals such as IIE
Transactions, Journal of Quality Technology, Metrika, Communications in Statistics,
International Journal of Production Research, European Journal of Operational
Research, and Journal of the Operational Research Society. He has been awarded
an NSF CAREER grant for research in semiconductor manufacturing process con-
trol. Dr. Castillo is an Associate Editor of the IIE Transactions on Quality and
Reliability Engineering journal and a member of the editorial board of the Journal
of Quality Technology.
Arnon Max Hurwitz, Ph.D., is Managing Director of Qualtech Productivity

Solutions, South Africa, and Vice President of MiTeX Solutions, Inc., Canton,
Michigan. He gained his M.S. in applied statistics from Oxford University, England,
and his Ph.D. in mathematical statistics from the University of Cape Town, South
Africa. Dr. Hurwitz lectured at the Graduate School of Business, Cape Town, and
at Guilford College, North Carolina, and was Head of the Mathematics Department
at Oak Ridge Military Academy, North Carolina. He was Quality Engineer at Corning

Glass, Inc., Telecommunications Division, in Wilmington, North Carolina, and Cor-
porate Statistician for HIMONT USA, Inc., in Houston, Texas. He was a Senior
Statistician and a Senior Project Manager at the U.S. semiconductor industry con-
sortium SEMATECH in Austin, Texas. In 1997 he became Vice President of MiTeX
Solutions, Inc., and also founded Qualtech Productivity Solutions, a corporation
supplying statistical analytic services to finance and industry.
Arnon lives near Cape Town, South Africa, and works internationally. He has
published a number of statistical and control-theoretic works in leading U.S. journals,
and has contributed chapters to several books. He has a wife and three children. His
hobbies are reading, writing, fly-fishing, and trying to play the fiddle.

Acknowledgment
The authors would like to thank those who contributed additional chapters for this
book, and those who co-authored chapters, for their excellent and invaluable con-
tributions. Names and contact information for all contributors follow, and are listed
in alphabetical order.
In addition, we would like to thank Nora Konopka of CRC Press for her
unflagging support and enthusiasm for the project, as well as all those at CRC Press
who translated a complex manuscript into publishable form.
Of course, technical work of this nature has required the support, over quite a
number of years, of many different entities and personalities, not the least of which
were the research institutions that gave the technology birth — namely Massachu-
setts Institute of Technology and the University of Michigan — and the institutes
that funded further research. In this case it was the semiconductor research corpo-
ration SEMATECH International, its member companies, and the tool vendors —
all members of SEMI/SEMATECH — who made their machines and their expert
staffs available for our numerous site experiments. There are too many names
involved to mention, and we thank them one and all.
Lastly, we thank the reviewers of our book for their valuable comments and
suggestions which added significantly to the value of the text.
James Moyne, Enrique Del Castillo, and Arnon Max Hurwitz

Contributors
Duane S. Boning Enrique Del Castillo
Microsystems Technology Laboratories Department of Industrial &
Massachusetts Institute of Technology Manufacturing Engineering
Cambridge, MA 02139 USA Pennsylvania State University
e-mail: boning@mtl.mit.edu 207 Hammond Building
University Park, PA 16802 USA
Jonathan Chapple-Sokol e-mail: exd13@psu.edu
IBM Microelectronics Division Chadi El Chemali
1000 River Road B975/E Electrical Engineering & Computer
Essex Junction, VT 05452 USA Science
e-mail: chapple@us.ibm.com University of Michigan
2360 Bonisteel Avenue
Nauman A. Chaudhry Ann Arbor, MI 48109 USA
One Oracle Drive e-mail: ccel@umich.edu
Nashua, NH 03062 USA
email: nchaudhr@us.oracle.com Ruey-Shan Guo
Department of Industrial Management &
Business Administration
Argon Chen National Taiwan University,
Graduate Institute of Industrial 50, Lane 144, Sec. 4
Engineering Keelung Road
National Taiwan University Taipei, Taiwan
1, Roosevelt Road e-mail: rsguo@ccms.ntu.edu.tw
Sec.1, Taipei, Taiwan 106
e-mail: achen@ccms.ntu.edu.tw Arnon Max Hurwitz
Qualtech Productivity Solutions
Jin-Jung Chen Sanclare Building,
Department of Mechanical Engineering Dreyer Street
National Taiwan University Claremont 7735 South Africa
Taipei, Taiwan e-mail: qualtech@iafrica.com
Kareemullah Khan
John Colt RA1-303
IBM Microelectronics Division Intel Corportaion
1000 River Road B975/E 5200 N.E. Elam Young Parkway
Essex Junction, VT 05452 USA Hillsboro, OR 97124 USA
e-mail: a442991@us.ibm.com e-mail: kareemullah.khan@intel.com

James Moyne Elke A. Rundensteiner
Electrical Engineering & Computer Department of Computer Science
Science Worcester Polytechnic Institute
University of Michigan 100 Institute Road
2360 Bonisteel Avenue Worcester, MA 01609 USA
Ann Arbor, MI 48109 USA email: rundenst@owl.WPI.EDU
e-mail: moyne@umich.edu
Paul H. Smith
William Moyne IBM Microelectronics Division
Virtual Ink 1000 River Road B975/E
56 Roland Street, Suite 306 Essex Junction, VT 05452 USA
Boston, MA 02129 USA e-mail: smitpaul@us.ibm.com
e-mail: william.moyne@virtual-ink.com
Taber Smith
Microsystems Technology Laboratories
Rock Nadeau Massachusetts Institute of Technology
IBM Microelectronics Division Cambridge, MA 02139 USA
1000 River Road B975/E e-mail: taber@mit.edu
Essex Junction, VT 05452 USA
e-mail: rnadeau@us.ibm.com Victor Solakhian
Brooks Automation, Inc.
Zhe Ning 15 Elizabeth Drive
(Information Unavailable) Chelmsford, MA 05124 USA
Victor.Solakhian@brooks.com
Tarun Parikh
Robert A. Soper
SEMATECH
Texas Instruments, Inc.
2706 Montopolis Drive
13570 N. Central Expressway, MS 3701
Austin, Texas 78741 USA
Dallas, TX 75243 USA
e-mail:
e-mail: soper@ti.com
Nital S. Patel Joe White

Texas Instruments, Inc. Crystal Semiconductor
13121 TI Boulevard, MS 352 USA
Dallas, TX 75243 USA e-mail: joew@crystal.cirrus.com
e-mail: nsp@ti.com
Jinn-Yi Yeh
Department of Industrial Engineering
The Dayeh University
112, Shan-Jiau Road
Da-Tsuen, Changhua, 5105
Taiwan, R.O.C.
email: jyeh@mail.dyu.edu.tw

Foreword
Mark Melliar-Smith, President and CEO, and Randy Goodall, Associate
Director of Productivity and Infrastructure
International SEMATECH, Austin, Texas
Control is essential for all manufacturing, but every day in the semiconductor
industry more than a quadrillion transistors, each with dimensions ranging from a
fraction of a micrometer down to tens of atoms, must be profitably fabricated. To
manage the exponentially rising cost of meeting this manufacturing challenge, pro-
cess equipment from each technology generation is increasingly pressed into service
to support the next generation. In the early years of the twenty-first century, new
processes for nearly every aspect of transistor fabrication, from thin gate and
source/drain to interconnecting metal and dielectrics, must be introduced in semi-
conductor factories around the world. The International Technology Roadmap for
Semiconductors shows starkly that the timing for these technology changes is so
short that we will necessarily “test them in combat.” Active control mechanisms,
such as the run-to-run methods described in this book, are mandatory if the industry
is to keep pace with the world’s demand for new electronic products.
During this period of unprecedented technological advancement, semiconductor
companies are also initiating the new generation of larger, 300 mm silicon wafers.
The product value of even a single 300 mm wafer containing more than 1000 advanced
chips dictates the use of active process control with a new level of urgency. Although
a staggering challenge, the 300 mm transition also brings with it a new opportunity.
International SEMATECH’s member companies have collectively and comprehen-
sively set a high bar for equipment performance in all areas, including factory
communications and recipe management. Process control implementations should
now become more straightforward.
Widespread deployment of run-to-run control has been somewhat of a struggle
because of the required critical mass of software and communications capability
necessary in both process equipment and factory systems. Equally scarce were the
people to drive the development, engineering, and adoption of these techniques.
With the new generation of software-savvy engineers at both semiconductor and
supplier companies, this is changing. In addition, new sensors and other lower-cost
measurement options are becoming available to reduce the time, money, and logistics
needed to support cost-effective control implementations.
Interest in better control of process equipment arose at SEMATECH in the early
1990s. The run-to-run method was then, and continues to be, the least equipment-
invasive control scheme that demonstrates real benefit. It is gratifying to see the
ideas supported by SEMATECH reach a level of maturity and industry acceptance
that supports treatment in a book of their own. This volume represents the continuance

of nearly a decade of active work and collaboration by these authors, in both the
academic setting of their respective universities as well as the industry context of
SEMATECH. Their long-time focus on the specific control problems of semicon-
ductor manufacturing imbue this effort with relevance and practicality. We believe
this book will find an industry ready for standard approaches and solutions for run-
to-run control. Our hope is that it accelerates the emergence of the new era of
sophistication in controlling the manufacturing marvel that is the semiconductor
industry.

Table of Contents
Introduction
James Moyne and Arnon M. Hurwitz
PART 1: FOUNDATION FOR CONTROL
Chapter 1
Process Control in the Semiconductor Industry
Taber H. Smith, Duane S. Boning, and James Moyne
Chapter 2
Process Control and Optimization Methods for Run-to-Run Application
Enrique Del Castillo and Arnon M. Hurwitz
PART 2: R2R CONTROL ALGORITHMS
Chapter 3
Basic R2R Control Algorithms
William Moyne
Chapter 4
Learning and Optimization Algorithms for an Optimizing Adaptive Quality
Controller
Enrique Del Castillo
Chapter 5
An Adaptive Run-to-Run Optimizing Controller for Linear and Nonlinear
Processes
Arnon M. Hurwitz and Enrique Del Castillo
Chapter 6
A Comparative Analysis of Run-to-Run Control Algorithms in the
Semiconductor Manufacturing Industry
Zhe Ning, James Moyne, Taber Smith, Duane Boning, Enrique Del Castillo,
Jinn-Yi Yeh, and Arnon M. Hurwitz

PART 3: INTEGRATING CONTROL
Chapter 7
Existing and Envisioned Control Environment for Semiconductor
Manufacturing
James Moyne and Joe White
Chapter 8
Design Requirements for an Integrative R2R Control Solution
James Moyne
Chapter 9
The Generic Cell Controller
James Moyne
Chapter 10
Derivation of a Piggyback Run-to-Run Control Solution Design
James Moyne
Chapter 11
Integrated Run-to-Run Control Solution Examples
James Moyne
Chapter 12
Design and Optimization of an Optimizing Adaptive Quality Controller,
Generic Cell Controller Enabled Solution
Enrique Del Castillo, Jinn-Yi Yeh, James Moyne, and Victor Solakhian
PART 4: CUSTOMIZATION METHODOLOGY
Chapter 13
Case Study: Furnace Capability Improvement Using a Customized
Run-to-Run Control Solution
Arnon Hurwitz and James Moyne
Chapter 14
Process Recipe Optimization

PART 5: CASE STUDIES
Chapter 15
Multizone Uniformity Control of a CMP Process Utilizing a Pre- and
Postmeasurement Strategy
James Moyne, Chadi El Chemali, Kareemullah Khan, Rock Nadeau,
Paul Smith, John Colt, Jonathan Chapple-Sokol, and Tarun Parikh
Chapter 16
Control of Photolithography Alignment
Nital S. Patel and Robert Soper
Chapter 17
Age-Based Double EWMA Controller and Its Application to a CMP
Process
Argon Chen and Ruey-Shan Guo
PART 6: ADVANCED TOPICS
Chapter 18
Advancements in Chemical Mechanical Planarization Process Automation
and Control
James Moyne
Chapter 19
An Enhanced Exponentially Weighted Moving Average Controller for
Processes Subject to Random Disturbances
Ruey-Shan Guo, Argon Chen, and Jin-Jung Chen
Chapter 20
Enabling Generic Interprocess Multistep Control: the Active Controller
Nauman Chaudhry, James Moyne, and Elke A. Rundensteiner
PART 7: SUMMARY AND CONCLUSIONS
List of Acronyms

Dedication
This book is dedicated to our wives,

Jennifer, Monica, and Mary Frances,
who make it all worthwhile.

List of Acronyms
AC Active Controller
AEC advanced equipment control
APC advanced process control
ARL average run length
AT&T American Telephone and Telegraph
BCAM Berkeley Computer-Aided Manufacturing
CDM (SAN) common device model
CIM computer-integrated manufacturing
CMP chemical mechanical planarization or chemical mechanical
polishing
COO cost of ownership
CORBA Common Object Request Broker Architecture
Cpk process capability
CSRS Control Systems Requirements Specification
CSSWG Control Systems Specification Working Group
CTE center-to-edge (nonuniformity)
CVD chemical vapor deposition
DBMS database management system
d-EWMA double exponentially-weighted moving average
DOE design of experiments
DOF depth of focus
ECA event–condition–action (rules)
ECS-TF Equipment Control Systems Task Force (of SEMI)
EPC engineering process control
E-R entity-relationship (database modeling)
EWMA exponentially-weighted moving average
FDC fault detection and classification
FWI full wafer interferometry
GCC Generic Cell Controller
GEM Generic Equipment Model
GM gradual mode (algorithm)
GMt time-based (extended) gradual model (algorithm)
GUI graphical user interface
HSMS high-speed message service
I/O input/output
I300I International 300-mm Initiative
IBM International Business Machines
ILD interlevel dielectric

IMA integrated moving average
IMC internal model control
KIRC knowledge-based interactive run-to-run controller
MES manufacturing execution system
MIMO multiple input, multiple output
MMSE minimum mean squared error
MSD mean square(d) deviation
MSE mean square error
NCS (SAN) Network Communication Standard
NP non-product (wafers)
NSF National Science Foundation
OAQC optimizing adaptive quadratic controller
OBEM Object-Based Equipment Model
OEE overall equipment effectiveness
OEM original equipment manufacturer
OES optical emission spectroscopy
OMT object modeling technique
PCC predictor–corrector controller
PFM Process Flow Specification Manager
PID proportional integral differential
PLS partial least squares
PM process maintenance
R2R run-to-run
RHS right-hand side
RLS recursive least squares
RR removal rate
SAN Sensor Actuator Network
SDM (SAM) specific device model
SECS SEMI Equipment Communication Standard
SEMATECH Semiconductor Manufacturing Technology
SEMI Semiconductor Equipment and Materials International
SIA Semiconductor Industry Association
SISO single input, single output
SPC statistical process control
SRC Semiconductor Research Corp.
TI Texas Instruments
USD United States dollars
VLSI very large-scale integration
WECO Western Electric Co. (SPC rules)
WMSE weighted mean-squared error

Introduction
James Moyne and Arnon Max Hurwitz
The semiconductor manufacturing industry is arguably the fastest evolving major

industry in the world. Success in the industry requires constant attention to the state
of the art in process tools, process chemistries and physics, and techniques for pro-
cessing and process improvement. The two major fronts along which product advance-
ments are made in this industry are minimum feature size and wafer dimension. At
the time of this writing, the “state-of-the-art” minimum feature size was in the 250 to
180 nm range, while processing on 300 mm wafers was becoming more prevalent.
As feature sizes shrink and wafer sizes increase, the industry must innovate to
maintain acceptable product yield, throughput, and overall equipment effectiveness
(OEE). Some manufacturing capability attributes, such as non-product wafer (NPW)
usage and wafer scrap, must actually be improved in the transition to larger wafer
sizes because of the increased value of 300 mm wafers (raw and processed). For
example, one user reported that a raw 300 mm wafer cost approximately $1500 to
$2000.* Although the cost of a raw 300 mm wafer may ultimately drop to a few
hundred dollars, the value of a processed 300 mm wafer increases during its many
process steps, ultimately representing more than 1000 devices worth $10 to $100
each. Faults introduced in any stage of manufacturing will often only show up in
final electronic testing, and the consequent device loss may be (cost-wise) quite
devastating — especially with these large-diameter wafers.
Although a number of solutions, including improved equipment design and
process innovation, will continue to aid in making these transitions cost effective,
it has become clear that they are no longer sufficient. Specifically, it has become
generally accepted that process and wafer quality sensing and subsequent process
tuning will be required to complement these equipment and process improvements.
The main form of process tuning that is being implemented as a standard process
and equipment control solution in the industry is run-to-run (R2R) control. As will
be shown throughout this book, R2R control is now a proven and available technol-
ogy, and has become a critical component of the success of existing and next-
generation fabrication facilities.
In this introduction we provide important information that lays a foundation for
understanding the concepts, motivation, and directions presented throughout the text.
Specifically, in the following sections we provide a definition of R2R control, explore
the qualities of a VLSI process candidate for R2R control, describe basic character-
istics of R2R control systems, provide a brief history of the development of R2R
control as a component of advanced process control, and summarize the layout of
the book.
* W. Rozich, IBM, SEMATECH AEC/APC Symposium XI, Vail, CO (1999).

1 WHAT IS RUN-TO-RUN CONTROL?
Run-to-run control is a form of discrete process and machine control in which the
product recipe with respect to a particular machine process is modified ex situ, i.e.,
between machine “runs,” so as to minimize process drift, shift, and variability. This
type of control is event-driven, where the events include the determination and
reporting of pre- and/or postprocess ex situ metrology data, and the requirement of
the tool to begin processing. The input/output structure of a typical R2R control
solution is shown in Figure 1. Note the granularity of control could be wafer-to-
wafer, or batch-to-batch, etc.
A typical scheme for utilization of R2R control for a CMP polishing tool is
illustrated in Figure 2. (Note: GCC stands for Generic Cell Controller, a control
structure to be discussed in Part 3 of this book.) Note that the metrology and
automation scheme for R2R control can vary widely. For example, the metrology
is generally limited to ex situ metrology, but could include in situ equipment state
FIGURE 1 Input/output structure of a typical R2R control solution.
FIGURE 2 Typical R2R control application — R2R control of a CMP process.

and wafer state information. The (ex situ) premetrology capability may or may not
be available. The metrology could be in-line or off-line, i.e., it could be directly
integrated (mechanically and electrically) into the process line, or could exist as a
stand-alone metrology station. The metrology could be fully integrated into a single
tool, or could be integrated into the process line as both a postmetrology capability
for a process and a premetrology capability for the subsequent downstream process.
2 VLSI TOOLS: THE EXAMPLE OF CMP

As VLSI (very large scale integration) technology advances, the feature sizes of both
the underlying devices and the underlying metal line widths decrease. With this
decrease comes increased transistor speed and density, but also a need for more
layers of metal interconnect. Thus interconnect technology is the center of much of
today’s VLSI research.
One of the major problems with fabricating additional layers of metal intercon-
nect is that the topography of the silicon wafer becomes increasingly nonplanar as
levels of metal are added. This, coupled with the demand for increasingly smaller
geometries, has led to some problems previously unseen. First, due to the clarity of
image needed for submicron geometries, the focal depth of lithography machines
has decreased. This reduced focal depth results in some of the topography of the
wafer being out of focus when other parts are in focus (see Figure 3). This is
unacceptable as geometries shrink.
In addition to lithography concerns, the nonplanar surface can lead to difficult
processing as the aspect ratio of the valleys of the wafer becomes great enough that
the interconnect metal is unable to fill and cover these areas. This effect can lead to
circuit failure due to metal fatigue or lack of connection entirely. Figure 4 shows a
typical nonplanar process as well as an ideal one.
There are many techniques used to increase planarity. Most involve applying a
level of glass or oxide in an attempt to fill the valleys that can lead to trouble later
on. The problem is that the peaks are also extended to some extent, so it is very
difficult to achieve planarity through this process alone. The process of etching peaks
Lamp
Mask
Enlarging Lens
Focusing Lens
Focal plane (clear)

Beyond focal depth
(blurred image)
P+ P+ P+ P+
N
Enlarging lithography system
FIGURE 3 Enlarging lithography system.

Non-Planar Process Ideal Process
Possible fault
P+ P+ P+ P+ P+ P+ P+ P+
N N
Oxide
Metal
Comparison between non-planar and planar processes
FIGURE 4 Comparison between nonplanar and planar processes.
Carrier (head) Slurry Feed
Wafer Slurry
Holder Carrier Feed
Platen
Polishing Pad
Platen
(a) Side View (b) Top View
FIGURE 5 Schematic of a CMP machine.
from the dielectric has also been attempted; again, this suffers from the inability to
etch peaks while leaving valleys unchanged. CMP (chemical mechanical planariza-
tion) solves this problem by using a combination of chemical etching and physical
abrasion to achieve global planarization.
CMP has its roots in the silicon wafer production machines used to polish the
wafers before processing. These machines provided a wealth of information that led
to the CMP machines of today. The basic process is the same for both. Wafers are
loaded into a vacuum grip carrier that can rotate. This is then pressed against an
abrasive pad that can also rotate. The lower pad is much bigger than the wafer, and
is continually coated with a chemical slurry by a nozzle. Figure 5 shows a schematic
of a simple CMP machine.
Through the use of CMP, near ideal planarization can be achieved. This has
allowed VLSI manufacturers to increase the number of interconnect layers. It has
also aided reliability by reducing the mechanical strain in metal lines resultant from
nonplanarity.
CMP is not without its flaws. In addition to its high cost, it has nonuniformity
issues that are the center of much CMP research. Nonuniformity issues can arise
both within a wafer and between two wafers. Within-wafer uniformity is measured
by comparing the relative thicknesses of the wafers along various sites located
radially from the center. The reason for this approach rather than a more uniform
pattern is that CMP involves rotating the wafer, which makes all sites that are radially
equal the same thickness. Figure 6 shows the two methods of measurement.

Radial Sites Uniform Sites
1 2345 678 9 6 7 3 8 9
Wafer measurement sites
FIGURE 6 Wafer measurement sites.
Uniformity between wafers is measured by comparing the average thickness

between two wafers. This measurement is related to the overall drift in a machine.
This drift can have many sources; among them are pad wear and changes in slurry
composition.
3 CHARACTERISTICS OF R2R CONTROL SYSTEMS

Although there is a wide range of R2R control system scenarios and solutions, there
are three basic characteristics common to all R2R control systems.
• Some form of postprocess quality measurement data is available. This

measurement data may be in the form of ex situ postprocess metrology
(traditional), but could also include in situ data compiled during the pro-
cess. Note that the data may or may not be available for every wafer,
batch, or control event. Note also that preprocess measurement data avail-
ability is not a requirement.
• A dynamic model of the process is maintained (explicitly or implicitly)
in the controller that relates the postprocess quality data to tunable process
“recipe” inputs. Using this model, the controller is able to provide “sug-
gestions” for process improvement as necessary based on postprocess
quality data values. The model is dynamic in that it attempts to track drifts
in equipment and process quality parameters on a run-to-run basis.
• Process improvement control actions, i.e., process input parameter adjust-
ments are instituted once during each “run” based on suggestions by the
controller. A “run” may be defined as a single wafer process event, batch
process event, etc. The control actions are generally instituted prior to the
commencement of a run event (i.e., between “runs”); however, this is not
necessarily required.
A typical R2R control solution was shown in Figure 2. Here, a wafer-to-wafer

control scheme is utilized to provide thickness and uniformity control of a chemical
mechanical planarization (CMP) process through R2R actuation of time and back-
pressure. Only postmetrology data is utilized, 50% of all wafers are measured, and
there is a two-wafer delay in actuation (i.e., data collected on wafer n is utilized
first in the control of wafer n + 2).

4 HISTORY OF THE DEVELOPMENT OF R2R CONTROL
Early algorithmic and system integration development for run-to-run (R2R) control
in the semiconductor industry was pioneered by researchers at MIT and at the
University of Michigan as well as by workers at various semiconductor manufac-
turing corporations in the U.S., most notably at Texas Instruments. In the early 1990s
some of this key research began to be sponsored by the Austin, Texas-based semi-
conductor research consortium, SEMATECH.* References to SEMATECH, its
research, and its affiliations may be found at the Web site http://www.sematech.org.
Continuous feature size reduction and wafer size increase have forced the players
in the semiconductor industry to innovate to remain competitive. The innovations
that have taken place to maintain and improve manufacturing capability attributes
have historically been in the form of (primarily) equipment design improvement,
process refinement, and, in a few cases such as chemical mechanical planarization
(CMP), new process conception and development. These innovations, for the most
part, could be characterized as process-centric; that is, a specific tool and/or its
specific process is improved with the expectation that it will lead to improvement
in overall factory throughput and yield.
In the mid-1980s the industry began to become more cognizant of other critical
avenues for maintaining and improving process and product metrics. One of these
avenues was improved process and product visibility, namely a much-improved
ability to view and understand aspects of the process and the wafer during processing.
This attempt at increased visibility was focused not only in the traditional off-line
process identification and development areas, but also on-line as part of the fabri-
cation scheme, i.e., attempting to ascertain the state of the wafer and process during
processing (in situ sensing) and the state of the wafer directly after processing
(ex situ metrology). Research and development organizations such as the Semicon-
ductor Research Corp. (SRC) and SEMATECH identified projects to develop metrol-
ogy technology (both in situ and ex situ) as well as physical and empirical process
models. Research investigators also began to look seriously for the first time at each
process as part of a total factory solution. Another force that appeared and provided
guidance toward the evolution of the industry in this area was the Semiconductor
Industry Association (SIA). The SIA began publishing a roadmap that attempted to
capture the state of the art in the semiconductor industry, “hot” areas where research
and development should be focused in the near future, and basic timelines for
achieving milestones in these areas.
With increased process and product data in hand, process engineers began to
investigate ways to put this sensory and metrology data to use. A natural first step
was to utilize the additional data to enhance existing process alarming and control
mechanisms. The predominant mechanism used in the industry at that time (and to
this day) is statistical process control (SPC). SPC is a method for detection of
statistically significant data patterns based on an assumption of a Gaussian distribu-
tion of data. Mean and variance parameters are determined for various data param-
eters through data collection and analysis. The sensory data are then monitored with
* SEMATECH has since changed its name to International SEMATECH.

respect to these mean and variance parameters and alarm events are generated.
Specifically, a number of detection rules, called the Western Electric Rules, are
applied to the data. When conditions of a rule are met, an alarm is generated.
While SPC is useful to detect and verify process stability and correctness, it is
not technically a “control” solution. This is because SPC provides a mechanism for
detecting aberrations but does not include mechanisms to correct for these aberrations.
As a consequence of this limitation, in the late 1980s and early 1990s researchers in
the industry began to complement sensory and metrology research with a focus on
utilizing the data to suggest corrective action. This effort, termed “advanced process
control” (APC), was spearheaded in the industry by efforts at SEMATECH and SRC.
The primary consideration in control solution development in the semiconductor
manufacturing arena that differentiated it from other arenas was the problem of lack
of available sensory capability, especially for in situ process and product identifica-
tion. The semiconductor industry is characterized by physically and chemically pro-
hibitive environments (e.g., high-temperature processes, corrosive and hazardous
processing chemistries, plasma environments, etc.), making sensor development and
use in many of these environments difficult or impossible. This, combined with the
fact that many process tools are not designed for the addition of in situ sensors (e.g.,
requiring the addition of quartz windows for in situ optical sensing), resulted in
inadequate sensing for in situ process identification and control. This in turn resulted
in labeling the control effort in the industry as “sensor-driven control,” where sensor
development drove and directed control development rather than the reverse.
The lack of adequate (especially in situ) sensing in semiconductor manufacturing
provided control systems researchers with unique challenges and opportunities for
advancement. The first innovations in semiconductor manufacturing APC were the
partitioning of the controlled process into the in situ control of the equipment
environment, the in situ control of the equipment environment operating on the
wafer, and the ex situ control of the final product for that process. This gives a
hierarchical, nested partitioning of the control problem, as illustrated in Figure 7
(from a factory operations perspective) and Figure 8 (from a controls perspective).
Each level of control is characterized by a set of sensory/actuation capabilities
(i.e., a process visibility and control capability) and control timing requirements.
For example, referring to Figure 7, in controlling the equipment environment, the
process is continuous. Thus the control should be continuous, or the time discreti-
zation should be sufficiently small so that the environment doesn’t drift significantly
between control events. Similarly, the wafer processing environment is also contin-
uous. However, timing requirements are generally more relaxed than with the equip-
ment environment because the wafer effect from the equipment environment is
cumulative and is impacted by factors such as the time constant of the process
chamber (i.e., the time required for an equipment environment actuation event to
begin to noticeably impact the wafer environment). At the outermost loop of the
control system depicted in Figure 8, the ex situ control environment is strictly event-
driven (and not continuous).
Wafers are analyzed after processing and corrective advice is fed back to the
tool for future wafer processing. Note that the outermost loop depicted in Figure 8

FIGURE 7 Typical R2R control utilization scheme, facility-wide.
FIGURE 8 Hierarchical partitioning of control problem.
does not necessarily represent the highest control loop in the control hierarchy.
Specifically, interprocess control could be implemented that “wraps” control around
a group of processes.
The partitioning of the control problem is powerful because it allows the devel-
opment of effective control solutions when “good” process visibility is limited to
one or two levels.
With the industry accepting the hierarchical nested control solutions approach,
research and development could now be focused on a particular level of control.
Terminology somewhat specific to the industry was attached to each of these control
levels. In-situ process environment and wafer environment control were collectively

termed real-time, in situ, or time-critical control, while ex situ process control was
termed run-to-run (R2R) control.* In partitioning the control problem and control
research, it became clear very quickly that, due to the available sensing capability
and process knowledge, R2R control represented the first primary area where process
improvements could be readily achieved.
During the 1990s innovation in R2R control development and deployment pro-
gressed on three basic fronts described below; this multidimensional approach rep-
resents a model for advancement that is also applicable to the other levels of process
control.
1. Sensor and Actuator Innovation: Progress along this front provides

increased process and equipment visibility.
2. Control Algorithm Solution Innovation: The development, analysis, and
parameterization of control algorithm solutions are necessary to address
the often unique process visibility and R2R controllability problems of
the industry.
3. Integration and Automation Innovation: The most often overlooked front
is the development of integration and automation techniques for rapid
deployment (re) configuration and reuse, and assimilation of R2R control
as part of multilayer control solutions.
Progress along these three fronts was paramount in determining the progress of the
various APC thrusts. Indeed, it was probably the determining factor that pushed R2R
to the forefront as the first widely implemented APC element. Specifically, the
following are a few of the important factors that pushed R2R control to the forefront
ahead of in situ control and interprocess control:
• Sensor and Actuator Innovation: R2R control is implemented where there

is the highest level of process visibility (or at least capability for visibility)
and actuation capability. As sensors can be implemented ex situ, issues of
harsh processing environments and lack of equipment design for pro-
cess/product inspection are nonexistent. Actuation is simply process recipe
modification between runs. Thus R2R control is, in most cases, just an
extension of process identification, design, implementation, and tuning
(i.e., R2R control reflects uploading/downloading and tuning of recipes
between runs similar to run-to-run actions of an operator). Additionally,
process engineers have much more knowledge and confidence in operating
and tuning a process R2R rather than either in situ or at an interprocess
level. This is because process knowledge in a fabrication facility is pri-
marily process-centric and run-based. A process engineer knows his/her
process well in terms of the product it produces. He/she is generally less
aware of the impact of up- or downstream processes, and does not have
as much knowledge of process dynamics during processing. Simply put,
* The term “run-by-run” or “RbR” control is also used.

the process engineer knows his/her process from the perspective of the
product it produces, and this is the perspective from which R2R control
is applied
• Control Algorithm Solution Innovation: R2R control addresses a relatively
straightforward process-centric control problem. Simple and intuitive dis-
crete control solutions can be applied in many cases. Further, as R2R
control addresses process tuning that is already conducted ad hoc by
operators and process engineers, it is already part of the semiconductor
manufacturing industry culture.
• Integration and Automation Innovation: R2R control is event-driven and,
thus, in most cases, not time-critical. In addressing integration and auto-
mation, attention could be focused on the solution architecture rather than
response time. This has led to the development of generic, portable, and
reusable software solutions that exist on common computer hardware/soft-
ware platforms. Further, because of the non-time-critical nature of R2R
control, stand-alone, nonintrusive prototype R2R systems can be deployed
in advance of the fully integrated systems to verify and quantify the
advantage of R2R. With these stand-alone systems, the user serves as the
communication link between the controller and both the tool and metrol-
ogy systems, and as a validation mechanism for controller advances. With
the stand-alone implementation intermediate step, a smooth migration
path is provided for acceptance of R2R control in the fabrication facility.
With the advantages of available sensory and actuation capability, straightfor-

ward control solutions, and integration and automation strategy giving a smooth
migration path to fully automated R2R control, the industry began to focus more
heavily on R2R control as the first advanced process control (APC) paradigm.
5 TEXT LAYOUT
This book is organized so the reader can quickly map his needs to the required parts
and chapters within those parts. The remainder of the book is subdivided into seven
parts; each part addresses an important aspect of R2R control development, deploy-
ment, and assessment. At the beginning of each part, a brief description is provided
as to the contents of that part. This is followed by chapters addressing specific topics.
Part 1 addresses foundational material including an overview of process control
in the industry and an overview of process control and optimizations. The two
fundamental components of a successfully deployed R2R control solution, namely
the control algorithm(s) and the integration methodology, are addressed in Parts 2
and 3, respectively; these parts also contain brief examples of R2R control solution
deployment. Methodologies for customization of R2R control solutions to actual
industry control problems are provided in Part 4. Part 5 contains actual detailed case
studies of R2R control solution deployment. Advanced “next generation” topics in
R2R control and semiconductor manufacturing process control in general are dis-
cussed in Part 6. Part 7, entitled “Conclusions,” provides a summary of what has

been presented and offers final thoughts on R2R control solution development,
deployment, and evolution.
One unfortunate characteristic of the field of R2R Control, and indeed, semi-
conductor manufacturing in general, is the extensive use of acronyms. To address
this problem, a complete listing of acronyms used in this text is provided at the end
of the book.
6 SUMMARY
This introduction serves to open the door to the subject matter of this book as well
as to general thinking about R2R control systems and their integration into manu-
facturing systems. It should be clear by now that the technology discussed is com-
pletely generic with respect to manufacturing control and integration. Even though
the experience of the authors, and all quoted examples, pertains to the semiconductor
industry, there is no reason why any other industry cannot take advantage of this
form of control. In this sense, R2R control is similar to the well-known SPC
(statistical process control).
To summarize some key features of R2R control, one may cite its wide appli-
cability to tools of all types, its dependence on certain algorithms that again have
wide generic applicability, its need for a coherent integration path in manufacturing,
and certain common measurement requirements. In exploring these features and
developing solutions, researchers and implementers have been able to take the
technology as presented in this book from a merely academic exercise into the world
of actual tool, and factory, application.
It is the authors’ hope that this text will not only serve to spread the use of R2R
control further into semiconductor manufacturing, but will also inspire and motivate
engineers, managers, and scientists in all branches of manufacturing to apply R2R
control in their particular areas.

Part 1
Foundation for Control
Process control is gaining recognition in the semiconductor industry as a means to
compensate for equipment changes due to inconsistent operation, process drifts, and
process shifts. In the Introduction to this book an overview was provided of R2R
control concepts and the history of the development of R2R control. In Part 1,
practical and theoretical components that comprise the foundation for R2R control
are presented.
In Chapter 1 several factors that led to the recent growth of R2R process control
are reviewed. The motivation for migration from traditional statistical process control
(SPC) techniques to adaptive control is explained. Problems are discussed that led
to the early interest in process control and the resulting solution of these problems.
Examples are drawn from semiconductor processes such as plasma etching, chemical
mechanical planarization (CMP), and metal sputter deposition. Several issues are
outlined that arose from the initial interest in adaptive process control, including a
lack of commercial solutions, a common framework, in situ sensors and on-line
metrology, and detailed studies of algorithm performance. A description is given of
how these issues were addressed as the new control technology matured, including
the development of a framework for control, the rise of commercial applications,
the development of new algorithms, and the introduction of new metrology.
Chapter 1 also explains why methodologies that have obeyed the “keep it simple”
rule have achieved widespread use. Suggestions are made for the future of process
control in the semiconductor industry. Process control application benefits are sum-
marized. Possible future trends in control are suggested that indicate a move toward
methodologies that replace “black-box” systems with those that incorporate
advanced models tightly coupled with the process, as well as methods that provide
multistep process optimization and control.

In Chapter 2, an overview of R2R optimization techniques is given. Three
methods are reviewed, namely (1) design of experiments (DOE)/response surface
methods (RSM), (2) the Ultramax® sequential optimization software, and (3) the
optimizing adaptive quadratic controller (OAQC), which is described in greater detail
in later chapters. The stability and robustness of exponentially weighted moving
average (EWMA)-based controllers, both single-weighted and double-weighted, are
discussed in detail, and methods for tuning these controllers are described. Other
important R2R control techniques are briefly reviewed. One of the goals of this
chapter is to give an up-to-date review of available R2R methods.

1 Advanced Process
Control in the
Semiconductor
Industry
Taber H. Smith, Duane S. Boning, and
James Moyne
1.1 INTRODUCTION
Advanced process control, or APC, has evolved rapidly in the semiconductor industry
during the 1980s and 1990s, with R2R control emerging as the first technologically
viable product of that evolution. In the Introduction to this book a detailed definition
of R2R control is provided and the evolution of R2R control is summarized from
the point of view of capabilities of the industry and organizations that had a signif-
icant impact on the evolution of APC. In this chapter we provide an in-depth view
of the evolution of advanced process control (toward R2R control) in the semicon-
ductor industry from a technical perspective, describe the issues that are guiding the
maturation of R2R control, and detail the benefits that can be achieved with effective
R2R control.
Specifically, in Section 1.2 we provide an historical summary of the evolution
of process control from alarm-based statistical process control toward model-based
control solutions such as R2R control. Further, we describe technical issues that
have proved to be a hindrance to this evolution and, subsequently, the widespread
acceptance of R2R control. In Section 1.3 we summarize advancements that have
been made in the field of R2R control that have helped to address these issues. Many
of these advancements are described in detail in later chapters. We follow this
summary with a discussion of the future of APC in Section 1.4. Here, we focus our
attention on the benefits of R2R control (current and future), as well as probable
directions for R2R control solution enhancement. This chapter concludes with a
summary of the information presented.
The main purpose of this chapter is to provide the reader with a snapshot of the
technical issues — past, present, and future — that are shaping the field of R2R
control in semiconductor manufacturing. With this information, the reader is pro-
vided with a foundation for understanding the detailed aspects of R2R control that
are described in the chapters that follow.

6400
+3σ
6200 +2σ
+1σ
6000 Target
-1σ
Deposition Thickness (A)

-2σ
O
5800
-3σ
5600
5400
5200
5000
4800
4600
5 10 15 20 25 30
Run #
FIGURE 1.1 An uncontrolled drifting process.
1.2 INITIAL STAGES OF CLOSED-LOOP

PROCESS CONTROL
1.2.1 EARLY SOLUTIONS: STATISTICAL PROCESS CONTROL
As semiconductor processing entered the late 1980s, process variability had been
substantially decreased.1 However, new problems were beginning to emerge. Many
processes were exhibiting steady drift in equipment performance. Such drifts were
often caused by the build-up of material on the interior components of the tools, or
gradual wear of components. For example, the deposition rate in a metal sputtering
process is highly correlated to the life of the components within the tool. The
resulting drift in the deposition thickness is shown in Figure 1.1.
Although not intended for process adjustment purposes, statistical process con-
trol (SPC) is often used to compensate for such problems. SPC is a technique aimed
at monitoring deviations from statistical control, a state of a process where mea-
surements follow a stable, uncorrelated process. Derivations are usually identified
through applying a set of rules or filters to the data. Adjustment to the process, i.e.,
removal of the assignable cause of variation, is usually left unmodeled, under the
assumption that a process engineer will try to fix the problem at its root. Removal
of the cause of variation avoids further occurrences of this problem in the future.
One set of violation rules used to determine the level of statistical control is known
as the Western Electric Company (WECO) Rules.* A subset of these rules follows:
* WECO rules are usually not recommended in the SPC literature since they may cause a considerable
increase in the number of false alarms given by the monitoring scheme.59

1. Last point of data is greater than three standard deviations away from the
process target.
2. Two of last three data points are greater than two standard deviations away
from the target.
3. Four of last five data points are greater than one standard deviation away
from the target.
4. Last eight data points are all above or all below the target.
In semiconductor manufacturing the process output is often shifted back to the

target by a simple adjustment to the process (in the sputter deposition case, this is
achieved by adjusting the deposition time). The amount of the adjustment is typically
equal to the sample mean of the data over the violation set (i.e., the last five data
points for WECO rule #3). As can be seen in Figure 1.2, the performance of this
method can be particularly poor in the sense that tools oftentimes experience regular
shifts or drifts in their outputs, and typical SPC detection methods such as the WECO
rule set are not very adept at distinguishing these shifts or drifts from process noise.
Although many process drift and shift conditions are eventually caught by SPC, the
problems are often only solved by warming up or otherwise “seasoning” the tool,
or by simply adjusting the processing time. In addition, the frequent occurrences of
these events were beginning to require significant manual monitoring efforts. Other
processes randomly drifted away from the target output, but then drifted back the
other way, continually wandering about the target.
Processes with these characteristics call for active adjustment strategies based
on control engineering principles, as opposed to the use of ad hoc SPC adjustments.
Furthermore, SPC implicitly assumes that adjusting a process is a very expensive
6400
6300 +3σ
6200 +2σ
O
6100 +1σ
6000 Target
5900 -1σ
5800 -2σ
5700 -3σ
5600
5 10 15 20 25 30
Run #
FIGURE 1.2 SPC control of a drifting process using tuning with WECO rules.

Disturbance
Set Linear Output

Point Controller
Process +
Affine
Model +
-
EWMA
Update
FIGURE 1.3 The EWMA controller. An “affine” function a linear function that does not pass
through the origin. More generally, in an affine function f (x), f (x) – f (0) is linear. For example,
if f (0) = a, then f (x) = Y = a + bx is an affine function.
activity to be utilized only when there is strong evidence that a process has been
affected by an extraneous source of variation. If adjustments are fairly simple and
inexpensive, as in many R2R control applications, a continuous “run-to-run” adjust-
ment scheme is preferable over SPC (see Reference 1 for a discussion on the
difference between SPC and engineering process control, EPC).
1.2.2 NEW SOLUTIONS — RUN-TO-RUN PROCESS CONTROL

In response to the need for continuous process tuning solutions, run-to-run (R2R)
process control algorithms began to emerge in university and industrial research.2–8
These methods were the first closed-loop feedback controllers to be used at the
process level in the semiconductor industry. They are similar to SPC in that they
monitor process parameters such as the deposition rate. However, unlike SPC tech-
niques, these methods make continual changes to the process, usually based on
dynamic modeling of process parameters. Many semiconductor fabrication facilities
(fabs) were already making frequent (though somewhat ad hoc) changes to processes
in order to compensate for drifts and shifts in the process outputs detected via
techniques such as SPC. Therefore, these controllers provided a natural step from
SPC to closed-loop feedback control.
One class of R2R controllers simply replaced the manual adjustment in SPC
with an automatic adjustment. This effort was generally aimed at automating current
practice within a fab. However, the controlled results were similar to those shown
in Figure 1.2. In some cases these controllers were expanded to include a group of
related processes. For example, SPC was used to control thicknesses of several
processes by utilizing a simple relationship between the deposition rate for thickness
and a common offset caused by equipment drift. This type of control was often very
effective for a large class of shifting processes in the industry. A second class of

R2R controllers was based on the exponentially weighted moving average (EWMA).6
This scheme is shown in Figure 1.3, and is explained in detail in Chapter 3.
Briefly, an EWMA was used to track changes in the process using the following
recursive algorithm:
a[n] = w ⋅ y[n] + (1 − w) ⋅ a[n − 1] (1)
where a[n] is the EWMA estimate of the process output, w is the EWMA weight,
and y[n] is a measurement of the process output or parameter to be estimated on
run. It can be seen that a higher EWMA weight means more recent measurements
are weighted more heavily. This weighted average of the process offset is used to
update the model of the process. This dynamic model is then used to adjust the
equipment settings to control the process outputs.
As an example, an EWMA controller may be used to track one or more process
outputs, such as deposition rate, and adjust the process inputs, such as process time,
to control one or more process outputs, such as the final film thickness. The results
of using an EWMA controller to control the deposition thickness of the sputter
deposition process above are shown in Figure 1.4. This figure illustrates that the
continual tuning of the process results in fewer regions where the control is off
target. Note also that there would be fewer points outside typical specification limits.
Acceptance of this class of feedback control was initially slow, largely due to
suspicion that frequent changes in the process settings would cause unseen changes
in critical film properties. However, several works demonstrated the effectiveness of
6400
6300 +3σ
6200 +2σ
O
6100 +1σ
6000 Target
5900 -1σ
5800 -2σ
5700 -3σ
5600
5 10 15 20 25 30
Run #
FIGURE 1.4 EWMA control of a drifting process.

the use of R2R process control,2–12 and acceptance of R2R process control began to
grow.
1.2.3 NEW ISSUES FACING R2R CONTROL ADOPTION

Those interested in fab-wide implementations of advanced process control, and
specifically R2R control, realized there were several major barriers to be overcome.
In particular, many fabs wished to implement R2R process control, but believed they
neither had nor wanted the necessary skills to develop a commercial system in order
to implement it. Unfortunately, there was no commercial solution that they could
turn to for implementing R2R control or providing R2R control expertise. In addi-
tion, it was soon recognized that adopting and integrating R2R control systems on
different tools in large numbers over a long period of time would require a substantial
upgrade to existing factory systems. The lack of a consistent standardized or proven
approach to integration of R2R process control presented a time and financial
resource barrier to implementation. Many tools also did not provide enough mea-
surement information to make R2R process control an effective tool. Another per-
ceived problem was that, in order to obtain the critical parameters required to
adequately control the process, a large amount of metrology and in situ sensor
development was necessary. Finally, many felt that the existing algorithms might
not be sufficient to control some processes, and there were concerns regarding the
stability, optimality, and robustness of these methods.
The issues that impeded the early adoption of R2R control are summarized in
Table 1.1. Note that this table also (briefly) summarizes the issues, presents concepts
and solutions that have been forwarded to address the issues, and provides references
to other chapters in this book where these concepts and solutions are described in
TABLE 1.1
Summary of Issues Impeding Early Adoption of R2R Control, Concepts
and Solutions, and References
Issue Solutions References in Book
Lack of commercial Third-party solution providers with standard Chapters 11, 13, 15
solutions solutions (see below)
No infrastructure for Standard framework for specification and Chapters 7–10
integration or integration: Chapters 8, 9, 11, 12
automation • Generic Cell Controller Chapters 7, 10, 20
• APC framework and enablers
Few on-line metrology New sensors and sensor integration standards Chapters 1, 7
and in situ sensors
Inadequate algorithms Verification of quality of existing algorithms Chapters 11, 13, 15, 16
Algorithm comparison: establishing domains Chapter 6
of applicability Chapters 4, 5, 17, 18, 19
Improved algorithms

detail. Further, an elaboration on these issues impeding the early adoption of R2R
control is provided in the remainder of this section, while a summary of some of
the concepts and solutions advanced to address the issues is provided in Section 1.3.
1.2.3.1 Issue: Lack of Commercial Solutions
Implementing control in a production environment proved much more difficult than

implementing it in a laboratory or research facility. This is due to a number of
factors. For example, many of the tools have only coarse adjustments on the equip-
ment settings, thus increasing the variability due to control actions. Further, these
tools are often shut down for maintenance, which causes large shifts in the process
outputs after being brought back up. Consider the deposition rate history of a sputter
deposition process shown in Figure 1.5. The abrupt changes in the deposition rate
are due to changes in the process kit. Notice that the starting values are very different,
and the drift in the deposition rates are slightly different for each process kit.
At the time that R2R control solutions began to appear (early 1990s), measure-
ments were almost exclusively performed off-line, and these were often slow, incon-
sistent, or skipped by operators. This caused delayed, inconsistent, and infrequent
measurements of the process outputs. As illustrated by our sputter deposition exam-
ple, this can have a large effect on the measured deposition thickness. Most of the
controller implementations developed at that time gave little attention to these minor
details. However, as shown in Figures 1.6 and 1.7, neglecting these details can cause
a large increase in the variability of the controlled output. Figure 1.6 shows a drifting
process with no delays, inconsistencies, or skipped measurements. Note that the
7.5
6.5
Deposition Rate (A /min)
6
O
5.5
4.5
3.5
0 200 400 600 800 1000 1200 1400
Kit Life (Kilowatt-hours)
FIGURE 1.5 Deposition rate of a sputter deposition process over several process kit changes.

1800
1600
1400

O
1200
1000
800
Target
Controlled
600
Uncontrolled
Measured Wafers
Update Time
400
0 100 200 300 400 500 600
FIGURE 1.6 Control of a drifting process with no nonperiodic time intervals, infrequent
measurements, or inconsistent delays.
1800
1600
1400
O
1200
1000
800
Target
600 Controlled
Uncontrolled
Measured Wafers
400
Update Time
200
0 100 200 300 400 500 600 700
FIGURE 1.7 Control of a drifting process with nonperiodic time intervals and infrequent
measurements with inconsistent delays.

controlled output is consistently on target. On the other hand, Figure 1.7 shows the
resulting control when measurements are often delayed, inconsistent, and skipped.
Another problem with implementing laboratory results in practice was that, for
the most part, little attention was paid to cost-effective, repeatable solutions for
integration and automation. The industry in general will not accept open-loop or
manual forms of R2R control as long-term solutions. Specifically, R2R control will
only be accepted if the user is not burdened with additional data entry at the controller
(e.g., entering metrology information) or at the tool (e.g., entering tool process
parameter update information).
In addition, the manual operation of most tools often left room for data-entry,
user-interface, and security problems within control software. For example, operators
manually entering data would sometimes use an incorrect metrology recipe, incor-
rectly enter data from the metrology tool, or make other minor errors. However,
recipe changes made by the controller based on these measurements could result in
several runs being significantly different from the target output.
Further, the nature of the process disturbances (e.g., drift, shifts, or wandering
noise) often changes, and many process engineers lacked the time or ability to
continually retune all the controllers in the manufacturing environment. This often
resulted in the controllers running in a suboptimal mode. The lack of commercial
solutions to address these issues was thus a serious impediment to the implementa-
tion of R2R techniques in the manufacturing environment.
1.2.3.2 Issue: No Enabling Technologies or Infrastructure

for Integration or Automation
Probably the single largest barrier to the implementation of R2R process control in
production facilities was the lack of a cost-effective enabling technology and infrastruc-
ture that would provide for (1) solutions to be rapidly prototyped and configured that
were flexible and process-independent to achieve cost-effectiveness; (2) integration of
software components, including third-party solutions, in a timely and cost-effective
manner to achieve the necessary customization and address unique end-user require-
ments as is typical with implementation of a new technology; (3) communication
capabilities where tools and sensors could be connected and data could be uploaded,
transferred, and saved to support fully automated solutions; and (4) commercial
quality applications to obtain the required level of software quality.
Specifically, an enabling technology was needed that would allow developers to
rapidly integrate and configure the necessary software components (including control
algorithms, data logging and presentation modules, communication drivers, and data
filters) to quickly prototype and customize R2R control solutions. This enabling
technology further had to provide for portability of these solutions between hard-
ware/software platforms and semiconductor processes to achieve the necessary cost
and technology leverage. It also had to provide a level of flexibility for rapid
reconfiguration (to new process paradigms) and rapid upgrade (to maintain compet-
itive advantage in the early stages of a technology market).
An infrastructure or framework was also needed to provide a consistent base
upon which current and future generations of controllers, including R2R control,

real-time control, and endpoint detection modules, could be built. The large amount
of research into on-line metrology and in situ sensors, as well as tool communication,
required standard methods for data upload, download, and storage. This was neces-
sary so that the factory system would be able to upload, download, store, and share
information; information regarding process recipes was particularly important. How-
ever, many tool, sensor, metrology, and factory systems use different operating
systems. Data formats for many of these pieces were completely different. In addi-
tion, tools in the semiconductor industry were generally not highly automated. This
was largely due to the rapid pace at which tool technology had changed within the
industry and the high cost of automation. Typical tool lifetime was on the order of
2 to 5 years, with costs typically being on the order of millions of dollars. Additional
efforts to configure and program a tool for automation were generally considered
cost prohibitive, time prohibitive, or not possible due to limited automation capa-
bilities of the tool or a limited automation skill set on site. This lack of automation
contributed to tool utilization typically on the order of 30%, and clearly pointed to
a need for a basic equipment and control framework.
1.2.3.3 Issue: Few On-Line Metrology and In Situ Sensors
In many complex processes, the lack of information available about the process state
and the state of the wafer during processing presented a major barrier to the effec-
tiveness of R2R process control. It was found that, for processes like plasma etching,
the complex interactions of the tool (e.g., the build-up of material on the chamber
walls) and the plasma chemistry make monitoring and controlling the process dif-
ficult. These processes were often difficult to model and control with ex situ mea-
surements. Because changing process settings resulted in unseen changes in the thin
film properties, scanning electron microscope (SEM) and other time-consuming
measurements were often the only means to develop and control processes. In order
to control such complex processes, more information about the state of the wafer
and plasma chemistry was needed.
In other processes, such as chemical mechanical polishing (CMP), processing
occurs in a much less controlled environment. In CMP, the wafer is pressed face
down on a polishing pad. Even though the chemical and physical mechanisms may
not be as complex as in plasma etching, obtaining access to the chemical and physical
mechanisms taking place during processing is extremely difficult (as explained in
the Introduction section of this book). Initially, this made ex situ measurements the
only information available on the process.
The lack of information available and the lack of access to the wafer being
processed forced R2R process control to rely largely on ex situ measurements. How-
ever, many felt that the speed at which these measurements were performed would
decrease the usefulness of R2R process control in a manufacturing environment, and
that if R2R was to be successful, the information necessary for control had to be
taken on the tool without operator involvement. This was particularly true for tools
that required frequent measurements (which were normally those most likely in need
of control). R2R process control for processes that relied heavily on ex situ metrology

were most likely to suffer a loss in throughput if measurements had to be taken
frequently. In addition, frequent measurement and recipe changes increased operator
error in the measurement data entry stage, as well as in the recipe adjustment stage.
These issues strongly suggested that, in many cases, R2R process control without
automated on-line metrology or in situ sensors was not practical or cost effective.
1.2.3.4 Issue: Inadequate Algorithms

Interestingly, algorithm development at this stage was generally ahead of implemen-
tation. This was largely due to the enormous task of creating an infrastructure,
developing on-line metrology and in situ sensors, and configuring tools for automa-
tion. At this stage most of the problems involving algorithms were those related to
implementation in production environments. However, a large amount of research
was still needed in order to address theoretical questions of stability, optimality, and
robustness, as well as practical issues of input/output bounding and weighting, advice
parameter discretization, and noise filtering.
1.3 MATURATION OF CLOSED-LOOP

PROCESS CONTROL
As R2R process control began to mature, a large amount of work was focused on
addressing the problems (summarized above) that were faced by the early adopters
of R2R process control. In particular, a generic enabler was developed to provide for
rapidly configurable, integrated control solutions;* this enabling technology has been
utilized in a large number of R2R applications in the industry from the beginning of
the R2R maturation process through present day. Somewhat later, a standard frame-
work was set up, upon which commercial applications could be developed; interest-
ingly, this framework specified an integration environment very similar to that utilized
by the generic enabler. The promise of R2R process control, real-time process control,
and fault detection and diagnosis sparked efforts to develop on-line metrology and
in situ sensors by both industry and academia.38–43,46,48,50,51 Finally, several works were
beginning to address stability, optimality, and robustness of R2R process control
algorithms, and practical issues associated with algorithm customization and
deployment6,26–36 (see Parts 2 and 6 of this book for additional references). In addition,
novel control techniques were beginning to address a wider range of control
problems15,29,38 (see Part 6 of this book for additional references).
In the remainder of this section, the efforts that contributed to the maturation of
closed-loop process control, and specifically R2R control, are described in more detail.
1.3.1 ENABLING TECHNOLOGIES FOR R2R CONTROL SOLUTIONS

In the late 1980s a research effort at the University of Michigan, sponsored in part
by the Semiconductor Research Corp. (SRC), focused on identifying (1) barriers to
* See Chapters 9 through 11.

advanced process control adoption in the industry, (2) user requirements for inte-
grated control solutions, and (3) a basic roadmap for developing and deploying APC
in the industry.13 An early result of that effort was the rather startling conclusion
that the major barrier to APC integration was not control technology, but rather
integration technology. Specifically, it was noted that there was very little reuse of
software in APC solutions, despite the fact that software was rapidly becoming a
larger component of tool cost and tool quality assessment. Further, it was noted that
the industry was suffering from a “not invented here” mentality, where software
solutions were often times proprietary and not developed by software engineers, and
there was no coordinated attempt to look beyond the semiconductor industry for
software solutions. It was also concluded that R2R control was the best initial
candidate for APC development and deployment due to (1) the infant state of
metrology and sensor technology at the in situ level, (2) a lack of consistent software
platforms at the equipment control level, (3) a process-centric — rather than interpro-
cess — mentality and knowledge base, and (4) a general unwillingness on the part of
users and OEMs* to deploy multivariate control solutions at the (invasive) equipment
control level or at the factory control level (where little was known about process-to-
process interaction, and few resources were available to support integration).
The researchers at the University of Michigan worked with industry and iden-
tified requirements for integrated control systems in semiconductor manufactur-
ing.** They then surveyed the software technology base, and utilized this foundation
to develop the Generic Cell Controller.14*** This enabling technology for integrated
control was developed to provide flexible, rapidly configurable, and portable inte-
grated control solutions for the industry. Its main features include a well-defined
and modular object-oriented integration environment, and a method for incorporating
control schemes in the (portable and flexible) data of a database (rather than in
procedural code or in scripts). Since the first GCC implementation was demonstrated
in 1989, a number of industrial R2R control solutions have been reported in literature
that utilize the GCC technology.10–12,15**** Novel R2R control results reported in
literature with these GCC solutions include first etch process control, first CMP
thickness control, first CMP uniformity control, first multivariate vapor phase epitaxy
multivariate control, and first fully automated control solution.11
During the mid- to late 1990s, the advanced equipment control (AEC) advanced
process control (APC) framework was set up by SEMATECH and several of its
member companies that were interested in promoting the development of commercial
hardware and software for semiconductor process control applications.16–20***** The
framework, which is based in large part on earlier work in Texas Instruments’
Microelectronic Manufacturing Science and Technology (MMST) program,20 is out-
lined in Figure 1.8. This framework provided a standard around which applications
from various companies could be built and integrated. These applications include
monitoring and control programs for R2R process control, fault detection and
* Original equipment manufacturers.

** The GCC concept is described in detail in Chapter 9.
*** GCC solution examples are reported throughout this text, especially in Chapters 11, 13, 15, and 18.
**** Requirements for R2R control solutions are presented in Chapter 8.
***** See Chapters 7, 10, and 20 for additional discussion of the APC framework.

APC Framework Components
Apps Plan Data Data Sensor Fault

Interface Manager Storage Collection Interface GUI
Machine Plug-In Plan Data Operator Fault

Interface Manager Executor History Interface Manager
Naming Events Trading System Logging Service

Manager Service Monitors
Signoff Registry
Manager
APC Framework Infrastructure
FIGURE 1.8 Advanced process control framework (adapted from Reference 12).
classification systems, and SPC monitoring packages. In addition, separate applica-

tions for data sampling plans, data collection, and data history maintenance could
be added. The framework also includes a structure for low-level equipment, sensor,
and metrology interfaces. Because a large portion of the benefits of R2R control are
derived from integration and automation, the standard interfaces for data storage
and retrieval outlined by the AEC/APC framework provide a basis for this to happen.
The standard allows semiconductor companies to adopt those packages and tech-
nologies that are best suited to their needs. In addition, the framework outlines
interfaces for collecting and storing data from equipment and sensors, as well as for
sharing these data with applications for fault detection and classification, R2R
process control, and factory-level computer integrated manufacturing (CIM) sys-
tems. These standards, then, if adopted, could provide IC companies with the ability
to obtain individual products from the vendors of their choice, while providing
vendors the ability to sell and market individual tools on the platform of their choice.
1.3.2 COMMERCIAL SOFTWARE

As APC and especially R2R control migrated from the laboratory to industry,
commercial software solutions began to appear. These solutions generally fell into
two categories, namely those developed as single point solutions, and those developed
to be reusuable and portable to multiple applications. Solutions in the latter category,
by and large, utilized enabling technologies similar to those described in
Section 1.3.1.21,22 The rise of commercial solutions accelerated in the late 1990s due
to a number of factors, including (1) the basic realization by the industry that APC

would eventually become an integral component of semiconductor manufacturing,
(2) the move toward 300 mm tooling and the opportunities for adding capabilities
both at the OEM and user levels, and (3) the substantial effort devoted to creating
a standard framework upon which applications could be built.
The rise of commercial R2R control solutions has seen an accompanying rise
in solution features. For example, many of these controllers directly accommodate
equipment maintenance events and provide solutions to rapidly adjust for such
changes.* Many control solutions also include the ability to control multiunit pro-
cessing tools within a single package. This often means separate controllers for each
unit, but allows the operators to easily control specific chambers of specific tools
within one common graphical user interface (GUI). Commercial packages often
contain built-in SPC or limit monitoring of values entered by operators. In addition,
many systems include separate interfaces and permissions for operators, engineers,
and administrators. Packages often significantly remove operator involvement by
incorporating communication with both the tool and on-line or ex situ metrology,
resulting in a fully automated solution.** These packages often offer the ability to
set up arbitrary inputs from various metrology tools on-line, in situ, and ex situ. This
allows a great amount of flexibility for the production facility to buy one package
for R2R control from one vendor, another package for database support from another
vendor, and work out the details of the automation of specific equipment on a tool-
by-tool basis. Finally, some commercial vendors are providing control “solutions,”
rather than software packages alone. These vendors provide software, consulting,
and may also completely integrate the controller into an existing factory system.
This eliminates or helps reduce the need for on-site control experts.
1.3.3 NEW ALGORITHMS

Since the development of initial R2R process control algorithms in the late 1980s
and early 1990s, many works have provided in-depth analysis of existing control
methods, making them more widely accepted and easier to use.23–30 Several methods
have been developed to address many of the practical issues involved with imple-
menting R2R process control in the manufacturing environment.30 Methods have
been developed to effectively accommodate delays and inconsistencies in the data
returning from ex situ metrology.26 Other works have focused on the need to effec-
tively tune the controllers,27 while still others have focused on the comparative
evaluation of control algorithms.31*** There has also been a significant effort to
bring standard techniques from the controls field, including proportional integral
differential (PID) control, internal model control (IMC), and robust control.28
In contrast to these developments, there has been a significant amount of work
to develop new methods for controlling semiconductor processes. These develop-
ments have included new algorithms such as neural network controllers,32–34 adaptive
controllers,35,36 and other techniques. These works have contributed significantly to
* See, for example, Chapter 18.

** See, for example, Chapter 11.
*** See, for example, Chapter 6.

the number of different tools available for addressing the wide range of situations
present in the manufacturing environment. Many aspects of algorithm advancement
are covered in Part 2 (Chapters 3 through 6), and in portions of Parts 5 and 6
(specifically Chapters 17 to 20) of this book
1.3.4 NEW METROLOGY

A significant effort in the early 1990s was dedicated to developing in situ sensors
and on-line metrology. This work has focused largely on the development of in situ
sensors for real-time endpoint detection and process control, as well as on-line
metrology for automated R2R process control. As a result, a large number of in situ
sensors have appeared for use in plasma etching, including temperature sensors,37,38
full-wafer interferometry (FWI),39 optical emission spectroscopy (OES),40 RF mon-
itors,41 scatterometry,42 and others. These sensors have been used in many applica-
tions, including endpoint detection on etch processes43 and R2R control of plasma
etching.44 Sensors have also been developed for chemical mechanical polishing
(CMP), including motor current sensing, interferometric sensing through a window
in the pad,45 thermal imaging of the pad,46 and other techniques.
Several on-line metrology tools have also been developed. These systems offer
significant throughput advantages with or without R2R process control. In particular,
on-line epitaxial thickness measurement tools have been developed and used for
R2R process control.47 An on-line metrology tool for chemical mechanical polishing
has been developed and used for R2R process control using several different tech-
niques.12,48,49 It has been shown that the cost of ownership (COO) for the CMP
process can be greatly reduced using this tool.12,48,49 It is likely that many more
metrology tools will be developed in the near future, and will provide the opportunity
for further advancements in process control and wafer processing.50,51 R2R control
could benefit from many forms of metrology, in-line (integrated) and off-line, but
also in situ, as R2R control solutions are developed to utilize in situ measurements.*
1.3.5 ACCEPTANCE OF RUN-TO-RUN CONTROL

With the development of enabling technologies and framework specifications, com-
mercial control software, new algorithms, and new sensors and metrology, advanced
process control, and specifically R2R control have matured significantly. R2R control
is now widely accepted as a means for production fabrication facilities to improve
processing quality, increase throughput, and decrease cost. The many works dem-
onstrating improvements gained by the use of R2R control over a wide range of
semiconductor processes** have resulted in advanced process control being recog-
nized as a key factor to achieving the performance and reliability requirements that
future semiconductor manufacturing will require. With this in mind, the future of
APC, and specifically R2R control in the semiconductor industry, will now be
discussed.
* See Chapter 18.

** See, for example, Chapters 11, 13, 16, 17, 18, and 19.

1.4 THE FUTURE OF ADVANCED PROCESS CONTROL
It has been suggested that feature size decreases and wafer size increases will not
continue at a pace necessary to produce a twofold improvement in performance-per-
dollar every 18 to 24 months.52 If this is true, then the twofold improvement in
performance-per-dollar must be achieved in other areas. Thus, the opportunity for
increased tool operating efficiency must be pursued using on-line metrology, in situ
sensors, process control, and endpoint detection to significantly contribute to cost
and performance improvements.12,53 In this section some of the possible benefits that
advanced process control could soon provide are discussed, an R2R control solution
example is presented to illustrate some of these benefits, and suggestions are given
for areas where future research and development is needed to maximize the impact
of APC on the semiconductor industry.
1.4.1 BENEFITS OF ADVANCED PROCESS CONTROL

1.4.1.1 Benefit: Increased Throughput
For many years it has been suggested that automation with advanced process control
will provide significant improvements in throughput, resulting in reductions in cost.
The increased throughput will likely be derived from the combination of on-line
metrology speed-ups (e.g., measurement and wafer processing occurring in parallel)
and the elimination of operator wait times (e.g., performing and inspecting metrology
results manually). In some applications there are expected to be added benefits such
as the removal of processing steps. For example, Figure 1.9 illustrates that a signif-
icant increase in throughput and a significant decrease in the number of clean steps
(i.e., cleaning after polishing and before reworking in CMP) can be achieved through
the addition of sensors and process control.48 Since OEE is largely governed by idle
equipment, downtime, and setup time, lessening of inefficient operation or “wait”
time could address about 15% of the loss in OEE.12,53
R2R control could also extend the period between some maintenance operations,
especially those associated with replacing consumable sets. Further, control algo-
rithms customized to the process could tune the process immediately after a con-
sumable set change, thereby reducing tool reconfiguration and increasing OEE.*
Note also that additional gains in this area will likely come from multiple-process-
step control solutions.**
While R2R process control may increase efficiency, the impact that increases in
setup and maintenance times could have on OEE should be carefully considered.
Setup and maintenance times often offset or overshadow the throughput increases
due to improved operational efficiency. Because the added parameters of more
complex controllers can make tuning and debugging difficult and time-consuming,
minimizing the complexity of a controller is critical to reducing the added setup and
maintenance times and maximizing the benefits. As a result, controllers that have

** See, for example, Chapter 15.

10 Minutes
5 Minutes
Polish Look-
Clean Measure
Ahead
30 Minutes
Calculate Polish
10 Minutes
Polish Lot Clean Measure
30 Minutes
90 Minutes
Calculate Polish
Rework Lot
Clean Measure
2/24 Wafers
30 Minutes 10 Minutes
10/45 Minutes
12 Minutes
Polish Look- On-Line Calculate
Ahead Measurement Polish Time
90 Minutes
On-Line Calculate
Polish Lot
Measurement Polish Time
Rework Lot On-Line

Clean
2/24 Wafers Measurement
30 Minutes
10/45 Minutes
FIGURE 1.9 Two CMP processes: one with a high-quality, low-throughput process using
ex situ metrology, and one with a higher quality, high-throughput process using on-line
metrology and R2R control.
followed the “keep it simple” approach have achieved the largest success.11,52 The
majority of commercial products are thus based on relatively simple integral con-
trollers,12,19,23 and have focused on resolving a wide range of practical implementa-
tion issues. This trend will likely continue until more complex controllers demon-
strate significant improvements in critical areas.

1.4.1.2 Benefit: Reduced Non-Product Wafers
An issue that has always plagued manufacturers attempting to improve process cost
of ownership and throughput while maintaining yield is the lost processing time and
cost associated with processing non-product (NP) wafers. These wafers are usually
required as part of the qualification of a process, e.g., after a process maintenance
(PM) event where a consumable set is replaced. For example, a CMP pad replace-
ment is often followed by a qualification period where NP wafers are used to “break
in” the pad. SPC techniques can be used to verify that the process is qualified and
the likelihood of misprocessing has been reduced to a level where processing of
product may resume. However, these techniques can be very inefficient, resulting in
lost OEE due to the extra time required to process NP wafers, and lost tool COO
due to the cost to the NP wafers and any pad life lost due to processing NP wafers.
Advanced process control can reduce the requirement for NP wafers by more
quickly qualifying the process. This capability is largely a function of the control
algorithm used and, more specifically, the capability of the control algorithm to
model the process shift associated with the PM event and any transient process
behavior that directly follows this event. This topic is explored further in Chapter 18.
1.4.1.3 Benefit: Improved Wafer-to-Wafer

and Lot-to-Lot Variability
It has been suggested that process control will greatly improve wafer-to-wafer or lot-
to-lot processing quality. It is likely that this area is where the greatest benefits of APC
will be derived, and will contribute to significant improvements in manufacturing
processes. A number of works suggest that APC techniques reduce process variability,
and more specifically, process capability.3–5,7–10,12,15,19,23,29,47–49 Process capability is a
function of process variability and process accuracy, i.e., closeness to target.* APC
improves process accuracy utilizing pre- and postprocess measurement, modeling of
process and equipment trends, and suggesting subsequent process parameter adjust-
ments (i.e., feedback control). Process variability is generally reduced through pre-
process measurement and subsequent process parameter adjustment (i.e., feedforward
control). Thus both pre- and postprocess metrology play a role in improving process
accuracy. Of the two, the impact of premetrology is often underestimated, even by
control engineers. Indeed, in scenarios where product variability dominates over
equipment or process variability and trends, utilization of premetrology has been
reported to account for up to 80% of the improvement in Cpk achieved with APC.54
The improved process capability can also result in reductions in process margins.
These reduced process margins could create the opportunity for new design rules
that lead to performance improvements. For example, tighter specifications on the
post-CMP within-die variability could lead to possible reoptimization of the follow-
ing lithography steps. These reoptimizations could lead to improvements in line
width variations, which in turn could allow tighter tolerances on device sizes. The
result would be higher performance-per-dollar devices. Improved process margins
* Process capability is defined in Chapter 11.

FIGURE 1.10 Improving the window of variability through CMP process control reduces
the amount of deposited oxide, leading to significant cost savings.
could also result in cost and waste reduction, as shown in Figure 1.10. In the CMP
process, the amount of deposited oxide for the inter-level dielectric (ILD) thickness
is equal to the amount of oxide that will be removed in order to achieve planarization,
plus the amount of variability of the final oxide thickness due to wafer-to-wafer and
lot-to-lot variability. Improving the control of the final film thickness reduces this
variability, and hence reduces the required amount of deposited oxide. In doing so,
this reduces the amount of processing in the CMP step, as well as the deposition
step. In both cases the result is reduced waste, power consumption, chemical usage,
and, ultimately, cost, as well as increased throughput.
1.4.1.4 Benefit: Reduced Within-Wafer

and Within-Die Variability
One of the most important improvements that R2R process control could address is
that of within-wafer and within-die variability. The difficult task of controlling
within-wafer and within-die nonuniformities will become particularly important as
wafer sizes move toward 300 mm, where wafer-level uniformity is expected to be
a major problem. This wafer-level nonuniformity will compound any within-die
nonuniformity superimposed on the wafer-level nonuniformity. In many applica-
tions, such as CMP, this within-die variability is generally quite large, often several
times larger than the across-wafer nonuniformities. Unfortunately, little work has
been done to incorporate these factors into R2R control algorithms. Doing so often
requires a significant understanding of the process being controlled, and thus control
engineers are unable to address these more complex factors when controlling a
process. It is also often the case that process engineers are unwilling to allow dynamic
changes in the process recipe in order to achieve improvements in these effects. This
resistance is generally due to process audit requirements, or a fear of scrapping
production wafers because of unseen problems in important wafer properties that
are not being directly controlled but are the result of changes in the process. Another
reason few controllers have addressed the within-wafer and within-die nonunifor-
mities is that there is often a need for more accurate process models in order to
control a process. The rapid pace of the semiconductor industry results in process
models being far behind current technology. These problems result in a retreat to

simply adjusting process time, or small process parameters that affect only the lot-
to-lot or wafer-to-wafer variability.
1.4.1.5 Benefit: Reduced Operating Errors
Finally, it is suggested that R2R process control will reduce misprocessing and other
operating errors. This reduction in operating errors could be achieved via automated
metrology upload and automatic recipe generation and download.12* This automation
is facilitated by utilizing appropriate control-enabling technologies and adhering to
a framework for integrated control, as described in Section 1.3.1. Reducing operator
errors through adoption of automated process control could drive a large improve-
ment in processing quality, particularly in the fab ramp-up period, where frequent
changes and tweaking are made to processes. The reduction in processing error
during this period is critical to the overall cost effectiveness of a new fab and its
ultimate profitability. This area is one that has received a lot of attention but is
difficult to demonstrate.12,54 Much more work is needed in this area in order to help
solidify the benefits of using APC in complex multistep fabrication processes. With
the maturation of R2R control and APC systems in general, the industry in a much
better position to begin further study of these benefits.
1.4.2 EXAMPLE OF APC BENEFITS: R2R CONTROL

OF A CMP PROCESS
The CMP process has been a prime early beneficiary of R2R control and serves as
an excellent example to illustrate the many benefits of R2R process control. A
schematic of a typical CMP R2R control solution is provided in the Introduction
section of this book. In general, current CMP R2R control solutions monitor post-
and possibly preprocess wafer thickness and center-to-edge uniformity, and modify
process parameters such as time, backpressure, carrier speed, and platen speed, in
a run-by-run fashion based on advice from the control solution. A typical example
of an uncontrolled CMP process is included in Figure 1.11 (Callout #1). Note that
the process is characterized by the following features: (1) a fairly continuous deg-
radation in pad removal rate over its life, (2) fairly regular pad replacement events
triggered either by the execution of a predetermined number of process runs or —
as in this example — the occurrence of an SPC alarm on process remaining thickness,
(3) a pronounced “spike” in removal rate directly after a pad replacement event, and
(4) a pad break-in phase directly after pad replacement where the pad is qualified
either by utilizing a predetermined number of NP wafers or by utilizing NP wafers
until the process is within acceptable limits.
The individual benefits of applying R2R control — and specifically tool and
process specific R2R control — are also illustrated in Figure 1.11 (Callouts #2
through #5). The first important improvement noted in the controlled solution is that
the process drift due to pad wear is eliminated during the useful life of the pad
(Callout #2). This, in turn, results in reduced process variability and improved

FIGURE 1.11 Example illustrating the many benefits of R2R control in controlling a CMP
process (controlled solution utilizes “new pad” feature*). Callout #1: Uncontrolled process;
note high process drift and variability, frequent pad replacement events, and process qualifi-
cation required after pad replacement PM’s. Callout #2: R2R control reduces process vari-
ability and drift. Callout #3: R2R control increases pad life, thereby reducing (pad)
consumable cost and reducing PM’s (thereby increasing OEE). Callout #4: Process-specific
R2R control reduces “spike” in removal rate associated with pad replacement, and more
quickly brings the process within acceptable bounds (thereby increasing OEE and reducing
requirement for NP wafers). (Reprinted with permission from MiTeX Solutions, Inc.,
www.mitexsolutions.com. “New Pad” process customization feature developed by MiTeX
Solutions, Inc. See Chapter 18 for a description of the algorithm utilized.)
process capability. The second related result is that pad life is extended through
adjustment of the process parameters to keep the product measured quality param-
eters within SPC limits (Callout #3). The benefits of extending pad life include not
only reduced cost of consumables, but also increased OEE due to the reduced
frequency of PM events to replace the pad. Note that these control benefits, illustrated
in Callouts #2 and #3 in Figure 1.11, can generally be achieved without tailoring
the control solution to the PM pad replacement event.
Another significant improvement noted with the controlled solution is the
reduced requirement for test wafers (Callout #4). This portion of Figure 1.11 illus-
trates that, with the controlled solution, the magnitude of the “spike” in removal
rate, associated with a new pad, is reduced. Further, the tool is brought to a process-
capable state more quickly, resulting in the use of fewer NP wafers and increased
OEE as a result of reduced pad qualification time. Note that this class of control
benefits can generally be achieved only if the controller includes a model of the pad
change event. In the control solution depicted in Figure 1.11 the controller contains
a model of the expected removal rate shift associated with a pad change. An enhance-
ment to this control solution is described in Chapter 18, where the controller models
not only the process shift associated with this PM event, but also the subsequent
process dynamics usually associated with pad break-in.

It is important to note that this example, while specific to CMP, could easily be
extrapolated to other processes. For example, a chemical vapor deposition (CVD)
process can be characterized by drift associated with source depletion, and shift
associated with a source replacement PM event. An etch process can be characterized
by drift associated with chamber wall seasoning (polymer buildup), and shift asso-
ciated with a chamber clean PM event. Thus, if the appropriate metrology capability
is available to measure process quality, and if process-specific control models can
be developed, these processes can also experience the same class of benefits dem-
onstrated for the CMP process.
1.4.3 AREAS FOR FUTURE RESEARCH AND DEVELOPMENT

Many of the R2R algorithm solutions currently being successfully applied to R2R
process control in semiconductor manufacturing are described in detail in Part 2 of
this book. In the remainder of this section, we will describe three possible avenues
for future R2R control algorithm advancement and discuss each possibility in terms
of the benefits outlined above, the effort required to achieve these benefits, and the
likely success of achieving them.
1.4.3.1 Complex, Adaptive, Self-Tuning Controllers
There has been a fair amount of research activity into process control strategies with
complex tuning algorithms.28–30,32–36,39 These works address issues such as the self-
tuning of parameters, optimality of controller parameters, rapid correcting algo-
rithms, robust process control, and other issues. These works often follow the work
done in the controls field and provide a natural progression for work in APC. The
controls field has dealt with many of these problems over the last few decades, and
this provides a nice vehicle for applying control algorithm developments and proofs
of stability and optimality to existing processes. It is often suggested that these
methods should be incorporated as soon as possible, and this would create the
greatest increase in process control performance in the semiconductor industry. In
light of this, we now consider the possible benefits of this approach, the impact
these benefits would have, and the likelihood of achieving them.
Consider the question of stability of a semiconductor process using R2R control.
Currently, most processes to which R2R control is being applied are generally “well-
behaved” in the sense that relatively simple model-based control solutions — such
as dynamic linear approximation solutions — can be effective over the process range
specified for a tool.7,9,11,12,15,23,44,47–49 For example, typical CMP control models
approximate monotonic, though multivariate, relationships between inputs and out-
puts.12 Further, the drifts in these processes are gradual, while shifts can generally
be detected using SPC techniques. Thus, using a combination of R2R control and
limits monitoring, R2R control solutions have been demonstrated to remain stable
in typical process scenarios.12 Therefore, stability of R2R control is not seen as a
major issue in semiconductor processing.
Reliability, on the other hand, is critically important to the operating time,
efficiency, cost, and profitability of a piece of equipment in a semiconductor facility.

This is another reason why controllers that have obeyed the “keep it simple” rule
mentioned earlier have had large success.52,11 Controllers of this type generally
provide good control because the drift rates of most semiconductor processes are
small relative to the amount of noise in the process. The simplicity of these control-
lers allows them to be easily understood by the many individuals working with the
processes, while at the same time allowing the control engineers to focus on the
many manufacturing issues (e.g., nonperiodicity of the measurements) that are
critical for reliable operation. The maturation of the APC infrastructure is likely to
improve on many of these issues, but these manufacturing issues will nevertheless
play an important part in the selection of any control system. In addition, most
increases in complexity focus on improving the performance of the controller. This
can sometimes result in a less user-friendly, less reliable system with a minimal
improvement in quality. However, addressing robust control for use in the semicon-
ductor industry may be an important exception to this rule of thumb, and could
result in significant improvements in both the reliability and quality of APC systems.
Optimality is also of noted importance in semiconductor process control. Many
control problems result from poor process models (either too simple or too complex)
and improperly tuned controllers. Many classical control techniques are based on
dynamic system modeling, and variations of these control approaches focus on
improving the control of wafer-to-wafer and lot-to-lot variability by tuning the
parameters of the controller.
However, addressing optimization of the parameters of a controller, while impor-
tant, is not always of primary concern in many APC applications in semiconductor
manufacturing. This is because such “optimized” APC solutions are usually aimed
at addressing wafer-to-wafer and lot-to-lot process variability; such sources of vari-
ation are, however, not always the largest to be considered. For example, in plasma
etching a large amount of etch rate variability is often observed. This variability
may be caused by device dependencies in the process that are the result of the
amount of open area on the different devices. So, in actuality, the variation is the
result of a lack of effective control or understanding relating to the device depen-
dencies in the process. The same may easily be true in other processes, such as CMP.
Consider a CMP process, and the within-die plot of 25 (postpolish) site thick-
nesses shown in Figure 1.12. Note that the range of these measurements is on the
order of 3000 Å. If we now consider a single site within the die plotted for several
dies across the wafer, as shown in Figure 1.13, we see that the (postpolish) within-
wafer variation range is only on the order of 500 Å. Further, consider the plot of
the (postpolish) mean thickness of a single device that was processed using a simple
EWMA controller shown in Figure 1.14. Here the wafer-to-wafer and lot-to-lot
variation range, which excludes effects due to the device, is also on the order of
500 Å.
The causes of the within-die variation, methods to measure and model these
variations, and mechanisms for assessing the impact of these variations on processing
are often unknown to process control engineers. This problem is often due to a lack
of a detailed understanding of the semiconductor process at hand, and the lack of
process visibility that can be provided by in situ sensors and metrology. Evidence,

8500
8000
7500
Post-Polish Thickness (A)

O
7000
6500
6000
5500
5000
0 5 10 Site # 15 20 25
FIGURE 1.12 The within-die variation of the postpolish oxide thickness measured at 25 sites
throughout one die (individual data point points are replicates from other die).
8500
8000
7500
Post-Polish Thickness (A)
O
7000
6500
6000
5500
5000
1 2 3 4 5 6 7 8 9 10
Site #
FIGURE 1.13 The within-wafer variation of the postpolish oxide thickness.
such as that cited above, suggests that focusing on improving our understanding of
the processes, how to measure the sources of variation, and how to build fundamental
process models for use in control would have a much larger impact on controlling

8500
8000
7500
Mean Thickness (A)

O
7000
6500 Lot 1 Lot 2 Lot 3 Lot 4
6000
5500
5000
10 20 30 40 50 60 70 80 90
Wafer #
FIGURE 1.14 The wafer-to-wafer and lot-to-lot variation of the postpolish oxide thickness
average of measurements taken at one location on 22 dies, plotted over four lots of 24 wafers.
semiconductor processes than would efforts focused on improving control parameter

optimization techniques for current algorithms — or incorporating more complex
algorithms to control problems of wafer-to-wafer or lot-to-lot variability.
1.4.3.2 Tool- and Process-Specific Models and Controllers
A major problem for many semiconductor processes lies in the control of device
dependencies. The die-level signature profiles for different devices often look com-
pletely different. This results in metrics such as the post-process mean thickness
being very different for different devices, and makes controlling the processing of
these different devices extremely hard. Current controllers only approximate these
effects by utilizing different models for different devices, or by using correction
factors. Using multiple models makes it difficult to track tool changes in the models
of devices other than the one being run. Therefore, running one product for a long
period before switching to another product can cause a serious degradation in the
quality of the second product. The device correction factors used to correct this are
an improvement, but inaccuracies in their values can result in high variability or can
require complex methods for updating model parameters such as deposition rate. In
addition, the device correction factors are often specific to the exact locations of the
measurements taken on the devices. While the monitored locations may be controlled
correctly, there is little indication of what is happening in the rest of the device.
Additionally, any change in the measurement plan can cause shifts or other unde-
tected errors in the resulting product wafers.

Other problems with process lie in qualifying and stabilizing the process after a
PM event such as replacing a consumable set. As an example, a polish pad replacement
event on a CMP tool is almost always followed by a pad qualification phase. The
nonproductive tool time associated with this pad “break-in” event reduces throughput
and OEE and requires the use of NP wafers. A control solution that does not model
the pad replacement transient signature does not address this problem, and in some
cases can actually increase the process shift associated with the PM event.
Significant opportunities exist to correct these problems by incorporating process-
specific models into existing control schemes.55–57 With respect to the device depen-
dency problem outlined above, models that provide approximations of the funda-
mental response of the process at hand, particularly with respect to device depen-
dencies, could greatly increase a controller’s knowledge about the controlled devices.
Correlating measured values with those expected from the process-specific model
would allow prediction and vitual monitoring of unmeasured regions of the con-
trolled wafers. Such fundamental models, while not necessarily precise, would allow
the user to greatly expand the degree at which different devices are monitored and
controlled. With respect to the post-PM process qualification problem outlined in
the previous paragraph, control solutions that model process and equipment shifts
and subsequent transients associated with common PM events can reduce the time
and NP wafer requirements for tool requalification, thereby increasing throughput
and OEE and improving COO.*
1.4.3.3 Multistep or Full-Flow Process Controllers
Finally, it is often the case that process control efforts are local; controlling param-
eters of one process on one tool neglects the larger picture of the manufacturing
process as a whole. The main reason for this process-centric control effort is that
process and control knowledge is also largely process-centric. Relatively little work
has been done to combine issues from multiple steps in the semiconductor manu-
facturing process into a process control effort aimed at solving problems related to
a series of steps.15,58 Multiple-step process control has the potential to have a large
impact on the industry, and very recently efforts have begun to focus on evaluating
the viability and effectiveness of multistep process control. For example, in
Chapter 15 a method is described for precompensation of CMP uniformity target
based on downstream etch uniformity data. In Chapter 20, techniques and results
for multiple-step feedforward control between lithography and etch processes are
reviewed, and a generic, multiple-step control-enabling technology is described.
These efforts represent the first steps in an area of control where the possible benefits
could be particularly rewarding. Solutions at this level would allow for focus on a
total factory control solution rather than process-centric, independent control solu-
tions. In addition, many integration issues are centered around device dependencies
in processing. As noted above, device dependencies arise in many processing steps
and interact between multiple processing steps. It is these interdependencies between
multiple process steps and device layouts that lead to significant manufacturability,

reliability, and performance losses. Combining the process-centric fundamental mod-
els mentioned above with multiple-step control methods is yet another area for
significant improvement in control.
A particular example of such a device dependency is that of postpolish, within-
die variation in CMP. This variation has a direct impact on the depth of focus (DOF)
of the following lithography steps. This DOF has a large impact on the variability
of the interconnect lines, and hence the performance of the resulting device. Post-
CMP measurements of the variation of the focusing mechanism in lithography tools
are often taken. Unfortunately, there is often little or no communication of these
results back to the CMP area. There exists an opportunity for future control algo-
rithms to take advantage of the APC framework in order to utilize these types of
process interactions to significantly improve the overall semiconductor manufactur-
ing process. Addressing control from a total factory solution standpoint will allow
for the incorporation of these interdependencies into the control strategy, and better
correlation of the controller assessment and tuning to the factory yield (rather than
individual process parameters).
1.5 SUMMARY
In this chapter we have reviewed the progression of control in the semiconductor
industry from statistical process control to run-to-run process control, which was
driven by the reduction of random tool processing variability and the increase in
steady long-term process drifts. We discussed how this trend toward R2R control
uncovered many new issues. These new issues were largely manufacturing related,
and several key barriers to process control were addressed. The resulting advance-
ments included: (1) the development of enabling technologies and a framework
around which process control could be developed, (2) the development of several
commercial applications for run-to-run control, (3) the introduction of many new
sensors aimed at real-time and run-to-run process control, and (4) several advances
in process control algorithms. Finally, we addressed the future of APC by first
discussing its many benefits, including increased throughput and OEE, reduced NP
wafers, improved process variability and capability, and reduced operator error. We
then summarized the future trends in process control for the semiconductor industry.
Specifically, we suggested that there will be a shift away from complicated tuning
algorithms with simple process models, toward more process-focused control
approaches with fundamental process models. Further, we outlined how multiple-
step process control methods could greatly increase the processing quality over
several complicated or difficult-to-control steps. We have suggested that these
approaches provide promise in dealing with the difficult task of controlling within-
wafer and within-die variation in the face of device-dependent processing.
The material presented in this chapter provides motivation for exploring (1) the
capabilities and limitations of current R2R control algorithm approaches being
applied in the industry (Part 2); (2) enabling technologies and frameworks for cost-
effective deployment, integration, and reuse (Part 3); (3) examples of solution
approaches and results (Parts 3 through 5); and (4) areas for advancement (Part 6).

With this motivation in hand we hope we have established a foundation for the
understanding of the material in the remainder of this book.
ACKNOWLEDGMENTS
We would to thank the NSF/SRC Engineering Research Center for Environmentally
Benign Semiconductor Manufacturing for supporting this work.
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2 Process Control and
Optimization Methods
for Run-to-Run
Application
Enrique Del Castillo and Arnon M. Hurwitz
2.1 INTRODUCTION
In a typical semiconductor manufacturing process, within-run (or batch) variation
is usually controlled by automatic controllers built into the equipment. Batch sizes
may be as small as one wafer in some processes. A run-to-run (R2R) controller is
necessary since specifications can change from batch to batch, the equipment may
experience aging or wearing-out phenomena, maintenance operations can change
the operating conditions of the process, or process disturbances may enter the system
suddenly. This implies that equipment controllers cannot be kept operating at a fixed
recipe. Thus, an R2R controller is needed to act as a supervisor, indicating whether
a recipe change is needed and suggesting a new recipe for use in the next batch.
Frequently, R2R controllers are model-based. Linear regression techniques are
used to estimate initial equipment models from experimental data. Here, the process
is seen as a “black box,” and models derived in this way are empirical in nature,
i.e., the models are not based on first physics/chemistry principles. We hasten to add
that this is not always the case in R2R control, as some first-principle state-space
controllers have been developed and implemented successfully. However, due to the
rapid technological change, empirical statistical models are widely used in relatively
new, poorly understood processes.
The development phases of a black box R2R control system are depicted in
Figure 2.1. During qualification of a new process or equipment, experimental and
statistical techniques are used for obtaining initial models and an initial optimal
recipe. Then, the R2R controller tunes or adjusts these initial models and recipe,
trying to keep the process at the optimized level (which becomes the target value
in case targets were not previously available). Due to their simplicity and robustness,
R2R controllers based on the exponential weighted moving average (EWMA) sta-
tistic are probably the most frequently used in industry.
The goal of this chapter is to provide a technical review of R2R control and
optimization methods. An overview of R2R optimization techniques is first provided
in Section 2.2. The stability and robustness of EWMA-based controllers are discussed

Response
(max. type)
baseline
run or batch
number
prior to optimization control

opt. (DOE/RSM)
qualification "release to manufacturing"
FIGURE 2.1
in detail in Section 2.3, where methods for tuning these controllers are also described.
Other important R2R control techniques are briefly reviewed in Section2.4. A review
of the literature up to 1995 was provided by Del Castillo and Hurwitz.11 One of the
goals of this chapter is to give a more up-to-date review of available methods.
2.2 R2R PROCESS OPTIMIZATION TECHNIQUES

For the qualification of a process and the development of mathematical models that
relate the process inputs to the corresponding outputs (responses), several techniques
have been reported in the literature, ranging from statistical methods such as design
of experiments (DOE) and response surface methods (RSM)2 to fuzzy logic models9
to the use of artificial neural network.38
DOE and RSM are widely used in industry for process characterization and
optimization, not only in semiconductor manufacturing. Given the relevance of these
methods, Chapter 14 provides an introduction to RSM techniques that will be useful
to process engineers working in semiconductor manufacturing. In this chapter we
discuss in detail the use of the Ultramax method,28,36 a commercial software devel-
oped by Ultramax Corp.
Sachs et al.31,32 illustrate the use of this software in semiconductor R2R pro-
cesses. Ultramax has been described19 as a Bayesian formulation of a ridge regression
estimator18 that works also in the rank-deficient case (i.e., the algorithm can be
launched even without observations). The appendix of this chapter provides a
detailed description of the inner works of the Ultramax algorithm.
An advantage that Ultramax displays over the usual “tweak and maintain” SPC
algorithms is its ability to “search” and characterize a feasibility region while seeking
an optimum; the run-to-run (sequential) optimization is accomplished by a “back-
wards and forwards” motion around the primary optimization region or point. The
utilization of this search facility prevents the algorithm from becoming trapped in

Selectivity Poly ER
15 500
13 400
Min Poly ER
Constraint
11 300
9 200
7 100
5 0
0 4 8 12 16 20
Run number
FIGURE 2.2
a relative maximum or minimum, and allows Ultramax to navigate through the

relative optima.
Ultramax is multiple input, multiple output (MIMO), and thus can support a
task such as the following application to a reactive ion etch (RIE) plasma system.28
The first problem formulation was “optimize selectivity subject to polysilicon etch
rate greater or equal to 250 Å/min.” An initial “optimum” recipe was derived via
classic design of experiments (DOE). The problem formulation was then entered
into Ultramax (in similar fashion to a DOE setup) and the sequential optimizer was
allowed to optimize the process on a run-to-run basis. The experimental results in
Figure 2.2 show that etch selectivity was improved by almost a factor of two over
a span of 20 runs, while the minimum etch constraint was not violated.
A second experiment (Figure 2.3) shows the effect of a deliberate system per-
turbation at run number 20. Here we see that the initial degradation in selectivity in
the few runs following the perturbation is followed by a period of system recovery,
where the selectivity is both improved and stabilized.
In experiments involving a planarization processes19 it was confirmed that Ultra-
max will act as a good R2R system optimizer for locating an optimum, or for
recovering from a system perturbation. Ultramax works remarkably well for a system
that requires quite a bit of “driving” toward a better operating point, and will function
robustly in a production environment through its recognition of input constraints as
well as output target ranges (specifications).
2.3 EWMA-BASED R2R CONTROLLERS

The EWMA statistic has been used for a long time for quality monitoring purposes.
Its use as the basis of a recipe adjustment technique is relatively more recent. The

System Perturbation
11
10
Selectivity 8
5
0 5 10 15 20 25 30 35
Run number
FIGURE 2.3
work of Box and Jenkins4 on minimum variance process control under the assump-
tion of IMA(1,1) noise is probably the first reference to this type of statistic for
process adjustment purposes. More recently, Sachs and his co-workers33 introduced
an R2R controller for semiconductor manufacturing purposes based on a single
EWMA statistic. This controller was termed a “gradual mode” controller to distin-
guish it from a “rapid mode” controller (not based on the EWMA) that recommends
more drastic recipe changes if there is statistical evidence the process is badly out
of control.
For a time series of measurements {Xt, Xt–1, …} where t denotes the run number,
the EWMA is given by
EWMA t = λXt + (1 − λ ) EWMA t −1 (1)
where the weight parameter λ (0 < λ ≤ 1) and some initial condition for the recursion
(1) have to be chosen. Evidently, the weight given to a measurement that occurred
j runs ago is
λ(1 − λ ) .
j
Therefore, it can be seen that the weights decrease geometrically (exponentially if

time is continuous) with the age of data. For a process that exhibits dynamic changes
in its model structure, such “discounting” of older data can be very useful. Intuitively,
in such a system, giving more weight to more recent measurements makes sense for
run-to-run control.
In this section, stability, robustness, and tuning aspects of EWMA-based R2R
controllers are presented. Our presentation is limited to the gradual-mode MIT
controller (based on a single EWMA equation) and the predictor–corrector controller
(based on two EWMA equations).

2.3.1 SINGLE EWMA-BASED R2R CONTROLLERS
Rather than deriving an optimal control law based on some optimality criteria (e.g.,
minimize output variance), the structure of EWMA-based controllers is first specified
and then justified by looking at how robust these controllers are with respect to
structural or parametric changes in the assumed models.
The single EWMA-based controller assumes the simple linear regression model
Yt = α + βUt −1 + ε t (2)
where the {εt} constitute a white noise sequence (i.e., they have zero mean, constant
variance, and are not autocorrelated), Ut denotes the controllable factor setting at
the end of run t (beginning of run t + 1), and Yt denotes the measured response at
time t. The parameter α is called the offset or bias and represents the mean value
of the response when the controllable factor equals zero (frequently, Ut is scaled
into the (–1, 1) range according to standard DOE coding conventions). The parameter
β is called the process gain and it is usually estimated off-line using DOE and
regression techniques conducted during the qualification of the process. We will use
the notation b = βˆ to denote the gain estimate.
If model (2) were known to be the true system description and T denotes the
target response value, then the minimum mean square error (MMSE) control strategy
is simply to fix the controllable factor at the value
T −α
Ut = (3)
b
which constitutes a feedforward controller. In practice, model (2) is not an accurate

description of the process due to disturbances. For this reason, Sachs and his co-
workers33 propose to reestimate the parameter α recursively from run to run using
the EWMA expression
αˆ t ≡ at = λ(Yt − bUt −1 ) + (1 − λ )at −1 (0 < λ ≤ 1) (4)
and the feedback control law is
T − at
Ut = . (5)
b
Equations (4) and (5) are referred to as “bias controllers.”

EWMA-based controllers are simple instances of internal model controllers.15
In an internal model controller (Figure 2.4), the differences between the prediction
of a model and the actual process response value are fed back to the controller via
a filter that attenuates large model errors and adds robustness against unmodeled
disturbances or unmodeled process dynamics. The controller is frequently the inverse

disturbance
+
T ∑ process ∑ Response
controller
+ +
-
+
prediction
model ∑
-
filter
FIGURE 2.4
of the model. For a single EWMA-based controller, the “model” is simply the
estimate of the gain, the process is simply given by the true gain β, the EWMA
filter given by Eq. (4) is used on the feedback loop, and the controller takes the
difference T – at as input, multiplies this times the inverse of the model, and generates
the control action given by Eq. (5).
2.3.1.1 Stability and Robustness Properties of Single

EWMA-Based Controllers
Ingolfson and Sachs20 investigated the gradual mode controller for the case when
the process obeys a slightly more complicated model:
Yt = α + βUt −1 + δt + ε t (6)
where δt is a deterministic trend component. If Eq. (6) is the true process description,
these authors show that the EWMA-controlled system will be asymptotically stable
if and only if
1 − λξ < 1 (7)
where ξ = β/b is a measure of the quality of the gain estimate. Furthermore, assuming
condition (7) holds, they show that the asymptotic mean square deviation (AMSD)
from target is given by
t→∞ [
AMSD DT (λ ) ≡ lim E (Yt − T ) =
2
] 2σ 2 δ2
+ 2 2
2 − λξ ξ λ
(8)
where Var(εt) = σ2. Ingolfson and Sachs show that the gradual mode controller is a
discrete integral controller of the form

t
Ut = K0 + K I ∑Y
i =1
i
with K0 = –λ/b and KI = T/b. These controllers are very well known and compensate
for process shifts and offsets. The robustness of this type of controller has been
emphasized in a recent book by Box and Luceño.6
An important question for EWMA-based controllers is how to select the λ weight
in Eq. (4), i.e., how to tune the controller. Smith and Boning34 show that the weight
that minimizes the AMSD (given by Eq. (8)) is given by the real root of
σ 2 ξ3λ31 − δ 2 ξ 2 λ21 + 4δ 2 ξλ1 − 4δ 2 = 0 (9)
that satisfies the stability condition. To solve Eq. (9), the probably unknown process
parameters σ, ξ and δ are needed, and this limits the practical application of this
result. In general, most authors agree that the larger the relative drift δ/σ, the closer
λ should be to one.
It is interesting to investigate what would happen if the single EWMA controller
is applied to a process in a perfect state of “statistical control,” namely, a process
such that
Yt = α + ε t
if Ut is always zero. In a recent paper, Del Castillo14 shows that the inflation in
AMSD over the minimum possible variance for Yt (given by σ2) is given by
AMSDDT (λ ) 2
= . (10)
σ 2
2 − λξ
which extends similar results by Box and Luceño,6 who analyze the case ξ = 1, i.e.,
the known gain case. This gives evidence in favor of using small values of λ
(around 0.1). In this way we have the assurance the controller will compensate
against process shifts and drift for a small price to pay (in terms of inflation of
AMSD), in the order of 10%, even if we grossly misidentify the process gain by a
factor of two. Note that even if ξ ≠ 1, the EWMA controller still contains “integral
action,” and this will compensate for offsets or shifts. A good part of the “robustness”
of these controllers (and also of PI controllers) comes from the integral action.
2.3.1.2 Other Process Disturbances
The performance of the single EWMA applied to disturbances other than a deter-
ministic trend has been studied recently.14 For the case where the process model is
Yt = α + βUt −1 + Nt (11)

with
Nt = Nt −1 + δ + ε t (12)
i.e., a random walk with drift disturbance, it is shown that the stability condition is
the same as before, namely, condition (7). Furthermore,
σ2 δ2
AMSDRWD (λ ) = + 2 2 (13)
ξλ(2 − ξλ ) ξ λ
is shown to be minimized by using an EWMA weight of
4δ 2 − σ 2 − σ 8δ 2 + σ 2
λ RWD = (14)
(
2 δ2 − σ2 ξ )
a weight that always satisfies the asymptotic stability condition. If, on the contrary,
the disturbance follows an IMA(1,1) process,5
Nt = Nt −1 − θε t −1 + ε t
where θ is a moving average parameter, then it is shown that
1 + θ2 − 2(1 − ξλ1 )θ 2
AMSDIMA (λ1 ) = σ
ξλ1 (2 − ξλ1 )
which is minimized by setting
1− θ
λ IMA = .
ξ
Note that if ξ = 1, then λIMA = 1 – θ provides the minimum possible AMSD, as

shown by Box et al.5
2.3.2 DOUBLE EWMA-BASED R2R CONTROLLERS

Butler and Stefani8 notice that for a severe drift per time unit, the offset of the
controlled response, as given by the second RHS term in either (8) or (13), can be
too large even when large weights λ are used. To avoid such undesirable situation
they propose to introduce a second EWMA equation in the controller,
Dt = λ 2 (Yt − b ut −1 − at −1 ) + (1 − λ 2 ) Dt −1 (0 ≤ λ 2 ≤ 1) (15)

and the controller is then given by
T − at − Dt
Ut = (16)
b
where at is as in Eq. (4). Double EWMA-based controllers (also called “predic-

tor–corrector” controllers) are internal model controllers where a double EWMA
filter is used on the feedback loop. Del Castillo13,14 has recently shown that if the
disturbance is any of the following,
Deterministic trend
Random walk with drift
IMA(1,1)
the system controlled with a double EWMA will be asymptotically stable if and
only if the following two conditions are satisfied:
1 − 0.5ξ(λ1 + λ 2 ) + 0.5z < 1 (17)
1 − 0.5ξ(λ1 + λ 2 ) − 0.5z < 1 (18)
where z =
(
ξ2 λ + λ
1 2 )2 − 4λ1λ 2ξ . For the listed disturbances, if the process is stable,
then, asymptotically, it will be on target on the average, thus the AMSD equals the
asymptotic variance. Expressions for AVAR are very complicated.13 However, if it
can be assumed the process gain is known (i.e., ξ = 1), the asymptotic variance for
a stable system under a deterministic trend disturbance is
σ2  λ2 λ + λ (λ − λ )2 λ (λ − λ )2 + λ λ2 
AVAR(Yt ) = 
1 2 2 1 2
+ 1 1 2 1 2
 + σ . (19)
2
( λ1 − λ 2 ) − λ − λ
2
 2 2 2 1 
The stability conditions for this controller define a circular region on the λ1, λ2 plane
(see Figure 2.5).
From Figure 2.5 and Eq. (19), it can be seen that to minimize the asymptotic
variance and obtain a stable response, we should use small weights λ1 and λ2. The
problem with this recommendation, originally given in the internal model control
literature, is that the transient effect will be too large for small weight parameters.
A measure of the severity of the expected transient up to a specified run number m
is given by the average mean square deviation:
∑ E[Y − T ]
1 2
MSD = t ≡ MSD .
m t =1

λ2
0 0.2 0.4 0.6 0.8 1
1
0.8
0.6
λ1
0.4
0.2
FIGURE 2.5
Del Castillo14 provides an expression for MSD for the algebraically simpler case
of ξ = 1 (known gain). A spreadsheet optimization model (downloadable from
http://www.ie.psu.edu/people/faculty/castillo/research.htm) is available to minimize
a weighted sum of the asymptotic variance and MSD :
min γ 1AVAR(Yt ) + γ 2 MSD (20)

λ1 , λ 2
subject to
0 < λ1 < 1
0 < λ2 < 1
where γ1 and γ2 (with γ1 + γ2 = 1) are two weights selected by the user. In Del
Castillo,13,14 it was recommended to simply give equal weight to each objective. A
more complete analysis for different objective weights can be performed from which
a process engineer can choose a particular set of optimal EWMA weights that solve
problem (20) according to his/her preferences. The value of m should be selected
based on the number of runs the process will operate. For example, consider the
case when α = 2, δ = 0.1, and σ = 1.0, that is, the case when we have a small relative
drift δ/σ. If m = 100 runs are going to be conducted, Figure 2.6 shows the optimal
(λ1, λ2) weights that solve Eq. (20) optimally.

m= 100
α=2, σ=1, δ=0.1
1.0 γ1=0.0, γ2=1.0
0.9
0.8
0.7
γ1=0.05, γ2=0.95
0.6
λ1
γ1=0.1, γ2=0.9
0.5
γ1=0.2, γ2=0.8
γ1=0.3, γ2=0.7
0.4 γ1=0.4, γ2=0.6
γ1=0.5, γ2=0.5
0.3 γ1=0.6, γ2=0.4
γ1=0.7, γ2=0.3
γ1=0.8, γ2=0.2
0.2 γ1=0.9, γ2=0.1
γ1=1.0, γ2=0.0
0.1
0.00 0.01 0.02 0.03 0.04 0.05
λ2
FIGURE 2.6
The plot reveals that unless we give more weight to the transient effect than to
the AVAR objective (i.e., unless γ2 > γ2), the optimal solution to (20) calls for using
λ2 ≈ 0, which implies the use of a single EWMA-based controller. In other words,
for small relative drift, single EWMA control is sufficient. This situation is further
emphasized if m = 20 is used instead (Figure 2.7). Note that the extreme cases (γ1 =
1, γ2 = 0, and γ1 = 0, γ2 = 1) in Figures 2.6 and 2.7 lead to the same (λ1, λ2) solutions.
In the first extreme case, all weight is given to the asymptotic variance, and this is
not a function of m. The second extreme case is more striking, since we are giving
all weight to MSD, which is clearly a function of m.
For large relative drift δ/σ, Figures 2.8 and 2.9 reveal that a double EWMA-
based controller is necessary (i.e., λ2 > 0 for all cases when γ2 > 0). As before, the
extreme cases yield the same EWMA weight solutions regardless of m.
More information on single and EWMA controllers can be found in Chapter 3
of this book.
2.4 OTHER R2R CONTROL METHODS

As mentioned before, a review of R2R control methods was provided in Reference 11
for up to 1995. Some newer developments are briefly discussed in this section.
Leang and Spanos22,23 propose to look at sequences of semiconductor manufac-
turing processes. They propose two control approaches, one in which feedback/feed-
forward techniques are applied to each pair of adjacent processes. They also sketch
in24 a global control approach that will improve the overall capability of the sequence.
Their approach can handle multiple inputs and outputs at each process step.
Stefani et al.35 propose to use a standard DOE/RSM approach to build quadratic
multivariate equipment models of the form

m= 20
α=2, σ=1, δ=0.1
1.0 γ1=0.0, γ2=1.0
0.9
γ1=0.05, γ2=0.95
0.8
γ1=0.1, γ2=0.9
0.7
γ1=0.2, γ2=0.8
0.6 γ1=0.3, γ2=0.7
λ1
0.5 γ1=0.4, γ2=0.6
γ1=0.5, γ2=0.5
0.4 γ1=0.6, γ2=0.4
γ1=0.7, γ2=0.3
0.3 γ1=0.8, γ2=0.2
γ1=0.9, γ2=0.1
0.2
γ1=1.0, γ2=0.0
0.1
0.00 0.01 0.02 0.03 0.04 0.05
λ2
FIGURE 2.7
m=100
α=2, σ=1, δ=0.5
1.0 γ1=0.0, γ2=1.0
0.9
γ1=0.05, γ2=0.95
0.8
γ1=0.1, γ2=0.9
0.7
γ1=0.2, γ2=0.8
γ1=0.3, γ2=0.7
0.6
λ1
γ1=0.4, γ2=0.6
γ1=0.5, γ2=0.5
0.5 γ1=0.6, γ2=0.4
γ1=0.7, γ2=0.3
γ1=0.8, γ2=0.2
0.4
γ1=0.9, γ2=0.1
0.3
0.2
γ1=1.0, γ2=0.0
0.1
0.00 0.05 0.10 0.15 0.20 0.25
λ2
FIGURE 2.8
Y = β0 + ∑β X + ∑β X + ∑ ∑β X X
i i ii i
2
ij i j (21)
where the X’s denote the controllable factors. These authors propose an adaptation
technique for tuning initial models of the form of (21) that selects “offset” parameters
oi and “gain” parameters gi in

m=20
α=2, σ=1, δ=0.5
1.0 γ1=0.05, γ2=0.95
γ1=0.0, γ2=1.0
γ1=0.1, γ2=0.9
0.9
γ1=0.2, γ2=0.8
0.8 γ1=0.3, γ2=0.7
γ1=0.4, γ2=0.6
0.7 γ1=0.5, γ2=0.5
γ1=0.6, γ2=0.4
0.6 γ1=0.7, γ2=0.3
λ1
γ1=0.8, γ2=0.2
0.5
γ1=0.9, γ2=0.1
0.4
0.3
0.2
γ1=1.0, γ2=0.0
0.1
0.00 0.05 0.10 0.15 0.20 0.25
λ2
FIGURE 2.9
Y = β0 +∑ β ( X + o ) + ∑ β (g X ) + ∑ ∑ β ( X + o ) (g X ) +
i i i i i i ij i i j j
∑β (X + o ) ∑β g X .
2 2
ii ii i ii i i
The offset and gain parameters are obtained by minimizing the sum of squared errors
of each response added up and weighted by each response prediction error variance.
That is, response k receives a weight 1/S 2k. This tuning technique, in effect, generalizes
the concept of “bias tuning” on which EWMA controllers are based, to the case where
not only the bias (offset) but also the gains are adapted in a full quadratic RSM model.
Baras and Patel1 present a worst-case R2R controller based on an ellipsoidal
algorithm that estimates a set of possible parameter values of RSM model. Within
that set, a recipe is obtained by taking a worst case (minimax) approach.
Work related to using information from an initial response surface model is that
of Hamby et al.17 They consider a multiple input, single output run-to-run system
described by a first-order linear regression equation and controlled by a single
EWMA controller. Their approach can be explained more simply by referring to the
single input, single output (SISO) case. From the stability condition 1 – λξ < 1,
the authors develop the interesting concept of probability of stability P(1 – λξ <
1) where the density of b = β̂ (obtained from regression analysis) is used for
integration and therefore can be computed analytically. A second interesting concept
used to determine λ is the probability of performance, Pi = P(AMSD(λ) < κ), which
is computed by Monte Carlo simulation of the density of b. The value of λ that
maximizes Pp is selected.
Equipment models with adaptation based on recursive least-square estimation
and self-tuning control techniques have been proposed for the SISO case,11 and the

MIMO unconstrained case.12 These papers are the predecessors of the OAQC algo-
rithm described elsewhere in this book.
Finally, we should mention that internal model R2R controllers based on first
principles — as opposed to based on empirical black-box models — have also been
developed.37
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31. Sachs, E., Guo, R.S., Ha, S., and Hu, A. (1991) “Process Control System for VLSI
Fabrication,” IEEE Transactions on Semiconductor Manufacturing, 4, 2, 134-143.
32. Sachs, E., Hu, A., and Ingolfsson, A. (1991b) “Modeling and Control of an Epitaxial
Silicon Deposition Process with Step Disturbances,” IEEE/SEMI Advanced Semicon-
ductor Manufacturing Conference Proceedings, 104-107.
33. Sachs, E., Hu, A., and Ingolfsson, A. (1995) “Run by Run Process Control: Combining
SPC and Feedback Control,” IEEE Transactions on Semiconductor Manufacturing,
8, 1, 26-43.
34. Smith, T.H. and Boning, D.S. (1997) “Artificial Neural Network Exponentially
Weighted Moving Average Controller for Semiconductor Processes,” Journal of Vac-
uum Science & Technology a, 15, 3.
35. Stefani, J.A., Poarch, S., Saxena, S., and Mozumder, P.K. (1996) “Advanced Process
Control of a CVD Tungsten Reactor,” IEEE Transactions on Semiconductor Manu-
facturing, 9, 3, 366-383.
36. Yunker, S. and Moreno, C.W. (1992) “Ultramax: Continuous Process Improvement
through Sequential Optimization,” Electric Power Research Institute, Palo Alto, CA.

37. Theodoropoulou, A., Zafirou, E., and Adomaitis, R.A. (1999) “Inverse Model-Based
Real-Time Control for Temperature Uniformity of RTCVD,” IEEE Transactions on
Semiconductor Manufacturing, 12, 1, 87-101.
38. Wang, X.A. and Mahajan, R.L. (1996) “Artificial Neural Network Model-Based Run-
to-Run Process Controller,” IEEE Transactions on Components, Packaging, and Man-
ufacturing Technology-Part C, 19, 1, 19-26.
APPENDIX. HOW THE ULTRAMAX® SOFTWARE WORKS

The software program called Ultramax* is a multivariate process optimizer that
builds a model of a running process in a sequential manner. Such an optimizer is
similar in its intent and action to the well-known EVOP strategy as described in
Box and Draper.3 Ultramax is, however, software-based, whereas EVOP is not. This
section describes in some detail the algorithm underlying the Ultramax optimizer.
The first step in running an application of the optimizer is to enter the problem
formulation into the software. This is akin to the design stage of an experimental
design–execute–analyze project. A list of input factors (design variables) and output
factors (responses) is given along with their operating constraints. Additionally, prior
regions are named; the prior region of a variable gives the area inside of which that
(input or output) variable has, in the past, occurred.
An objective or goal function is also defined; this may be a single output or a
function of outputs (for example, a sum of loss functions). Output constraints are
typically the process or product specifications that we desire, and the input con-
straints define the low to high regions of input factor allowances.
Three features of Ultramax are of particular note.
1. The optimization can begin with little or no data. This is of great value
in production when, as is usually the case, no screening experiments have
been run ahead of the optimization. If such data are available, they can
be entered into the Ultramax database and the program will use them
appropriately.
2. As experimental data are added more parameters are estimated and, if
enough runs have been accomplished, the data are selected and weighted
according to a heuristic method. In this latter case, all (model) coefficients
of a second-order Taylor series approximation to the underlying process
response surface are the parameters that are estimated.
3. The program recommends one or more advices to be taken as future run
settings (recipes). The advice may be strictly adhered to, modified, or
dropped if necessary. The advice given is a result of optimizing on the
goal function while at the same time respecting all input and output
constraints; an advice is a prediction based on the latest version of the
response surface that the software has at its disposal. In this sense one
can regard it as a feedforward, model-based adaptive optimizer.
* Ultramax is a registered trademark of Ultramax Corp., Cincinnati, Ohio. Thanks to Dr. Carlos Moreno
of the Ultramax Corp. for his assistance in this regard.

Item 1 above relates to the estimation algorithm, and we discuss it in some detail
below. Item 2 relates to the weighting, or screening, of the accumulated database,
a topic that we will not discuss. Item 3 is the well-known topic of constrained
optimization (see Press et al.30) and needs no further discussion here.
Ultramax estimates a process response surface as a second-order Taylor series
approximation. Let us adopt the standard regression model formulation:
y = Xββ + ε (22)
with X and n × p matrix, β a p × 1 vector, ε an n × 1 error vector which is normally

distributed with zero mean and covariance matrix σ2In. Let the ordinary least squares
(OLS) estimator of β be b, where
b = ( X ′X ) X ′y
−1
(23)
The Ultramax version of b is B, with
B = ( X ′X + K ) X ′y
−1
(24)
where K is a diagonal matrix, diag(ki), with ki constants, (i = 1, … , p).

B reverts to b when enough data have finally been observed. As we can see, B
is similar to a ridge-type estimator of the kind proposed by Hoerl and Kennard18
where ki = k for all i. Hoerl and Kennard developed their estimator for X of full
rank, whereas we see that B is proposed for the rank-deficient case as well.
A RANK-DEFICIENT BAYES ESTIMATOR

For X of full rank it has long been recognized that a correction to the b of Eq. (23)
in the form of a small, positive quantity added to each diagonal element of X′X has
certain desirable features, particularly if X′X is ill-conditioned, that is, has some
very small eigenvalues. Piegorsch and Casella29 have traced this development as far
back as 1944 with Duncan10 and Levenberg,25 as well as to 1963 with Marquart.27
It is of some interest to note that Levenberg’s development was in response to
problems of estimating first-order Taylor series approximations to non-linear func-
tions problems that arose due to the omission of second- and higher-order terms.
For convenience, let us assume that the independent variables of (22) are scaled
so that X′X is in correlational form, that is, that diagonal elements of X′X are unity
and the off-diagonals are the same correlations. The Hoerl–Kennard ridge regression
estimator mentioned above is
( )
−1
β* = X′X + kI p X ′y (25)
where k > 0 is a constant that is chosen by graphical means or by some other plausible
criteria.

As is well known (see, e.g., Graybill16), there exists a p × p matrix Q such that
QX′XQ′ = Λ = diag(λi) with the λ2i being the eigenvalues of X′X. Now suppose
that Q is chosen such that λ2i ≥ λ2j for all i > j, and that λ2r+1 , … , λ2p are all assumed
to be zero for rank(X′X) = r ≤ p. Partition Q′ into {Q′r : Q′p–r}, where Q′r is p ×
r and Q′r is p × (p – r), and define Λ2r = diag{λ21, … , λ2r}.
If we define (X′X)r = Q′r Λ2rQr, then b+ = Q′r Λ–2rQrXb′y is a generalized inverse
estimator for β since (X′X) +r = Q′r Λ–2rQr is a generalized inverse estimator for X′X.
This fact was noted by Marquart,27 who also suggested a combined generalized
inverse-ridge estimate for β as
{ }
−1
b +* = (X′X)r + kI p X ′y (26)
An estimator that is close to (26) in form may be derived by considering a set

of parametric constraints of β of the form Hβ = 0, where H = Qp–r . Brown7 notes
that the estimator b+o = X+y, where X+ is the Moore–Penrose generalized inverse for
X′X, may be viewed as the limit of the Hoerl–Kennard ridge estimator as k → 0+.
A Bayesian approach to (26) is to adopt a Bayesian prior for β such that the
prior expectation of Hβ is zero. One such form, given by Goldstein and Smith,21 is
(
Φ(β) ∝ exp − 1 2σβ2

) ( Hβ)′ ( Hβ) (27)
The Bayes estimator with respect to quadratic loss is given by the posterior mean
of β, and is
−1
( )
b Φ = (X′X) + σ σβ H′H X′y
2
(28)
 
−1
  2 0 0   
 
(
= Q′ Λ2 + σ σβ )
0
 Q X ′y
I p − r   
(29)
 
If (σ/σβ)2 λ2i for all i, … , r, then
−1

( 
)
b Φ = Q′ Λ2 + σ σβ I pQ X′y
2
(30)
   
−1
( )
= X′X + σ σβ I p  X′y
2
(31)
 
That is, we have a plausible estimator that will work even in the rank-deficient case.

Note that this type of estimator is akin to the wider class of estimators derived
by Lindley and Smith.26 Lindley and Smith’s derivations turn on a concept called
“exchangeability,” which is here evidenced in (27) by the presence of a common σβ
for the coefficient vector β. The presence of exchangeability can here be justified
by our device of X′X in correlational form.
THE ULTRAMAX FORMULATION

Turning to the Ultramax formulation, we learn that X of Eq. (24) is in deviational,
not correlational, form, that is, centered but not standardized. Let us write this special
case of X as x; that is, for any column of x, xj = (xij – mj), where xij are the raw
observations on independent factors or second-order terms, and mj is its sample
mean. Let sj be its observed sample standard deviation, and let M = {diag(sj n)–1}
be a p × p diagonal matrix, n > 2. Then M′x′xM = (rjk), the p × p matrix of
correlations. Substituting xM for X in Eq. (31), we obtain
−1
( )
b Φ ≅ ( xM )′ ( xM ) + σ σβ I p 
2
( xM )′ y (32)
 
Noting that M′ = M, and M–1 = diag(sj n), we can derive
b Φ ≅ M −1{x ′x + K} x ′y
−1
(33)
with K = diag{n(σsj/σβ)2}, thus
b B = {x ′x + K} x ′y
−1
(34)
is an appropriate Bayesian shrinkage estimator for full or rank-deficient cases.

Part 2
R2R Control Algorithms
Several different algorithmic approaches have been proposed in the last few years
for R2R process control. The earliest work in this area is that of Sachs and his co-
workers at MIT who proposed to use a feedback controller based on the so-called
exponentially weighted moving average (EWMA) statistic. In the past, the EWMA
statistic had been used widely in industry for process monitoring purposes, but in
R2R control it is used as part of a simple feedback controller that suggests when
and how to adjust a process. In Part 2 of this book, R2R control algorithms that are
based on the EWMA statistic and algorithms based on some other approaches are
presented.
Specifically, in Chapter 3, two basic R2R algorithm approaches are described
that utilize EWMA data filtering. Included in this chapter is the “gradual mode”
controller of Sachs et al., which uses a single EWMA equation, and the so-called
“predictor–corrector” controller, developed at Texas Instruments, which uses two
coupled EWMA statistics. These two algorithms have been effectively utilized in
practical R2R control application in the semiconductor industry; examples of such
applications are presented in Chapters 11, 13, and 15.
Chapters 4 and 5 detail a different class of controllers based on a further
development of the R2R adaptive control concept. The inner works of an R2R
algorithm, termed OAQC, are described. The OAQC can act both as a controller (if
the responses should track given targets) or as an optimizer (if responses need to be
maximized or minimized). As was mentioned in Chapter 2, the application of
optimization techniques usually precede the use of control techniques, since the first
are used to find an initial recipe during the qualification of a tool. Thus, there is an
inherent advantage in an R2R algorithmic solution that incorporates both optimiza-
tion and control.

Another important distinction can be made between the EWMA controllers of
Chapters 3 and the OAQC and similar controllers of Chapters 4 and 5. EWMA run-
to-run algorithms are based on a linear first-order approximation around the current
recipe to a possibly nonlinear and drifting process. The EWMA statistics act as a
filter of large system/model deviations caused by the nonmodeled dynamics, pro-
viding a robust approach to control (see Chapter 2). In a variety of semiconductor
processes such local linear approximation becomes necessary. The OAQC and sim-
ilar methods (e.g., the Ultramax method, see Chapter 2) can be seen as providing
second-order (quadratic) polynomial approximations of the process responses around
the current recipe. The parameters in these quadratic polynomials are continuously
tuned by a learning mechanism (see Chapter 4), and this allows tracking of nonlinear
changes in the process that occur from run to run.
The algorithms presented in Chapters 3 through 5, while addressing R2R control
using a variety of approaches, do not represent the complete set of algorithms
available for R2R control. For example, neural network and expert-systems-based
solutions have been proposed. While each of these algorithms has its own strong
points, and effective R2R control can often be accomplished using basic R2R control
techniques (see Chapters 1 and 2), a detailed comparative analysis nevertheless
should be attempted as part of the process control solution development and deploy-
ment process. Chapter 6 provides one of the few studies that compares the perfor-
mance of various R2R control algorithms presented in the literature. More impor-
tantly, it identifies aspects of an R2R control algorithm that should be explored as
part of the selection process.

3 Basic R2R Control
Algorithms
William Moyne
3.1 INTRODUCTION
In the Introduction and Part 1 of this book we illustrated the many current benefits
and discussed potential future benefits of R2R control. These benefits can be realized
to a large extent utilizing straightforward and uncomplicated control algorithms.
Having an understanding of these algorithms will provide the reader with ammuni-
tion to help develop simple but effective R2R control solutions.
The focus of this chapter is to explain two of the more basic R2R control
algorithms used today in the semiconductor industry, namely the “EWMA gradual
mode” and the “predictor–corrector controller (PCC).” Both of these algorithms are
multiple input, multiple output (MIMO) first-order polynomial control approaches.
That is, they approximate the system they are controlling as a set of polynomial
equations containing only constant and first-order terms. This may at first seem
limiting, but with these algorithms it is assumed that R2R control will be applied
to a relatively stable process, subjected to noise and drift, and other techniques will
be used when the process becomes unstable (mechanisms such as SPC could be
utilized to identify the need to transition to these other techniques — see Chapter 1).
The process drift may be monotonic or cyclical. Once the nature of the system has
been established, both the EWMA gradual mode and PCC algorithms act as piece-
wise linear approximators over many runs. Using this strategy, complex models can
be linearized around an optimal point and, as such, are presented to the controller
to maintain that point.
3.2 ALGORITHM FORMULATION

Since both of the algorithms being described in this chapter are polynomial-based
and linear, they can be represented using standard linear equation techniques. Spe-
cifically, the algorithm uses an ‘m’-by-’n’ (inputs-by-outputs) linear model with an
additional constant term.*
Y = Ax + c (1)
* Equations will use the following notation: Arrays will be capitals, vectors will be lower case, and
indexing within a vector or matrix will be lower case with subscripts. In addition, the special subscript
t will be reserved for time or run number information.

where y = system output,
x = input (recipe),
A = slope coefficients for equation,
c = constant term for linear model.
This matrix notation can be expanded into the familiar simultaneous equations
notation. Each output represents a target of control, and each input represents an
adjustable parameter in the recipe.
y1 = a11x 1 + a12 x 2 +…a1m x m + c 1
L (2)
y n = a n1x 1 + a n 2 x 2 +…a nm x m + c n
The algorithm operates under the assumption that the underlying process is locally
approximated by the first-order polynomial model, and that this polynomial model
can be maintained near a local optimal point solely by updating the constant term
c. In order to allow maximum flexibility for algorithmic development, the compu-
tational engine associated with the R2R algorithm is divided into two parts:
• Model update
• Recipe update
This division applies to both the EWMA gradual mode and predictor corrector
algorithms. In the remainder of this section we will describe the methods used for
both model and recipe update in each of these algorithms.
3.2.1 MODEL UPDATE

Updating the model is the first step in the control process. Currently (with these two
algorithms) this entails updating the constant term used in the polynomial model
equation. This step of the control process determines how aggressive the controller
acts, as well as its ability to handle different conditions such as drift.
3.2.1.1 Model Update in the EWMA Gradual Mode Algorithm

The EWMA gradual mode algorithm uses one of the simplest methods of model
update (see Chapter 1). As its name implies, it filters historical data with an expo-
nentially weighted moving average (EWMA) filter to prevent overcontrol. A single
weighting factor α is used.
ct = ∑ α(1 − α)
i =1
t −i
( yi − Axi ) (3)
Although (3) would provide the desired EWMA weighting, it also requires data
from all previous runs. Luckily, this can be simplified using the additive nature of
the series to generate an iterative expression for the constant term update:

ct = α( yt − Axt ) + (1 − α ) ct −1 (4)
Using an EWMA filter to smooth the control action on a linear process has been
shown to provide good results in a number of applications.1–5 The simplicity of the
algorithm also makes it a natural starting point for an R2R control strategy.
3.2.1.2 Model Update in the Predictor–Corrector Control

(PCC) Algorithm
The PCC algorithm is an expansion on the EWMA gradual mode that adds an explicit
model for drift. Drift is present in many VLSI processes that can “age.” Examples
include pad wear on a chemical mechanical planarizer, or buildup on the wall of a
plasma etcher (examples of this type of drift are described further in the Introduction
section of this book). The PCC algorithm uses two parameters, α and β, to weight
noise and drift, respectively. EWMA weighting is used for both the constant term
update and for the drift estimation.
nt = α( yt − Axt ) + (1 − α )nt −1
( )
dt = β yt − Axt − ct −1 + (1 − β)dt −1 (5)
ct = nt + dt
where n = estimation of noise for run

d = estimation of drift for run
A = slope coefficients for model
y = measured output of the system
x = input (recipe)
c = constant term for model
α = EWMA weighting for noise estimation
β = EWMA weighting for drift estimation
Simulations of PCC vs. EWMA on processes with and without drift show that PCC
provides better drift response with no noticeable penalty when drift is absent.
Changes in the drift rate, however, can lead to potential overshoot based on the time
averaging of the PCC drift estimator. Figure 3.1 shows a comparison between PCC
and EWMA control under both drift and noise conditions.5
3.2.2 RECIPE UPDATE

Once a suitable constant term has been chosen for each of the model equations
separately, the task of determining a new recipe must be addressed. This solution
must take into consideration many conditions and constraints that affect the process.
Although, in the actual controller, the final recipe is calculated in the presence of
all conditions and constraints, they will be discussed separately. The remainder of

FIGURE 3.1 PCC vs. EWMA.
this section will be devoted to presenting the algorithm used for fitting a solution
to the numerous outputs. Parameters and constraints that can affect this solution,
and methodologies for dealing with them, are discussed in Section 3.3.
3.2.2.1 Curve Fitting
At the heart of the R2R recipe algorithm is a matrix least-squares routine. Least-
squares is a method for determining the optimal solution (curve fit) for an overde-
termined (#outputs > #inputs) system.6,7 The method has the favorable property of
providing the “best” solution even if an “exact” solution does not exist. In this case,
“best” refers to the solution that minimizes the squared error between itself and the
exact solution, and “exact” refers to input values to the model that generate the
desired target value exactly. Care must be taken when formulating the problem. The
absolute scale of the inputs can cause certain inputs to be favored over others when
an optimal solution is chosen. This is beneficial when used to modify the behavior
of the controller, but is not desirable if it is not controlled (see input/output weights
discussed in sections 3.3.3 and 3.3.4). To prevent unwanted bias, all inputs can be
normalized (as shown in Eq. (6) below) to between –1 and 1 before any computation.

x−
( xmax + xmin )
xn = 2 (6)
 xmax − xmin 
 2 
where xn = normalized recipe

xmin = lower bound for recipe
xmax = upper bound for recipe.
Based on the formulations of the problem and possible boundary constraints, the
least-squares solution can take on three forms:
• Exact solution
• Overdetermined
• Underdetermined.
Figure 3.2 illustrates examples of the three possible forms of the solution to a control
problem. Each of these must be solved in a different manner. For the underdetermined
case (Figure 3.2a), the system has two inputs (x1 and x2) and one target output (3).
This problem would normally lead to an infinite number of solutions (represented
by a line). Since all solutions are “correct,” it would serve the purpose of the algorithm
FIGURE 3.2 Three possible solution domains.

to simply pick one of the values. This extra degree of freedom is instead used to
bring the solution as close to the previous recipe as possible, minimizing least-
squares distance. This not only reduces the solution to a single value, but also has
the positive effect of minimizing the extent of the changes to the input parameters
of the system.
Figure 3.2b illustrates the effects that two conditions have on a two-input system.
These constraints, which are represented by two lines, create a problem that has
only one solution. This solution (represented by the intersection of the two lines)
satisfies both conditions exactly. Due to the lack of freedom in the problem, the
previous solution information is not used.
With the addition of a third condition, an overdetermined problem arises
(Figure 3.2c). In this formulation there are more conditions than degrees of freedom
in the inputs, so there is no exact solution. A least-squares algorithm is used to
minimize the error between the target for each output and the final solution. Again,
the previous solution is not used to avoid further constraining the problem.
In order to provide a flexible environment that can handle any input/output
combination, the algorithm must first determine which case is occurring, and then
generate the solution accordingly. This could require three separate computational
routines, but luckily this can be reduced to one. Since the least-squared solution is
guaranteed to be the best, it can be used to solve the exact and overdetermined cases
directly and the underdetermined case with some preprocessing of the data. The
mathematical formulation of the recipe update problem for each of these cases is
described in more detail in the following subsections.
3.2.2.1.1 Exact solution
If the number of inputs (n) to a system is equal to the number of outputs (m), then
there is exactly one solution that satisfies the desired outputs. The calculation of this
solution is straightforward:
y = Ax + c
(7)
x = A−1 ( y − c)
Note that here are two uses for the symbol y in the equations used for control. First,
it represents the output of the system. This is what is measured as the real value of
the system output. This value is primarily used to update the constant term c, as
discussed earlier. Second, it is used to denote the target that is desired for that output.
This second use is how it is used in the remainder of this chapter. The two meanings
are similar in that they are the observed and ideal values, respectively, of the system
output.
3.2.2.12 Overdetermined
There are two events that could lead to an overdetermined problem. The first is that
the problem was formulated with fewer inputs than outputs (n < m). Second, the
controller could have originally been underdetermined or exactly determined, but

input bounds forced certain inputs to be locked, thus decreasing the number of
controllable inputs.
Once an overdetermined case is encountered, a least-squares error fit is applied.
This ensures, in a least-squares sense, that the solution places the output as close as
possible to the target. The calculation of the solution is as follows6:
y = Ax + c
AT ( y − c) = AT Ax (8)
( )
−1
x = AT A AT ( y − c )
3.2.2.1.3 Underdetermined
In contrast to the overdetermined case, the underdetermined case is encountered
when the number of inputs exceeds the number of outputs (m > n). This is often the
case in a process. Several inputs can be modified to help maintain a certain output,
so the possible solutions are infinite.
Although being able to reach target is always desirable, the choice of the “best”
solution from the set of all possible solutions must be done in a consistent manner.
Again we turn to least squares. This time, however, instead of merely obtaining an
answer that hits the target, we can also select an answer that is closest to the previous
recipe while still exactly solving the original problem. In this way we can ensure
both that our output is guaranteed to be correct, and that the associated inputs are
modified as little as possible.
The actual formulation of the problem is a little more complex than the other
cases. It involves the use of a Lagrange multiplier (λ) to take the two constraints
and merge them into a single equation.6,7 This method of obtaining “best” results
for underdetermined systems has been used with many of the very first R2R control
solutions applied to actual process control,8 and continues to be used today.9 The
calculation of the updated recipe parameters “x” for the underdetermined case is as
follows:6
2
min x − x0 Ax = b
1
( x − x0 ) ( x − x0 ) + λT ( Ax − b)
T
L=
2
= ( x − x0 ) + λT A = 0
dL T
dx (9)
x − x 0 = − AT λ
Ax − Ax0 = − AAT λ
Ax = Ax0 − AAT λ = b

AAT λ = Ax0 − b
( ) ( Ax − b)
−1
λ = AAT 0
( ) ( Ax − b)
−1
x = x0 − AT AAT 0
where b = t – c (Target – constant term)

x0 = recipe from previous run
λ = Lagrange multiplier
A = slope coefficients for model
L = equation to minimize
3.3 CUSTOMIZATION OF ALGORITHMS

TO PRACTICAL APPLICATIONS:
PARAMETERS AND CONSTRAINTS
The formulations given in the previous section provide “correct” mathematical
solutions to control problems. In the industrial application of R2R control, however,
there are a number of practical issues that must be addressed by the algorithm that
may alter the solution advices generated by these algorithms. These additional
constraints and parameters must be taken into consideration along with those given
by the R2R control equations themselves before a final solution can be found. This
is what often separates a theoretical solution from a “feasible” or “practical” solu-
tion.10 When the controller incorporates these constraints and parameters, the recipe
“advice” generation is altered in a predictable manner. Although these parameters
can complicate an otherwise simple control approach, they can also provide for
valuable operator influence to complement the theoretical controller.
A list of some of the constraints and parameters that impact (e.g., limit or bias)
the answers provided by the theoretical solutions of Section 3.2 is as follows:
Constraints Bias parameters
Input bounds Output weights

Input resolution Input weights
In the remainder of this section, these constraints and parameters are described
in more detail, and algorithm enhancements are presented to incorporate the impact
of these factors into the mathematical formulations presented in Section 3.2.
3.3.1 INPUT BOUNDS

The R2R controller is generally designed to control actual machinery and, as a result,
must account for limitations in the range of possible settings that an input may have.
These limitations could be machine imposed (e.g., specified in a user manual), or

FIGURE 3.3 Input bounds algorithm.
operator imposed (e.g., input range for a parameter that has been qualified for a
process). One way to address input bounding with control is to simply determine
the optimal recipe without input bounds, then fix all input R2R control advices that
exceed these bounds to the closest valid (within bounds) setting. This approach
provides the necessary constraints, but generally results in a less than optimal setting
for the equipment. It is important that the final recipe is chosen in the presence of
these constraints. To achieve this the R2R algorithm can be modified to use an
iterative approach as shown in Figure 3.3.
This approach differs from the one-pass approach in one key area. After the
variables have been modified to respect their maximum ranges, these variables are
removed from the system and the process is repeated. This reduces the possibility
of a nonoptimal solution, but does not guarantee an optimal solution. It is provided
as a computationally inexpensive alternative to a full optimization that can at least
guarantee valid if not optimal results.
3.3.2 INPUT RESOLUTION

A major problem faced when applying R2R control to a real process is input
resolution. Even a perfectly modeled system can suffer from this. Control decisions
based on infinite resolution must be rounded by the operator (or the machine) to
acceptable increments. This can often lead to unacceptable control, and as a side-
effect can give false information back to the controller algorithm: namely that the
suggested recipe was used when, in fact, a rounded version was used.

FIGURE 3.4 Input resolution methodology.
As a first step to addressing this problem, a simple iterative method is proposed

to provide resolution control. Inputs are ordered from least to most adjustable (using
their input weights — see Section 3.3.4) and then sequentially rounded and removed
from the equation. The remaining inputs are then adjusted to obtain the best solution
for the new problem. This is repeated until all inputs have been rounded. Figure 3.4
shows a diagram of the method used.
3.3.3 OUTPUT WEIGHTS

It is often the case that the desired target of a process cannot be reached given the
constraints of the system. If this is the case, a decision must be made as to the relative
importance of each output. The default is, of course, equal weighting, but this may
not be desirable. For example, if a process has two outputs, thickness and uniformity,
the operator may want optimal thickness with a secondary requirement of good
uniformity. The weights could also be set inversely proportional to the variance of
the output variable. This would put greater importance on those variables with low
variance, e.g., those that can be more accurately controlled. The controller accom-
modates output weighting by applying an output weighting matrix W to the system.
w1 0 0
 
W=0 … 0 (10)
 0 0 wm 

where w1 … wm are the relative weights for outputs 1 … m.
The system equation for the output becomes
Wy = Wax + Wc
W ( y − c) = WAx
(11)
(WA)T W ( y − c) = (WA)T WAx
(A W )
−1
T T
WA AT W T W ( y − c ) = x
The weighting works by biasing the magnitude of certain outputs so that when a
least-squared solution is calculated, outputs with higher weights contribute a greater
penalty to the solution if they are off target. Thus, higher-weighted outputs are set
closer to their targets than other outputs. Application of output weights in an exact
or underdetermined system has no effect on the output; in both cases there is no
reason to sacrifice one output to obtain another, as there is an infinite solution set.
Other bias terms related to direct output weights are the model update weights.
These weights (α for EWMA, α and β for PCC control) determine the aggressiveness
of the controller for each of the outputs. These parameters can be used to minimize
the impact of certain noisy outputs on the model update and recipe generation of
the controller, while increasing the impact of more stable outputs. The result is that
a system can quickly adapt to changing conditions while being somewhat resistant
to process noise. An added benefit of these parameters is that they provide these
biased noise filtering capabilities regardless of the type of control problem (i.e.,
underdetermined, exact, or overdetermined).
3.3.4 Input Weights (Input Adjustability)
Although the inputs to the system can be normalized to ensure consistent operation,
weights can also be applied to these inputs to add yet another level of control. Input
weights enable the user to set the adjustability of the inputs. That is, heavily weighted
input variables are adjusted with greater magnitude relative to lightly weighted
variables to achieve process control.
Application of the weighting is achieved by adjusting the normalized input
variables so that the least-squared distance incurred by each variable (distance of
new control advice xt from xt–1 where t is the run number) is adjusted by its input
weight. This should not be confused with the output weighting mechanism discussed
in the previous subsection. In the underdetermined systems where the model indi-
cates a set of solutions where all outputs are met, the recipe is determined with the
added constraint of being as close to the old recipe as possible. This can be biased
by the relative weighting of the inputs. Inputs that are weighted heavily are forced
to be the least adjustable due to their relatively large effect on the error calculation
for the recipe (i.e., the difference between the target and value predicted by the
suggested recipe applied to the model). A matrix V and its inverse V –1 are used to
apply the input weighting.

v1 0 0
 
V = 0 … 0 (12)
 0 0 vn 
where v1 … vn are the relative weights for inputs 1 … n. Note that the input weighting
has no effect on both overdetermined and exact solution problems. In those cases,
the inputs are not factored into the calculation of the error for the final solution, so
the magnitude of the inputs, which is the key to their weighting, is irrelevant.
Once a weight matrix has been defined it must be applied in such a manner as
to ensure that the formulation of the problem leads to a correct solution. In order
to achieve this, the weight must be applied to both the recipe and the slope (first-
order) term. First, the application of the weight term V to the recipe x modifies the
least-squared error generated by these inputs when determining the solution closest
to the previous solution (see Section 3.2.1.3). The side-effect of this weighting is
that the new output generated by these inputs is not consistent with the original
problem formulation. To remedy this, the slope term A is weighted with the inverse
of the recipe weight. The system equation for the output then becomes
Y = Ax + c
( )
Y = A ⋅ V −1 ⋅ (V ⋅ x ) + c (13)
y = A * x * +c
This new formulation can be used in place of the original variables to provide the
necessary weighting. The problem is then treated as before (see Section 3.2.1.3),
but with the new scaled values.
2
min x * − x0 * A* x *= Ax = b (14)
The solution, however, is based on these scaled values, so it must be scaled back to
the original domain.
x = V −1 ⋅ x * (15)
3.4 CONCLUSIONS AND FUTURE IMPROVEMENTS

Two basic R2R algorithms have been introduced in this chapter. Both the EWMA
gradual model and PCC algorithms utilize a MIMO linear polynomial modeling
approach with R2R updates of the constant terms of the equations. The PCC addi-
tionally adds an explicit model for drift. These basic R2R algorithms have been
proven effective in a variety of semiconductor manufacturing applications (see, for
example, Chapters 1, 11, 13, and 15); a key element of the successful application
of these algorithms, however, is their customization/enhancement to address practical

issues such as input and output bounding, discretization, and weighting, as described
in Section 3.3.
There are a number of other algorithms that can be applied to R2R control; some
of these algorithms are detailed in the remainder of this section of the book. Many
new algorithms will undoubtedly be developed in the near future. Since the two
algorithms presented in this chapter are modularized into two components, the model
update stage and the recipe update stage, these algorithms can benefit from advance-
ments at either stage. A key component of the successful utilization of these enhance-
ments, however, will be the ability of these enhanced solutions to accommodate the
practical issues in R2R control introduced in Section 3.3.
ACKNOWLEDGMENTS
Much of the material presented in this chapter is derived from Reference 11 and is
reprinted with permission.
REFERENCES
1. Sachs, E., Hu, A., and Ingolfsson, A., “Run by Run Process Control: Combining SPC
and Feedback Control,” IEEE Transactions on Semiconductor Manufacturing, Oct. 1991.
2. Moyne, J., Curry, J., Solakhian, V., Weaver, T., and Gwizdak, R., “Improving Reli-
ability, Yield and Throughput of Chemical-Mechanical Planarization through Process
Automation and Control,” Advanced Semiconductor Manufacturing Conference:
SEMICON Taiwan ‘98 (Nov. 1998).
3. Moyne, J., “Run-to-Run Control Success Stories,” SEMATECH AEC Workshop VIII,
Santa Fe, NM (Oct. 1996).
P., and Parikh, T., “Multizone Uniformity Control of a CMP Process Utilizing a Pre
and Post-Measurement Strategy,” 46th International Symposium of the American Vac-
uum Society, Seattle, Washington, (Oct. 1999); also accepted for publication in the
Journal of the American Vacuum Society (accepted December 1999).
5. Butler, S. and Stefani, J., “Application of Predictive Corrector Control to Polysilicon
Gate Etching,” American Control Conference, June 1993.
6. Hilderbrand, F.B., Advanced Calculus for Applications, 2nd ed., Prentice-Hall, Engle-
wood Cliffs, NJ, 1976, pp. 357-364.
7. Press, W., Teukolsky, S., Vetterling, W., and Flannery, B., Numerical Recipes in C,
2nd ed., Cambridge University Press, 1994.
8. Kim, M. and Moyne, J., Multiple Input Multiple Output Linear Approximation Run-
to-Run Control Algorithm — User Manual ver. 1.0, The University of Michigan, Nov.
22, 1993.
9. Discussions with MiTeX Solutions, Inc., Canton, MI, suppliers of R2R control solu-
tions for semiconductor manufacturing (www.mitexsolutions.com).
10. Boning, D., Moyne, W., Smith, T., Moyne, J., and Hurwitz, A., “Practical Issues in
Run by Run Process Control,” Proc. Sixth Annual SEMI/IEEE ASMC, Boston, (Octo-
ber 1995).
11. Moyne, W., “Run by Run Control: Interfaces, Implementation, and Integration,” S. M.

4 Learning and
Optimization
Algorithms for an
Optimizing Adaptive
Quality Controller
4.1 INTRODUCTION
The OAQC (optimizing adaptive quality controller) is a process optimization and
control software tool recently developed for application in run-to-run (R2R) manu-
facturing environments. Its most recent version is the result of the evolution of R2R
applications of adaptive control techniques for linear unconstrained single input,
single output (SISO) systems;5 liner unconstrained multiple input, multiple output
(MIMO) systems;3 and nonlinear, constrained MIMO systems.8 The OAQC has been
implemented on the NextStep (Mach) and Windows NT platforms. The NextStep
OAQC has been integrated with the Generic Cell Controller (GCC, see Reference 14
and Chapter 11 of this book) whereas the WinNT version is not integrated as of this
writing. This chapter will specify which feature applies to each version. When no
specification is made, the feature applies to both versions.
Many R2R controllers are based on response surface models that are obtained
through experimentation during the “qualification” of a process. After qualification,
an R2R controller will determine recipes at run t based on the estimated model
parameters at that run. For a SISO system, a common response model is simply
Y ( x )t = α + βxt −1 + δ t + ε t
where α and β are parameters, Y is the response, x is the level of the controllable
factor, δ t models a deterministic drift, and the {εt} constitutes a white noise sequence
with variance σ2. The so-called EWMA controllers2,15,16 popular in R2R applications
and used as a “benchmark” in the area of R2R control, modify the estimate of α +
δ t by computing the estimate at + Dt(t) and updating the estimates at and Dt at every
run t using EWMA equations. The estimate of the process gain, b = βˆ , is obtained
during qualification experiments and is usually not updated during the control phase.

As mentioned in Chapter 2, these controllers are in fact internal model controllers10
and their properties have been studied in considerable detail.4,11,16
Rather than performing the two phases, “qualification” and “control,” separately,
the OAQC can start without prior response models and simultaneously build models
and optimize a process, keeping the performance at its optimum as long as it is
possible. In contrast to EWMA controllers, estimation (i.e., adaptation) of all param-
eters, including the gains, can take place. This chapter describes the learning and
optimization characteristics of the optimizing adaptive quality controller. Section
4.2 discusses the optimization problems solved by the OAQC. In Section 4.3 we
describe the OAQC learning algorithm. The important concept of a local model is
explained in Section 4.4. Finally, some additional features of the OAQC controller
are discussed in Section 4.5.
4.2 OPTIMIZATION
To better understand the OAQC approach for process optimization, it is useful first
to look at how design of experiments (DOE) and response surface methodology
(RSM) typically work.
ˆ
When building a response surface model of a response, Y(x), DOE approaches
recommend different settings (recipes) x based on some optimality criteria for the
design or for the estimated responses such as orthogonality, rotatability, or D-opti-
mality. These criteria do not consider whether one wishes to maximize or minimize
a particular response; they concentrate only on model-fitting properties. Suppose
that, after factor screening experiments have been conducted, there is a single
response Y(x) that is known to be affected by n controllable factors, where x ∈ ℜn.
The experimental design problem is then to find
 x 1′   x 11 x 12 L x 1n 
   
x′ x x 22 L x 2n 
X =  2  =  21
 M  L L O L
   
 x k′   x k 1 xk2 L x kn 
such that some criteria for X is optimized. For example, for D-optimality, X′X is
maximized, which implies that the volume of the confidence ellipsoid of the param-
eter estimates is minimized (Var (θ̂) is “minimized” in this sense). Note that this
minimization is achieved regardless of our goals or objectives for Y. If we ignore
the response objectives, D-optimality is a useful design criterion when there are
several bounds or constraints that limit the possible values that x can take.
Once an experiment is designed, the k trial recipes are run and the parameters
θ ∈ ℜk(k ≥ l) are estimated using some variant of the least-squares method:
∑ (Y − Yˆ (θ; x ))
2
min t t t
θ
t =1

where the x’s are fixed and the optimization is over θ-space. The end result is a
parametric model Yˆ (θˆ ; x). The last step in the qualification of a process using DOE
and RSM techniques is the optimization of the recipe x, namely
(( ) )
2
min Yˆ θˆ ; x − T “target is best”
x
or
min Yˆ θˆ ; x
x
( ) “smaller the better”
or
max Yˆ θˆ ; x
x
( ) “larger the better”
Here, the optimization is over the recipe (factor) x space, perhaps subject to one or
more constraints in x.6,7 Note that during this step θ̂ remains fixed. Actually, RSM
usually starts with a series of steepest ascent/descent searches based on a first-order
model until a second-order model can be fit. For simplicity of presentation, we
assume here that Y has been determined to be of second-order after steepest ascent
searches.
An R2R controller like the EWMA controllers will take the models Ŷ(x) and
will try to keep the responses Y at the optimal performance in the presence of process
noise and drift. As can be seen, building models for R2R control consists of three
optimization processes performed sequentially: (1) an experimental design is defined
based on some optimality criteria, (2) a model-fitting (e.g., least-squares) minimi-
zation step is performed, and (3) a recipe-finding optimization step is performed.
The OAQC, instead of solving these three problems in series, attempts to solve them
simultaneously in an incremental way at each run, speeding up the qualification
phase of a process and reducing extreme disruptions to the process while the OAQC
learning algorithms are running.
4.2.1 SIMULTANEOUS RESPONSE OPTIMIZATION

AND MODEL FITTING
For ease of presentation, assume again that there is a single response Y that is known
to depend on n controllable factors. It is desired to keep Y as close as possible to a
target T. However, the input–output relation is unknown and a model Yˆ initially may
not be available. The OAQC solves, at each run t, the following problem:
(
min (1 − λ t ) Yˆt +1 t ( xt +1 ) − T ) − λ (Var(Yˆ (x )) σ )
2
2
t t t +1 (1)
xt +1 ∈ Ω1
where the first term is the squared deviation from target of the one-run-ahead
predicted response, and the second term is the scaled variance of the current estimated

response. The optimization is carried over the factor space within a set Ω1 defined
by factor bounds. The constants {λt} are such that 0 ≤ λt ≤ 1, and give relative
weights to the two objectives in the function: (1) optimization of the response (first
term) and (2) model fitting (second term). As t increases, the value of λt decreases
from 1 to 0. Notice that if λt = 1, the second term is equivalent to a conditional
D-optimality criterion (see Reference 13), i.e., the next run factors are selected where
current prediction is worse as measured by the response variance. Performance
measure (1) is implemented only in the OAQC WinNT. For the corresponding
performance criterion used by the NextStep version, see Reference 8.
4.3 LEARNING ALGORITHM

At each run, the solution to problem (1) provides a new set of factors xt+1 to try
next. Initially, optimization of the objective function (1) will tend to favor factor
settings that will lead to obtaining good response models, as opposed to factor
settings that achieve desired response performance. Learning is conducted through
the estimation of the response parameters using a multivariate recursive least-squares
(RLS) algorithm.12 The RLS algorithm finds θˆ such that it minimizes 1/N ∑ Ni=1 e 2i
where et = yt – θˆ ′tϕt is the residual at time t and ϕ is a l × 1 vector of regressors
(typically, the x’s). The algorithm is
Pt −1ϕ t
Kt = (2)
1 + ϕ ′t Pt −1ϕ t
(
θˆ t = θˆ t −1 + Kt yt − ϕ ′t θˆ t −1 ) (3)
[ ]
Pt = In − Kt ϕ ′t Pt −1 (4)
where Kt is an (l × 1) vector of gains or weights and Pt is an (l × l) matrix proportional

to the matrix of covariances of the parameter estimates at run t.
Note that we do not specify any structural requirement on θ and ϕ. Therefore,
response models can be linear, linear plus 2-factor interactions, or fully quadratic
polynomials, depending on the process engineer’s needs. Models can also contain
a drift parameter. Once the model orders are defined, the dimension l is adjusted in
the recursive estimation algorithm accordingly.
4.4 LOCAL VS. GLOBAL RESPONSE SURFACE MODELS

The OAQC algorithm* constructs local models that are updated as each run is
conducted. This is in sharp contrast to traditional RSM-based run-to-run control
techniques where a response model is first fit, then used by an R2R controller. In a
* Sections 4.4 and 4.5 apply only to the Windows NT OAQC.

classical R2R controller, inadequate performance can occur if the controller recom-
mends factor settings outside of the region where the response model was fit in
factor space, or if the model–system mismatch is large. Rather than using such a
“global” model that hardly can be valid over a large region in the factor space, the
OAQC constructs response models that are valid locally. Local models are achieved
by the OAQC using a variety of techniques. First, an “initial region” of factor settings,
Ω1, is selected by the process engineer. This will limit the values that controllable
factors can take, and will usually be located around a baseline x0 where the process
has been operating in the past. As more runs are conducted, if the OAQC determines
that better operating conditions might exist outside Ω1, the initial region is dropped
and the OAQC will move outside of the initial region. At this point the OAQC will
select controllable factors that (1) satisfy only operational region (Ω2) constraints,
and (2) satisfy a local model constraint, defined as an ellipsoid of controllable factors
x computed based on the most recent recipes. The centroid of this ellipsoid moves
according to an EWMA, giving more weight to the more recent factor settings. The
operational region should be such that Ω1 ⊂ Ω2. This defines limits a process engineer
does not want to exceed in the interest of safety. The main advantage of using an
initial region and a local model constraint is that changes in the operating conditions
of the process are not abrupt, and therefore the process is minimally disrupted from
its regular operation during learning/optimization. If the initial region limits are
dropped, the local model constraint guarantees that the next run will not differ greatly
from the most recent experimental runs. These goals are similar to the goals in
evolutionary operation techniques.1 Figure 4.1 illustrates the idea of local models
and an initial region.
In the figure, there are two factors (x1, x2) that affect the response. Two quadratic
models were sequentially fitted, both of them based on information collected within
an initial region. Eventually, the OAQC finds a small region (depicted as Model 3)
where a better performance is achieved outside the initial region Ω1, but inside of Ω2.
Recently, Hurwitz and Del Castillo9 studied the performance of the OAQC-WinNT
learning and optimization algorithms. They considered a simulated, 3 × 2 highly
nonlinear CMP process with large trends, a particularly difficult system to control. It
was found that the OAQC keeps the responses consistently closer to their targets with
a performance considerably better than a simple open-loop operation of the process
when not much room for improvement was available over the open-loop scenario. For
an account of the performance of the OAQC, see Chapter 5 in this volume.
4.5 RESET ACTION

During a control session, desired targets may change or a response type may need
to be changed. The OAQC defines four types of responses, in a way similar to
Taguchi*:
1. target (the closer to target the better)

2. max (the larger the better)
* The OAQC NextStep version allows only target responses subject to constraints.

x1
model 3
model 2
baseline
model 1
initial region
operational region
x2
FIGURE 4.1
3. min (the smaller the better)

4. constraints only (response should satisfy constraints only).
Suppose that at some point in an optimization/control session, considerably dif-

ferent (new) targets are desired. When the targets change significantly, any control
algorithm should contain an adequate “reset” action that will adapt future recipes to
the new desired performance. A reset action should also be triggered when a response
type changes, for example, from max type to target type. In the OAQC, a reset action
is triggered if any of the changes or transitions shown in Figure 4.2 occur.
We point out that some of the transitions are unlikely to occur in practice (e.g.,
changing a response from “max” to “min” or vice-versa). Once one of the transitions
in Figure 4.2 occurs, the OAQC will try to find a new recipe x that meets the new
objectives. If unsuccessful, it will “explore” the factor space to fit a better model
and get new recipes. This will occur if it is concluded that the local models are no
longer locally valid.
4.6 OTHER FEATURES

This chapter describes the main details of the optimization and learning capabilities
of the OAQC. There are many other features that are useful in run-to-run applications
that we briefly describe here.*
* Features 1 and 2 apply only to the WinNT OAQC.

Max (uncommon) Min
Check new
targets
Check new
targets
Check new
Constraint targets
Target
only Check new
targets
FIGURE 4.2
1. Uncontrollable and controllable factors. A subset of the input factors

that affect the responses may not be controllable; however, they might
affect the responses of the process and they may be observable. Including
these uncontrollable factors in the response models will improve their
prediction capabilities. The OAQC enables definition of these two types
of factors. The sets Ω1 and Ω2 will be defined by controllable factors only.
Once a subset xc ⊂ x of controllable factors is defined, the optimization
of Eq. (1) is carried out by leaving the uncontrollable factors xu fixed and
optimizing (1) only with respect to xc.
2. Nonoptimizable responses. It may be of interest to measure and model
some response without optimizing it, perhaps simply for monitoring pur-
poses. This can be done by defining it as a “constraint only” response and
not defining any constraint. Thus, prediction models will be built for such
responses, but no optimization will take place with respect to them. In
this way, the ability to build regression models (of up to second order) of
nonoptimizable responses of interest is incorporated into the system.
These responses, however, must depend on the same factors x as the
optimizable responses.
3. Factor and responses weights. Not all controllable factors are equally
easy to adjust, and it is frequently desirable to define relative weights that
will make a factor less likely to be varied from its previous run. Similarly,
not all optimizable responses will be equally important, and the OAQC
allows us to define relative weights for each response. For example, once
models have been fit with enough precision by optimizing Eq. (1), we will
have λt → 0. Then, a standard way of incorporating response weights is
(Yˆ t +1 ) (
′
− T Γ Yˆt +1 − T )
where Ŷ and T are p × 1 vectors of estimated (optimizable) responses and
response targets, respectively, and Γ is a p × p diagonal matrix of response
weights, i.e., the i-th diagonal element of Γ (i = 1, 2, … , p) is the relative
weight given to response i. The higher the weight given to a response,
the more penalized its deviations from target are, and the more strict
control of that response we will have.
4. Initial models. The OAQC can start its optimization/learning routine
without prior information about the responses. However, if prior models
are available (perhaps based on previous process data), these can be used
in two different ways: (1) as initial models that will speed up the optimi-
zation/learning process, and (2) for simulation purposes. For the learning
and estimation process, a vector θ0 of initial parameter estimates may be
defined together with its associated precision matrix P0. The more confi-
dence we have in the estimates θ0, the smaller the diagonal elements in
P0 should be. This corresponds to a Bayesian interpretation of the recursive
least-squares estimation algorithm.12 The OAQC allows us to simulate
MIMO systems with responses of up to quadratic order with linear drift
and additive normally distributed white noise. The OAQC optimization
and control algorithm can then be applied to the simulated responses as
if they were the true (unknown) system responses.
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Manufacturing, 7, 2, 193-201.
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Review and Extensions,” Journal of Quality Technology, 29, 2, 184-196.
6. Del Castillo, E. and Montgomery, D.C. (1993) “A Nonlinear Programming Solution
to the Dual Response Problem,” Journal of Quality Technology, 25, 4, 199-204.
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5 An Adaptive Run-to-Run
Optimizing Controller
for Linear and Nonlinear
Processes
Arnon Max Hurwitz and Enrique Del Castillo
5.1 INTRODUCTION
Manufacturing processes encounter many hindrances to fulfilling operational equip-
ment efficiencies. In the Introduction to this book we noted that two causes of trouble
on the manufacturing floor are typically the batch-to-batch or “run-to-run” (R2R)
drift of the actual output performances from the desired level, and also an inherent
inability of the process to deliver consistent high quality. This last-stated problem
has usually been tackled in an off-line manner by statistically designed optimization
experiments. Designed experiments are very effective for developmental work, but
are seldom used in an actual production situation. The first-stated problem (i.e., R2R
control) of tool drift, or shift, has traditionally been managed by the tool operator
tweaking various recipe setpoints of the process, such as temperature. The problem
here lies in varying operator experience levels and attitudes to control. In addition,
it is typical that only one input gets tweaked, whereas, in truth, a number of inputs
affect the various process outputs in some multivariable, cross-correlated manner.
A need is thus identified for an automated R2R control solution that is self-
adapting to optimized control of a process. In this chapter we address the dual
“optimization-control problem” by introducing a multiple input, multiple output
(MIMO) R2R controller that can act as an optimizer and/or a controller. Specifically,
in the first part of this chapter we briefly discuss the original “linear” model control
approach to R2R where model development is done off-line using traditional exper-
imental design. This approach, which is detailed in Chapter 3, has been proven
effective, and a commercial application is mentioned.
We then present a solution to the dual optimization-control problem by intro-
ducing a multiple input, multiple output (MIMO) R2R controller that can act as an
optimizer and/or a controller. This controller — the optimizing adaptive quadratic
controller (OAQC) — can develop equipment models on-line if none are available
(see also Chapter 4). Once a satisfactory model is determined, OAQC will switch
to R2R control mode. The OAQC can also be used in either pure optimization or
in pure batch control mode.

At the conclusion of this chapter we introduce a commercial integration platform
control called the generic cell controller (GCC), which enables “plug-and-play” of
production R2R control solutions such as OAQC solutions. The GCC is described
in Part 3 of this book, and the integration of the OAQC in the GCC integration
platform is presented in Chapter 12.
5.2 “LINEAR” R2R CONTROL

The evolution of linear constrained multiple input, multiple output (MIMO) R2R
control is reviewed in Del Castillo and Hurwitz.5 In its simplest form, for a single
input, single output (SISO) system, a common response model is
y( x )t = α + βxt −1 + δt + ε t (1)
where y is the estimated response, α and β are parameters, x is the level of the
controllable factor, δt is a deterministic drift with t being time, and {εt} a white
noise sequence with variance σ2. This model — called a gradual mode model — is
used as a local approximation to a drifting, possibly nonlinear, response surface as
shown in Figure 5.1.
So-called EWMA controllers11 model (α + δt) as ct and update it using an
exponentially weighted moving average, i.e.,
ct = λ( yt − βxt ) + (1 − λ )ct −1 (2)
The basic mechanics of this simple R2R control scheme is as follows: It is desired
that the output Y equals target T which occurs if the controllable input is set at X
since y = c + bX, where y, estimates E[Y], b is the estimated linear slope, and c the
estimated Y-intercept (Figure 5.2). If there is evidence of a process shift, c is rees-
timated using the above EWMA method (Figure 5.3). X is then recalculated to give
X′ so that Y again equals its target T, that is, X′ = [T – c]/b (Figure 5.4).
Output (Yt)
Model Compensation (Yt)
Process Drift (Yt)
'Gradual Mode'
Control Model
lnitial Process
Operating Point
Process
Response
Surface lnput (Xt)
FIGURE 5.1 “Gradual mode” linear model.

Y
T
X
FIGURE 5.2 Input X gives E[Y] at target T.
T
C
FIGURE 5.3 C is reestimated if process shifts.
T
X'
FIGURE 5.4 X is recalculated so that Y = T.
FIGURE 5.5 A three-table CMP tool.
The parameter b is typically estimated off-line using formal designed experi-

ments, such as Box–Behnken or two-level factorial designs.2 The parameter b then
is assumed fixed. This leads to a control scheme that appears, at first sight, to be
very simple. However, any commercial realization has to go much further.
Boning et al.1 pointed out some practical issues that the design of a R2R controller
should consider. Among these are the importance of considering input constraints; the
weighting of inputs (as some may be required to vary less frequently than others); the
weighting of outputs (as some outputs are more important than others); the resolution
or “granularity” of the input settings; and accountability of uncontrollable inputs.
A solution for the above has been found10 and incorporated into a commercial
controller. This controller is installed in the most recent three-table CMP tool in the
semiconductor industry (see Figure 5.5).*
* By MiTeX Solutions, Inc. of Ann Arbor, MI, in the Strasbaugh, Inc. “Symphony” planarizer.

5.3 NONLINEAR R2R CONTROL
If the process response surface is fairly “flat” in the region of control model approx-
imation, then a linear controller of the type given above should be expected to work
well. Experience in CMP, epitaxial deposition, and etch has borne this out. However,
there exist processes where response surface nonlinearities are features. Even pro-
cesses that exhibit linearity over one region of operation might easily show nonlin-
earity when the operating window is moved to a different part of the response space.
An illustration of a model nonlinear in the inputs is a “Hammerstein” model.6
A SISO example of this type is
yt = axt2−1 + bxt −1 + c + ε t (3)
This model is linear in its parameters, and may thus be estimated by a least-squares
technique such as recursive least squares (RLS).8
Another approach to a nonlinear R2R control solution is to use neural nets for
the response model.11 This will work if enough data are available to construct the
neural weightings. In production processes with many different regimes/recipes, it
is not always easy to get sufficient data for neural modeling, and a more parsimonious
approach is useful. One such approach devised by Del Castillo and Yeh12 and called
the “optimizing adaptive quadratic controller” (OAQC) is now described.
The OAQC assumes that equipment behavior can be modeled according to a
second-order MIMO Hammerstein model of the form
(
yt = y(0) + Nzt −1 + Mt + I p − CB ε t ) (4)
where z ′t = (ut, ut2, ut(i) ut(j), i < j) is a vector of length (2n + (n(n – 1)/2) that contains
the quadratic expansion of ut ; yt is a p × 1 vector of quality characteristics; y(0) is
a p × 1 vector of intercepts; ut is a vector of controllable factors; t denotes a vector
containing the time index t in its p components, {εt} is a sequence of multivariate
white noise random vectors; and B is the one-lag backward shift operator. This
model is general enough for most equipment response surfaces.
A minimum means square error forecast developed by Del Castillo4 may be
applied to the model given in (4) to give a forecast equation:
ϒ t +1 t = Lyt + M (t + 1) + Nzt (5)
where ϒt +1|t is the one-step-ahead forecast of y, and the (p × 2n + (n(n – 1)/2)) matrix N
contains parameters for both first-order and quadratic terms. The quadratic expansion
provides a second-order polynomial approximation to the system nonlinearity. On-
line parameter estimates of L, M, and N are provided by a recursive least-squares
(RLS) algorithm,8 and then (5) may be used to derive the control rule for the current
run.

The OAQC uses a multivariate version of the Clarke and Gawthrop3 one-step
controller performance index,
( ′
) ( )
J = ϒ t +1 t − T W ϒ t +1 t − T + (ut − ut −1 )′ Γ(ut − ut −1 ) (6)
which is minimized subject to the input and output constraints:
Lu ≤ u t ≤ U u (7)
L y ≤ ϒ t +1 t ≤ U y (8)
where T denotes a p × 1 vector of targets, W is a p × p diagonal matrix with entries

representing the relative priorities of each response, and Γ is a n × n diagonal matrix
of cost coefficients — the larger a cost coefficient, the closer the factor i will remain
to its previous setting. J is minimized with respect to the controllable factors u t.
5.4 THE OAQC NONLINEAR CONTROLLER

The traditional form of R2R control as described above proceeds according to the
following three steps: (1) an experimental design based on some design optimality
criterion is performed, (2) a model is fitted using some form of minimization (e.g.,
least squares), and (3) a search-and-locate optimization step is done to find an
“optimal” process recipe. The OAQC attempts to address these three steps simulta-
neously (rather than sequentially) in an incremental way at each run, thereby speed-
ing up the qualification of the process and reducing process disruptions.
For ease of presentation, assume that there is a single response Y that is dependent
on n controllable factors. It is desired to keep Y as close as possible to target T. The
exact input–output relationship is, however, unknown. The OAQC solves the fol-
lowing problem at each run:
(
min  (1 − λ t ) ϒ t +1 t ( xt +1 ) − T ) − λ (Varϒ ( x ) σ2 
2
(9)
 t t t +1 
where the minimization occurs as {xt+1 ∈ Ω1}, a region of factor space defined by
input factor bounds, and ϒ is the estimated response.
The first term of (9) is the square deviation of the one-step-ahead predicted
response, and the second term is the scaled variance of the current estimated
response. The constants {λt} are such that 0 ≤ λt ≤ 1, and give relative weights to
the two objectives in (9), namely the optimization of the response (first term) and
model fitting (second term). Note that if λt = 1, then the second term is equivalent
to a conditional D-optimality,* a useful criterion in the presence of factor bounds.
* D-optimality ⇒ |X′X| is maximized ⇒ Var (ϒ) minimized, where X = (xij), the matrix of j = 1, …, n
factor inputs over i = 1, …, k trials.

At each run the solution to problem (9) provides a new set of factor settings
xt+1 to try next. Initially, optimization of the objective function (9) will tend to favor
factor settings that will lead to good response surface models as opposed to factor
settings that achieve desired response performance. Learning proceeds via estima-
tion of the response parameters using a multivariate recursive least squares (RLS)
algorithm.8
5.5 OAQC: SIMULATED TRIALS

The OAQC software has a simulation facility that is used to demonstrate optimization
and control against “open loop” (i.e., no control) in two different settings. In both
trials a three-input, two-output quadratic CMP process model with linear drift is
installed in the simulator as the “truth.” This model is given by Khuri.7
y1 = 2756.5 + 547.6u1 + 616.3u2 − 126.7u3 − 1109.5u12 − 286.1u22

(10)
+ 989.1u32 − 52.9u1u2 − 156.9u1u3 − 550.3u2u3 − 10t + ε1t
y2 = 746.3 + 62.3u1 + 128.6u2 − 152.1u3 − 289.7u12 − 32.1u22 + 237.7u32

(11)
− 28.9u1u2 − 122.1u1u3 − 140.6u2u3 − 1.5t + ε 2 t
where ε1t ~ N(0,602) and ε2t ~ N(0,302). The ui were constrained to the (–1,1) range.
y1 is removal rate, y2 is within-wafer nonuniformity.
The first trial introduced as a given (prior), a fairly good initial model for the
controller to start with. The second trial started with no prior model at all. The model
given in the first trial was
y1 = 2500 + 400u1 + 500u2 − 100u3 − 800u12 − 200u22 + 1000u32

(12)
− 40u1u2 − 100u1u3 − 100u2u3 − 7t
y2 = 600 + 50u1 + 100u2 − 100u3 − 200u12 − 50u22 + 300u32 −

(13)
− 30u1u2 − 100u1u3 − 100u2u3 − 3t
In the first trial, a target of 2700 was set for the output y1, while a constraint on y2
between –100 and 700 was set as a goal. Both optimization and control were
requested. Fifty (50) simulation runs were executed.
The graph of Figure 5.6, with “target” lines at 700 and 2700 added, shows the
results for y1 and y2 (the outputs resulting from optimization and control) as well as
the open loop or “uncontrolled” outputs. As can be seen, after the optimization phase
ended — at about run 13 — the controlled outputs stayed closer to the target (or
upper constraint in the case of y2) than the uncontrolled outputs.

4500
optimization phase
4000
3500 control
3000
2500
2000
1500 no control
1000
500
control
0
0 10 20 30 40 50
FIGURE 5.6 3 × 2 R2R simulation with prior model, y1 target = 2700, y2 constraints.
4000
optimization phase
3500
3000 control
2500
2000
1500 no control
1000
500
control
0
0 10 20 30 40 50
FIGURE 5.7 3 × 2 R2R simulation with no prior model, y1 constraints and y2 constraints.
The second trial was executed for 50 simulated runs and in all details was
identical to the first trial except that no prior model was specified, and y1 was given
no target, but desired constraints of 2700 ≤ y1 ≤ 100,000 were imposed. As can be
seen again, in Figure 5.7, once the optimization phase is over, the controlled
responses better match their constraints than for the open responses.
These graphical intuitions may be confirmed by examining a table of summary
statistics (Table 5.1) for the trial runs (excluding the first 15 “optimization” runs in
all cases). The means (µ) of the controlled outputs (y1c, y2c) are closer to or more
consistently within the limiting constraints than are the open responses (y1o, y2o).
There is not much to choose between when examining the response standard
deviations (σ) except that in the case of y2, the open responses have smaller varia-
tions. This is probably caused by the control action itself pushing against difficult-
to-accomplish constraint limits due to the rather severe nature of the assumed trends.
The mean square deviation (MSD) for the y1’s is taken as the square root of the
average of Σ(y1* – 2700)2, and again for y2 but using the sum Σ(y2* – 700)2, where
“*” is either c for controlled or o for open loop. In all cases the controlled responses
show improvement over the uncontrolled responses.

TABLE 5.1
Performance Statistics for Two
Simulation Trials
Trial #1 y1c y1o y2c y2o
µ 2570 2426 713 795

σ 103 104 44 33
MSD 162 287 45 99
Trial #2
µ 2757 2432 665 793
σ 134 134 45 32
MSD 142 294 55 97
In trial #1, the y1c mean of 2570 is closer to the target (2700) than the mean for
y1 . The y2c mean of 713 is also closer to the constraint (700) than the mean for y1o.
o
MSDs in both cases are also smaller for the controlled than the open case. For trial
#2, control performance remains superior to open loop except, as before, in the case
of σ for y2.
It should be noted that in the Khuri model, all signs in both model equations
are the same for matching terms except for the signs of the trend terms. This makes
the system inherently more difficult to control: a few differing signs would give
added latitude to the controller in the face of opposing drifts.
5.6 CONTROLLER IMPLEMENTATION

A step in the commercialization path of any software is some means to embody it
within a robust factory control framework. We note that Moyne and McAffee9 have
given a structure for generic cell controller technology that is ideal for this type of
R2R control, and that has also been commercialized.* The GCC technology is
detailed in Part 3 of this book (specifically Chapters 9 through 11). An integration
path to ultimate system linkage has thus been well established in addition to the
control theoretic foundation. An integrated GCC-enabled solution is shown in
Figure 5.8. The GCC system accepts pre- and postmetrology process inputs and
performs process optimization, modeling and/or control depending on the capabil-
ities provided by the optimization/control algorithm incorporated in the particular
GCC solution. As detailed in Chapter 12, an OAQC solution has been incorporated
into a GCC system, thereby providing the adaptive control capabilities described in
this chapter in an industrial quality solution.
* See http://www.mitexsolutions.com.

Factory Controller lnter-Cell Control
Cell Control
(Run-to-Run Control)
Post
Recipe Process
Results
Advice
Equip. Cntrlr.
(Real-Time Control)
Equipment
Product Flow
FIGURE 5.8 Cell control for R2R.
5.7 CONCLUSIONS
Run-to-run control is now an industrially proven batch control strategy that has a
considerable body of theoretical work behind it as well as a tested integration path.
In this chapter we have shown that R2R control can be extended to nonlinear systems,
and to systems about whose response patterns little or nothing is known, by the use
of the optimizing adjusting quadratic controller. This approach integrates process
model estimation, model updating, and recipe optimization in one seamless on-line
entity.
ACKNOWLEDGMENTS
The authors are grateful to Strasbaugh, of San Luis Obispo, California, for permis-
sion to use diagrams appearing on their commercial Web site. Thanks are also due
for the helpful comments of Dr. James Moyne of the University of Michigan. An
earlier version of the material presented in this chapter was presented at the 1999
International Conference on Quality Manufacturing.
REFERENCES
1. Boning, D.S., Moyne, W., Smith, T., Moyne, J., and Hurwitz, A. Practical issues in
run-by-run process control, Proc. 6th Annual IEEE/SEMI Advanced Semiconductor
Manufacturing Conference, Boston, MA (1995).
2. Box, G.E.P., Hunter, W.G., and Hunter, J.S. Statistics for Experimenters, John Wiley
& Sons (1978).
3. Clarke, D.W., and Gawthrop, P.J. Self-tuning controller, Proc. IEE, 122, 9, pp. 929-935
(1975).
4. Del Castillo, E. A multivariable self-tuning controller for run-to-run process control
under shift and trend disturbances, IIE Transactions, 28, 12, pp. 1011-1021 (1996).
5. Del Castillo, E., and Hurwitz, A.M. Run-to-run process control: Literature review
and extensions, J. Quality Technol., 29, 4, pp. 199-204 (1997).

6. Golden, M.P., and Ydstie, B.E. Adaptive extremum control using approximate process
models, AIChE J., 35, 7 (1989).
7. Khuri, A. I. Response surface methods for mutiresponse experiments, 13th SEMAT-
ECH Statistical Methods Symposium (ref. Sematech at http://www.sematech.org)
(1996).
8. Ljung, L., and Soderstrom, T. Theory and Practice of Recursive Estimation, Cam-
bridge, MA, The MIT Press (1987).
9. Moyne, J.R., and McAffee, L.C. A generic cell controller for the automated VLSI
manufacturing facility, IEEE Transactions on Semiconductor Manufacturing (May,
1992).
10. Moyne, J.R., Telfeyan, R., Hurwitz, A.M., and Taylor, J. A process-independent run-
to-run controller and its application to chemical-mechanical planarization, Proc. 6th
Annual IEEE/SEMI Advanced Semiconductor Manufacturing Conference, Boston,
MA (1995).
11. Smith, T.H., and Boning, D.S. Artificial neural networks exponentially weighted
moving average controller for semiconductor processes, J. Vacuum Sci. Technol., a,
15, 3 (1997).
12. Del Castillo, E., and Yeh, J. Y., An adaptive run-to-run optimizing controller for linear
and nonlinear semiconductor processes, IEEE Transactions on Semiconductor Man-
ufacturing, 11, 2, 285-295 (1998).

6 A Comparative Analysis
of Run-to-Run Control
Algorithms in the
Semiconductor
Manufacturing Industry
Zhe Ning, James R. Moyne, Taber H. Smith,
Duane S. Boning, Enrique Del Castillo,
Jinn-Yi Yeh, and Arnon M. Hurwitz
6.1 INTRODUCTION
In Chapters 3 through 5 we described a number of R2R control algorithms. This
chapter provides a comparative analysis of R2R control algorithms, focusing on
their ability to provide robust and stable control in the face of linear and quadriatic
drift.1 This chapter is not meant to be an exhaustive analysis of algorithm robustness
and stability, but rather an illustration of the pros and cons of the various R2R
algorithm candidates, and a description of a methodology for comparative evaluation
of R2R control algorithms.2 Specifically, the chapter is organized as follows. Fol-
lowing this introduction, background information is provided on each of the algo-
rithms that are investigated, as well as the multialgorithm R2R control solution
enabler. The testing benchmarks are then presented, followed by simulation results
of the application of the algorithms to these benchmarks. This chapter concludes
with a comparative analysis and a discussion of additional tests that could be
performed to further qualify the algorithms.
6.2 BACKGROUND
The apparatus required for testing multiple R2R control algorithms and realizing
multiple algorithm control solutions necessarily includes the algorithms themselves
as well as the multialgorithm control system enabler. In the following subsections,
summary information on each these elements is provided for completeness. Note
that more detailed treatment of the polynomial-based R2R control algorithms can
be found in Chapters 3 through 5, while the multialgorithm solution is detailed in
Chapter 9.

6.2.1 RUN-TO-RUN CONTROL ALGORITHMS
6.2.1.1 The EWMA “Gradual Mode” R2R Controller
The EWMA “gradual mode” controller (GM) is a linear approximation model-based

controller with an exponential weighted moving average (EWMA) “forgetting fac-
tor” that provides for control of noisy processes.3,4 The GM begins with a linear
model of the process,
yt = Axt + ct , (1)
where yt = vector of n process outputs

xt = vector of m process inputs (e.g., machine settable parameters)
ct = vector of n constants
A = an n by m matrix (of first-order coefficients)
The controller updates the offset term ct on an R2R basis using an EWMA approach:
ct = α(Yt −1 − Axt −1 ) + (1 − α ) ct −1 , (2)
where 0 ≤ α ≤ 1. By adjusting ct in (1), the GM is able to track and compensate for

gradual changes in the process as well as filter out random talk noise in the process.
A controller “module” implementation of the GM was developed for integration
into R2R control systems. In order to make the GM implementation practical on the
factory floor, a number of features have been added to accommodate control of
typical semiconductor processes. These features include (1) recipe parameter bound-
ing to force the controller to search for a control solution in a user-definable recipe
region, (2) input weighting to allow the user to trade off recipe advices between
different inputs, (3) output weighting to allow the user to provide preferential control
for important outputs, (4) an input discretization capability to accommodate the
discrete nature of equipment settings, and (5) controller tuning parameters to provide
maximal controller performance in the particular controller environment. Note that
all of these features are dynamically settable in the implementation developed.5
6.2.1.2 The Time-Based EWMA R2R Controller (GMt)
The GMt controller extends the GM controller to more accurately provide control
in environments where some or all of the process quality measures (outputs) cannot
be accurately approximated as a linear function of the process inputs.4 As an example,
consider the following multivariate process control problem:
(Amount Removed, Nonuniformity) = f (Time, Speed, Pressure) (3)
A linear solver cannot accurately model situations where an output parameter such
as Amount Removed is a function of an input parameter such as Time multiplied
by a linear function of other input parameters (i.e., Speed and Pressure).

The GMt provides a more accurate model and controller for systems of this type
by breaking the system outputs down into two sets, namely primary outputs, which
are directly impacted by primary inputs, and secondary outputs, which are functions
of primary output(s) and secondary inputs. The GMt then provides control by imple-
menting a two-step linear solution process that approximates a nonlinear solver. In
the first step, the controller uses the EWMA GM method (as shown in (1) and (2))
to compensate fully for those primary outputs that do not have corresponding sec-
ondary outputs, and to partially compensate (in a weighted fashion) for those primary
outputs that also have corresponding secondary outputs. Thus, for the system described
in (3), the GMt would first compensate for Removal Rate in part and Nonuniformity
in full by adjusting Speed and Pressure (in the manner of (1) and (2)), and then (in
the second step) adjust Time to compensate the rest of the way for Amount Removed.
As with the GM, a controller “module” implementation of the GMt has been
developed for integration into R2R control systems that contains all of the “industrial
quality” features implemented in the GM application.
6.2.1.3 The Knowledge-Based Interactive

Run-to-Run Controller
The knowledge-based interactive run-to-run controller (KIRC) is a machine learning

algorithm for R2R control that uses leaves in a classification decision tree to suggest
control actions for process improvement.6 KIRC generates nonlinear response sur-
faces from experimental data using neural networks. Points are calculated on each
response surface and discretized into output classes to form training examples. The
size of the outputs classes is typically determined by statistical process control limits.
The GID3 algorithm generates a decision tree by using an information entropy metric
to recursively partition the operating space with attribute tests. The starting operating
point is chosen from the largest leaf in the decision tree where all outputs are inside
the target range. As gradual drifts or sudden changes occur in the process, the output
values may leave the region of the target leaf. The decision tree is searched for a
neighboring leaf that matches the current output classification. By comparing the
attribute ranges of (1) the leaf matching the new process state and (2) the original
target leaf, a control action is computed to move the process back in the target output
region.
Most of the work with KIRC has focused on compensating for process shifts
caused by disturbances during a reactive ion etching process in a hexode reactor.
An EWMA drift compensation component has recently been added to the algorithm
so that control actions can be taken before a predicted gradual drift moves the process
outside the control limits.
6.2.1.4 The Optimizing Adaptive Quality Controller (OAQC)
The optimizing adaptive quality controller (OAQC) is designed to seek and maintain
optimum operating conditions for a multiple input, multiple output (MIMO) pro-
cess.7 The controller is to be used in a run-to-run manner. Work on this controller
originated from previous developments in self-tuning MIMO controllers.8

yt + yt - T MULTIVARIATE
in
keep ut-1
ut-1 SYSTEM ∑
SPC CHART
out
implement u
-
targets
RECURSIVE
initial estimates
ESTIMATOR
Hammerstein model
yt-1
OAQC
NON-LINEAR input and output constraints
targets
OPTIMIZER
priorities
ut
FIGURE 6.1 The OAQC controller.
The OAQC is comprised of the following elements:
1. A recursive multivariate least-squares estimation algorithm.

2. A nonlinear constrained optimization algorithm.
3. Various utilities, including experimental designs for fitting quadratic
responses and obtaining initial estimates, multivariate SPC charts that can
be added to the controller and act as deadbands or be used to supervise
the recursive estimation procedure, diverse tuning functions that allow the
process engineer to modify the controller, history plots for inputs and
outputs, and discretization of the inputs.
The basic idea of an optimizing controller is to provide on-line estimation of a

nonlinear (in the controllable factors) regression model (a Hammerstein model) that
is optimized in order to obtain the best control action. Once optimal operating
conditions have been achieved, the OAQC will seek to maintain the process under
control running at such conditions. Therefore, the OAQC acts both as an “optimizer”
and as a “controller.” If equipment models are available from previously conducted
off-line experiments, the corresponding parameter estimates can be entered into the
OAQC to speed up the optimization phase.
Figure 6.1 shows a block diagram of the multivariate controller. The controller
contains a multivariate recursive estimation algorithm to update the model parame-
ters. Also, and most important from a practical point of view, the proposed OAQC
explicitly considers input and output constraints.
6.2.2 MULTIPLE ALGORITHM SYSTEM ENABLER

6.2.2.1 The Generic Cell Controller (GCC)
The Generic Cell Control (GCC) is a discrete control enabling mechanism that
utilizes distributed object-based communication and a relational database (as

G C C R 2 R Controller
Multiple Control
Algorithms
Rule Base Optimization

Which Alogirthm(s) / Control
GCC DB Recipe
Metrology DownLoad
Process
Monitoring
FIGURE 6.2 GCC-enabled R2R solution supporting multiple control algorithms.
opposed to procedural code) to store and execute sequential control information.

The theory of operation of the GCC is documented in literature.9,10
Because the GCC provides for modular and configurable control solutions, it is
well suited as an enabler for R2R control implementations that make use of multiple
control algorithms operating in a complementary fashion.1,11 An example of such an
implementation is shown in Figure 6.2. Note that the implementation contains a
rule-based decision-making module that utilizes metrology information along with
process history and a rule base to determine the optimization or control algorithm(s)
to invoke for each run. Note further that the rule base contains rules that identify
the domain of applicability of the various algorithms; information on these domains
(such as that presented in this chapter) could be used to develop these rules.
6.3 ALGORITHM TEST BENCHMARKS

There is a large variety of multivariate processes in the semiconductor industry that
are candidates for R2R process control. These processes exhibit many qualities over
their input parameter space of operation as well as over time (i.e., from run to run),
that could impact (and be impacted by) an R2R controller. For example, the process
response surfaces may be linear or nonlinear. Further, the processes may be subject
to different drifts, noise, and other disturbances. Thorough testing of R2R algorithms
for the semiconductor manufacturing industry would then necessarily include an
exhaustive benchmarking of the algorithms to these process qualities. As a first step,
results are presented on algorithm operation against the following two benchmarks:
1. A linear process with linear drift buried in white noise.

2. A full quadratic, severely nonlinear process with linear drift buried in
white noise.
As a test vehicle, process models originating from a CMP process are used as
an example process. These models each have four inputs (Platen Speed, Back-
Pressure, Polish Head Downforce, and Profile) and two outputs (Removal Rate and

Nonuniformity). Factors are included in the models to account for process noise and
run-to-run process drift. No discretization limits in the inputs are imposed.
Specifically, the linear process utilized has the form
y[n] = C + Ax + ω[n] + δn , (4)
where n is run number and w[n] is normally distributed white noise with zero mean
and covariance matrix Λ. We will use
−1382.60 
C= 
 −627.32 
50.18 −6.65 163.4 8.45

A=
13.67 19.95 27.52 5.25
−17
δ= 
 1.5
665.64 0 
Λ=
 0 5.29
The second-order process has the form
y[n] = C + f (u[n]) + ω[n] + δn , (5)
where drift and noise are the same as in (4) and f(u[n]) is a full second-order
polynomial function of the inputs with the following form:
3 3
f (u[n]) = ∑ ∑ β(i, j) u (i) u ( j)

i=0 j=0
We will use
1386.5 381.02 −112.19 3778.8 −21.301 8.7159 24.953

β=
1520.8 2365.6 2923.5 281.66 −3.9419 −1.0754 1.406
37.082 −17.642 −11.974 −164.99 28.150 249.17 0.025067

0.33797 −72.274 −94.222 −26.175 −13.505 36.691 32.929 
In both cases, the targets are 1700 Å for Removal Rate and 150 Å for Nonuniformity.
For simplicity, only Removal Rate control is evaluated in our comparison.

 −138.21
C= 
−627.32 
5.018 −0.665 16.34 0.845

A=
13.67 19.95 27.52 5.25 
The process designed to test the performance of the GMt controller against the GM
controller has the following form:
y[n] = C + Ax + ω[n] + δn , and (6)
Amount Removed = Removal Rate * Time, (7)
where Removal Rate is one of the outputs in the vector y[n] and noise and drift
terms in (6) are the same as in (4). The outputs for this process are Amount Removed
and Nonuniformity with targets of 1700 Å and 150 Å, respectively.
6.4 TEST RESULTS

Given the test benchmarks described in the previous section, controlled responses
from different control algorithms (introduced in Section 6.2) are presented in this
section. As a quantitative comparison metric, we use a weighted mean-squared error
(WMSE). This quantity is computed as the squared error of each output from target
summed over the run, divided by the respective process targets and total run number,
and summed together.
6.4.1 CONTROL OF THE LINEAR PROCESS

Figure 6.3 shows the controlled responses (Removal Rate) from GM, OAQC, and
KIRC controllers in controlling a linear process with drift and noise. The weighted
mean-squared errors (for 30 runs) were 3.2 × 10–2 for GM controller, 2.50 × 10–2
for OAQC and 2.52 × 10–2 for KIRC, indicating that all three algorithms kept very
good control of the process with linear drift.
6.4.2 CONTROL OF THE QUADRATIC PROCESS

Figure 6.4 shows the controlled responses (Removal Rate) from GM, OAQC, and
KIRC controllers in controlling a full quadratic (nonlinear) process with linear drift
and noise. Here we see that the OAQC, which is based on a nonlinear model, keeps
good control of the process, while both GM and KIRC lost control of the process
after eight runs. The WMSE for OAQC was 3.67 × 10–2.
6.4.3 GMT CONTROLLER VS. GM CONTROLLER

Controlled responses for the process given in (6) and (7) (Section 6.3) are displayed
in Figure 6.5. Both the GMt and GM controllers were run 40 times on the process.

GM Control of Linear Process
1800
1600
Removal Rate
1400
EWMA-Linear
1200 Uncontrolled
Target
1000
0 5 10 15 20 25 30
Run#
OAQC Control of Linear Process
1800
Removal Rate
1600
1400
OAQC
1200 Uncontrolled
Target
1000
0 5 10 15 20 25 30
Run#
KIRC Control of Linear Process
1800
Removal Rate
1600
1400
1200 KIRC
Uncontrolled
Target
1000
0 5 10 15 20 25 30
Run#
FIGURE 6.3 Control of linear process.
The weighted mean-squared errors were 2.434 × 10–2 for the GMt controller and
12.521 for the GM controller. As can be seen from the figure, the GM controller
lost control of the process after 36 runs due to its linearized approximation of the
nonlinear process, while the GMt controller maintained a good control of the process
during the entire period of runs by providing a two-step linear solution.

GM Control of Non-Linear Process
1800
Removal Rate
1600
1400
EWMA-NL
1200 Uncontrolled
Target
1000
0 5 10 15 20 25 30
Run#
OAQC Control of Non-Linear Process

1800
1600
Removal Rate
1400
OAQC-NL
1200 Uncontrolled
Target
1000
0 5 10 15 20 25 30
Run#
KIRC Control of Non-Linear Process

1800
1600
Removal Rate
1400
KIRC
1200 Uncontrolled
Target
1000
0 5 10 15 20 25 30
Run#
FIGURE 6.4 Control of quadratic (non-linear) process.
6.5 COMPARATIVE ANALYSIS

A review of the test results presented in Section 6.4 indicates that all three algorithms
(GM, OAQC, and KIRC) provide good control of the simulated linear process (with
linear drift and white noise); the differences between the control provided are
minimal. With the simulated full-quadratic non-linear process, both the GM and
KIRC controllers were unable to provide control beyond the first few runs due to
the severe non-linearity in this test case; however, the OAQC provided control for
the duration of the simulated process, with a relatively small WMSE.
The results presented in Section 6.4.3 illustrate the utility of the GMt control
approach for a class of non-linear systems. As illustrated in Figure 6.5, the GMt is
able to provide control for some processes where the GM controller eventually fails.

GM Control of Non-Linear Process
1.6 104
Amount Removed
1.2 104 GM-Controlled
Uncontrolled
Target
8000
0 5 10 15 20 25 30 35 40
Run #
GMt Control of Non-Linear Process

4
1.8 10
1.6 104
Amount Removed 1.4 104
1.2 104 Controlled

Uncontrolled
1 104 Target
8000
0 5 10 15 20 25 30 35 40
Run #
FIGURE 6.5 Control of non-linear process.
6.6 CONCLUSIONS
A comparative analysis of four algorithms (GM, GMt, OAQC, and KIRC) has been
presented in this chapter. The algorithms were evaluated in the control of both linear
and non-linear processes that experienced linear R2R process drift as well as white
noise. The results indicate that all algorithms were able to provide good control of
the linear test process, while only the OAQC was able to provide control of the
severely non-linear process. (There are many classes of non-linear drift processes
for which the GM is able to provide a level of control.) Additionally, it has been
shown that the GMt provides good control for a class of non-linear control problems
such as those where the measured output is related to an intermediate process variable
by a multiplicative factor such as time.
Although the test results presented here help to identify the domains of accept-
able operation of the tested algorithms, they represent only a first step in determining
the suitability of a control algorithm to a particular process. There are many other
factors that must be considered before making the final evaluation of the control
algorithm. For example, the non-linear model utilized in the test process represents
only one case of non-linear control; the specifics of the non-linear process and the
region of operation within the process model will have a significant impact on the
suitability of the control algorithm. Also, the characteristics of the process noise
may impact algorithm performance. Further, the impact of model error should be
evaluated. Finally, the maturity of the algorithm implementation, capability for
integration, and features (such as bounding of inputs and other practical factors)

should be considered in any comprehensive evaluation. In summary, a complete
algorithm solution comparative evaluation should address the qualification of the
controllers with respect to factors such as non-linear process drift, various noise
patterns, controller model error, and usability in an industrial setting.
ACKNOWLEDGMENTS
Much of the material presented in this chapter is derived from Reference 1, and is
reprinted with permission. The authors gratefully acknowledge the contributions of
William Moyne and Victor Solakhian in developing the GM, GMt, and GCC soft-
ware, and Matt Hankinson for developing the KIRC software and providing KIRC
algorithm test results.
REFERENCES
1. Boning, D., Castillo, E., Hurwitz, A., Moyne, J., Ning, Z., Smith, T., and Yeh, J., “A
Comparative Analysis of Run-to-Run Control Algorithms in the Semiconductor Man-
ufacturing Industry,” Seventh Annual SEMI/IEEE ASMC, Boston (October 1996).
2. Moyne, J., Chaudhry, N., and Telfeyan, R., “Adaptive Extensions to a Multi-Branch
Run-to-Run Controller for Plasma Etching,” Journal of Vacuum Science and Tech-
nology A, Vol. 13, No. 3, (May/June 1995), pp. 1787- 1791.
3. Moyne, W. “Run by Run Control: Interfaces, Implementation, and Integration,” S.M.
4. Smith, T., “Novel Techniques for the Run By Run Process Control of Chemical-
Mechanical Polishing,” S.M. Thesis, MIT EECS (May 1996).
5. Boning, D., Moyne, W., Smith, T., Moyne, J., and Hurwitz, A., “Practical Issues in
Run by Run Process Control,” Proc. Sixth Annual SEMI/IEEE ASMC, Boston (Octo-
ber 1995).
6. Hankinson, M., Vincent, T., Irani, K., and Khargonekar, P., “Integrated Real-Time
and Run-to-Run Control of Etch Depth in Reactive Ion Etching,” IEEE Transactions
on Semiconductor Manufacturing (1996).
7. Del Castillo, E., and Yeh, J.-Y., “Optimizing Adaptive Controller for Run-to-Run
Process Control: Software Implementation and Algorithmic Details,” technical report,
Dept. of Industrial Engineering, University of Texas at Arlington, Box 19017, Arling-
ton.
8. Del Castillo, E., “A Multivariate Self-Tuning Controller for Run-to-Run Process
Control Under Shift and Trend Disturbances,” IIE Transactions (1996).
9. Moyne, J., “Generic Cell Controlling Method and Apparatus for Computer Integrated
Manufacturing System,” U.S. Patent Number 5,469,361, (Filed, August 1991; Issued,
November 1995).
10. Moyne, J. and McAfee, L., “A Generic Cell Controller for the Automated VLSI
Manufacturing Facility,” IEEE Transactions on Semiconductor Manufacturing (May
1992).
11. Boning, D., Chaudhry, N., Hurwitz, A., Moyne, J., Moyne, W., Shellman, S., Smith,
T., Telfeyan, R., and Taylor, J., “A Multi-Level Approach to the Control of a Chemical
Mechanical Planarization Process,” Journal of Vacuum Science and Technology A
(May/June 1996), pp. 1907-1913.

Part 3
Integrating Control
In Part 1 we noted that integration and automation innovation are key factors that
pushed R2R control to the forefront ahead of in situ control and interprocess control
in the movement toward advanced process control (APC) implementation. Indeed,
the integration of control is often the most overlooked challenge in pursuing APC
development and deployment. Attention must be paid to integration aspects through-
out the APC process or the control solutions developed will be too costly or cum-
bersome to be useful.
In Part 3 of this book we explore the methods and solutions for integrating
control. Information presented in this part is useful to anyone trying to implement
and/or integrate R2R control. It addresses issues such as solution robustness and
portability, design for flexibility and future enhancement, and identification of met-
rics of capability and success. Specifically, in Chapter 7 we define the existing and
future-envisioned control environment in semiconductor manufacturing that might
incorporate R2R control. This environment is defined in terms of specifications from
three sources that are shaping the control integration environment for the industry:
(1) the Semiconductor Industry Association and the SIA roadmap, (2) Semiconductor
Equipment and Materials International (SEMI) and SEMI standards, and
(3) SEMATECH and the SEMATECH Control Systems Requirements Specification
(CSRS) output. For each source, the specific impact on R2R control integration is
discussed. Following this discussion we identify the design requirements for an
integrateable* R2R solution in Chapter 8. We then turn our attention in Chapter 9
to a specific R2R control enabler design and solution, called the Generic Cell
Controller (GCC), which conforms to these design requirements. We include a
* Both “integrateable” and “integrable” are commonly utilized in the industry to mean “capable of
integration.”

description of the GCC concept, provide a straightforward example of a GCC
implementation, and discuss the utilization of the GCC flexible control system
concept to realize a multialgorithm R2R control solution.
The information in Chapters 7 through 9 presents external and internal R2R
controller design requirements, and provides examples of enabling technologies.
However, it doesn’t suggest a complete design for an integrated R2R control solution.
We address this problem in Chapter 10 by presenting a design for a “piggyback”
R2R control solution that conforms to the integration requirements identified in
Chapter 8. This is followed, in Chapter 11, by two examples of R2R control solution
integration: (1) a “piggyback” tool retrofit solution, and (2) a fully integrated solution
for a next-generation tool. These example presentations include descriptions of
integrated solution design and software user interface, methodology for deployment,
and evaluation in terms of process improvement. One other important aspect for
R2R control solution development and integration is the development of the control
algorithm solution to the control environment. This issue is addressed in Chapter 12
with a case study of the design and implementation of a GCC-enabled optimizing
adaptive quality controller R2R control solution.

7 Existing and Envisioned
Control Environment
for Semiconductor
Manufacturing
James Moyne and Joe White
The industry as a whole has been pursuing the identification, specification, and
standardization of control integration for semiconductor manufacturing along many
fronts. The three major players in this arena are the Semiconductor Industry Asso-
ciation (SIA), Semiconductor Equipment and Materials International (SEMI), and
SEmiconductor MAnufacturing TECHnology (SEMATECH). The SIA is an orga-
nization of leaders in the semiconductor manufacturing industry. Members of the
SIA have been instrumental in the process or addressing the technology needs of
the industry by establishing precompetitive partnerships and consortiums such as
the Semiconductor Research Corp. (SRC) in 1982, SEMATECH in 1987, and the
International 300-mm Initiative (I300I) in 1996. The SIA membership also publishes
a National Technology Roadmap for Semiconductors, which will be discussed further
in Section 7.1.1 SEMI is a global trade association, founded in 1970, that represents
the semiconductor and flat panel display equipment and materials industries. With
over 2000 members, the primary goal of SEMI is to help its members expand their
global marketing opportunities and relationships by providing industry-specific
information and educational resources. SEMI is the primary standards organization
for the semiconductor industry.2 SEMATECH is a nonprofit technology development
consortium originally created to reinvigorate the U.S. semiconductor industry, but
it has evolved since 1998 into an international research consortium.3
In this chapter we provide a discussion of significant contributions to control
integration by the Semiconductor Industry Association (SIA Roadmap), SEMI (stan-
dards), and SEMATECH (Control Systems Requirements Specification).
7.1 THE SEMICONDUCTOR INDUSTRY

ASSOCIATION AND THE SIA ROADMAP
The SIA has provided direction for research, development, and deployment of control
solutions in semiconductor manufacturing by presenting a roadmap for advancement.
The National Technology Roadmap for Semiconductors is a 15-year projection of

the integrated circuit technology characteristics required to maintain the historical
rate of performance and cost improvements.1 In providing this projection along with
an analysis of the current state of the art, the roadmap identifies the research needs
that must be fulfilled to realize the required technology advancements. The roadmap
addresses the many aspects of semiconductor manufacturing from front-end pro-
cesses through assembly and packaging.
Run-to-run control technology is addressed in the roadmap as a component of
factory integration. The roadmap clearly identifies R2R control as a technology
whose development is underway and whose full deployment should occur by the
year 2003. The roadmap also identifies R2R control as an integral component of a
larger advanced process control (APC) framework. Developers should continue to
look to the SIA roadmap for indications of future directions in R2R control tech-
nology development, deployment, and integration.
7.2 SEMICONDUCTOR EQUIPMENT AND MATERIALS

INTERNATIONAL AND SEMI STANDARDS
Semiconductor Equipment and Materials International (SEMI) has been pursuing
standards in the area of communication and integration ever since the development
of the SEMI Equipment Communication Standard (SECS) in the late 1970s.4 From
that time to the present, SEMI experts have focused on defining communication
mechanisms between the various elements of the control and operations hierarchy
in the fabrication facility. Figure 7.1 is an illustration of various SEMI standards
and SEMI standards efforts mapped into the logical semiconductor facility hierarchy.
Note that this figure includes existing standards supported by SEMI as well as
FIGURE 7.1 SEMI standards and standards efforts mapped into control hierarchy.

working standards specifications under development by SEMI members. The fol-
lowing is a brief description of SEMI communication control standards relevant to
the integration of R2R control.4
SEMI Equipment Communications Standard (SECS — E4 and E5)*: SECS
is a standard for communications between intelligent equipment and a host. The
standard has two parts that define the communication protocol interface (SECS-I)
and the messages exchanged (SECS-II). SECS-I, which specifies point-to-point
communications over a (slow) R2-232 interface, is somewhat obsolete; high-speed
message service (HSMS) is a high-speed Ethernet-based replacement for SECS-I,
but retains many of the deficiencies of SECS-I (e.g., point-to-point only communi-
cations, host-equipment master/slave only operation, etc.). The Computer Integrated
Manufacturing (CIM) framework specification and Object Based Equipment Model
(OBEM) point to future alternatives to SECS (see below).
Generic Model for Communications and Control of SEMI Equipment
(GEM — E30): The GEM standard defines the generic behavior of semiconductor
equipment as viewed through a communications link in terms of SECS-II messages
communicated over that link. The GEM standard impacts equipment control and
equipment to “host” communications. Note that GEM does not comply with the
distributed object-based control description paradigm; this paradigm is being pur-
sued through OBEM, which may become a replacement for GEM (see below).
Recently, the GEM standard has been enhanced to include an application note
defining a methodology for process parameter update.5 This enhancement is impor-
tant to the standardization of R2R control implementation because it defines a
common way for providing R2R control advice information to a tool.
Object-Based Equipment Model (OBEM — under review)**: The OBEM
specification defines concepts, behavior, and message services to realize equipment
control systems. The OBEM standard defines the operation of the equipment control
systems, including utilization of sensor actuator network (SAN)-compliant device-
level systems and visibility to higher level control systems. Specifically at the equip-
ment control level, requirements addressed by the OBEM standard (either directly or
through reference) include integration of control algorithms at equipment control
levels, real-time in situ control capabilities, synchronization of data, object-based solu-
tion, visibility of equipment objects to higher level systems (i.e., data accessibility),
aspects of volume data management, integration of device control algorithms, and
remote monitoring. OBEM achieves specification for these requirements by providing
an aggregate description of an equipment class and identifying structure and behavior
that provides links to other detailed object-oriented SEMI specifications.2,6
Sensor Actuator Network (SAN — E54): This suite of standards defines con-
cepts, behavior, and message services to facilitate device level communication over
a sensor/actuator bus, thereby integrating sensors and actuators into the equipment
control system.4,7 Examples of devices include mass flow device, particle counter,
capacitance manometer, etc. Components of the standard include sensor/actuator
* SEMI standards in equipment automation/software are delineated by an “E” number designation.

** At the time of this writing, the OBEM specification was under review as a provisional SEMI standard.2

network (i.e., sensor bus) communication standards (NCSs), a common device model
(CDM), and specific device models (SDMs).
CIM Application Framework and APC Framework (under review): This
suite of framework documents specifies a common object-oriented environment for
integrating applications and sharing information in a CIM factory domain.2,8,9 These
specifications are derived from a SEMATECH CIM framework specification. They
define a “plug-in” environment for the definition, partitioning, and integration of
CIM applications such as schedulers and work-in-progress trackers. The plug-in’s
interfaces are specified in terms of exposed object attributes and methods. The APC
framework component specifies framework applications related to control.
Figure 7.2 provides an illustration of some of the components of the APC Frame-
work, and shows the integration of the APC Framework with the other frameworks
in the suite. Figure 7.3 shows the fundamental components in an APC framework-
compliant advanced process controller.
Referring to Figure 7.1, each of the aforementioned standards is part of the
hierarchical control solution specified for the industry. An example of a typical R2R
control solution that might utilize these standard specifications is shown in Figure 7.4.
Note that in this example (1) a SAN is utilized to collect data within an in-line
metrology system; (2) the metrology system communicates metrology information
FIGURE 7.2 CIM Framework components.

FIGURE 7.3 Structure of CIM Framework advanced process control component.
FIGURE 7.4 An example of R2R control solution utilizing SEMI standards.
of interest to an R2R controller via SECS messaging; (3) the R2R control solution
communicates to the metrology system via SECS and to the tool via GEM (SECS);
(4) the internal architecture, as viewed from above, is APC framework compliant;
(5) the equipment presents a GEM/SECS interface to both the R2R control element
and a host controller;* and (6) the equipment implements R2R control advices (i.e.,
recipe modification suggestions) via sensor/actuator commands implemented over
the equipment SAN.
* There are many different architectures for providing connectivity between equipment and both an R2R
controller and a factory host. This two-equipment-port solution is merely one example and is not meant
to suggest a preferred architecture.

7.3 SEMATECH AND THE CONTROL SYSTEMS
REQUIREMENTS SPECIFICATION
The efforts by the SIA, and especially SEMI, clearly address aspects of definition
of the integration environment for APC, including R2R control. However, they don’t
provide a concise “big picture” that illustrates how all of the standard elements fit
together, and specifically how R2R control should be integrated. SEMATECH real-
ized this deficiency and established a Control Systems Specification Working Group
(CSSWG) in early 1996 to pursue a Control Systems Requirements Specification
(CSRS) for the industry.10 In researching these requirements through interviews of
users, integrators, OEMs, standards leaders, and CSSWG members, it became clear
that the specification of methods and components for adding a new control capability
into a control system is a fundamental requirement that should be addressed in a
CSRS. Specifically, users, working with integrators and OEMs, would like the
flexibility to easily and reliably add, delete, or modify a sensor, algorithm, applica-
tion, or control capability in an equipment control system. In further identifying this
capability, the following guidelines were identified:
1. The specification should be defined so that the capability could be under-

stood and added at the user skill level — that is, a skill level that doesn’t
require technical intervention of the OEM or third-party integrator.
2. The specification should address current-generation and next-generation
systems. It should provide a migration path so that current solutions can
be reused to a large extent in next-generation CSRS-compliant systems.
3. The specification should reference SEMI standards wherever possible and
should be aligned with SEMI directions in standardization.
4. The specification should be aligned with current efforts in advanced con-
trol systems specification such as APC Framework and the International
300-mm Initiative (I300I).8,9,11
The two primary components of the CSRS are (1) a specification for the enhance-
ment of existing equipment control systems, and (2) a specification of future control
systems. The first component was developed for users, integrators, and OEMs to
utilize as when they wish to add a control capability (sensor, algorithm, application,
etc.) to an existing system. The CSRS indicates the standards and specifications to
which the sensor supplier, OEM, and integrator should adhere so that capability can
be easily added to the system. The second component was developed to be utilized
as an aid for envisioning future equipment control systems and could thus be an aid
in the specification of these systems.
The list of requirements of control systems addressed by the CSRS is shown in
Table 7.1. As shown in the table, these requirements are specified across a number
of domains to ensure interoperability in each of these domains. Specifically, the
CSRS is divided into control and reliability domains. The control domain specifies
the structure and operation of the entire factory control systems. The reliability
domain addresses issues such as equipment up-time, maintenance, etc.

TABLE 7.1
Control Systems Requirements Issues
Issue Domain
1. Specification for synchornization/time-stamping of data Control

2. Real-time (in situ), run-to-run, and factory-level control capabilities Control
3. Specifications for combining run-to-run and in situ control Control
4. Specifications for combining run-to-run and factory-level control Control
5. Defining equipment, run-to-run, and factory-level control systems utilizing Control
a standard object-based paradigm
6. Specifications for sensor integration into the control system (models, Control
communication protocols, etc.)
7. Specifications for integration of third-party) control algorithms at equipment Control, Reliability
and run-to-run level (without affecting integrity of control system or tool)
8. Defining data accessibility/visibility at equipment and run-to-run control Control
levels
9. Specs. for remote monitoring Control
10. Specifying wafer state information Control
11. Supporting wafer-driven processing Control
12. Specifications for volume data management Control
13. High-speed network compliance Control
14. Defining a successor to SECS-II GEM that delivers higher throughput Control
15. Specifications defining visibility of machine operations Control, Reliability
16. Deterministic performance requirements Control, Reliability
17. Configuration management requirements Control, Reliability
18. Specifications for equipment transition between up/down time, Reliability
maintenance, etc.
19. Specifications for equipment maintenance Reliability
20. Specifications for testability requirements Reliability
21. Specifications for fault detection and end-point control Control, Reliability
22. Alignment with the APC Framework efforts Control
23. Alignment with 300-mm ECS efforts Control
24. Alighment with I300I efforts Control
25. L
In mapping the list of requirements to the available standards provided by SEMI,

a CSRS for current and near-term next-generation systems is defined. This definition
is summarized in Figure 7.5. Referring to this figure, note that the following are
specified for a run-to-run control solution:
1. Use of GEM/SECS for communication to equipment (and to metrology

system as necessary).
2. Capability for migration to OBEM connectivity to equipment.
3. Implementation of R2R controller as a “piggyback” solution (see below).
4. Internal R2R controller architecture that is APC Framework “compatible”
with capability for migration to framework compliance.

FIGURE 7.5 CSRS for current and near-term next-generation systems.
These specifications define elements of the internal structure and communication

capability of a “piggyback” controller. A piggyback controller refers to a class of
controllers that are integrated with traditional equipment control systems and perform
selected control functions that are generally beyond the capability of these traditional
control systems. For example, at the real-time level, a piggyback controller running
a real-time operating system and utilizing high-speed data interface cards may utilize
in situ measurement data such as optical emissions spectral data and Vbias (bias volt-
age) data to stabilize an etch process through adjustment of power, pressure, and flow
equipment inputs (see Figure 7.6). The equipment controller purchased with the
system is still utilized to control the sequential operation of the tool (e.g., pumpdown,
gas flow, light plasma, etc.); however, as it is not equipped to modify equipment
inputs during a run, this task is accomplished by the piggyback controller.
In the R2R control regime, a piggyback controller must be integrated with
existing equipment and metrology and perform automatic updates of equipment
input parameters as necessary to achieve R2R process control.12 In evaluating a
capability for practical integration (in terms of cost and time), a number of design
requirements can be identified for the integrateable R2R control solution. These
design requirements are detailed in the next chapter.
7.4 SUMMARY
Insight has been provided in this chapter into contributions of three players in the
industry that are shaping the roadmap of R2R control development and integration.

FIGURE 7.6 Example of in situ piggyback control solution.
The SIA provides a timeline for the development and deployment of R2R control
and gives an understanding of the positioning of R2R control with respect to other
advancements in the industry. SEMI provides guidance toward interoperability and
interchangeability of R2R solutions through standards developed generally in a
bottom-up, “grass-roots” fashion. SEMATECH, through its CSRS effort, provides
a level of organization to SEMI communication and control standards, and provides
a roadmap for users, OEMs, and integrators to specify and verify requirements of
control systems for both retrofit and next-generation applications.
These three players have contributed valuable input to the specification of
requirements for control solutions in the industry. The derivation of these design
requirements for R2R control solutions is provided in the next chapter, followed (in
Chapters 9 and 10, respectively) by the description of an enabling technology and
an R2R control solution design that meet these design requirements.
ACKNOWLEDGMENT
Much of the material presented in this chapter is derived from Reference 8, and is
reprinted with permission. The authors also acknowledge the contributions of the
members of the Control Systems Requirements Working Group sponsored by Inter-
national SEMATECH.
REFERENCES
1. The National Technology Roadmap for Semiconductors, Semiconductor Industry
Association (1997), available at www.sematech.org.
2. www.semi.org.
3. www.sematech.org.

4. SEMI International Standards: Equipment Automation/Software 1 and 2, Semicon-
ductor Equipment and Materials International, 1999.
5. Document 3022A: Revision to SEMI E30, Addition of Application Notes for Recipe
Parameter Modification, Semiconductor Equipment and Materials International,
(October 1999).
6. Rumbaugh, J. et al., Object-Oriented Modeling and Design, Englewood Cliffs, NJ,
Prentice Hall, 1991.
7. Moyne, J., Najafi, N., Judd, D., and Stock, A., “Analysis of Sensor/Actuator Bus
Interoperability Standard Alternatives for Semiconductor Manufacturing,” Sensors
Expo ’94, Cleveland (September 1994).
8. SEMATECH CIM Framework Architecture Guide 1.0, SEMATECH Technology
Transfer Document #97103379A-ENG (1997).
9. SEMATECH Advanced Process Control Framework Initiative (APCFI) Project:
Detailed System Description, SEMATECH Technology Transfer Document
#99053736A-TR (1999).
10. SEMATECH Control Systems Requirements Specification V2.0, SEMATECH Tech-
nology Transfer Document #96123222B-ENG (December 1997).
11. CIM Global Joint Guidance for 300 mm Semiconductor Factories, Release One,
International 300-mm Initiative (I300I) and Japan 300-mm Semiconductor Technol-
ogy Conference (J300) (December 1997).
12. Moyne, J., Etemad, H., and Elta, M., “Run-to-Run Control Framework for VLSI
Manufacturing, Microelectronic Processing ’93 Conference Proceedings (September
1993).

8 Design Requirements
for an Integrative*
R2R Control Solution
James Moyne
The lack of immediate widespread acceptance of R2R technology in the semicon-

ductor manufacturing area, despite its proven capabilities, indicates that adequate
R2R controller design requirements have not been met for the painless integration
of industrial quality R2R control. Design requirements for integrated cost-effective
R2R control solutions are presented in this chapter.1–4
Clearly the primary concern of integrators is the short- and long-term cost of
developing, integrating, utilizing, and maintaining systems utilizing R2R control. To
a large extent, these issues impacting cost must dictate the design of the controller.1
In order to understand the issues that impact the cost of R2R control it is necessary
to describe the technical and practical semiconductor manufacturing R2R control
environment. First and foremost, semiconductor processes are complex, not well
understood (thus physical models are generally nonpredictive), and very dynamic.
Further, the control technology applied to these processes is basically sensor-driven,
and there is generally an insufficient number of sensors and actuators at each level
of control. Thus, there is a tendency to rely on empirical methods for control. A
number of empirical control algorithms have been developed for applications to R2R
control in semiconductor manufacturing; many have been discussed in detail in Part
2 of this book. Algorithm implementations and other supporting software elements
(communication drivers, user interface modules, etc.) have been made available from
a number of sources, both commercial and noncommercial. However, in general, the
domain of applicability of each algorithm is limited or not well understood.2,3
This unique control environment imparts a number of requirements on practical
and integratable R2R control solutions. A fundamental set of these requirements is
listed in Table 8.1. Additional information on each requirement is provided in the
following sections.4
8.1 PROCESS INDEPENDENCE

As noted above, the R2R control solutions for the semiconductor industry are generally
empirical in nature. Further, a set of empirical algorithms have been proved effective
for R2R control in a number of process scenarios. The R2R control environment should
* Sometimes referred to as “integrateable.”

TABLE 8.1
Summary of R2R Control System Design Requirements
in the Semiconductor Manufacturing Industry
Section # Requirement
1 Process independence
2 Plug-and-play integration of external software modules
3 Dynamic control scheme
4 Complementary operation of multiple control and optimization methods
5 Ability to provide R2R control with or without in situ control
6 Platform independence
7 User friendliness and control integration migration path
take advantage of this multiprocess control capability and provide a level of process
independence of the control solution. This will enhance the cost-effectiveness of R2R
control by providing a high level of cross-process portability and reusability of the
control solution. Design requirements of an R2R control system that will maximize
process independence include (1) separation (modularization) of process-specific
control capability from generic control capability, (2) capability for (re)configuration
of process control I/O for adaptation to a new process, (3) dynamic internal R2R
controller control scheme (see below) for rapid reconfiguration to new process control
schemes, and (4) capability for plug-and-play of third party modules (see below) for
incorporation of new required features in a process control environment.
8.2 PLUG-AND-PLAY INTEGRATION OF EXTERNAL

SOFTWARE MODULES
The R2R control solution must be able to interoperate with software programs such
as process model builders, optimizers, control algorithms, equipment and metrology
interfaces, data presentation and storage mechanisms, and user interfaces. Thus, the
control solutions must define a generic interface to all such types of software
programs. These types of programs, or modules, should be able to dynamically
connect and disconnect to/from the control environment without any code modifi-
cation. There should be a module interface, which facilitates the passing of arbitrary
data, determined at run time between the controller and the module. The module
interface must also allow users to develop custom modules, and third-party devel-
opers to produce shrink-wrapped modules that can be incorporated in the control
scheme dynamically (i.e., so that the control solution can be updated dynamically
at run time). Note that this generic and dynamic software interface requirement is
critical to achieving the requirement of process independence described above.
8.3 DYNAMIC CONTROL SCHEME

The controller’s source of control knowledge (i.e., the knowledge of navigation
through execution of software modules to achieve control tasks) should be persistent

yet dynamic, capable of being updated in mid-process, and capable of being adapted
to many different processes by the user. One way to achieve these goals is to have
the control knowledge stored in a database rather than in static code. Storing the
control knowledge in a database makes the knowledge capable of being changed or
modified quickly, easily, and at any time (including during run time). Further, it
provides a level of portability of the control scheme.
8.4 COMPLEMENTARY OPERATION OF MULTIPLE

CONTROL AND OPTIMIZATION METHODS
In analyzing the control algorithm alternatives applied to the full spectrum of process
conditions in the semiconductor manufacturing industry, it is clear that none of the
available R2R control algorithms cover the entire spectrum of process optimization
and control (see Part 2 of this book).2,3 This fact imparts two requirements on the R2R
control solution if it is to be applicable industry wide. First, there must be a capability
for plug-and-play of control algorithm modules (see above) so that the “best” algorithm
can be utilized in the control scheme for a process. Second, in many cases the controller
must utilize a framework that supports the complementary utilization of a number of
sequential optimization and control algorithms. This framework must contain a mech-
anism that can capture the state of the system after each process run and determine
which of the available control algorithms is best suited to the process.
8.5 ABILITY TO PROVIDE R2R CONTROL WITH OR

WITHOUT IN SITU CONTROL
In the Introduction to this book (see Figures 7 and 8) we noted that R2R control is
merely a component of an envisioned multilevel control system that includes real-
time equipment and process control as well as potentially soft-real-time process
control components operating in conjunction with the sequential R2R control com-
ponent. Currently, in many cases, these in situ control components are nonexistent;
thus, the R2R control component must be capable of providing control in the absence
of these components. However, in other cases in situ control elements (notably
endpoint capabilities) are available. The R2R controller should be able to utilize the
in situ capabilities in conjunction with R2R control capabilities to provide improved
process control. Further, the controller should have a reconfigurable dynamic control
scheme (see above) so that in situ control capabilities can be easily added (as they
become available) to complement the control scheme.
8.6 PLATFORM INDEPENDENCE

Due to the software development and corporate environments, there are no clearly
identifiable software or hardware platform standards (de facto or otherwise) in the
semiconductor industry. At the time of this writing, the majority of applications
operating at the (non-real-time) level of R2R control utilized the Pentium* (or
* Intel Corp.

similar) hardware platform running Windows NT.* However, there are a few orga-
nizations that produce or utilize rival hardware or software platforms demanding
solutions for alternative platforms such as UNIX. A key source of cost leverage of
any R2R solution, then, is platform independence or, at the very least, a level of
portability of solutions between Windows NT and UNIX.1
8.7 USER FRIENDLINESS AND CONTROL

INTEGRATION MIGRATION PATH
Though not a quantifiable design requirement, user friendliness is perhaps the most
important requirement for the acceptance of R2R control technology in the main-
stream of semiconductor manufacturing. In most cases sequential control represents
a new technology in fabs. Since processes are not well understood in general, and
the control solutions are generally based on empirical data, there is a valid level of
hesitation among process engineers and operators in accepting R2R control. There
are a number of requirements of R2R control solutions that address this user friend-
liness issue and provide for a migration path toward full acceptance of R2R control
as an integral part of mainstream semiconductor manufacturing. The most important
of these requirements is the separation of details of the control algorithm operation
in the controller from the overall R2R operation of the controller. The operator or
process engineer should not be burdened with a requirement of understanding or
even viewing control algorithm operation when he/she is utilizing the system in a
production environment. The controller should be presented as a very simple I/O
solution, similar to that depicted in Figures 1 and 2 in the Introduction to this book,
where, for each control run, the controller utilizes a small amount of metrology data
(e.g., average thickness and uniformity) and generates an advice consisting of tuning
suggestions for a small number of process parameters (e.g., time and pressure). Note
that this I/O solution is the same no matter what control algorithm is utilized;
therefore, the portion of the GUI associated with controller operation should remain
the same, regardless of the control algorithm utilized. One way to provide this level
of consistency is to separate the user interface into operation modes such as Operate
and Configure, where the overall R2R operation is viewed in the Operate mode and
the algorithm details are viewed and configured in the Configure mode. A security
log-in system could then be used to insulate the operator for accessing the Configure
mode.
Another user interface requirement is that it be rapidly (re)configurable. Unfor-
tunately, despite efforts at standardization of user interfaces by the semiconductor
industry, there are many “standard” user interface forms that vary widely from
company to company. A requirement of any R2R control solution is that its GUI be
generally configurable to the look and feel specified by the user. Some parameters
and ideas for GUI design and configurability are provided in SEMI and SEMATECH
user interface specifications.5,6 These specifications suggest another important
requirement of user interfaces, namely that they comply with (SEMI) standard
specifications wherever possible.
* Microsoft Corp.

8.8 SUMMARY
Some of the important requirements of R2R control solutions for semiconductor
manufacturing have been detailed in this chapter. They address not only the technical
capability of the solution, but also its economic feasibility. While not all of these
requirements apply to every application, they should be utilized in the assessment
process of an R2R control solution.
In the following chapters in this part of the book these requirements are utilized
in the design and assessment of R2R control-enabling technologies, and R2R control
integrated solutions.
REFERENCES
1. Moyne, J., Telfeyan, R., Hurwitz, A., and Taylor, J., “A Process-Independent Run-
to-Run Controller and Its Application to Chemical-Mechanical Planarization,” Proc.
Sixth Annual SEMI/IEEE ASMC, Boston (October 1995).
nology A, Vol. 13, No. 3, (May/June 1995), pp. 1787- 1791.
3. Telfeyan, R., Moyne, J., Chaudhry, N., Pugmire, J., Shellman, S., Boning, D., Moyne,
W., Hurwitz, A., and Taylor, J., “A Multi-Level Approach to the Control of a Chemical
(May/June 1996), pp. 1907-1913.
4. Telfeyan, R., Moyne, J., Hurwitz, A., and Taylor, J., “Demonstration of a Process-
Independent Run-to-Run Controller,” 137th Meeting of the Electrochemical Society
(May 1995).
5. Document 2783A: Human Interface Standard for Semiconductor Manufacturing
Equipment, Semiconductor Equipment and Materials International (June 1998).
6. SEMATECH Strategic Cell Controller User Interface Style Guide 1.0, SEMATECH
Technology Transfer Document #92061179A-ENG (1992).

9 The Generic Cell
Controller (GCC)
James Moyne
The Generic Cell Controller, or GCC, represents a solution to address the require-
ments of R2R control in the semiconductor manufacturing industry (as detailed in
Chapter 8). The GCC design and a GCC-enabled R2R control solution are presented
in this chapter.1-3 Specifically, the design of the GCC is presented, in Section 9.1,
as a solution to any form of discrete control (including R2R control). Simple
examples are used to illustrate the application of the GCC concept to control. A
specific solution of GCC application to R2R control is presented in Section 9.2. This
presentation includes a detailed description of the GCC operating environment,
software components, and process optimization and control environment. This is
followed in Section 9.3 by a detailed mapping of the solution design to the design
requirements of Chapter 8.
9.1 GENERIC CELL CONTROLLER DESIGN

9.1.1 INTRODUCTION
A perception of the layout of the automated facility is a prerequisite to a study of
its control structure. The widely accepted vision of the fully automated manufactur-
ing facility is a hierarchical logical structure that is paralleled by a hierarchical
control structure. At the top of the manufacturing hierarchy, a factory controller acts
as a global production facility controller, and as a gateway to higher levels of
company management. At the bottom of the hierarchy, the “leaves” of the tree are
the various types of equipment in the facility involved in product manufacturing.
Each piece of equipment has an equipment controller that provides for detailed
operation of the equipment, and provides for network access to the facility hierarchy.
Between the facility controller and the equipment controllers, numerous cell
control elements are networked in a hierarchy and divide the complicated task of
wafer processing. Generally, this hierarchy consists of two or three physical levels.
In any manufacturing facility a cell controller is defined as follows:
A cell controller is a unit in a facility that accepts commands from a parent (controller)
and implements these commands by instructing children units under its control. These
children may also be cell controllers, or may be equipment controllers with sufficient
intelligence to interpret the commands sent from a parent cell controller.

Note the distinction between a cell controller — which is not involved in direct
equipment control — and an equipment controller. The interface to the cell controller
is, to some extent, a function of its role in the facility. Efforts in CIM framework
component standardization seek to standardize the interface to these controllers as
well as communications between control elements over the factory backbone.4-6
In understanding the above description of a cell controller, it is clear that,
although the tasks assigned to the various cell controllers in the facility may vary,
cell controllers have common basic functionality. The implementation of a cell
controller design that isolates the generic functionality common to all cell controllers
would result in a significant reduction of programming effort, as well as in cost in
facility startup and facility update.2 Software portability would be increased while
system complexity would be decreased.
The remainder of this section contains a description of a Generic Cell Controller
(GCC) design for facility automation.1-3 A requirements analysis and list of design
assumptions are first presented. This is followed by a general description of the
design and a more detailed description of the GCC components and component
interactions. A special capability of the GCC, namely its ability to be taught “on the
fly” to adapt to a new control environment, is then discussed. Following a summary
of the GCC design description, this section concludes with examples (in semicon-
ductor manufacturing) that illustrate GCC operation. Note that throughout this sec-
tion the GCC design is presented in generic terms and not applied to R2R control;
this approach is taken to give the reader a better understanding of the range of
applicability of GCC concepts. The specific application of GCC to R2R control is
presented in Section 9.2.
9.1.2 GCC DESIGN GOALS AND ASSUMPTIONS

In determining design specifications for a generic cell controller in the semiconductor
facility, careful consideration must be given to aspects of the facility environment
and to the goals of facility automation implementers. The automated semiconductor
manufacturing facility is a hybrid environment consisting of multivendor controllers,
networks, and equipment.2,7 The product line and even aspects of the facility structure
and operation may be ever-changing (i.e., dynamic within the limits imposed by the
hierarchical facility definition). The facility control structure must support this hybrid
dynamic environment in real time and at a minimum cost.7
Therefore, the following design goals are realized for GCC design:
1. The controller design must accommodate the hybrid and dynamic oper-
ational environment. Included in this goal is the implication that the
controller design must not be a function of the facility hardware, software,
and networking base.
2. The controller design specification should provide for the maximization
of generic attributes of the cell controller so that development costs are
minimized as redundancy of programming effort is minimized.
3. The cell controller performance should be maximized with respect to
development speed, operating speed, software size, memory requirements,

etc. A minimum performance requirement is the ability to function in a
sequential control environment.
To completely specify the role of the cell controller in the facility, a few assumptions
about facility structure and operation must be made. The overall facility structure
must be specified. For this design effort, a hierarchical facility structure is assumed.
Thus, it will be assumed that a cell controller functions in the hierarchical facility
structure as described above. Important properties of the hierarchical structure that
should be considered in attempting a cell controller design include:
1. The controller accepts commands from, at most, one parent and imple-
ments each command by passing a set of commands to one or more
children under its control.
2. The scope of influence of a controller is its immediate parent and imme-
diate children.2 (Any cell controller design must reflect a clear understand-
ing of the internal operations of the controller as well as its interaction
with its immediate parent controller or children (other generic cell con-
trollers and/or equipment controllers)).
It should be noted that the assumption of a hierarchical facility as described above

is not a prerequisite for the realization of this GCC design. This point will become
clear as the description of the design proceeds. The assumption of a hierarchical
facility is made so that the GCC description can be more easily understood.
Assumptions are also made with respect to facility-wide communication. The
first assumption is that any communication protocol in the facility between cell
controllers or between cell controller and equipment controller satisfies the following
additional properties:
3. The communication protocol provides for communication of application-

level information to/from the controller that has error-free communication
transmissions.
4. The communication protocol will support the communication (between
controller applications) of any message that conforms to the specified
facility message format (see next paragraph).
5. The communication protocol provides end-to-end delivery of messages
between controller applications in a “reasonable” length of time (reason-
able such that delays in message delivery in general do not grossly affect
the timely operation of the controller).
6. The communication protocol functionality is partitioned such that a clear
separation exists between the functionalities of the application and the
functionalities of the communication protocol.
Another assumption made concerning facility communication is that a facility-wide

message format specification exists. This specification should indicate a well-defined
message information format and should allow for the communication of any and all

necessary information between controllers in a facility. As an example, one appro-
priate message format specification for semiconductor manufacturing is SECS (see
Chapter 7).6 The CIM framework standards efforts are also aimed at defining stan-
dardized interfaces and interactions between control components.4-6
Other assumptions are made concerning the development environment. It is
assumed that the cell controller hardware environment is such that it does not impose
any controller design limitations (such as memory space and hardware interface
compatibility). (Of course this assumption is not valid in a practical implementation,
but is useful in developing generic design specifications.) It is also assumed that
because of the structure, potentially large quantity, and dynamic property of the
control information to be stored, any data storage and management in the cell
controller will make use of a relational database management system (DBMS)
(although this assumption does not restrict the eventual incorporation of other data-
base systems such as object-oriented database application systems8).
9.1.3 GENERAL DESCRIPTION OF GCC

With the foundation for the design in place, the design process may begin. An initial
concern is that the design goals for operation in a heterogeneous environment and
the design goal of a generic cell controller tend to conflict (because the more
heterogeneous the environment, the greater the number of factors that must be dealt
with to achieve a generic controller design). Any cell controller design that maxi-
mizes generic functionality should provide for the isolation of that functionality
from the expected hybrid of communication protocols and hierarchical facility archi-
tectures. To provide for this isolation, the cell controller design should be modular;
generic modules should exist in the cell controller design to provide for the truly
generic aspects of functionality of the controller, while nongeneric modules should
also exist in the design to isolate the majority of the cell controller functionality
from the specifics of facility communication and facility structure.
The isolation from facility communication is provided by an interpreter module
that converts information from a cell controller communication network interface
into information with a common message format (and vice-versa). Note that mes-
sages converted by the cell controller interpreter module into the common message
format are passed on to a message parser for use by the rest of the generic cell
controller. Note also that the communication network could be any network that
satisfies conditions 3 through 6 above. Because of the modular nature of the com-
munication protocols (see assumption 6), the function of the interpreter module
generally is to strip off protocol control information from incoming messages or to
encapsulate outgoing messages with protocol control information.
The necessary isolation from changes in the facility structure already exists as
restrictions have been placed on the facility structure concerning hierarchy and scope
of influence (see assumptions 1 and 2). Thus, the components of interaction with
the cell controller are well known and definable from a generic perspective.
A conclusion of this analysis, then, is that a generic environment is created for
the development of a cell controller specification for use in the specified hierarchical

facility and with the implementation of the appropriate communication interpreters
isolating the protocol-specific aspects of communication.
When developing a cell controller specification in this generic environment, a
first step is to characterize the desired functionality of the controller. A controller
with the design described here reacts to three sources of stimuli (also called events):
(1) messages received from above (the parent controller), (2) messages received
from below (a child cell controller or equipment controller), and (3) an internally
triggered event (such as a timeout on a message transaction). The method of reaction
to these sources of stimuli is also (generically) definable as follows:
The cell controller, initially in an idle state, receives stimulus in the form of either a
message of a specified format or an internal event indication. The cell controller parses
the information, interprets the information, and takes action as a result. The cell
controller then returns to an idle state.
There are many cell controller designs that would potentially achieve the desired
functionality, however, the inclusion of performance and cost considerations in the
design requirements greatly reduces the number that are acceptable. Usually software
complexity is proportional to its size, so a specification that minimizes application
software size is desirable. A modular specification is also desirable because, as stated
earlier, it provides isolation from facility structure and communication. Modular
design then results in increased flexibility and portability of the design, and decreased
update costs. From the performance standpoint, sequential control performance
consistent with process events in the factory is a requirement. Finally, and perhaps
most importantly, it must be emphasized that the specification should be generic
and therefore applicable to any cell controller in the hierarchical facility.
The cell controller design schematically represented in Figure 9.1 incorporates
all of the above analysis and design considerations. The overall operation of this
cell controller design can be summarized as follows:
The cell controller is a reactive device and therefore begins in an idle state. It responds
to message events received from the parent or children controllers, or to internally
triggered events. All message events received are stripped of control information
(specific to the communication protocol) by I/O interpreter modules, and the generic
portion of the cell controller is presented with internal or message “event” indications
structured in a common facility-wide message format. A message parser makes use of
the well-defined structural properties of the message format to extract the event data
from the message. A main program kernel module called a “conductor” matches the
event data received from the message parser or from an internal event to an entry in
the controller database. (The database is structured such that the event formats are
embedded in the data dictionary; therefore, the database is capable of storing the event
data of any event — externally or internally generated — that complies with the
specified format.) Through relations implied by the database, the conductor determines
the unique action to take as a result of an event received. Also through relations implied
by the database, the appropriate action may be invoked. to invoke this action the
conductor first scans the database to determine the necessary routines (or methods) to
call as well as parameters to pass to the routines, and an order to call the routines. The

FIGURE 9.1 Generic Cell Controller schematic.
conductor calls these routines in the specified order and with the specified parameters.
A routine may update the database. A routine may also send message data (derived from
the database) to the message parser to be formatted and forwarded to the I/O interpreter
so that the message data may be communicated in the specified format and appropriate
communication protocol to a parent or child controller. Upon return of control to the
conductor from the routines called, the cell controller returns to an idle state.
The event posting and servicing style of operation of the controller is illustrated by
the flow diagram of Figure 9.2. In analyzing the figure it is clear that the macroscopic
view of controller information flow is uncomplicated and well defined because
(1) the sources of controller stimulation “events” are well defined as is the message
format, and (2) much of the control information is embedded in the database struc-
ture. It is also clear that the system is heavily data-driven; indeed, all events result
from data received (via a formatted message) or from an internal event (e.g., timeout
on data expected). Thus, the database component of the controller plays a large role
in determining controller operation.
9.1.4 SPECIFIC DESCRIPTION OF GCC MODULES

The following is a detailed description of the various modules of the GCC introduced
in the previous section and illustrated in the GCC block diagram of Figure 9.1.
9.1.4.1 I/O Interpreter and Message Parser
These GCC modules perform data conversion between the facility-wide message
format and the internal GCC event format. In this way, the I/O interpreter isolates

FIGURE 9.2 Flow diagram of cell controller operation (internal event is stated here as
“Timeout Indication”).
most of the functionality of the controller from communication protocol-specific

information. This allows for a more generic controller specification. As an example,
in the automated semiconductor manufacturing arena, the common message format
is SECS-II. The controller interpreter module provides a two-way translation from
SECS information over a communication network to SECS-II formatted messages.
The message parser in turn formats and deciphers SECS-II formatted message
information to and from GCC event messages. Note that the communication network
could be any Ethernet, RS-232, etc., network. The functionality of the communica-
tion hardware (e.g., an RS-232 communication board) may be considered as part of
the functionality of the I/O interpreter. The functionality of the I/O interpreter and
message parser that is important to the GCC algorithm is that these modules, working
together, present/accept application level information to/from the GCC that is inde-
pendent of the physical and application communication protocol through which it
was/will be communicated.
As a specific example, suppose an equipment controller is reporting its model
number and software revision number to the GCC using a SECS Stream 1 Function
2 message.6 Suppose the model number is “EQUIP1” and the revision number is
“Ver1.0.” The I/O interpreter module would provide support of communication of
data into the GCC via an RS-232 or Ethernet interface, and present the message
parser module with the SECS-II message syntax. This incoming SECS message
would be of the format:
Message (Stream 1, Function 2)

List of two items
Item 1 == Model number == “EQUIP1”
Item 2 == Version number == “Ver1.0”.

The information communicated to the parser would be the same SECS-II syntax
regardless of the lower-level communication medium (e.g., RS-232 or Ethernet)
utilized.
9.1.4.2 Main Program Kernel Module (or “Conductor”)
This module coordinates all controller activity. Its functionality is quite simple and
well defined. This module is event-driven, reacting to message events from its parent
and children, and internal events. For each stimulus event, the module uses the
database to interpret the event and determine the action to be taken (i.e., the rou-
tines/methods in modules to be called). The conductor then calls the specified
routine(s) in the order and with the parameters specified by the database. Upon
return from these routine(s) the conductor returns to a state of rest/idle. Figure 9.2
is a flow diagram illustrating conductor functionality. The elements of the flow
diagram may be explained as follows.
1. Start/Idle: The conductor is a reactive, event-driven module. Thus, for the

case where no event stimulus is received and all (previous) stimulus
reaction transients have ended, this module remains in an idle state,
continuously checking for an event stimulus (see next item).
2. Stimulus to Module: When in an idle state, the conductor continuously
checks for an incoming stimulus (external message or internal event). All
message events received have been parsed by the message parser and
saved as message information in a structure defined in the conductor. If
no event is posted, the conductor continues to poll. If an event is detected
the conductor “wakes up” and services the event (see item 3 below).
Incoming event detection may be accomplished in a number of ways,
such as with a mailbox mechanism. With this method, a memory location
(variable) may be designated as a mailbox, accessible by the message
parser module, an internal timer module, and the conductor. The mailbox
is normally empty (contains a null value) and is polled by the conductor.
When an event, external or internal, is to be posted, the mailbox flag is
raised and an address in the mailbox points to the variable instance
containing the event information. Upon receiving the information (upon
its next poll) the conductor clears the mailbox message/timeout pointer,
thereby lowering the mailbox flag.
3. Match Event to Database: As stated in the general description of the GCC,
the conductor services event stimuli by matching the information of the
event to information in the GCC database and, through relations implied
by the database, taking the appropriate action. Thus, when the conductor
has detected that an event stimulus has occurred, it must first attempt to
find a match between information associated with the event and an entry
in the database. The way in which event information is stored in the
database (i.e., the database schema) is dependent on a variety of factors
including the message format specification, the DBMS used, as well as
user storage, performance, and interface objectives. Regardless of the

storage format, the conductor must contain an algorithm that will search
through the database and indicate a match between stored information
and the current message or timeout associated with the event. This algo-
rithm will be a function of the database schema as well as the event data
structure and the message protocol.
The interaction of the conductor with the database is described further
below. Also, later in this section, examples are presented that illustrate
the matching of a message to the database (where the messaging format
is SECS), and the matching of a timeout internal event to the database.
For these examples the database schema and message and timeout event
data structures are detailed.
4. Determine Action to Take: Each message and timer instance stored in the
database is linked to a single action identified by an action number. After
the conductor has found a match between the incoming event (message
or timeout) and an entry in the database, it retrieves the associated action
number.
5. Determine Routine(s) to Call (in Order) and Parameters to Pass: In the
database, each action (identified by an action number) is associated with
(is linked to) one or more routines (each identified by its routine number),
and a set of parameters to be passed to each routine. Note that in an object-
oriented paradigm these “routines” may be equated to methods.9 After the
main program has determined an action number in response to the incom-
ing event (see item 4 above), it retrieves the associated routine numbers
and parameters. It then compiles an ordered list of routines to call, and
the parameters to pass with each call. An example of such a list is indicated
in Table 9.1. In this example the action to be taken is action number 5.
The purpose of this action is to read the values of two sensors on a piece
of equipment and store them for later use. Four routines are to be called
to implement this action: (1) “Initialize() — no parameters” — wakes up
the piece of equipment; (2) “GetData(Ch, 1, 2)” — sends a message to
the equipment requesting the values of channels 1 and 2;
(3) “PollACK(Val_1, Val_2)” polls the equipment for a response message
containing the sensor values “Val_1” and “Val_2”; and (4) “UpdatesDB(1,
Val_1, 2, Val_2)” updates the database with the new values of channels
1 and 2.
6. Another Routine to Call?/Call Routine(Parameters): From the compiled,
ordered list of routines to call (see item 5 above), the conductor takes the
necessary steps to implement the action indicated (see item 4 above). This
is accomplished by calling each routine in the list in order with the
indicated parameters. In the example relating to Table 9.1, the routines
“Initialize,” “GetData,” “PollACK,” and “UpdateDB” are called in order
and the values of equipment channels 1 and 2 are read and updated in the
local database. After control has returned from the last routine called in
the ordered list, the conductor returns to an idle state, polling for the next
event stimulus.

TABLE 9.1
Ordered List of Routines to Call from the Conductor
Action# Order# Routine# RoutineName Parameters
5 1 6 Initialize None
5 2 5 GetData Ch, 1, 2
5 3 11 PollACK Val_1,Val_2
5 4 2 UpdateDB 1, Val_1, 2, Val_2
9.1.4.3 Database
The database is the central source of information for the controller. The database
contains the necessary information so that the conductor can match any valid incom-
ing event to a database entry. The database also relates event information to actions
to be taken and routines to be called. The general structure of such a database is
indicated by the Entity Relationship (E-R) diagram of Figure 9.3 (which is a sim-
plification of the detailed E-R diagram of the actual controller database). The Entity
Relationship technique is commonly used to model data storage systems. A brief
tutorial on the E-R modeling technique is given in Appendix A (found at the end of
this chapter). An in-depth presentation of the E-R approach is found in Teorey.10
Referring now to Figure 9.3, the structure and use of the database will be described
in detail.
The database contains the seven entities “Routine," “Invocation," “InternalEv-
ents," “InternalEvent Instance,” “Action," and “Message.” A set of candidate rela-
tions (or tables) for a relational database schema can be derived from the model
using well-documented techniques.11 In the basic implementation each of the entities
would be a table in the GCC relational database. Further, the relationship “Invoked
By” would also be a table in the database. Relationships between these entities
would be implemented as foreign keys in the relational tables. Table 9.2 is an
example of such a basic schema. Note that Keys and Foreign Keys of tables are
FIGURE 9.3 Simplified E-R model of Generic Cell Controller database.

TABLE 9.2
Basic GCC Schema
ENTITIES:
Message(Message#, Message_Data, Action#, …)

InternalEvent(InternalEvent#, Description, Default_Value, …)
InternalEvent_Instance(InternalEvent_Inst#, InternalEvent#, InternalEvent_Data, Action#, …)
Action(Action#, Description, …
Routine(Routine#, Description, …)
Invocation_Num(Invocation#)
RELATIONS DERIVED FROM ENTITY RELATIONSHIPS:
Invoked_by(Invocation#, Action#, Routine#, Parameter_Ptr, …)
KEY:
Candidate Keys are Underlined

Foreign Keys are in Boldface
The “Invocation_Num”relation would most likely be deleted in a revised (normalized) schema
indicated. In the following paragraphs, each entity/relationship resulting in a table

(or tables) in Table 9.2 is described in detail.
1. Message: The Message entity is perhaps the most complex entity in the
database. The database table or tables corresponding to this entity would
store information about every message event stimuli that the GCC is to
receive. This includes messages from its parent controller and messages
from child controller(s). Upon detecting a message event, the conductor
services the event by first attempting to find a match between the message
event and an instance of the Message entity in the database. If a match
is found, the conductor can determine (also from the Message entity
instance) a unique action number that serves as a key in determining an
action to take to service the event (see also below).
The database must provide the capability to store the information of
any message to be sent or received by the controller. This requirement
impacts on the design of the message storage portion of the database. The
database schema incorporates the entire message structure definition into
its data dictionary. The result is that any message with that message
structure definition can be stored in the database, however, the structure
of the database is independent of the message data itself, and is therefore
generic to the facility.
2. InternalEvent: This relation contains information on all possible internal
events that could have instances managed by the GCC. Note that this table
is not accessed by the conductor in servicing an event, as it does not
contain direct information on currently active internal events (see item 3
below). The existence of this table, however, may be necessary as it

contains information on internal events that may not be presently active.
Thus deletion of this table could result in loss of information. As an
example, a “Conversation Timer” may be defined and may be used to
monitor the timely receipt of a reply message in response to a request
message sent. The entry in the InternalEvent table may contain a descrip-
tion of the timer as well as other parameters such as a Timer# and the
default timeout value. If, at some time, there are no active instances of
this timer (i.e., if there are no outstanding conversations with the GCC)
then there would be no instances of the timer in the InternalEvent_Instance
table (see next item). Deletion of the InternalEvent table in this situation
would result in critical loss of information.
3. InternalEvent_Instance: The InternalEvent_Instance table contains infor-
mation on internal events being monitored in the system. This table would
contain the foreign key of InternalEvent#, indicating the type of internal
event of which this is an instance. This relation also contains the foreign
key of Action# indicating a “one-to-many” relationship between the
Action entity (described below) and the InternalEvent_Instance entity.
Note that the foreign key of Action# cannot be null, i.e., every internal
event monitored must correspond to an action (note that the action may
be “no action”).
The InternalEvent_Instance and Message entities provide similar func-
tionality to the GCC system of mapping the event to a single action. Thus,
if internal and external events are defined utilizing a common format, the
tables corresponding to these entities can be combined into a single
“Event” table.
4. Action: In servicing an event, the conductor first attempts to find a match
with an instance of the Message (or InternalEvent_Instance) entity. If a
match is found, the message or timer database record contains a value for
foreign key parameter Action#. This value corresponds to an instance of
the Action entity (see Table 9.2).
5. Invoked_By: The Invoked_By table results from the ternary relationship
between Action, Routine, and Invocation (see Figure 9.3). From this table,
the conductor can determine, for a desired action, the routines to call, the
parameters to pass to each routine, and the order in which to call the
routines. To accomplish this, the conductor queries the database for all
entries in the Invoked_By table that contain the desired value for the
Action# parameter. These entries are then ordered by the value of the
Invocation# parameter. The routines (identified by their Routine#) are then
called in order with the parameters indicated by the Parameter_Pointer
value.
6. Routine: This table results from the Routine entity and contains information
on each of the routines in the GCC. Note that the Routine table does not
have to be accessed by the conductor in servicing an event as the necessary
information on routines to call (e.g., Routine#, Parameter_Pointer, etc.)
can be found in the Invoked_by table. The existence of the Routine table,

however, may be necessary as it contains information on routines that
may not be presently involved in the Invoked_by relationship. Thus,
deletion of this table could result in loss of information.
7. Invocation_Num: This table results from the Invocation entity and, in this
example implementation, only contains a single parameter used in the
Invoked_By table to indicate an ordering of routines associated with an
action. As this table does not provide any additional significant informa-
tion, it would be deleted from a revised database schema.11
As a final note to the description of the database module, examples are presented
at the end of this section that illustrate the servicing of message and timeout events.
Included with these examples is an illustration of the function of matching the
message/timeout to the database, where the messaging format is SECS and the
database schema is as indicated above.
9.1.4.4 Internal Event Monitor Module
This optional module manages the internal GCC events. For instance, it may manage
timeout events and pass the appropriate information to the conductor.
9.1.4.5 Routines
The routines contain the functionality necessary to implement the details of control-
ler actions. As noted earlier, routines may be components or methods of program
modules. The routines are called by the conductor, as shown in Figure 9.1. Using
information stored in the database, the conductor determines which routines to call,
the order in which to call the routines, and the parameters to pass to the routines.
The execution of a routine may result in any combination of the following four
actions.
1. The database is modified. Entries may be added, deleted, or modified

(within the obvious limitations that the modification is permitted and data
integrity is maintained). For example, the data parameter of a message
may be altered to reflect a recipe change. A timer instance may be created
to reflect the fact that a request message has just been received (and no
reply yet sent). Note that routines are the only system components that
can alter the data in the database because all actions (including database
updates) are implemented through calls to routines.
2. A message(s) is sent to a higher- or lower-level controller(s). The routine
may access the database to determine the data to be sent in the message.
The routine then passes the information to the message parser module
where it is formatted into a message conforming to the specified facility-
wide format (see Figure 9.1). Note that routines are the only system
components that invoke the sending of a message to any source outside
the controller.

3. An event is posted to the GCC. The routine may generate an event to the
GCC. This event is serviced per normal GCC operation.
4. Elements outside the GCC are impacted, i.e., the routine interacts with
elements not defined within the realm of the GCC (see below).
The routines then are defined to have the role of implementing the details of actions
that result from the servicing of an event to the controller.
Examples of some of the roles of routines include:
1. Initiating a timer instance. For example, a message has been sent to a

child controller and a timely reply is expected. A routine would establish
a timer for the conversation in the Timer Instance database table. The
timer would be monitored by the Internal Event module.
2. Deleting a timer instance. In servicing a timeout event, a routine would
probably be called to remove the appropriate timer event entry from the
InternalEvent_Instance database table.
3. Retransmitting a message. If, after a message has been sent to a remote
controller, a negative acknowledgment message event or a timeout event
is detected, a retransmit routine might be called to service the event. This
module would retransmit the initial message.
4. Updating message information in the database. If a message has been
received that indicates a change in the state of a machine or process, the
information in the database may be modified by a routine to reflect the
change in the state of the system and the change in expected incoming
information.
5. Generating a message event to the GCC. For example, as part of an
equipment diagnostic action event service, a routine may determine that
an alarm has occurred at the equipment and may generate a message to
the GCC to shut down the equipment.
6. Reading and/or writing from/to an external data structure, i.e., a data
structure that is not directly part of the GCC database. For example, a
routine might be directed to update an expert systems knowledge database,
or a routine might print results to a log file.
Note that, within the definition of routines, a possible role of a routine is to serve
as an interactive window to application modules (such as expert systems, simulation
software, etc.) or directly to a user. (Note that these modules could be operating
concurrently with the generic controller modules.) As an example of the use of an
interactive application module, a user interface routine might be invoked in a situ-
ation where a correctly formatted message received does not have a match in the
database. The user interactive routine might be called to determine the course of
action from the user and to update portions of the database. Thus, the cell controller
information can be modified while in operation such that it adapts to new stimuli;
the user interactive window interface is used to teach the controller how to react to
new stimuli. This learning mechanism is considered to be an important feature of

the GCC. A detailed discussion of such a learning mechanism for the GCC is
discussed in the next subsection.
It should also be noted that issues of serializing message events are not addressed
here, as this issue is, to a large extent, implementation-specific. As an example, a
GCC solution implemented on a high-bandwidth processor may allow for parallel
servicing of GCC events, with appropriate database access serialized to ensure
database information integrity. On the other hand, a more simplified GCC imple-
mentation may queue events as they are received and address them serially.
9.1.5 A LEARNING MECHANISM FOR THE GCC

This section contains a description of a special capability of the GCC, namely its
ability to be taught “on the fly,” i.e., while in operation.1 This capability of the GCC
is given special attention for many reasons, including (1) the feature and its imple-
mentation are not necessarily intuitively obvious from the description of the GCC
in previous sections, (2) the capability is rare in current (non-GCC) controller
implementations as most current implementations do not have a dynamic control
algorithms (because the control algorithms are “hard coded” rather than incorporated
into a database), and (3) the capability is very desirable in flexible manufacturing
systems, as these systems are dynamic with respect to product and product flow,
and possibly equipment.
The GCC is defined as reacting to an event by trying to find a match between
the event and an entry in the database, and then, through relations implied by the
database, calling routine(s) in a specified order with specified parameter(s) to service
the event. In many situations, however, especially when a system is in its infancy,
many unexpected events may occur for which there is no match in the database. The
GCC can be structured to detect these events and learn from an expert on the fly, i.e.,
while in operation, how to service these events. This is accomplished with a set of
routines that serve as an interactive window to an expert user. These routines are
called as part of an action linked to any message or timeout event that does not have
a match in the database. The routines inform the expert of the anomalous event and
query the expert for the appropriate action (new or existing) to take to service the
event. Assuming the response from the expert is valid (i.e., it satisfies existing system
and database integrity rules) the information is entered into the database. The GCC
has “learned” how to service the event; if the event occurs at a later time, the GCC
has developed the necessary knowledge to service the event. Figure 9.4 is an expanded
view of the GCC flow diagram of Figure 9.2, illustrating the system learning capability.
It should be noted that the expert described in the previous paragraph does not
necessarily have to be a human expert. It could be a knowledge base, artificial
intelligence system, or any other qualified decision-making body.
9.1.6 IMPLEMENTATION OF GCC LEARNING MECHANISM

The implementation of a GCC learning mechanism could vary greatly from system
to system. As noted above, the expert could be any (human or nonhuman) decision-
making body. In early GCC implementations, however, the expert will most likely

FIGURE 9.4 Generic Cell Controller flow diagram expanded to illustrate system learning
capability.
be human. A GCC interface will most likely be menu-driven, guiding the expert
through the update process.
As an example, when an unknown message event is detected, the expert may
be greeted with a menu system to guide him/her through the GCC control knowledge
update process. Note that the expert may bypass the learning process by allowing
the GCC to return to the idle state without servicing the event. The expert may also
bring the system to a halt if the event warrants such extreme action. In the general
case, however, the expert is expected to teach the GCC to service the event on the fly.
If the user chooses to teach the GCC on the fly, the system should allow the
expert (through the user interface) to view the unknown message in detail. Note that
the message can be easily inserted into the existing database, as it complies with
the facility-wide message format. The expert should also be allowed to view the list
of currently available actions and the routines, parameters, etc., linked to them. The
expert could then be prompted to enter an Action# to be associated with (linked to)
the message event. The expert may chose an existing Action# to service the event.
At this point, assuming the entry passes any system and database integrity checks,
the learning process is complete as the existing event is already linked to a set of
routine calls. However, if the expert chooses to create a new action to service the
event, the GCC must learn the routine calls to be associated with this new action.

Thus, for this case the user interface should allow the expert to view existing routines.
The expert enters a sequence of routines to be called and the parameters to pass to
these routines to implement this new action. After the sequence has been entered,
and assuming the entries pass any system and database integrity checks, the learning
process is complete. The GCC is now equipped to service this and future instances
of the event.
It is important to note that the time needed to teach the GCC to service an event
may vary greatly depending on the type of event, the type of teacher, as well as the
teacher-to-GCC interface. In some cases the learning process may be too slow to
effectively service the event that initiated the learning sequence. Thus, the learning
interface may also contain options so that the current event instance may be treated
differently from future occurrences of the event. For example, the GCC may be
instructed to inform the operator of an error in response to a current event; however,
the appropriate service response is formatted through the learning process as the
appropriate response to future occurrences of that event type.
9.1.7 EXAMPLES
Examples presented here serve to illustrate generic cell controller operation. They
also serve to illustrate the various functionalities of routines that might exist in a
generic cell controller. For all examples, the generic cell controller operation is
analyzed in a scenario that might occur in a semiconductor manufacturing facility.
The facility-wide message format is SECS-II. Note that these examples do not
address providing an R2R control capability utilizing a GCC-enabled solution;
examples of this type are provided in Chapter 11.
9.1.7.1 Example 1 — Etching a Wafer
In this example, a generic cell controller, initially in an idle state (see Figure 9.2),
receives a message from its parent to etch 500 Å of SiO2 on a wafer. The generic
cell controller reacts to the message as described above, finding a match to the
message in the database and, through relations implied by the database, taking the
appropriate action. The portion of this generic cell controller database that pertains
to this example is shown in Figure 9.5. Note that some implementation-specific
parameters have been added to the database tables. Specifically, an “Active?” param-
eter has been added to the message table. This parameter is used to indicate whether
a message is expected; for this implementation the generic cell controller should
only take the action indicated by the message table entry if that entry is tagged as
active. In the following paragraphs a detailed description is included of the actions
taken by this generic cell controller to service this message.
This example begins with a parent controller generating an event to the generic
cell controller in the form of an SECS-II message indicating that 500 Å of SiO2
should be etched in a wafer residing in Equipment#1.6 The command enters the
generic cell controller through an I/O interpreter module where it is stripped of all
protocol-specific control information (see Figure 9.1). The SECS-II message is then
parsed by the message parser and presented to the conductor. The conductor services

FIGURE 9.5 Portion of a GCC database pertaining to Example #1 — Etching a Wafer.

the event by first searching the Message portion of the database (i.e., tables Message,
List, and Item*) to find a match with the incoming data. Assume that in comparing
the message received the database records in Figure 9.5, a match exists with Mes-
sage# 7. From the Message table, the conductor determines that Action#4 should
be taken to service the message event. The Action table indicates that Action#4 is
“REQ_LOAD_RECIPE_ETCH_500_RIE#1,” i.e., the action will result in a variety
of tasks being completed, including the issue of a request to Reactive Ion Etcher #1
to download a recipe to etch 500 Å.
To implement the above action the conductor makes five routine calls. The
conductor determines the routines to call, the order in which to call the routines,
and the parameters to pass to the routines, from the Invoked_By table shown in
Figure 9.5. The sequence of routine calls for this action are:
1. RemoteCommandACK(SUCCESS, 0);
2. PPLoadInquire(“Etch500”, 1000, 1);
3. ActivateDBMessage(7, 2, OK, 1);
4. TimerAdd(CONVERS, 7, 2, 99, 0, 1);
5. LogEvent(“Etch.Request.500.Ang.SiO2.RIE1”);
This sequence of routines, when executed, first sends an acknowledgment message

to the parent controller indicating that the etch job will be initiated. A message is
then sent to the appropriate equipment controller requesting that it accept a download
of a recipe to perform the etch. An acknowledgment (accept or deny) is expected
as a response to this request; thus, the appropriate accept and deny messages in the
database are tagged ACTIVE to indicate that they are expected. As the reply is
expected in a timely fashion, a conversation timer instance is added to the
InternalEvent_Instance table in the database. Finally, the etch request event is logged.
A detailed description of the activities associated with the calling of each of the
routines is provided in Appendix B.
After control returns to the conductor from the last routine call, the event is
considered serviced and the generic cell controller returns to an idle state (see
Figure 9.2). Note that although the completion of these tasks (through routine calls)
results in the etch request event being serviced, the etch job itself if not complete.
The completion of the etch job would require additional stimuli from the equipment
(e.g., a Stream 7 Function 2 response to the Process Program Load Inquire message);
this could generate an action to download the recipe (see Action #15 in Figure 9.5)
and send a final job report message to the parent controller.
9.1.7.2 Example 2 — Servicing a Timeout
In this example, a generic cell controller is initially in an idle state, polling for a
message received or a timeout indication. A conversation timer instance has been
* “List” and “Item” refer to the components of an SECS message.6 A Message consists of zero or more
lists and zero or more items. A list consists of zero or more items. Items are the usuable data components
of the message.

created previously in servicing an earlier event. The InternalEvent_Module, in scan-
ning the InternalEvent_Instance table, deduces that the conversation timer instance
has timed out. The generic cell controller reacts to the timeout event as described
above, finding a match to the timeout indication in the database and, through relations
implied by the database, taking the appropriate action.
As an example, if the InternalEvent Module detects that timer instance 3 of type
Timer#4 has timed out, the module passes the appropriate information to the con-
ductor through a structured variable. The conductor services the event by first
searching the InternalEvent_Instance table in the database to find a match with the
incoming data. The conductor then determines the appropriate action number from
the database relations. The ordered execution of routines called to carry out this
action could cause, for example, the issuing of a report to the parent controller
indicating that a timeout has occurred with the appropriate identifying parameters.
9.1.8 GCC DESIGN SUMMARY

In this section, a GCC design has been presented. It is important to note that the
GCC design is applicable to a number of sequential control scenarios in addition to
R2R control. Specifically, the design is applicable in areas where flexibility, porta-
bility, and capability for integration are important. For example, a GCC framework
could be utilized as an enabler for an advanced process control station that includes
Fault Detection and Classification, Statistical Process Control, process monitoring
and diagnostics, and off-line data analysis, in addition to R2R control.
The R2R control arena, though, represents the first arena where the approaches
such as the GCC have proved effective. In the next section the application of the
GCC concept to R2R control solutions is discussed in detail.
9.2 GENERIC CELL CONTROLLER IMPLEMENTATION

The GCC solution presented in this section is comprised of a suite of software
applications that work together in the manner of the GCC operational model
described in Section 9.1 to provide an automated R2R control capability. As shown
in Figure 9.6, the system consists of the GCC kernel and a set of modules (these
modules contain the “routines” defined in Section 9.1). One of the modules is a
GCC GUI, which presents an abstract view of the cell. It shows the high-level
commands that the GCC implementation can accept on behalf of the cell, together
with the list of modules containing the routines that will actually carry out the work
to execute high-level commands.
9.2.1 MODULE DESCRIPTIONS

The following is a description of the components that comprise the GCC R2R
solution system. Although the description is, to some extent, implementation-spe-
cific, it serves to provide insight into the design specifications that are necessary to
achieve the solution requirements identified in Chapter 8. Further, the design
described contains components that may not be required in some R2R control

FIGURE 9.6 Typical GCC software solution.
applications; the specific implementation utilized would probably implement a sub-

set of components described here. Note that the operation of practical systems that
utilize a subset of the components defined here are described later in this book (e.g.,
Chapter 11 and Part 5).
9.2.1.1 GCC Kernel
The GCC Kernel contains the Main Program Module or “conductor” as described
in Section 9.1. It waits for events and reacts with corresponding actions. When the
GCC receives a command, an event is posted and the GCC consults its database to
determine a corresponding action, which is an ordered list of invocations. An invo-
cation is a message sent to a target. The targets in this case are the various modules
connected to the GCC.
9.2.1.2 The GCC Graphical User Interface
The GCC solution provides a three-mode graphical user interface, as shown in

Figure 9.7. By separating the GUI at the high level into Operate, Setup, and Access
modes, and by limiting access to the setup mode based on the log-in security level,
the control-specific aspects of the solution are separated from the operation-specific
aspects. GCC GUI design requirements and compliance with standards are discussed
in Chapter 8, as well as later in this chapter.
9.2.1.3 GCC Modules
The GCC modules identify themselves and the cell to which they belong by name,
as a character string. The database can be modified or modules can be interchanged,

FIGURE 9.7 Illustration of a three-mode graphical interface (traversed through mode buttons at
the bottom of the screen — Operate mode shown here).
thereby allowing dynamic binding of the software modules to the distributed GCC
application suite. What this means is that the GCC solution can be modified during
run time through the plug-and-play of module application modules and the corre-
sponding modification to the data in the GCC database (as necessary) to specify the
utilization of these modules.
All modules have certain common attributes and behaviors. If one runs a module
with the kernel not running, one will notice that the module automatically tries to
find the kernel and bind to it. If the module cannot find the kernel, it allows one to
either
1. Try a search for the kernel again.

2. Specify a host name (either a specific name, or have it dynamically search
for the kernel running on any local host within a local area network).
3. Run the module in stand-alone model. (For passive modules, such as a
GUI module, the passive run mode has no utility; however, for an active
module, such as an algorithm module, it allows for utilization of the
module, for example, to configure process control models.)
9.2.1.4 GCC Module-Control Algorithm
This module or set of pluggable modules provides dynamic algorithmic solutions

for sequential process parameter modification based on previous process outputs,
possibly previous and current process inputs, and historical process data. For exam-
ple, the algorithm could dynamically model a first-order approximation of the
response surface model of the process at the process operating point (see Chapter 3).
Regardless of the specific algorithm, its run-time “operate” behavior is as follows:
given pre- and postprocess metrology as available, it updates the dynamic model
and delivers the appropriate parameter modifications to achieve specific targets.
“Setup” behavior includes a capability for creation, modification, and loading of
control model configurations, viewing of model parameter evolution and configura-
tion, possibly moving back the controller to a specified control run (i.e., deleting a
portion of the recent controller evolution), turning the model adaptation behavior
on and off, turning the control behavior on and off, executing the control behavior
in a single-step mode, and configuring a process simulator.
9.2.1.5 GCC Module–Equipment Interface
This module provides an interface to the equipment. For example, it encodes and
parses SECS communications to support download of equipment parameter updates.
It also provides a capability to maintain synchronization with the tool application.
9.2.1.6 GCC Module–Metrology Interface
This module provides an interface to the metrology system. For example, it could
encode and parse SECS communications to support upload of (pre- and/or postpro-
cess) metrology parameters. It also provides a capability to maintain synchronization
with the metrology application. Note that in cases where the metrology is fully

integrated (hardware and software) into the tool, the tool and metrology tool com-
ponents may utilize the same physical interface. In this case the Tool and Metrology
Interface GCC modules may share I/O resources.
9.2.1.7 GCC Module–History
This module produces dynamic graphical or tabular information of the event traces
and control history of the process. Specifically, it displays and logs the controller
inputs, controller outputs, and control run number. Note that this module does not
impact the operation of the control system in providing R2R control advices.
9.2.1.8 GCC Control Rule Database
The GCC database data contains the control routing scheme that defines the meth-
odology for servicing events to the GCC through invoking methods in the various
GCC modules. Specifically, the database defines, for each event, the module invoca-
tion order, and the methods and I/O parameter types associated with each invocation.
9.2.2 PROCESS OPTIMIZATION AND CONTROL SCHEME

The process optimization and control scheme utilized by the control solution is
illustrated in Figure 9.8.12 This multibranch selection mechanism is enabled by the
GCC methodology, and allows for the complementary utilization of process control
FIGURE 9.8 Process optimization and control scheme.

and optimization methods for R2R control. Each branch consists of a single optimi-
zation or control algorithm (e.g., a commercially available algorithm). These branches
are utilized in complementary fashion to enhance the robustness of the controller. In
order to achieve complementary utilization of these algorithms, a mechanism must
be utilized to identify which combination of the available process analysis branches
should be invoked so that the (statistically/heuristically) optimal or “best” advice for
the process recipe will result. Further, after the process has been analyzed by the one
or more indicated algorithm branches, a “best” set of advices (recipe) must be derived
that results from comparing the weighted advices of the selected branch algorithms.
This “best” recipe is the main output of the R2R controller.
The branch selection algorithm utilized by the R2R control paradigm addresses
a number of issues in combining algorithms. First, the knowledge of the state of the
process that could be utilized to select R2R control algorithms is diverse, oftentimes
vague, and generally difficult to capture in crisp form. Second, the same can be said
of the knowledge pertaining to the domain of applicability of each branch algorithm.
Indeed, this knowledge is also vague. Third, as there is no common taxonomy for
defining the domain of applicability, it is difficult to combine the knowledge into a
deterministic knowledge base. Fourth, as there are differing degrees of confidence
associated with the advices provided by algorithms, a weighting capability must be
associated with algorithm advices in a multialgorithm scheme.
The branch-selection algorithm that is part of the implementation description
presented in this section is based on a fuzzy logic multibranch solution.12,13 This
solution addresses the aforementioned issues by utilizing fuzzy logic applied to a
knowledge base to determine branch selection.14 A review of the requirements of
the branch selection algorithm and the available methods for its implementation
reveals that fuzzy logic is indeed an ideal mechanism for the development and use
of the required knowledge base.12,13 Specifically, the fuzzy system is attractive for
many reasons. First, it makes effective use of vague or nonexact information in
conjunction with deterministic information, and it can provide suggestions with a
limited amount of knowledge. This is important because, in many cases, the available
knowledge on branch selection for R2R control is somewhat vague and limited.
Second, the developed fuzzy system effectively captures knowledge in “human
language” format (a form in which much of R2R process control knowledge exists).
Third, the system is capable of suggesting the “best” alternative(s) in situations
where there may be many viable solutions. This is important because in many cases
the domain of applicability of R2R algorithm branches overlap. Finally, the devel-
oped system can relate degrees of confidence with suggested solutions. Thus, it
inherently provides a mechanism for the weighting of advices from each branch
invoked for a particular process run.
The fuzzy mechanism developed incorporates both fuzzy and nonfuzzy knowl-
edge into a data knowledge base. This knowledge base is incorporated/linked into
the database of the GCC R2R control enabler, and the resulting system is thus able
to enforce routing information relating to which control thread(s) to invoke for a
particular process run (see Figure 9.8).8,12,13 Thus, the database contains a schema
for the storage of fuzzy and nonfuzzy rules as well as the interaction with the GCC

FIGURE 9.9 Fuzzy rule base for a two-branch controller.
database. It also contains a “fuzzifier” that categorizes process run data as necessary
so that it may be utilized by the available rules.13
The rule syntax allows expression of rules that advise for or against an action.
As an example, Figure 9.9 is an illustration of a valid rule base. The rule base
contains rules that relate the usefulness of one of two algorithms (a linear approx-
imation control algorithm and a quadriatic approximation optimization algorithm)
to the correction of process error. Note that each rule contains a predicate, operator,
action, and certainty factor (a number between zero and one indicating the confidence
or believability of the rule).
In order to handle information that is somewhat contradictory (e.g., rules 2 and
4 in Figure 9.9) we utilize a method introduced by Chaudhry et al.13 With this
method, all rules associated with a particular action (i.e., the action of choosing a
particular branch) are partitioned into two sets, those recommending for the action
and those recommending against the action. For each of these sets a confidence is
derived (a number between zero and one) by applying fuzzy set theory. Thus, an
Upper Confidence level advising for an action and a Lower Confidence level advising
against an action are both derived.
After both confidences are derived, we then provide the following technique for
making a decision of branch selection.12
1. Upper and Lower Confidence levels computed are combined into a tuple
(X 1, X 2), where X 1 represents the degree of support for an action, and
X 2 represents one minus the degree of support against an action (0 ≤ X
1, X 2 ≤ 1).
2. The tuple is then plotted as shown in Figure 9.10. This graph is a two-
dimensional representation of the support associated with an action. Thus,
the tuple associated with an action plotted on the graph depicts the degree
to which the action is confirmed or refuted, and the degree to which the
rule set associated with the action is contradictory or supplying a low
amount of information. In Figure 9.10, rules strongly advise for choosing
algorithm “A” and against algorithm “B.” Rules associated with algorithm
“C” are contradictory (i.e., some are expressing strong support for the
algorithm while others are expressing strong support against its utilization).
There is little confidence in the knowledge-base information associated

FIGURE 9.10 Two-dimensional representation of action support.
with algorithm “D.” Placement of points “E” and “F” indicate intermediate
levels of confirmation and rejection support.
3. Steps 1 and 2 are applied to rule sets associated with other actions (that
suggest other branches).
4. The graph is partitioned into three regions as shown in Figure 9.10: a
triangular region of strong confirmation recommendation, a triangular
region of strong rejection recommendation, and the remaining area rep-
resenting weaker recommendation. Note that the two partitioning lines
are lines of equal confidence.
5. A rule is applied to the graph to determine which action(s) to take, i.e.,
which optimization and/or control algorithm(s) to invoke. An example of
such a rule might be:
if (there is at least one action in the strong confirmation region)
then (take all actions in the strong confirmation region)
else if (there is at least one action not in the strong rejection region)
then (take the action closest to the strong confirmation region)
else (take no action)
Note that if this rule were applied to the event depicted in Figure 9.10,
then algorithm “A” would be invoked for the current process run.
In summary, the branch selection method developed utilizes fuzzy logic theory
to recommend optimization and/or control branches to be invoked for a particular

process run. The method is flexible in that it supports fuzzy rules, such as rules that
might be attained from the process engineer, as well as nonfuzzy rules. Further, the
method is adaptive as it can incorporate new rules (relating to existing or new branch
selection decisions) on-the-fly. This property combined with the GCC learning
mechanism capability results in an R2R control framework that is very dynamic and
adaptable.
9.3 MAPPING THE GCC DESIGN TO R2R

CONTROLLER DESIGN REQUIREMENTS
The design requirements for integrateable R2R control were presented in Chapter 8.
The GCC concept was developed to address these requirements. In this section we
analyze the GCC design and implementation to illustrate that this approach does
indeed address the design requirements. We provide this analysis by restating each
requirement and describing how this requirement is addressed with GCC-enabled
solutions. The mapping exercise is presented here to illustrate its utility as a tool to
evaluate the capability of an integrated R2R control solution.
1. Process Independence — The GCC has a well-defined generic interface

to the process and equipment being controlled. Because the control scheme
mechanism is dynamic, the GCC can be programmed with control knowl-
edge for any process. Because software modules and equipment interface
modules (including third-party modules) can be integrated into the system,
any appropriate process or equipment-specific modules can be integrated
into the generic R2R control scheme. In other words, the modularity of
the system also allows for the modularization of generic capability from
process-specific capability. The dynamic capability allows for quick
(re)configuration to new processes and new process control schemes.
2. Plug-and-Play Integration of External Software Modules — As defined
above, the GCC provides a well-defined interface for dynamic integration
of external software modules. These modules include control algorithms,
data loggers, equipment and metrology interfaces, etc. The use of the
object-oriented approach in some GCC implementations, which will be
discussed further in Chapter 11, further simplifies the plug-and-play capa-
bility. The key to this capability is the utilization of the GCC database as
the (sole) interface point between modules and the elimination of all direct
module-to-module interaction.
3. Dynamic Control Scheme — When the GCC receives an event (message
or timeout), the control scheme determines the action to be taken in order
to service that event. That control action consists of a sequence of mes-
sages (i.e., routine calls) sent to modules to carry out the desired task. In
other words, the control scheme is a list of event–action pairs, where an
event represents a high-level command or message to the GCC, and the
action is a list of module invocations. The control scheme is stored as the
data in a database rather than in static code (see Section 9.1); thus, it is

persistent, portable, and able to be modified, even during the execution
of a process if necessary. This dynamic control scheme is also critical to
the GCC’s qualities of process-independence, and plug-and-play integra-
tion of external modules.
4. Complementary Operation of Multiple Control and Optimization
Methods — While multiple control algorithms are not always required to
achieve effective R2R process control today, the GCC has the ability to
utilize several controllers and optimizers concurrently, as defined in
Section 9.2, taking the advice given by the most appropriate controller or
optimizer to use for the current run.
5. Ability to Provide R2R Control with or without In Situ Control — The
GCC is designed as a major component of a multilevel control system
that includes in situ equipment and process control operating in conjunc-
tion with sequential control components such as R2R control. These
control loops operate concurrently in a hierarchical feedback fashion, as
shown in Figure 9.7 and Figure 9.8 in the Introduction to this book. At
the factory level, the GCC R2R control elements interface with factory-
level control (potentially enabled through the GCC engine or with the
active controller, see Part 6 of this book), also in a complementary fashion.
6. Platform Independence — The GCC implementation utilizes an open
CORBA development and runtime platform.8 It provides a graphical,
object-oriented user and software-development environment that is oper-
ating-system-independent, i.e, applications developed on one platform can
be recompiled and utilized on another supported platform (current operat-
ing environments supported include Windows NT*, UNIX, and MacOS**).
7. User Friendliness and Control Integration Migration Path — While the
evaluation of user friendliness is somewhat subjective, the GCC solution
has a number of qualities that enhance the user friendliness of the solution.
For example, the ability to incorporate third-party modules, which provide
a necessary functionality but also may have familiar user interfaces and
familiar operation, facilitates user friendliness. The modular design of the
system enhances user friendliness by allowing for modularization of the
user interface as well as system understanding, and minimizing the com-
plexity associated with modular interaction. The fully object-oriented,
event-driven design of the system also enhances user friendliness because
it results in operation that is more intuitive, and can be more easily
represented graphically. Other factors that enhance user friendliness and
the ability to provide a control integration migration path include (1)
independence of the internal control solution from the I/O characteristics
of the integration environment (see Section 9.1), (2) capability for (re)con-
figuration of the system to evolving control needs, (3) capability for GUI
reconfiguration, and (4) compliance of the implementation with SEMI
standards for communications and architecture.6
* Microsoft Corp.
** Apple Computer Corp.

9.4 SUMMARY
The generic controller approach to portable and configurable sequential systems has
been presented in this chapter. The GCC is applicable to a number of control
paradigms; however, it is especially suited to address the requirements of R2R
control solutions in semiconductor manufacturing. The example presented in
Section 9.2 illustrates many of the advantages of the GCC when applied to R2R
control, such as the capability of incorporating third-party modules to achieve desired
functionality while maintaining flexibility of the control scheme. This allows, for
instance, the complementary utilization of multiple control algorithms to achieve
more robust control (as described in Section 9.2.2). It also allows the utilization of
a “learning mechanism,” as described in Sections 9.1.5 and 9.1.6, to enhance the
control scheme in response to new or unforeseen events.
The qualities of the GCC or any other solution enabler complying with the R2R
control system requirements of Chapter 8 allows for the specification of (cost- and
quality-) effective designs for R2R control. One such design, applicable especially
to retrofit R2R control applications, is presented in Chapter 10. This is followed, in
Chapter 11, by examples of utilization of GCC-enabled R2R control solutions in
process control.
APPENDIX A: OVERVIEW OF ENTITY RELATIONSHIP

(E-R) THEORY AND CONSTRUCTS
The E-R approach to database modeling provides semantics for conceptual design
of databases.10-11 With the E-R approach, database information is represented in
terms of entities, attributes of entities, and relationships between entities, where the
following definitions apply. A common form of modeling semantics corresponding
to each definition is illustrated in Figure 9.11.
Entity Many-to-One Relationship
Many-to-One Relationship with Optionality

Descriptor Attribute
on the “One” Side” (i.e., Cardinality = 0 to 1)
Many-to-Many Relationship with Optionality

Identifier Atribute on a “Many” Side (i.e., Cardinality = 0 to
Many)
Ternary Relationship
One-to-One Relationship (Binary) (One-to-One-to-One for This Example)
FIGURE 9.11 Entity relationship modeling semantics.

1. Entity: A principle object about which information is collected. For exam-
ple, in a database containing information about personnel of a company,
an entity might be “Employee.” In E-R modeling an entity is represented
with a box.
2. Attribute: A label that gives a descriptive property to an entity, e.g., name,
color, etc. Two types of attributes exist. Identifier attributes distinguish
among occurrences of an entity, e.g., social security number. Descriptor
attributes merely define an entity occurrence, e.g., gender, weight, etc. In
E-R modeling an attribute is represented with an oval tied to the entity
(box) to which it pertains. In many cases, attributes are not included in
the E-R model.
3. Relationship: A relationship is a connectivity exhibited between entity
occurrences. Relationships may be one to one, one to many, or many to
many, and participation in a relationship by an entity may be optional or
mandatory. For example, in the database containing information about
personnel of a company, a relation “married to” among Employee entity
occurrences is one to one (if it is stated that an employee has, at most,
one spouse). Further, participation in the relation is optional, as there may
exist unmarried employees. As a second example, if company policy
dictates that every employee have exactly one manager, then the relation-
ship “managed by” among Employee entity occurrences is many to one
(many employees may have the same manager), and mandatory (every
employee must have a manager). In E-R modeling a relationship is rep-
resented with a diamond if it relates one or two entities, and is represented
with an n-sided polygon if it relates n entities (where n is greater than
two). Connectivity in a relationship is denoted with shading of the dia-
mond; a connectivity of “one” is denoted with the appropriate portion of
the diamond unshaded while a connectivity of “many” is denoted with
the appropriate portion of the diamond shaded. Optionality of entity
participation in a relationship is indicated with a ring around the line
segment between the entity and the relationship.
A detailed description of E-R model semantics, extensions, and E-R modeling

techniques may be found in Teorey.10
APPENDIX B: DESCRIPTION OF ACTIVITIES

ASSOCIATED WITH ROUTINE CALLS ASSOCIATED
WITH EXAMPLE 1 — ETCHING A WAFER
The following is a detailed description of the activities associated with the calling
of each of the routines associated with “Action #4” in Example #1 (Section 9.1.7).
Routine#27: RemoteCommandACK(SUCCESS, 0): This routine prepares the
data to send a Remote Command Acknowledge message (Stream 2 Function 22) to
Port#0 (for export to the parent controller). The first routine parameter is the data

item to be sent in the message while the second parameter indicates the port number
to which the message is to be sent. For this call to the routine, the data item to be
sent with the message is SUCCESS, which is defined to be a 2-byte signed integer
with a value of zero. The message and destination information is passed to the
message parser by this routine, which directs the formatting of a Stream 2 Function
23 message. The routine then returns control to the conductor. The message parser
will format the message into the proper SECS-II syntax and forward it to the I/O
interpreter module associated with Port#0 for transmission to the parent controller.
Routine#29: PPLoadInquire(“Etch500”, 1000, 1): This routine prepares the data
to send a Process Program Load Inquire message (Stream 7 Function 1) to initiate
the download of a recipe to an equipment controller. The first two routine parameters,
respectively, are the Process Program ID and Length data items to be sent in the
message, while the third parameter indicates the port number to which the message
is to be sent. For this call to the routine, the routine passes the “Etch500” and 1000
data items to the message parser and directs the formatting of a Stream 7 Function
1 message. The routine then returns control to the conductor. The message parser
will format the message into the proper SECS-II syntax and forward it to the I/O
interpreter module associated with Port#1 for transmission to the RIE#1 Equipment
controller.
Routine#2: ActivateDBMessage(7, 2, 1, 1): This routine modifies an entry in the
Message table, tagging it as active. A tag (described above as the “Active?” param-
eter) is used with this implementation to indicate whether a message is expected. If
a message is expected, it is tagged “YES.” If an expected message arrives, the foreign
key of Action# indicates the action to take to service the message event. However,
if a match is found between an incoming message and a message tagged “NO,” the
message is unexpected; the generic controller may invoke a user interface routine
in this instance to learn how to deal with the unexpected event. The four routine
parameters, respectively, are the Stream#, Function#, Data, and Port#. In this instance
the above PPLoadInquire() routine call has resulted in the scheduling of a Stream
7 Function 1 message to be sent to the RIE#1 Equipment Controller. To be compliant
with the SECS protocol, the recipient of the message is expected to respond with a
Stream 7 Function 2 message in a timely fashion. The generic cell controller should
be made aware that such a response is expected, i.e., the appropriate database
message table entry(s) should be tagged as active. This is the function of the
ActivateDBMessage routine. For this call to the routine, the message portion of the
database would be searched for the Stream 7 Function 2 message, associated with
Port#1. The routine assumes that a single match will be found. When a match is
found, the routine modifies the database, tagging the entry as “ACTIVE,” as shown
in Figure 9.5 (bubble call-out annotation). The routine then returns control to the
conductor.
Routine#4: TimerAdd(CONVERS, 7, 2, 99, 0, 1): This routine adds an entry to
the InternalEvent_Instance table (not shown in Figure 9.5). The parameters of the
routine call indicate, respectively, the type of timer, the Stream and Function numbers
of the message associated with the timer, the Action# to be associated with the timer,
the timeout value (zero indicates use default — the default value may be found in

the Timer table), and the Port# associated with any message timer. For this particular
call, a conversation timer is to be entered where the reply expected is a Stream 7
Function 2 message arriving via Port#1. The routine searches the InternalEvent table
for the (requested) default value and creates a new entry in the
InternalEvent_Instance table with the indicated parameters along with TimeStart
(the current time). The routine then returns control to the conductor.
Routine#3: LogEvent(“Etch.Request.500.Ang.SiO2.RIE1”): For this implemen-
tation all events are logged. This routine opens up a log file, creates a new line at
the end of the file, and enters the text “Etch.Request.500.Ang.SiO2.RIE1” along
with the current date and time. The routine then returns control to the conductor.
Note that this routine does not impact the generic cell controller database and does
not result directly in the sending of any SECS-II formatted messages.
ACKNOWLEDGMENTS
Portions reprinted with permission from IEEE Transactions on Semiconductor Man-
ufacturing, Vol. 5, No. 2, pp. 77-87,3 © 1992 IEEE, and from Journal of Vacuum
Science and Technology A, Vol. 13, No. 3, pp. 1787-1791.12
REFERENCES
Manufacturing System,” U.S. Patent Number 5,469,361 (Filed, August 1991; Issued,
November 1995).
2. Moyne, J., System Design for Automation in Semiconductor Manufacturing, Doctoral
Thesis, University of Michigan, (May 1990).
3. Moyne, J., McAfee, L.C., “A Generic Cell Controller for the Automated VLSI Man-
ufacturing Facility,” IEEE Transactions on Semiconductor Manufacturing (May
1992).
Transfer Document #97103379A-ENG, (1997).
#99053736A-TR (1999).
Association, (1997), available at www.sematech.org.
Sixth Annual SEMI/IEEE ASMC, Boston (October 1995)
9. Rumbaugh, J. et al., Object-Oriented Modeling and Design, Englewood Cliffs, NJ,
10. Teorey, T., Database Modeling and Design: The Fundamental Principles, 2nd ed.,
Morgan Kaufmann, 1994.
11. Date, C.J., An Introduction to Database Systems, Addison-Wesley, 1986.

12. Moyne, J., Chaudhry, N., Telfeyan, R., “Adaptive Extensions to a Multi-Branch Run-
to-Run Controller for Plasma Etching,” Journal of Vacuum Science and Technology
A, Vol. 13, No. 3 (May/June 1995), pp. 1787- 1791.
13. Chaudhry, N., Moyne, J., and Rundensteiner, E., “An Extended Database Management
Design Methodology for Uncertain Data Management,” Information Science Journal
(accepted for publication, August 1999).
14. Zadeh, L., “Fuzzy Sets,” Information and Control 8 (1965), pp. 338-353.

10 Derivation of a Piggyback
Run-to-Run Control
Solution Design
James Moyne
In Chapters 7, 8, and 9 we defined requirements and described technologies for

providing integrateable R2R control solutions in semiconductor manufacturing. Uti-
lizing these requirements and technologies, there are a number of plausible R2R
control solution designs. The particular design depends to a large extent on the
processing environment and, specifically, the capability for modification of the
existing equipment and factory control systems.
In this chapter we explore an R2R control solution design in a retrofit environ-
ment where the equipment and factory control systems are in place and there is a
desire to add an automated R2R capability to the system with minimal modification
to the existing software.1–4 Thus, the only available interface to the equipment,
metrology, and factory host elements is generally through SEMI standard
GEM/SECS communication links.5 The SEMATECH Control Systems Require-
ments Specification (CSRS — see Chapter 7) provides elements of an integration
requirements specification for APC whose main component is SEMI standards.2 In
applying these requirements to existing systems in which R2R control is to be
integrated, we see that a piggyback solution is suggested (a definition is provided
in Chapter 7). In this chapter we provide a specification for this piggyback solution
in terms of the basic internal architecture and the integration environment. Note that
this is not a standard solution, but merely one solution design that meets the require-
ments for integration identified in Chapter 8. We conclude this chapter by identifying
advantages and disadvantages of this solution and suggesting alternative design
possibilities.
10.1 REQUIREMENTS OF A PIGGYBACK R2R

CONTROL SOLUTION DESIGN
The SEMATECH CSRS provides elements of an integration requirements specifi-
cation for APC. The CSRS for current and near-term next-generation systems pro-
vides a partial requirements specification using existing standards that specify in a
common and reusable way the addition, deletion, or modification of sensors, algo-
rithms, applications, and control capabilities in semiconductor processing systems
at the user skill level. This CSRS is considered a partial solution because the standard

(plus additional, not-yet-standard specifications) set does not yet exist to specify a
complete CSRS. A migration path to future CSRS systems is also provided to
maintain alignment with the envisioned CSRS.2
Although the CSRS and the related SEMI standard set is incomplete with respect
to completely specifying an R2R integration solution, they can be utilized to identify
requirements and design parameters for adding an R2R capability to an existing
system.
The requirements of a piggyback R2R controller can be generally stated as
follows:
1. The system must integrate a metrology capability that captures one or

more process quality parameters on a run-to-run basis. An example is a
postprocess thickness sensor that could evaluate the remaining thickness
of a layer and the uniformity of that layer. A second example is a metrol-
ogy system that delivers an in situ “footprint,” or process/wafer parameter
trace, for a process run from which process and product health may be
derived.
2. The process must utilize the integrated metrology and provide automated
run-to-run control process improvement via the automatic adjustment of
recipes on the tool. The recipe input parameters to be adjusted are deter-
mined by the control systems integrator working within the constraints
supplied by the user and the equipment.
3. The piggyback controller configuration must operate within the existing
control, computer-integrated manufacturing (CIM), and manufacturing
execution system (MES) environments. That is, there should be minimal,
if any, reprogramming of the equipment control system or factory-level
CIM and MES systems required.
4. The software solution must be reliable and maintainable and allow for
integration of third-party software.
5. The solution must utilize existing SEMI standards wherever possible and
provide a migration path to the envisioned long-term CSRS.5
10.2 RUN-TO-RUN PIGGYBACK

CONTROLLER DESIGN
In order to achieve these requirements, the following design parameters, based on
the CSRS for current and near-term next-generation solutions, are specified:2,3
1. The controller shall utilize GEM to communicate with the metrology and
process tools. Additionally, if supported, the controller shall also utilize
any applicable specific equipment model (SEM) standard such as the
pending metrology SEM standard.5 Current process and metrology system
tools should support GEM. GEM provides a mechanism for gathering
metrology data. It also provides a mechanism for adjusting process program

FIGURE 10.1 Illustration of CSRS for piggyback “pass-through” operation.
parameters via equipment constant settings;* this capability is not required

for GEM compliance, but is specified as an application note in GEM to
support process parameter modification for APC.6**
2. The internal structure of the controller shall be of a form that can migrate
to an APC Framework-compliant solution.7,8 What this means is that the
software structure of the controller should be object-oriented, should
utilize CORBA*** or a similar object communication mechanism to
support communication between functional modules, and should define a
pluggable capability for the functional modules (i.e., a well-defined,
object-oriented interface to each module). In order to support this internal
structure in a GEM communication environment, software conversion
modules or wrappers should be provided that convert the internal CORBA
communication to GEM messaging as necessary to achieve run-to-run
control.
3. The controller should provide a GEM pass-through capability, thereby
maintaining equipment connectivity with the host, MES and factory level
* There are a number of methods that could be utilized to update process program parameters to achieve
APC. Depending on the capabilities of the tool equipment control system software, equipment constants
could be used to relate parameters of the updated process program. Equipment constants could also be
used to relate suggested modifications to process program parameters from the stored process program,
i.e., the constants contain only the +/– “tweaks.” The former method is preferred because it ensures data
integrity between the controller and tool. Alternatively, the entire process program could be downloaded,
but this results in an enormous amount of communication overhead. Finally, remote commands or variable
parameters could be used. The reader should refer to the latest versions of appropriate SEMI standards
(e.g., GEM) as well as equipment control systems specifications when determining which process program
parameter update method to utilize.5,6
** This effort is being pursued by the SEMI Equipment Control Systems Task Force (ECS-TF). For
more information on this task force, refer to the CSRS document,6 or contact SEMI at www.semi.org.
*** Common Object Request Broker Architecture (CORBA) is a concept published by the Object
Management Group (OMG), which specifies a common architecture for distributed object systems.9

CIM system. The pass-through operation is illustrated in Figure 10.1 and
is described in more detail in Section 10.3. The controller communicates
with the equipment, metrology system, and host in such a way as to
provide the host with an interface that is the same as the original equip-
ment and metrology systems interface.
The resulting specification for the piggyback system addresses all of the system
requirements identified, is realizable with today’s technology and standards, and is
compliant with the CSRS specification, Version 2.0.2
10.3 PASS-THROUGH OPERATION

A key component of the controller design is the implementation of the SECS “pass-
through” capability. As noted in Section 10.1, the piggyback controller configuration
must operate within the existing CIM and MES systems, i.e., there should be no
reprogramming of the factory-level CIM and MES systems required. What this
means is that the SECS interface factory host presented by the controller should be
the same as that presented by the tool and/or metrologer. In other words, the factory
host software should not require modification and should see (interface to) a system
that looks the same as a tool and/or metrologer without a piggyback controller
inserted. In order to achieve this transparent capability, the following requirements
must be met (using the tool as the example):*
1. The piggyback control must provide a synchronization capability between

the communication state of the tool, as specified in the SEMI GEM
standard, and the communication state presented to the host.2,5 The pig-
gyback control system must move the tool communication system to a
COMMUNICATING state, as shown in Figure 10.2, before it can effect
run-to-run control.** Since the factory host did not move the tool into
this state, it should still perceive the tool as being in the NOT COMMU-
NICATING state. Thus, the piggyback controller must provide an inter-
face to the factory host indicating a NOT COMMUNICATING state until
such time as the host wishes to communicate with the tool; at that time
the controller will guide the factory host, utilizing the state model pre-
sented in Figure 10.2, to synchronization with the tool to the COMMU-
NICATING state.
2. The piggyback control must provide a synchronization capability between
the control state of the tool and the control state presented to the host.
The piggyback control system must move the tool communication system
to an EQUIPMENT ON-LINE state as shown in Figure 10.3 before it can
effect run-to-run control. Since the factory host did not move the tool into
* The same requirements apply to the pass-through capability to be provided between the metrology
system and the factory host.
** The state table illustrations in this subsection utilize Harel notation to depict (nested) states and state
transitions.10 Note that these equipment behavior models are specified in the GEM standard.5

FIGURE 10.2 The GEM communications state diagram (for a description of state transitions —
numbered arrows — see E30 in Reference 5). (Courtesy of Semiconductor Equipment and
Materials International.)
FIGURE 10.3 The GEM control state diagram (for a description of state transitions —
numbered arrows — see E30 in Reference 5). (Courtesy of Semiconductor Equipment and
Materials International.)
this state, it should still perceive the tool as being in the UNKNOWN
state until such time as it begins to bring the equipment ON-LINE. Thus,
the piggyback controller must provide an interface to the factory host
indicating the appropriate default state, and guide the factory host, utilizing
the state model presented in Figure 10.3, to synchronization with the tool.
3. The piggyback controller must simultaneously support R2R control mes-
saging along with factory host-to-tool messaging. This is accomplished
utilizing a priority-based scheme. R2R control messages are of a lower
priority than pass-through messages. Thus, an R2R message transaction
can only be initiated when there are no outstanding pass-through trans-
actions. If a pass-through transaction is initiated while an R2R transaction
is open, both transactions must be serviced concurrently.

4. The piggyback controller may have to provide a “heartbeat” capability
with the tool and the host. This capability, usually accomplished with
periodic S1F1/F2 transactions, verifies the health of the SECS link.5 If
the equipment supports a heartbeat capability, the host must also be
presented with this heartbeat capability.
5. SECS transaction timing issues are complicated by the insertion of the
piggyback controller between the factory host and the tool.5 SECS T1 and
T2 timers can be supported at tool-to-host direct link levels (i.e., can
remain unchanged); however, the T3 (transaction) timeout value may have
to be lengthened to take into consideration any delay added by the pig-
gyback controller. In most cases, however, T3 is set to a large value (10’s
of seconds) and the piggyback delay is insignificant.
10.4 MIGRATION OF THE PIGGYBACK SOLUTION

A specification for a piggyback controller that supports R2R control that has been
presented utilizes GEM at all interfaces and provides a pass-through capability
between the tool and the host. The internal structure of the specified controller is
such that can easily migrate to an APC Framework-compliant solution when such
solutions are fully realizable.
The piggyback solution, though representing a method for rapidly incorporating
an APC capability, is not considered a final solution for that capability. As imple-
mentations verify the capability, this capability may be migrated into the tool or up
into the factory control system as illustrated in Figure 10.4, while the piggyback
controller may be retained for rapid deployment and testing of new APC capabili-
ties.11 Adherence to the CSRS in developing the piggyback controller and migrating
to the final solution will facilitate the migration and result in a more cost-effective
and reliable system.2
FIGURE 10.4 Migration of the piggyback control capability.

10.5 ADVANTAGES AND DISADVANTAGES OF THE
PIGGYBACK APPROACH, AND ALTERNATIVES
The piggyback design just presented represents just one solution design for integrat-
ing an R2R control capability into an existing system. This design has a number of
advantages, including the following:
1. It utilizes existing (SECS/GEM) interfaces on the equipment, metrology,

and host components.
2. It maintains the connectivity between the equipment and the host; in many
cases the host software and host operation are not impacted by the addition
of the R2R control component.
3. A well-defined mechanism is specified for integration of R2R controller
SECS/GEM commands with the existing communication between the host
and equipment.
4. The internal architecture of the controller is such that a migration path is
available toward integration directly into a next-generation tool, or onto
a (APC Framework-compliant) factory backbone network.11
Experience in utilizing this pass-through piggyback form of control solution has

also revealed a number of disadvantages to this approach:
1. Because the piggyback solution is part of the equipment-to-host commu-

nication link, a failure in the piggyback system would generally cause a
failure in that line. This problem may be addressed by providing a relay-
invoked hardware bypass system similar to that shown for the real-time
control piggyback system in Figure 7.6 of Chapter 7.
2. The fact that the R2R controller is modifying recipe parameters on the
tool could lead to synchronization and traceability problems between the
tool and the host. For example, over time, parameters being controlled
may be altered significantly, which may impact the operation of host-level
applications such as schedulers. It is important that the R2R controller
actuation capability be limited so that it does not impact the host operation,
or that the appropriate GEM event reports be set up so that the host is
informed when parameters of interest are altered to the point that they
may change host operation. Note that this may already be common prac-
tice in systems where the host downloads the baseline recipe for a process,
but the operator is allowed to modify the recipe within certain bounds.
3. Although the piggyback specification defines a run-to-run (i.e., wafer-to-
wafer or batch-to-batch) control solution, it does not indicate when, within
a run, the control modification should take place. For example, if the
metrology and run-to-run modeling and control for run n is completed
while run n + 1 is being processed, should the control advice be executed
on run n + 1 as soon as it is available, or should the control recipe
modification only occur between runs (i.e., after run n + 1 has completed,

but before run n + 2 commences)? Unfortunately, considering the wide
variety of process types and equipment solutions for a particular process,
there is no clear answer to this question. One plausible solution might be
to implement the control actuation capability to mimic the actuation
capability provided to the user (through the equipment user interface) for
the particular process instance.
4. The GEM standard specifies a point-to-point, host-to-equipment commu-
nication line. Therefore, because both the factory host and R2R controller
are communicating with the equipment, the piggyback solution techni-
cally violates the GEM standard. This issue can be addressed by migrating
the R2R controller to the factory backbone or into the equipment as shown
in Figure 10.4. Note that this issue is also addressed in the APC Frame-
work environment where host-to-equipment communications are peer-to-
peer and multiple peer-to-peer connections are allowed.7,8
5. Although the GEM standards provide mechanisms for the reporting and
modification of recipe (“process”) parameters, it doesn’t explicitly require
that process parameter modification be supported. Recent efforts within
SEMI are focused on addressing this issue by providing application note
additions to GEM to specify preferred methods for “process program
parameter modification.” 6
6. Space in a cleanroom fabrication environment is generally very costly.
The cost of the footprint of additional computer (including monitor) may
be unacceptable in many cases. This issue may be addressed by having
the R2R control element exist logically as a separate application entity in
either the equipment control system or in the factory control system, as
shown in Figure 10.4. Depending on the desired method for interaction
between applications on a single hardware platform, there may be a need
for GEM connectivity to the R2R controller. This issue is discussed later
in this chapter.
The piggyback solution presented here is provided as one example of a solution

for adding an R2R control capability to an equipment system. The following is a
list of alternative solution approaches:
1. Second GEM Port on Tool: Using the same communication capability

defined for the piggyback controller, an integrated R2R control capability
can be achieved by adding a second GEM port to the tool. The advantage
of this approach is that the pass-through capability required for the pig-
gyback controller defined in this section may not have to be implemented,
since connectivity between tool and factory host is supported through the
original GEM port. Further, each GEM port has a single host that is
consistent with the GEM specification. The obvious disadvantage is that,
in most cases, tools do not support a second GEM port; thus, a significant
amount of communication software enhancement may be required at the
tool. Also, since the R2R host has no capability for monitoring the com-
munications between the tool and factory host, there is a potential for

conflict between the two hosts. For example, each host could provide
different process parameter values for the same run.
2. Additional Non-GEM Port on Tool: If a pass-through capability is not
required for the piggyback controller, there may be no requirement that
the R2R integration capability be GEM-compliant. If this is the case, a
second communication port can be configured on the tool to support
communications for R2R control. The advantage of this solution over a
GEM port is that a much simpler communication capability can be utilized
that only supports messaging required to implement R2R control. Another
advantage of this solution, in addition to those identified for alternative 1
above, is that more common interface development tools, such as Ethernet
TCP/IP builders, could be used. In addition to the disadvantages defined
for alternative 1, the primary disadvantage of this alternative is that the
solution is nonstandard.
3. Fully Integrated Equipment-Level Solution: As illustrated in Section 10.4
(see Figure 10.4), a possible migration path for the piggyback controller
is to move the capability into the equipment controller. An important
consideration is the impact of the piggyback controller operation on the
reliability of the equipment controller software. One way to minimize this
impact is to structure the R2R system as a separate set of applications
that communicate with the equipment control application(s) via distrib-
uted object techniques such as CORBA.9 The advantages of such a solu-
tion are numerous. The footprint and additional screen required for the
piggyback system are eliminated. The interface between the tool and host
is simplified. The connectivity to the tool (applications) and metrology
can also be simplified. The functionality, synchronization, etc., between
the tool and R2R controller can be enhanced. The main disadvantage of
this approach is the effort required to integrate the R2R and equipment
control applications on a single (computer) operating system platform.
The communication integration can actually be more straightforward than
with many piggyback scenarios. There is an added effort, however,
required to integrate the GUIs.11
4. Factory-Level Backbone Solution: As also illustrated in Section 10.4 (see
Figure 10.4), a possible migration path for proven piggyback R2R control
solutions is up onto the factory backbone. This concept is supported in
SEMI APC standardization efforts, where elements of the interface of this
APC “plug-in” are defined.5,7,8 The advantages of this approach are numer-
ous and are illustrated in Figure 10.5, using a Generic Cell Control (GCC)-
enabled R2R control solution as an example (see Chapter 11). The back-
bone solution allows greater access to the capability by tools as well as
users. As shown in Figure 10.5, this allows metrology to be reused as
premetrology and postmetrology, thereby reducing metrology system
costs. The R2R controller can be set up to provide R2R control for multiple
tools (e.g., in this example, through multiple instantiations of the GCC
R2R controller class in GCC implementations). Perhaps the largest advan-
tage, though, is the visibility of the controller to factory level, multiprocess

FIGURE 10.5 GCC R2R controller implemented on factory backbone (DB = = database,
CVD = = chemical vapor deposition, CMP = = chemical mechanical planarization).
data, and process targets. This allows the control solution to be tuned to
factory-level control as opposed to equipment-centric control. This con-
cept of R2R control as part of a total factory solution is discussed further
in Part 6 (Chapter 18) . The main disadvantage of this solution is the effort
required to integrate the R2R solution on the factory backbone. This effort
is compounded by the fact that there is a relative lack of standardization
of communications at this level (the APC framework specification is not
widely implemented and does not completely specify the operation of the
controller at the factory level). Note that in many instances, the “optimal”
integration strategy for the R2R capability is to limit the interaction to
the factory database that contains the metrology data and process recipes.
The controller simply accesses the metrology data and updates the appro-
priate recipe process parameters. This approach limits the requirement of
interaction of the controller with tool and metrology systems, thereby
providing a highly nonintrusive enhancement to the factory.
10.6 SUMMARY
A piggyback controller design has been presented in this chapter that supports
flexible R2R control in the semiconductor manufacturing SEMI standard environ-
ment. Further, a migration path is supported for integration of the R2R capability
at the factory level or equipment level, while retaining the piggyback capability for
testing new advanced process control capabilities. Alternative piggyback controller
designs have been presented to various interface and performance requirements
imposed by equipment and/or factory systems.
In the next chapter we explore the application of R2R controller design by
describing two integrated R2R control solution examples, namely a GEM/SECS
piggyback solution and a fully integrated (at the equipment level) solution.

ACKNOWLEDGMENT
Some of the material presented in this chapter is derived from Reference 2, and is
reprinted with permission.
REFERENCES
1. Moyne, J., “Integration of Run-to-Run Control into Existing and Next Generation
Chemical-Mechanical-Planarization Tools,” SEMATECH AEC/APC Workshop IX,
Lake Tahoe (September 1997).
3. Moyne, J., “Application of AEC/APC Requirements Specifications to Enhancement
of Existing Control Systems,” (invited tutorial), SEMATECH AEC/APC Workshop
IX, Lake Tahoe (September 1997).
4. Moyne, J. and Curry, J., “A Fully Automated Chemical-Mechanical Planarization
Process,” VLSI Multilevel Interconnection (V-MIC) Conference, Santa Clara, CA
(June 1998).
6. Document 3022A: Revision to SEMI E30, Addition of Application Notes for Recipe
Parameter Modification, Semiconductor Equipment and Materials International
(October 1999).
Transfer Document #97103379A-ENG (1997).
#99053736A-TR (1999).
9. OMG CORBA/IIOP and OMG CORBAservices Specifications, Object Management
Group (1999). (Available at www.omg.org)
10. Harel, D., “State Charts: A Visual Formalism for Complex Systems,” Science of
Computer Programming, 8 (1987).
11. Moyne, J., Solakhian, V., Curry, J., and Gwizdak, R., “Migrating a SCADA Control
Capability into an Equipment Controller for a Fully Integrated and Automated Tool
Solution,” SEMATECH AEC/APC Workshop X, Vail, CO (October 1998).

11 Integrated Run-to-Run
Control Solution
Examples
James Moyne
In Chapters 8 through 10 we presented (1) key requirements for the internal structure
of the R2R controller, (2) an example R2R solution-enabling technology meeting
these requirements, (3) a design for an R2R piggyback controller, and (4) design
alternatives including fully integrated solutions at the factory and equipment level.
In this chapter we provide brief examples of two R2R control solution designs
presented, namely a piggyback solution, and a fully integrated equipment solution.1
In both examples, the process being controlled is chemical mechanical planariza-
tion (CMP, or “polishing”), which is described in detail in the Introduction to this
book. For purposes of discussion in this chapter, the CMP process being controlled
is described as follows: the process is basically a surface planarization method in
which a wafer is affixed to a carrier and pressed face-down on a rotating platen
holding a polishing pad. Typical process control metrics are remaining thickness
and radial uniformity control, while tunable inputs include polish time, platen speed,
carrier speed, downforce, backpressure (between wafer and carrier), and various
conditioning parameters. It is the relationship between process control metrics and
tunable inputs that motivates process control.
The fundamental R2R control-enabling technology utilized is the Generic Cell
Controller (GCC — see Chapter 9), and all solution requirements defined in
Chapter 8 are met.2,3 The GCC solution incorporates (1) interface modules for
interfacing to the equipment, metrology, and factory host; (2) a control module; (3) a
history module for data logging and presentation; and (4) an alarms module that
monitors R2R data with respect to control and specification limits, and reports limits
violations to the equipment. The interface modules in the piggyback solution provide
a pass-through capability (external to the GCC) and prioritize pass-through commu-
nication over R2R control communication. The internal architecture of the GCC is
CORBA,* and the GCC database provides the control scheme for servicing events
through routing information between the various modules.
* Common Object Request Broker Architecture, see Chapter 10.

11.1 R2R CONTROL AND THE CMP PROCESS
Chemical mechanical planarization (CMP) is accepted as a critical component of
semiconductor manufacturing. As the migration to 300-mm wafers and smaller
features continues, issues such as increased equipment reliability and up-time,
increased throughput, and reduced scrap will have even greater impact on the cost
of ownership (COO). As a result, efforts will continue to be focused on improving
these parameters to maintain competitive advantage.
Two major sources of lost productivity in CMP tools are process drift and
operator error. Process drift, away from target thickness and uniformity, leads to
lost wafers (scrap) and equipment downtime for consumable replacement. Operator
error results in lost wafers and equipment downtime, while operator unavailability
results in unnecessary equipment idle time and lost production. According to one
SEMATECH study, these factors collectively account for up to 50% of overall
equipment effectiveness.4 Thus, there is potential for significant benefit through
addressing these factors.
The application of process automation and model-based R2R process control in
CMP wafer fabrication has been recognized as having the potential to significantly
impact these factors.1,5,6 The fully integrated and automated R2R solutions presented
here for CMP process control greatly reduce process drift along with operator error
and unavailability, thereby reducing scrap, equipment downtime, and cost of con-
sumables, while increasing yield and throughput. In the remainder of this chapter
the design of automated process control solutions for current (piggyback) and next-
generation (fully integrated) CMP tools is presented, followed by an analysis of
results and conclusions.
11.2 SOLUTION DESIGN

The automated R2R process control solution has been developed as a retrofit for
currently existing CMP tools (Figure 11.1) and as an integral component of next-
generation tools (Figure 11.2). The retrofit solution is an example of a piggyback
solution, while the next-generation design is an example of a fully integrated solution
(alternative 3 in Chapter 10, Section 10.5). Either system solution consists of three
major components, namely the tool, metrology unit, and controller. In the retrofit
solution the R2R controller resides on a separate computer and utilizes a SECS/GEM
interface with the tool for communication.7 In the integrated solution, the R2R
controller resides as an application on the equipment controller computer and utilizes
the CORBA distributed object methodology to communicate with ActiveX* equip-
ment controller applications. The single platform integrated software architecture is
illustrated in Figure 11.3.
Automated R2R control is achieved because the tool, metrology, and control
components each have inherent characteristics that collectively provide the run-to-run
control capability. Specifically, the tool is a Strasbaugh 6DS-SP or 6ED “Symphony”
* ActiveX is a product of Microsoft Corp.

FIGURE 11.1 Automated control system solution (retrofit solution for existing tools).
FIGURE 11.2 Fully integrated automated control system solution (solution for new tools).
polisher that has a capability for recipe modification via a remote entity.* In the
case of the 6DS-SP retrofit solution, this capability is achieved through the tool
GEM interface, while in the next-generation Symphony tool, an internal object-based
interface is used (see Figure 11.1 and Figure 11.2, respectively). The metrology unit
is a Nova Measuring Instruments thickness sensor that computes average remaining
* 6DS-SP and 6ED “Symphony” are products of Strasbaugh, San Luis Obispo, California.

FIGURE 11.3 Integrated solution software architecture.
thickness and wafer uniformity and has an SECS interface for reporting this infor-
mation.* The controller is a MiTeX Solutions multivariate run-to-run controller that
is capable of simultaneously controlling thickness and uniformity to target.** The
controller utilizes the GCC enabling technology described in Chapter 9. The con-
troller implementation automatically accepts both preprocess and postprocess
metrology information from the metrology unit. This is accomplished directly
through the SECS interface in the retrofit solution, and indirectly through the equip-
ment controller in the next generation solution (see Figure 11.1). The controller is
capable of utilizing both premetrology and/or postmetrology measurements, and is
capable of providing a level of R2R control regardless of whether these measurements
are available for a particular run. The controller utilizes model-based control
techniques and a two-stage linear approximation control algorithm with EWMA
filtering (see Chapter 3) to derive recipe improvements (e.g., time and backpressure),
and automatically delivers these recipe advices to the CMP tool. In the retrofit
solution, parameter updates are delivered according to the specification of the GEM
application, not for updating recipe parameters.7 In this retrofit solution, the con-
troller further provides a pass-through communication capability to a GEM compat-
ible host (see Figure 11.1), thereby allowing a host to maintain full GEM commu-
nications with the tool (and potentially the metrology unit). Note that this capability
is not required in the next-generation fully integrated solution for reasons identified
in Chapter 10, Section 10.5.
The R2R controller achieves CMP process control by utilizing metrology data
along with dynamic process models and a process history to determine optimal
recipe parameters (i.e., advices) for the next process cycle.5 Further, the control
system utilizes an alarms “plug-in” module to monitor both metrology and recipe
advice data with respect to control and specification limits. As shown in Figure 11.4,
this fully configurable alarms module links limits violations to actions that can be
performed by the tool (such as “alarm, finish cycle, and stop”). The controller then
* Nova Measuring Instruments, Rehovoth, Israel.

** MiTeX Solutions, Inc., Canton, Michigan; www.mitexsolutions.com.

FIGURE 11.4 Excerpt of user interface to configurable alarms-based control module (piggyback
solution).
FIGURE 11.5 Excerpt of operator interface to the automated run-to-run controller (piggyback
solution).
automatically downloads both recipe optimization advices and any alarming action
data to the tool and informs the tool to start processing the next wafer.
Figure 11.5 shows the user monitor interface to the run-to-run controller when
performing automated run-to-run process control. Note that communication inter-
faces to the metrology and tool elements display the uploaded metrology data and
downloaded tool recipes, respectively, while a graphical display keeps track of tool
input and metrology output history. Note also that details of control algorithm
operation are not presented at the operator interface login level, so the controller is
viewed as a simple I/O “black box” at this level.
One novel aspect of this solution is that it provides for fully automated CMP
process operation. That is, an operator is not required to monitor or operate the tool.
The alarms monitor and control capability provides for automatic response to any
alarm condition, while the run-to-run process tuning capability keeps the process
within specification limits for significantly longer periods of time. The communica-
tion capability between the metrology system, control system, and tool completes
the automation process while maintaining a pass-through communication capability
between the tool and a host.
11.3 R2R ARCHITECTURE

The R2R enabler for both the retrofit and next-generation solutions is the GCC (see
Chapter 9).8 In fact, the same internal architecture is utilized for both solutions, and
this same solution has been applied to the control of other process types (see, for
example, Reference 9). The GCC solution is implemented as a suite of application
“modules,” including third-party modules, that are coordinated by the GCC kernel
to provide automated R2R control utilizing the GCC paradigm. Some of the modules
utilized in this solution (also see Chapter 9) include (1) the tool interface, which

downloads control advices and alarm indications — see (5) below — to the tool;
(2) the metrology interface, which uploads pre- and postwafer metrology data from
the metrology system; (3) the control module, which utilizes two-stage dynamic
linear approximation modeling and EWMA filtered model evolution (see Chapter 3
and 6); (4) a history module, which displays and logs all data received and generated
by the GCC system; (5) an alarms module, which monitors metrology data received
and control advices generated against control and specification limits and determines
appropriate alarm action requests to be sent to the tool; and (6) a GUI module, which
provides a user interface platform for viewing the operation of the system and
accessing the individual module GUIs.
The GCC defines a generic module interface, which allows modules to dynam-
ically connect and disconnect from the GCC without any code modification. This
module interface facilitates the passing of arbitrary data, determined at runtime,
between the GCC and the module. It also allows users to develop custom modules
or third-party developers to produce shrink-wrapped modules. This generic and
dynamic interface to software modules contributes to the GCC’s quality of process
independence, and allows the rapid customization of the same basic solution to both
retrofit and next-generation environments as defined above.
The GCC module interface relies on a distributed objects architecture that allows
objects to send messages to other objects in other tasks, or have messages executed
in other threads of the same task.10 In general, an object sends a message to a remote
object by communicating its own address space with a proxy for the remote object.
The proxy assumes the identity of the remote object; it has no identity of its own.
The application is able to regard the proxy as if it were the remote object. Note that
proxy does not require access to the remote object’s class. It isn’t a copy of the
object, but a substitute for it. Its main function is to make a remote object appear
as if it were local.
The GCC mechanism relies on a special object, called a message event object,
to exclusively provide for interaction between the GCC kernel (“conductor”) and
the various modules. The message event object travels to the modules in an order
specified by the GCC database to execute the plan to service a message or timeout
event. The object carries with it the required methods to invoke and appropriate data
to send to and receive from the module. The common message object approach
further simplifies the module interface to the GCC.11
In migrating from the piggyback solution to the fully integrated solution, the
object-oriented modular architecture allows the R2R control system to act as a
separate set of applications residing on the (Symphony) equipment controller. These
applications interact utilizing the CORBA approach. The primary advantages of this
approach are (1) the interface between the R2R control system and the equipment
controller is well-defined and relatively small, thereby tending to minimize the
software integration task; (2) the operation and any failure of the R2R control system
has minimal impact on the equipment controller application(s), thus minimizing any
negative impact on software reliability; and (3) the modular application design and
interaction allows independent maintenance and upgrade of the R2R control and
equipment control systems. One potentially difficult task in integrating R2R control
and equipment control applications is the integration of the user interface components.

FIGURE 11.6 Screen shot of symphony user interface illustrating fully integrated R2R com-
ponent (compare to Figure 11.4).
FIGURE 11.7 Screen shot of symphony user interface illustrating fully integrated R2R com-
ponent (compare to Figure 11.5).
Adherence to standard user interfaces, as described in Chapter 8, as well as object-

oriented design and flexible object-oriented user interface design tools, lessens the
user interface integration task.10 As an example, Figure 11.6 and Figure 11.7 are user
interface screen shots from the Symphony equipment controller illustrating the
integration of the R2R component. Note that the user interface of the piggyback
solution is maintained (see Figure 11.4 and Figure 11.5, respectively).

FIGURE 11.8 Utilizing the CMP automated run-to-run process controller to control process
thickness and uniformity; comparison of controlled vs. uncontrolled operation.
11.4 RESULTS OF DEPLOYMENT

The run-to-run component of the control solution described above has been applied
in production to simultaneously control both process remaining thickness and uni-
formity for CMP oxide removal processes.1 The results (Figure 11.8) compare the
process with and without R2R control. Specifically, they show that (1) the controller
provides for rapid compensation (tuning) of the standard recipe to bring the process
in tune and better achieve multivariate process targets, and (2) the controller com-
pensates for process drift over time and keeps the process in tune, thereby continuing
to better achieve multivariate process targets. There are a number of metrics that
can be used to quantify this benefit. One of the more common is process capability
or Cpk, which is a measure of process accuracy and variability. The results shown
in Figure 11.8 indicate that Cpk is improved by over 50% for both thickness and
uniformity when compared to the uncontrolled case.* Thus, the effects of the run-
to-run control solution include significantly improved process quality, improved
* Cp is a simple process capability index that relates the spread of the specification limits (i.e., the
difference between the upper and lower specification limits, USL, and LSL) to the variation of the process,
represented by six standard deviations or 6 Sigma. Thus Cp = (USL – LSL) / (6 Sigma). Cpl and Cpu
relate the process limits to the process average, divided by 3 Sigma. That is, Cpl = (Av – LSL)/3 Sigma
and Cpu = (USL – Av)/3 Aigma. Cpk is the minimum of Cpl and Cpu. Note that a higher Cpk is always
preferred.13

process efficiency (due especially to lack of need for rework), and lower scrap that
results from process limits violation.
Results of applying the fully automated run-to-run control solution are shown
in Figure 11.9. This figure illustrates that the controller automatically modifies time
and backpressure individually for each wafer spindle to achieve control of both
process remaining thickness and uniformity. The system also monitors both metrol-
ogy and recipe suggestions against control and specification limits, and generates
alarms as necessary to the tool to automatically shut down the tool in the event of
a specification limit violation.
11.5 DISCUSSION
Although results presented above have focused on quantifying the process capability
and reduced scrap benefits of this R2R control solution, a number of other benefits
are also apparent. Specifically, additional benefits resulting from the run-to-run
control component of the solution include lower number of required test wafers and
increased life of consumables. Test wafer requirements can be reduced because the
controller can adjust the process quickly during the pad break-in phase, allowing
the transition to product wafers much sooner in the pad break-in curve. This advan-
tage has been further amplified with a “new pad” feature that has been added to the
controller.12 This R2R enhancement, which is described in detail in Chapter 18, gives
the controller the capability to remember the initial characteristics of the pad (e.g.,
removal rate) and allows the controller to revert to this remembered state when the
pad is replaced.
Another important, but as yet not quantified, benefit of run-to-run control in this
example is the increase in consumable life (i.e., pad life). This occurs because the
process is continually adjusted within established bounds to compensate for pad
wear; thus, the number of runs between SPC-triggered pad replacement events is
increased.
The benefits arising from the automation aspect of this example solution have
not been quantified. However, noting the hands-off capability for operation with the
automated control system in place, it is projected that process performance degra-
dation due to operator error and lack of operator availability (i.e., idle operator)
would be virtually eliminated.
11.6 CONCLUSIONS REGARDING R2R

CONTROL IMPLEMENTATIONS
A fully automated advanced process control solution for CMP has been described
in this chapter. This example application of automated process control clearly illus-
trates not only the advantages, but the requirement of automated process control as
an integral component of next-generation tools. The solution has been developed
for application to both existing (retrofit) and next-generation tools and has been
shown to significantly impact cost of ownership of these tools. Specifically, this
control solution has been shown to reduce process variability, reduce scrap, increase

FIGURE 11.9 The fully automated CMP R2R process control solution; inputs — a) and b) — are modified to keep
outputs — c) and d) — on target.
life of consumables, and increase yield and throughput. It is further anticipated that
this capability will also be proven to reduce equipment downtime and reduce test
wafer requirements. The impact of the automation aspect has not yet been quantified;
however, with run-to-run operator intervention drastically reduced, it is likely that
the yield and throughput losses due to operator-induced idle and downtime will be
reduced.
The controller has been developed as a fully object-oriented solution and is
compatible with existing standards and trends in semiconductor manufacturing. It
address all of the design requirements for an integrated R2R control solution iden-
tified in Chapter 8; most of these requirements are met due to utilization of the GCC-
enabling technology implemented in an object-oriented environment. Further, due
in part to this object-oriented structure, the controller has been developed so that it
can be easily enhanced to support future control environments such as multistep
process control, interprocess feedforward control, and combined in situ and run-to-
run control.
ACKNOWLEDGMENTS
Portions reprinted with permission from proceedings of Advanced Semiconductor
Manufacturing Conference: SEMICON Taiwan ’98 (see Reference 1). The develop-
ment of an R2R control capability for the Strasbaugh tools presented in this chapter
required a significant collaborative effort between the tool supplier (Strasbaugh) and
the control solution integrator (MiTeX Solutions). The authors would like to
acknowledge John Curry and Tim Weaver from Strasbaugh, and Victor Solakhian
and Richard Gwizdak from MiTeX Solutions, for their efforts in making possible
the solutions presented in this chapter.
REFERENCES
SEMICON Taiwan ‘98 (November 1998).
November 1995).
3. Telfeyan, R., Moyne, J., Hurwitz A., and Taylor, J., “Demonstration of a Process-
Independent Run-to-Run Controller,” 137th Meeting of the Electrochemical Society
(May 1995).
4. SEMATECH AEC Workshop VIII, Santa Fe, NM (October 1996).
5. Moyne, J., “Integration of Run-to-Run Control into Existing and Next Generation
6. Boning, D., Moyne, W., Smith, T., Moyne, J., Telfeyan, R., Hurwitz, A., Shellman, S.,
and Taylor, J., “Run by Run Control of Chemical-Mechanical Polishing,” IEEE Trans.
Components, Packaging Manufacturing Techn. Part C, Vol. 19, No. 4 (October 1996).

8. Moyne, J. and Curry, J., “A Fully Automated Chemical-Mechanical Planarization
Process,” Fifteenth International VLSI Multilevel Interconnection Conference, Santa
Clara, CA (June 1998).
9. Khan, K., Solakhian, V., Ricci, A., Gu, T., and Moyne, J., “Run-to-Run Control of
ITO Deposition Process,” Society for Information and Displays ‘98 International
Symposium, Anaheim, CA (May 1998).
10. http://www.apple.com/webobjects.
Sixth Annual SEMI/IEEE ASMC, Boston (October 1995).
12. Moyne, J., “Advancements in CMP Process Automation and Control,” (invited) Third
International Symposium on Chemical Mechanical Polishing in IC Device Manufac-
turing: 196th Meeting of the Electrochemical Society, Hawaii (October 1999).
13. The Memory Jogger: A Pocket Guide of Tools for Continuous Improvement, SEMAT-
ECH, GOAL/QPC, 1988.

12 Design and Optimization
of an Optimizing Adaptive
Quality Controller,
Generic Cell Controller-
Enabled Solution
Enrique Del Castillo, Jinn-Yi Yeh,
James Moyne, and Victor Solakhian
12.1 INTRODUCTION
In Chapter 11 we presented the design and implementation of two R2R control
solutions. In this chapter we present a third R2R control solutions example, focusing
on the use of the control algorithm and the integration of the algorithm with the
control enabling mechanism. The control algorithm utilized is the optimizing adap-
tive quality controller (OAQC), as described in Chapter 4, and the control-enabling
technology is the Generic Cell Controller (GCC) as described in Chapter 9.
The OAQC acts both as a controller and an optimizer, maintaining optimum
operating conditions for multiple input, multiple output processes.1,2 The controller
will suggest a recipe of operating conditions to be implemented in the next run of
a particular process. The OAQC algorithm has been implemented in two software
platforms: (1) NextStep-OpenStep (Mach),3 and (2) Windows NT.
The objectives of this chapter are (1) to illustrate the NextStep implementation of
the OAQC with a simple case study, and (2) to present the integration of the OAQC
controller with the GCC.4,5 The chapter is organized as follows: Section 12.2 presents
a case study using the NextStep software implementation of the OAQC. Then,
Section 12.3 shows how the integration between the OAQC and the GCC was achieved.
12.2 USE OF THE OAQC: A CASE STUDY

The OAQC (NextStep/OpenStep) system can run in a stand-alone mode or integrated
with the GCC system. This section provides a case study that illustrates the stand-
alone form of operation. A 4 × 2 chemical mechanical planarization (CMP) process
will be used for this purpose. This illustration is based on equipment models
developed in Chapter 6.6 Controllable factors (scaled in the (–1, 1) coding conven-
tion) are platen speed (υ1), back pressure (υ2) polishing downforce (υ3), and the
profile of the conditioning system (υ4). Each factor is constrained to lie on the (–1, 1)

FIGURE 12.1 OAQC’s NextStep user interface.
range. The two responses of interest are removal rate (y1) and within-wafer nonuni-
formity (y2). The fitted equipment models are:
y1 = 3233.25 + 1833.08 υ1 − 96.83 υ 2 + 3005.34 υ 3 − 614.51 υ 4 − 5453.06 υ12
+ 54.47 υ 22 + 1597 υ 32 + 83.43 υ 42 − 705.68 υ1υ 2 − 1532.67 u1u3 3959.76 u1u4
+ 563 u2 u3 + 934.39 u2 u4 + 0.3 u3 u4 − 17 t + ε1,t
and
y2 = 326.5 − 5483.85 u1 − 169.4 u2 + 338.87 u3 + 176.62 u4 − 1009.13 u12 − 6.72 u22
+ 89.98 u32 + 0.76 u42 − 2890.96 u1 u2 − 12060.42 u1 u3 − 628.2 u1 u4
− 270.1 u2 u3 + 137.59 u2 u4 + 395.15 u3 u4 + 1.5 t + ε 2,t
where ε1,t ~ N(0,25.82) and ε2,t ~ N(0,2.32). For illustration, Eqs. (1) and (2) were
simulated and correspond to the system to be controlled. We will proceed as if
nothing is known about the system parameters with exception of prior intercept
estimates for each response. This will provide a realistic setting in which equipment
models are not available but only some basic information about the responses is.
12.2.1 ENTERING THE OAQC INITIAL SETTINGS

After starting the system, the OAQC graphical user interface (GUI), as shown in
Figure 12.1, appears on the screen.
The user must enter some basic information through the GUI prior to running the
OAQC, such as the number of factors (3), the number of responses (3), positive ranges
for all factors (in this case –1 ≤ µ i ≤ 1), non-zero intercept estimates for each response
(we entered 3233 for y1 and 326 for y2), and non-zero minimum resolutions for each
factor (we entered 1 for µ 1, and 0.1 for µ 2, µ 3, and µ 4). The minimum resolutions refer
to the minimum change to a controllable factor (i.e., the “discretization” of the inputs).
In addition to entering this basic information, the following steps must be performed:

FIGURE 12.2 Change order of the models.
1. Change order of the models. Assuming the process engineer suspects there
is curvature for all responses, full quadratic models are selected by click-
ing on all three types of effects (linear, two-factor interaction, and pure
quadratic), as shown in Figure 12.2.
2. Change response constraints. The constraints were set at y1 > 1700 and
y2 < 250.
3. Change response targets and weights. The target values were set at 1700
for y1 and 150 for y2 (by default, all response weights are set equal to one).
4. Change gain estimates. Assume approximate initial models given and
quadratic models selected. The initial models were specified as follows:
y1 = 3233 + 1800 u1 − 90 u2 + 3000 u3 − 600 u4 − 5000 u12 + 50 u22
+ 1500 u32 + 80 u42 − 700 u1 u2 − 1500 u1 u3 − 4000 u1 u4
+ 500 u2 u3 + 900 u2 u4 + 0.3 u3 u4 − 10 t

and
y2 = 326 − 5000 u1 − 170 u2 + 300 u3 + 170 u4 − 1000 u12 − 6 u22
+ 90 u32 + u42 − 2800 u1 u2 − 12000 u1 u3 − 600 u1 u4
− 270 u2 u3 + 140 u2 u4 + 400 u3 u4 + t
Thus, the OAQC is given a priori information about the system to be

controlled. Figure 12.3 shows the change gain estimates window where
the user can enter those gain estimates in Eqs. (3) and (4).

FIGURE 12.3 Change gain estimates.
FIGURE 12.4 Change tuning parameters.
5. Change tuning parameters. A three-level factorial experiment was selected

for the first ten runs. Figure 12.4 shows the Change Tuning Parameters
window.
6. Multivariate exponential weighted moving average (EWMA) SPC chart.
This option implements the Lowry et al. chart.7 It asks for initial estimates
for the variances of the responses (the default is all variances equal to
1.0, and all covariance equal to 0.01), SPC EWMA weight (0.3 is the
default), and the constant upper limit (10 is the default). All defaults were

FIGURE 12.5 Multivariate EWMA SPC chart setup.
used in this option. The Multivariate EWMA SPC chart windows is shown
in Figure 12.5. By default, the chart is used just for monitoring out-of-
control events. If used as a deadband, the OAQC will be invoked (and a
new recipe will be computed) only when there is evidence of an out-of-
control state; otherwise, the previous recipe is kept.
12.2.2 FIND NEXT RECIPE

The user should click on the “Find Next Recipe” button whenever it is desired to
invoke the OAQC’s optimizer to find the suggested recipe to use for the next run.
After entering initial settings, bounds, constraints, intercepts, and perhaps parameter
estimates, a normal iteration will then consist of the following:
1. Clicking “Find Next Recipe”

2. Reading the solution
3. Entering the recipe in the equipment
4. Obtaining the metrology
5. Entering the metrology information in the “Update Observed Responses
(metrology)” option
Then, we repeat the same steps run by run until the control session terminates. The
recipe and metrology information is automatically displayed in “history plots” that
show the levels of the controllable factors and of the responses for each run.
Figures 12.6 and 12.7 show the inputs and outputs, respectively, of a 50-wafer (runs)
session for this CMP process. In this simulation, target values were set at 1700 for
y1 and 150 for y2, and constraints were set at y1 > 1700, y2 < 250, and –1 ≤ µ i ≤ 1.
The open-loop responses (what we would get if the recipe were maintained constant

0.6
0.4
0.2 Speed
Pressure
0
Downforce
-0.2 Profile
-0.4
-0.6
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
Run Number
FIGURE 12.6 Computed recipes (inputs) for 50 runs of a 4 × 2 CMP process.
3500
3000
2500
Removal rate (closed loop)
2000 Nonuniformity (closed loop)
1500 Removal rate (open loop)

Nonuniformity (open loop)
1000
500
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
Run Number
FIGURE 12.7 Resulting responses (outputs) for 50 runs of a 4 × 2 CMP process.
1.5
T2
1
Upper limit
0.5
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
Run Number
FIGURE 12.8 EWMA chart for 50 runs of a 4 × 2 CMP process.
at the zero level) are also shown in Figure 12.8. The constraints on the outputs
together with the strict target values are useful in this example as removal rate is
usually a “larger the better” response and nonuniformity a “smaller the better”
response. The EWMA chart (Figure 12.8) indicates that there is no “out of control”
signal. Thus, this 4 × 2 CMP process is in control.

12.3 INTEGRATION OF THE OAQC WITH THE
GENERIC CELL CONTROLLER (GCC)
In Chapter 9 we showed that the GCC-R2R controller (GCC-R2R) is a discrete
control mechanism that utilizes a relational database to store and execute sequential
control information (a sequence of command–action pairs used to control a manu-
facturing process). The GCC implementation described here further uses object-
oriented technology and distributed object-based communications to implement a
suite of client/server applications designed to work in a distributed computing
environment provided by the NextStep/OpenStep operating system. The solution is
portable to many hardware and software platforms (Intel, Motorola, SUN Sparc,
Power PC processors; Mach, Windows NT, Solaris operating systems; and Sybase,
Oracle, OpenBase, and other industry standard database servers).8
Specifically, the GCC utilizes a relational database along with a GccEvent object
to direct execution order and data flow, respectively, as illustrated in Figure 12.9.
The GccKernel queries the database to determine a module execution order required
to service a control command. The GccEvent objects travel between the modules
and serve as containers for all the GCC data needed to relate the current state of the
run-to-run control system. In this way the modules may execute the desired actions.
The modules then perform their intended actions and the results of those actions are
stored back to the GccEvent. Thus, the instance of GccEvent class is passed from
one module to another as directed by the GccKernel as an argument of a command
(message to an object). Each module contributes some data (such as the recipe,
measured or simulated output, etc.) to the instance.
Metrology
Module
target target
recipe recipe
run number run number
getMetrology metrology output
download
recipe and
start GccKernel
Equipment
Module
plot action
History-Plot
Module command
Database
getRecipe,
control
target
recipe
run number
metrology output
target new recipe
recipe
run number
Control
Algorithm
Module
FIGURE 12.9 The GCC-R2R data flow diagram.

Metrology Equipment
Equipment Equipment
Module such as CMP
Module
or Epi Tool
metrology
output download recipe
recipe and
Inter-Process getMetrology start
Controller high-level
command command
Database
GUI high-level GccKernel
command Control Rules
System State
action
run data
plot
getRecipe
control
recipe simulate
History-Plot next recipe
simulated
Module metrology
output
Command Flow OAQC Simulator
Data Flow
Process Optimization and Control Module
FIGURE 12.10 Generic cell controller block diagram.
This version of the GCC-R2R contains a set of modules that, collectively, are
capable of providing R2R control of a variety of manufacturing processes. This set
includes three control algorithm modules:
1. The linear approximation multivariate “Gradual Mode” (GM) control

algorithm (MIT)
2. The time-based extended GM (GMt) control algorithm (MIT)
3. The optimizing adaptive quality controller (OAQC) (PSU)
Since the GCC-R2R provides a modular and configurable control environment,

it is suited for managing the required communications between a control algorithm
module, a processing equipment interface module, a metrology equipment interface
module, and other modules (such as a history-plot module) that are part of the control
solution. Figure 12.10 shows the general schema of the GCC. The heart of the GCC
is the GccKernel, which coordinates all controller activity (by coordinating command
and data flow between the various R2R control modules running on any computer
in a network). The GCC-R2R accepts commands either from a parent interprocess
controller or from the process engineer/operator (via the graphical user interface)
and performs corresponding actions fetched from the database. Those actions involve
the coordination of any number of the aforementioned modules to achieve a desired
result.
Of the many features of GCC-enabled R2R control solutions described in
Chapters 9 and 10, the example provided in this chapter illustrates the feature of
capability for integration of third-party software, namely the OAQC algorithm solution,
into the GCC module. The OAQC controller can be used either in stand-alone mode
or as part of the GCC. The stand-alone mode usage was described in Section 12.3.

The GCC mode of operation is somewhat different. Once a user has entered and
saved the initial settings (see 12.2.1) for the process being controlled, it is not
necessary to use the OAQC user interface. As the OAQC is used as part of the GCC
system, the GccKernel takes control of all its activities. It sends to the OAQC module
commands in order to get a suggested recipe for the next run or to simulate the
process and metrology outputs. This is implemented via a distributed objects para-
digm (see Figures 12.9 and 12.10). As part of the execution of sequential control,
information is first fetched from the database for a high-level command. The GccKernel
then sends messages to the OAQC system object and gets the results encapsulated
in the GccEvent distributed object, which is used by the GCC as an information
medium.
The following is a real example of commands sent to the GCC modules by the
GccKernel to implement high-level “planarize”* command for one control “loop.”
Each command explanation is commented to its right.
[OAQC getRecipe:] /* Get the process recipe for this run */

[GccTool recipeDownload:] /* Download that recipe to the equipment
(either automatically via a SECS interface or
manually with the aid of the equipment
operator) */
[GccTool start:] /* Start the process */
[GccMetrology getMetrology:] /* Enter in metrology data (either automatically
via a SECS* interface or manually through a
Graphical User Interface) */
[OAQC control:] /* Determine a process recipe for the next run */
[GccHistory plot:] /* View the process history either in tabular
form or graphically */
[GccKernel runAgainIfNecessary:] /* Repeat the loop according to the “repeat
number” set by the operator */
There are numerous advantages to the GCC-integrated form of OAQC operation.

This form of operation
1. Can be integrated into a hierarchical control system within a semiconduc-

tor manufacturing factory
2. Allows automatic uploading of metrology data and automatic download-
ing of recipes to the equipment
3. Provides a database management system for analyzing historical
input–output data
4. Enables the OAQC to run in parallel with other controllers9
5. Provides different authorization levels for users
* “Planarize” is a typical command process action for a chemical mechanical planarization (CMP) tool;
see Introduction.
SEMI Equipment Communication Standard, a communication protocol commonly utilized in the semicon-
ductor manufacturing industry. See Reference 10 for a complete description, and Chapter 9 for examples.

12.4 SUMMARY
A design for integration of an OAQC algorithm implementation into a GCC-enabled
R2R control solution has been described in this chapter. As a complement to the
examples in Chapter 11, which focused on the integration of R2R control into the
factory and the operation and evaluation of the controller in that environment, this
chapter focuses on the algorithm implementation and the integration of the algorithm
into the R2R control solution. The solution developed is illustrated to be flexible
and allows for operation of the algorithm in stand-alone and integrated model. The
integration meets the requirements of integrated control defined in Chapter 8, thus
the solution, if deployed, should provide for effective R2R control in a factory
environment, similar to the solutions described in Chapter 11.
REFERENCES
1. Del Castillo, E., “A Multivariate Self-Tuning Controller for Run-to-Run Process
Control under Shift and Trend Disturbances,” IIE Transactions, Vol. 28, No. 12, 1996,
pp. 1011-1021.
2. Del Castillo, E. and Yeh, J., “An Adaptive Run-to-Run Optimizing Controller for
Linear and Nonlinear Semiconductor Processes,” IEEE Transactions on Semiconduc-
tor Manufacturing, Vol. 11, No. 2, May 1998.
3. Garfinkel, S.L. and Mahoney, M.K., NeXTSTEP Programming Step One: Object-
Oriented Application, Springer-Verlag, New York, 1993.
4. Moyne, J.R. and McAfee, L.C. Jr., “A Generic Cell Controller for the Automated
VLSI Manufacturing Facility,” IEEE Transactions on Semiconductor Manufacturing,
Vol. 5, No. 2, 1992, pp. 77-87.
November 1995).
6. Ning, Z., Moyne, J.R., Smith, T., Boning, D., Del Castillo, E., Yeh, J., and Hurwitz,
A., “A Comparative Analysis of Run-to-Run Control Algorithms in the Semiconductor
Manufacturing Industry,” 7th Annual IEEE/SEMI Advanced Semiconductor Manu-
facturing Conference and Workshop, Cambridge, MA, Nov. 1996, pp. 375-381.
7. Lowry, C.A., Woodall, W.H., Champ, C.W., and Rigdon, S.E., “A Multivariate Expo-
nentially Weighted Moving Average Control Chart,” Technometrics, Vol. 34, No. 1,
Feb. 1992, pp. 46-53.
8. Telfeyan, R., Moyne, J., Hurwitz, A., and Taylor, J., “Demonstration of a Process-
Independent Run-to-Run Controller,” Electrochemical Society, May 1995.
nology, Vol. 13, No. 3, May/June 1995, pp. 1787- 1791.

Part 4
Customization Methodology
Thus far in this book we have provided motivation for R2R control in the industry
(see Introduction), described elements of the foundation of process control (Part 1),
presented information on R2R control algorithms (Part 2), and described R2R control
deployment and integration-enabling mechanisms (Part 3). While each of these
components is important to the R2R control solution, successful utilization of R2R
control in practice additionally requires adherence to a procedure for process control
deployment that includes process identification, control solution customization, inte-
gration, test, and validation. In Part 4 of the book we focus on the methodology for
R2R control solution deployment and customization.
We present this methodology in Chapter 13 through a case study based on an
example of an R2R implementation on a production tool. The device type, input/out-
put detail, measurement units, and exact numerical results have been changed to
protect the confidentiality of the customer. The implementation now refers to a
“furnace for producing a ceramic used in the manufacture of superconducting wire.”
The effort was motivated by the customer’s desire to improve the performance
of their ceramic furnaces without requiring substantial, costly hardware upgrades.
A team made up of expert personnel from the customer and the control vendor was
organized to carry out the initial implementation and show process improvement
under R2R control.
The main feature of the chapter is the establishment of a well-defined method-
ology for implementing R2R process control. Detailed discussions were first con-
ducted with the customer’s personnel to identify the control problem, and a design
of experiment (DOE) on the furnace was executed so that a model of the process
could be derived for control purposes. From the results of the experiment, regression
models of the process were developed. Utilizing these as control models within the
R2R controller, the controller was deployed on the most stable furnace in the plant;

any improvement in furnace performance could then be seen as a bottom-line
advantage for the whole furnace line.
Results were gathered for 60 runs (furnace cycles) and compared to previous
runs of the same furnace without the controller present. Notable improvement ratios
were observed.
The operation of a run-to-run system usually takes place in two phases or stages.
In the first stage, a new piece of equipment or tool is “qualified,” which means that
experiments are conducted in order to characterize and possibly also optimize the
performance of the tool. This qualification stage is based on design of experiment
(DOE) techniques. DOE is widely known and practiced in modern process engi-
neering, and enjoys many popular references such as References 1 and 2; it is
therefore not further discussed. Any optimization part of a tool qualification uses a
set of experimental optimization techniques called response surface methods. Once
the process has been qualified, equipment models and process targets become avail-
able, and the goal of an R2R controller is to keep the process responses at the
optimized levels in the presence of drift and disturbances that occur from run to run.
This constitutes the second stage of the operation. Although some optimizing con-
trollers can provide optimization and control capabilities in the same tool set (e.g.,
the OAQC algorithm described in Chapters 4 and 5), the use of classical response
surface methods (RSM) is much more widespread. RSM methods are also the topic
of Chapter 14.
REFERENCES
[1] Box, G.E.P., Hunter, W.G., and Hunter, J.S., Statistics for Experimenters, John Wiley
and Sons, New York, 1978.
[2] Montgomery, D.C., Design and Analysis of Experiments, John Wiley and Sons, New
York, 1997.

13 Case Study: Furnace
Capability Improvement
Using a Customized R2R
Control Solution
Arnon Hurwitz and James Moyne
Control algorithms and enabling technologies for R2R control are described in
Parts 2 and 3 of this book, respectively. In this chapter a case study of developing,
deploying, and evaluating an R2R control solution for a furnace process is presented.
The R2R control solution development and deployment effort was successfully
carried out on a production tool in a production environment. The effort utilized a
team with members drawn from the tool owner (the “customer”) and the vendor of
the control solution. In presenting this case study, the device type, input/output detail,
measurement units, and exact numerical results have been changed to protect the
confidentiality of the customer; at the same time we have closely paralleled the
implementation steps and the improvement ratios of the original outcome. The
implementation now refers to a “furnace for producing a ceramic used in the man-
ufacture of superconducting wire.”
The purpose of this chapter is to chronicle the complete R2R control customi-
zation and deployment process. Specifically, it addresses gathering user require-
ments, design and execution of process characterization experiments, development
and customization of R2R control models, deployment, evaluation of results, and
integration. The reader may wish to use elements of this chapter as a template for
developing and deploying his/her own R2R control solution.
13.1 PROBLEM SETUP

The effort was motivated by the customer’s desire to improve the performance of
his ceramic furnaces by using R2R control. A team made up of expert personnel
from the customer and the control vendor* was organized to carry out the initial
implementation and show process improvement under R2R control.1 The vendor’s
personnel had expertise in R2R control solution development, deployment, and
integration; the customer’s personnel were expert in the needs and the operation of
the process.
* MiTeX Solutions, Canton, Michigan.

TABLE 13.1
Multivariate Control Model
Y = C1 + 1.4 * E – 0.01 * R1 + 0.03 * R2 – 0.01 * R3
Z1 = C2 + 0.04 * R1
Z2 = C3 + 0.03 * R2
Z3 = C4 + 0.06 * R3
Utilizing a methodology (presented below) defined by the vendor and agreed to

by the customer, the R2R control system deployment effort was initiated; detailed
discussions were conducted with the customer’s personnel to identify the control
problem, and a design of experiment (DOE) on the ceramic furnace was executed
so that a model of the process could be derived for control purposes.
From the results of the experiment, as well as additional discussions with the
customer, regression models of the process were developed. From these models the
4 × 4 multivariate R2R control model shown in Table 13.1 was derived. In this
model, the process outputs to be controlled were Y = ductility measurement, Zi =
superconductivity measurement i; (i = 1, 2, 3), Ri = furnace temperature ramp profile
i; (i = 1, 2, 3), E = amount of trace element additive, and Cj a constant; (j = 1, 2, 3, 4).
Utilizing this control model, the controller* was set up by entering the model
coefficients and other parameters detailed below. The controller was then deployed
on the most stable furnace in the plant; any improvement in furnace performance
could then be seen as a bottom-line advantage to using R2R control.
The R2R controller was deployed and results gathered for 60 runs (furnace
cycles) and compared to previous runs of the same furnace without the controller
present. The results are summarized as follows:
1. The ratio of noncontrolled standard deviation for output Y to controlled

Y is 2.29.
2. The ratio of noncontrolled standard deviation for output Z1 to controlled
Z1 is 1.92. Similar ratios apply for Z2 and Z3.
In summary, R2R control cut the standard deviation of both Y and Z performance
parameters in half.
13.2 BACKGROUND: DESCRIPTION

OF PRODUCTION TOOL
In the case study application, the customer was interested in improving the capability
of his furnaces used to produce ceramic material for superconducting wire. An
informal analysis of the process indicated that the deployment of R2R control might
provide significant process improvement. The furnace type in question has the
construction shown in Figure 13.1.
* The MiTeX Generic Cell Controller run to-run (GCC-R2R) controller.

ZONE 1 ZONE 2 ZONE 3
FURNACE CERAMIC INDUCTION

BODY MATERIAL COILS
FIGURE 13.1 Induction furnace with three heating zones.
The furnace is divided into three zones with a separate crucible of ceramic
material placed in each zone. Each zone is heated directly with its own set of
induction coils, and indirectly by the adjacent coil(s). Each coil can be ramped up
to full power with an independently controlled ramp gradient Ri for Zone i. The
ceramic material for a load was mixed in one batch with a trace element additive E
and then evenly divided into three crucible batches for simultaneous insertion into
the three furnace zones at the start of each cycle, or “run.” The percentage of the
trace element for any one furnace run could be varied between strict specification
limits from run to run, but could not be varied separately for the material in the
three separate crucibles for any single run.
On completion of a furnace cycle the ceramic material was removed, drawn into
wire, and tested for a physical property Y called “ductility.” As the Y test was
expensive and destructive, only one test was made from a piece of wire taken from
the material of the first furnace zone (Zone 1). A nondestructive test for “conduc-
tivity” Zi was made on a sample of wire from each separate zone.
There were thus four controlled inputs {E, R1, R2, R3} and four measured
outputs {Y, Z1, Z2, Z3}.
13.3 METHODOLOGY FOR CONTROL DEPLOYMENT

In order to ensure that a consistent approach was followed when deploying a control
solution, the control solution vendor established a methodology to be followed.1
This allows for checking and corrective action as the implementation project pro-
ceeds. The steps of the methodology are laid out in Table 13.2.
13.4 APPLICATION OF METHODOLOGY

The above steps of the methodology were implemented as specified in Table 13.2.
Details are provided in the following subsections.
13.4.1 QUANTIFY PROBLEM WITH PROCESS ENGINEERS

In the first step of the application of this procedure, extensive discussions were
conducted with customer personnel to identify process quality metrics and process

TABLE 13.2
Methodology for Control System Deployment
Step Activity Conducted by
1 Quantify problem with process engineers on site: identify Vendor and customer at customer
process, extract available process knowledge, identify site
basic quality metrics and tunable parameters, etc.
2 Design of experiments for process characterization and Vendor
R2R control model development
3 Execution of DOE, data collection Customer (vendor can provide
assistance)
4 Data analysis: process response surfaces Vendor or suitably qualified
statistician
5 R2R controller: final parameter specifications Vendor and customer
6 Customization and delivery of a test R2R system Vendor
7 On-site testing, training, technical support during testing Vendor hand-off to customer
through on-site training
8 Results analysis and feedback to customer Vendor
9 Deployment, integration Vendor and customer
10 Technical support, upgrades, additional training Vendor
TABLE 13.3
Bounds for Inputs
Input Parameter Lower Bound Upper Bound
E 16.3 20.0
R1 159 161
R2 159 161
R3 159 161
quality improvement goals. From these discussions it was agreed that the ideal run-
to-run controller would provide multivariate (concurrent) control of ductility (Y) as
well as three-zone superconductivity (Z1, Z2, Z3).
The process engineers further related that Y was a fairly well-behaved signal
and a strong (qualitatively stated) function of the additive (E) level, although Y was
also notorious for strong downward drift. In fact, the furnace had to be taken apart
and rebuilt after every 20 to 30 cycles to “reset the drift factor back to zero.”
Conductivity (Z) was less well behaved* than Y, and its correlation to input variables
(induction ramp Ri, and E level) was not as well understood.
As stated in Section 13.1 above, there were four controllable inputs {E, R1, R2,
R3} and four measured outputs {Y, Z1, Z2, Z3}. The input factors were constrained
by safety and other considerations to lie within certain upper and lower bounds as
shown in Table 13.3.
* Higher relative variability, and metrology noise.

TABLE 13.4
Experimental Design Matrix
Pattern R1 R2 R3 E
1 0000 160 160 160 18.1

2 –++– 159 161 161 16.3
3 +–+– 161 159 161 16.3
4 0000 160 160 160 18.1
5 –––– 159 159 159 16.3
6 ++– – 161 161 159 16.3
7 –+–+ 159 161 159 20.0
8 0000 160 160 160 18.1
9 ++++ 161 161 161 20.0
10 – – ++ 159 159 161 20.0
11 +––+ 161 159 159 20.0
12 0000 160 160 160 18.1
13.4.2 DESIGN OF EXPERIMENT(S)

Using the information provided by the engineers, an experiment was designed to
quantify the process control problem. This entails designing and running a formal
experiment to optimally collect data that can be used to construct a linear model of
the process. This model is subsequently used in the R2R controller to guide the
process.
Given the resources and constraints of the situation at hand, it was decided to
design a basic experiment with eight “experimental” runs plus four runs set at the
process standard recipe setpoints — a total of twelve runs. The experimental matrix
was based on a half-fraction of a two-level, four-input-factor design; that is, a 24-1
fractional factorial design.* The design matrix is given in Table 13.4.
The “Pattern” column indicates the high (+) and low (–) settings of the inputs
according to the bounds given in Table 13.2.
13.4.3 EXECUTION OF THE EXPERIMENTAL DESIGN

The customer’s project team engineers and line operators executed the experiment.
Note that the standard process recipe settings (i.e., “0000”) were run at roughly even
intervals throughout the experiment, and started and ended the experiment. The
results from these standard-setting runs were used to check that no abnormal tool
behavior occurred during the experiment. The 12 runs were completed over a short
time period, but if they had been run over a long period when tool drift could manifest
itself, the standard run results could be used to de-trend the final experimental
outcomes before the subsequent model-building. The results of measuring Y, and Z1,
Z2, and Z3, are given in Table 13.5.
* For details about factorial designs, see Reference 2.

TABLE 13.5
Measured Outcomes of Experimental Runs
Pattern R1 R2 R3 E Y Z1 Z2 Z3
1 0000 160 160 160 18.1 37.3 10.39 11.44 10.41

2 – ++– 159 161 161 16.3 34.8 10.30 11.47 10.42
3 +–+– 161 159 161 16.3 34.7 10.49 11.37 10.47
4 0000 160 160 160 18.1 37.4 10.42 11.36 10.47
5 –––– 159 159 159 16.3 34.7 10.35 11.29 10.42
6 ++– – 161 161 159 16.3 34.8 10.49 11.44 10.29
7 –+– + 159 161 159 20.0 40.1 10.34 11.45 10.29
8 0000 160 160 160 18.1 37.4 10.41 11.40 10.48
9 ++++ 161 161 161 20.0 40.0 10.48 11.40 10.41
10 – – ++ 159 159 161 20.0 39.9 10.34 11.38 10.47
11 +– – + 161 159 159 20.0 40.0 10.45 11.36 10.36
12 0000 160 160 160 18.1 37.3 10.43 11.42 10.40
TABLE 13.6
Parameter Estimates
Term Estimate Std. Error t Ratio Prob. > t
Intercept 10.646146 2.617284 4.07 0.0048

R1 –0.012211 0.009434 –1.29 0.2366
R2 0.0330125 0.009434 3.50 0.0100
R3 –0.012872 0.009434 –1.36 0.2147
E 1.4041711 0.006709 209.31 <0.0001
Note also that the (nonstandard) experimental runs* are arranged in random
order through the design matrix. If the experiment were to be replicated, the standard
runs would stay in their unaltered run order; however, the other experimental runs
must have their order randomly shuffled to prevent introduction of any experimental
bias or unwanted systematic structure.
13.4.4 DATA ANALYSIS

The results of Table 13.5 were entered into a statistical analysis program,** and
linear regression models were requested for Y and the Zi’s. The next set of three
tables shows the output for the analysis of the Y data.
Table 13.6 shows the coefficients (parameters) of the model estimated from the
experimental data for Y. Writing down the model using these coefficients, we obtain
Y − 10.65 + 1.4 * E − 0.01 * R1 + 0.03 * R2 − 0.01 * R3 (1)
* Rows: 2, 3, 5, 6, 7, 9, 10, 11.

** JMP by the SAS Institute of Cary, North Carolina.

TABLE 13.7
New Parameter Estimates for Y
Intercept 9.4057562 2.963697 3.17 0.0113

E 1.3909428 0.013129 105.94 <0.0001
R2 0.0172799 0.018463 0.94 0.3737
TABLE 13.8
Lack of Fit for Y Model
Source DF Sum of Squares Mean Square F Ratio
Lack of fit 4 0.00448778 0.001122 0.7697

Pure error 3 0.00437278 0.001458 Prob. > F
Total error 7 0.00886056 0.6101
From Table 13.6, only the inputs R2 and E have coefficients with t-statistics that are
significantly different from zero; the coefficients for R1 and R3 are marginal (about
77% significance level for the t ratios). We can, therefore, try a model for Y that has
only R2 and E on the right-hand side (RHS). The new parameter estimates are listed
in Table 13.7.
Table 13.7 shows that the significance level for R2 collapses; only E remains as
significant. One could have a control equation for Y, which is driven by E alone, and
it might work quite well. However, the engineers were convinced that the form given
in Eq. (1) was preferable for control, and that the signs and sizes of the coefficients
for all three R inputs were correct. For this reason the controller was programmed
with Eq. (1) for Y. As it turned out, this gave good Y control in the trials.
The goodness of fit of Eq. (1) for Y is also determined as a whole by the
R-squared adjusted statistic, which was greater than 99%. This means that the model
given in (1) “explains” more than 99% of the variation observed in the Y of the
experimental data.
Table 13.8 addresses possible lack of model fit to the data. The model we have
fitted for Y is strictly a linear one in the input factors; if the true nature of Y contained
quadratic or other nonlinear terms we would expect the fit to be not as good, and
to show up formally as a significant lack-of-fit F-ratio. In Table 13.7 the probability
of such a lack of fit is seen to be small because the lack-of-fit F-ratio statistic has
a high probability (61.01%) of occurring by chance alone.
Next, we need to derive the equations for the conductivity Z1, Z2, and Z3. Only
R1 was found to be significant for Z1. Table 13.9 shows the estimation results for
Z1 regressed against R1.
The chosen model for Z1 is thus
Z1 = 3.9 + 0.04 * R1 (2)

TABLE 13.9
Parameter Estimates for Z1
Intercept 3.9323351 0.884476 4.45 0.0012

R1 0.0404374 0.005528 7.32 <0.0001
TABLE 13.10
Control Model System
Y = C1 + 1.4 * E – 0.01 * R1 + 0.03 * R2 – 0.01 * R3
Z1 = C2 + 0.04 * R1
Z2 = C3 + 0.03 * R2
Z3 = C4 + 0.06 * R3
R-squared adjusted for model (2) was 83%; no lack of fit was detected. Similarly,
the models for Z2 and Z3 were
Z 2 = 6.8 + 0.03 * R2 (3)
Z 3 = 0.5 + 0.06 * R3 (4)
R-squared adjusted for model (3) was 34%, and for model (4), 55%. These indicate
a weak explanatory power; however, the individual t-statistics showed significance
for both ramp (Ri) parameters and, in addition, the signs of the parameters were in
accordance with engineering theory and consistent with (2). No lack of fit was
detected* for either (3) or (4). The final model system chosen for the controller can
as shown in Table 13.10. Note that the values of the constant terms are not given
explicit values here: they are initialized at the start of a control run to bring the tool
outputs to target, and thereafter they are estimated on a run-to-run basis by the
control software itself.
13.4.5 CONTROLLER PARAMETER SPECIFICATION

A minimal set of control parameters needs to be specified before the controller can
be deployed for action. A list of these parameters follows:
1. The weights of the input parameters, the relative weights of which reflect
preference for adjustment (higher weight implies greater preference).
2. The weights of the output parameters, the relative weights of which reflect
priority in control.
* Although in the case of models (3) and (4) this could mean noise-obscured structure.

TABLE 13.11
Output Parameter Specifications
Output Parameter Weight EWMA (alpha) Targets
Y 1 0.7 37.3
Z1 1 0.4 10.5
Z2 1 0.4 10.5
Z3 1 0.4 10.5
TABLE 13.12
Input Parameter Specifications
Input Parameter Upper Bound Lower Bound Resolution Weight
E 16.3 20.0 0.1 2.0

R1 159 161 0.01 1.0
R2 159 161 0.01 1.0
R3 159 161 0.01 1.0
3. The smoothing parameters (EWMA weights, or alphas — see Part 2 of

this book), one for each output parameter, the weights of which, lying
between 0 and 1, reflect more or less smoothing of input metrology noise;
the closer to zero, the more smoothing.
4. The output targets for the product type.
5. The upper and lower control bounds for the input parameters. These may
be the same as the bounds for the designed experiment, and are usually
contained within the bounds of the designed experiment.
6. The resolution, or “granularity,” of each input parameter; this value indi-
cates the smallest control adjustment possible for that input.
7. The control model equations.
Utilizing these control parameter specifications, the control system model of

Table 13.10 is augmented by the specifications of Tables 13.11 and 13.12 to complete
the specification for this application.
Table 13.11 indicates that all output parameters are considered of equal impor-
tance. Also, more metrology noise is expected for the Z outputs, and so an alpha
closer to zero is specified. The alpha for Y is high, indicating high confidence in the
precision of the measured value for Y and in the controller action.
13.5 CUSTOMIZATION AND DELIVERY

OF CONTROLLER
The parameters of Tables 13.10, 13.11, and 13.12 were entered into the controller
software. In addition, certain custom additions such as password protection were

enabled for the specific needs of the customer. The controller was then delivered to
the customer’s site and set up for the test runs.
13.6 ON-SITE TESTING, TRAINING, TECHNICAL

SUPPORT DURING TESTING
The controller was deployed at the customer site on the “most stable” furnace.
Because R2R control serves to reduce process shift and drift, performance improve-
ment of a stable process would serve to identify a lower bound on the impact of
R2R on process capability for this type of process. The testing proceeded as follows.
1. Vendor’s personnel visited the customer test site and installed an R2R
controller on the target furnace. The controller was deployed on a stand-
alone computer with communication between the metrology tool, control-
ler, and process tool achieved through human interaction.
2. Vendor’s personnel remained at the site for a period of one week. During
that time the vendor completed training of three shifts of customer’s
personnel (process engineers and technicians) on the use of the R2R
control system, and delivery of a customized user manual for the R2R
control system that covered controller operation as well as model setup
for change of process. The training process entailed two hours of hands-
on training followed by four hours of monitoring by vendor personnel.
3. The stand-alone test controller was left at the vendor site for a period of
six weeks. During that time the vendor was available for 24-hour phone
technical support. A day’s visit was also made after three weeks to check
the progress during the test period.
4. Customer’s personnel delivered to the vendor the process recipe logs and
metrology data collected during the test period. The data for 60 control
runs are included in the Appendix of this chapter. The customer also
delivered a sample of metrology data for a fixed recipe (i.e., noncontrolled)
run of 60 furnace cycles that occurred prior to the deployment of the
controller.
13.7 RESULTS ANALYSIS

The controller eliminated the typical downward drift of the Y parameter and enabled
the process to run for 60 cycles without noticeable degradation in performance. The
standard deviation of the Y measurement was, in comparison to the noncontrolled
Y, cut by more than half. The standard deviation for the Z outputs was also cut almost
by half. Table 13.13 summarizes the improvements for Y and Z1. Results for Z2 and
Z3 were similar. Graphs of the output metrology for Y clearly show the improvement
(Figure 13.2). For Z1 (Figure 13.3), there is no trend to begin with, but the controller
appears to reduce the number of process interventions, and thus leads to a more
stable, less noisy process. Similar results can be noted for all three Z outputs
(Figure 13.4).

TABLE 13.13
Performance Improvement with R2R
Control: Y and Z1
Metric Y Z1
Standard deviation (controlled runs) 0.32 0.14

Standard deviation (non-controlled) 0.73 0.27
Standard dev. ratio (noncontr./contr.) 2.29 1.92
Y: Controlled vs Non-controlled
40.00
39.00
38.00
37.00
36.00
Y-units
Controlled Y
35.00
Non-control Y
34.00
33.00
32.00
31.00
30.00
1
4
7
10
13
16
19
22
25
28
31
34
37
40
43
46
49
52
55
58
Run #
FIGURE 13.2 Controlled vs. non-controlled Y performance.
Z1: Controlled vs Non-controlled
12.00
11.50
11.00
10.50
Z-units
Controlled Z1
Non-control Z1
10.00
9.50
9.00
8.50
1
4
7
10
13
16
19
22
25
28
31
34
37
40
43
46
49
52
55
58
Run #
FIGURE 13.3 Controlled vs. non-controlled Z1 performance.
The actual moves made by the R2R controller, in the form of instructions for
tweaking the inputs E and Ri (i = 1, 2, 3), are shown in Figures 13.5 and 13.6. Note
that while R1 tended to begin and end the 70-run campaign at about the same average
level, R2 and R3 ended somewhat higher than where they began.
These good results were communicated to the customer in the form of a pre-
sentation to all who had been involved in the project, as well as interested managers
from different production branches.

Z1: Controlled
11.20
11.00
10.80
10.60
10.40
Controlled Z1
Z-units
10.20
Controlled Z2
10.00
Controlled Z3
9.80
9.60
9.40
9.20
9.00
1
4
7
10
13
16
19
22
25
28
31
34
37
40
43
46
49
52
55
58
Run #
FIGURE 13.4 Z1, Z2, and Z3 performance under control.
E: Controller moves
18.4
18.2
18.0
E-units
17.8
E
17.6
17.4
17.2
17.0
10
13
16
19
22
25
28
31
34
37
40
43
46
49
52
55
58
61
1
Run # RUN #
FIGURE 13.5 Control moves made by input E.
R: Controller moves
160.60
160.40
160.20
R1
R-units
160.00
R2
159.80 R3
159.60
159.40
159.20
1
4
7
10
13
16
19
22
25
28
31
34
37
40
43
46
49
52
55
58
Run #
FIGURE 13.6 Control moves made by inputs R1, R2, and R3.
13.8 DEPLOYMENT, INTEGRATION

At the conclusion of the test, a determination should be made to deploy the controller
in production. A deployment plan and integration path must be decided. R2R controller

integration is covered in depth in Chapter 10, and especially Chapter 11. In terms
of the case study, the R2R controller solution had been installed in other tools and
the integration path was clear enough to the vendor personnel. The integration can
be made completely “closed loop” if there exists automated metrology for the output
parameters. If automated metrology does not exist for all or some of the output
parameters, then some human interaction will remain necessary; this is feasible,
provided the run-to-run cycle leaves sufficient time for the human interaction to
occur.
In the case of the induction furnace, several hours elapsed between runs, and
this would make it possible to do metrology and/or data entry by hand in sufficient
time before the occurrence of the next run. It is also possible, and has been shown
for other tools,* for several runs to elapse before a new recipe needs to be generated.
This time lapse also allows for human interaction in the control loop. Ideally,
however, full automation is preferred, and this is possible, provided that a proper
production robust integration entity is available.**
13.9 CONCLUSIONS
The successful development, customization, and deployment of an R2R control
solution has been presented in this chapter. The development and deployment effort
utilized is an orderly, systematic methodology that is process-independent. Thus,
this methodology could be and has been applied to a wide variety of R2R control
problem scenarios. Deployment of this specific methodology has yielded numerous
successes in CMP, etch, and deposition control. With respect to the case study,
performance improvement of the magnitude demonstrated opens the door to tool
upgrades costing far less than buying the latest and most expensive tool. This is
especially desirable if there are a number of similar tools needing to be replaced or
upgraded in any one site. Thus, R2R controller technology gives production man-
agers a new option for cost–benefit decision making.
REFERENCES
Santa Fe, NM, (October 1996).
2. Box, G.E.P., Hunter, W.G., and Hunter, J.S., Statistics for Experimenters, John Wiley
& Sons (1978).
* For example, in the case of semiconductor planarization devices.

** In the present case study, the MiTeX Generic Cell Controller (GCC) serves this purpose.

APPENDIX: DATA FROM PRODUCTION RUN WITH
AND WITHOUT R2R CONTROL
INPUTS ---TARGETS--- OUTPUTS

Run # E R1 R2 R3 Y Z Cntrl Y Cntrl Z1 Cntrl Z2 Cntrl Z3 No-ctrl Y No-ctrl Z1
1 17.5 160.00 160.00 160.00 37.3 10.5 36.71 10.45 10.40 10.45 37.08 10.39
2 17.5 160.00 160.00 160.00 37.3 10.5 36.67 10.45 10.51 10.45 37.82 10.50
3 17.5 160.00 160.00 160.00 37.3 10.5 36.53 10.45 10.40 10.45 37.01 10.39
4 18.0 160.00 160.13 160.00 37.3 10.5 37.11 10.45 10.12 10.45 36.43 10.12
5 18.0 160.00 160.13 160.00 37.3 10.5 37.11 10.45 10.51 10.45 37.72 10.50
6 18.0 160.00 160.13 160.00 37.3 10.5 37.47 10.45 10.73 10.45 36.40 11.72
7 18.0 160.00 160.13 160.00 37.3 10.5 37.36 10.45 10.56 10.45 37.41 10.56
8 18.0 160.00 160.40 159.87 37.3 10.5 37.32 10.45 10.01 10.45 36.29 10.01
9 18.0 160.00 160.13 159.87 37.3 10.5 37.43 10.45 10.45 10.45 37.31 10.45
10 18.0 160.13 160.13 159.87 37.3 10.5 37.54 10.01 10.34 10.45 36.40 10.34
11 18.0 160.13 160.13 159.87 37.3 10.5 37.50 10.45 10.51 10.45 37.51 10.51
12 18.0 160.13 160.13 159.87 37.3 10.5 37.43 10.45 10.45 10.45 37.20 10.45
13 18.0 160.13 160.13 159.87 37.3 10.5 37.32 10.45 10.45 10.45 37.17 10.45
14 18.0 160.27 160.13 159.87 37.3 10.5 37.29 10.45 10.40 10.45 36.63 10.40
15 18.0 160.27 160.27 159.87 37.3 10.5 37.58 10.45 11.06 11.11 36.04 11.06
16 18.0 160.27 160.13 159.73 37.3 10.5 37.54 10.45 10.40 10.45 36.56 10.40
17 18.0 160.27 160.13 159.73 37.3 10.5 37.43 10.45 10.56 10.45 37.06 10.57
18 18.0 160.27 160.13 159.73 37.3 10.5 37.54 10.45 10.45 10.45 36.99 10.46
19 17.8 160.27 160.00 159.73 37.3 10.5 36.82 10.45 10.18 10.07 35.90 10.19
20 17.8 160.27 160.00 159.73 37.3 10.5 37.03 10.45 10.29 10.45 35.91 10.30
21 18.0 160.27 160.13 159.87 37.3 10.5 37.65 10.45 10.34 10.45 36.02 10.35
22 18.0 160.27 160.13 159.87 37.3 10.5 37.58 10.45 10.29 10.12 35.84 10.30
23 18.0 160.27 160.13 159.87 37.3 10.5 37.47 10.45 10.34 10.45 35.95 10.35
24 18.0 160.27 160.13 159.87 37.3 10.5 37.65 10.45 10.67 10.45 35.93 10.69
25 18.0 160.27 160.13 159.87 37.3 10.5 37.29 10.95 10.29 10.45 35.73 10.30
26 18.0 160.13 160.13 159.87 37.3 10.5 36.71 10.45 10.40 10.45 36.21 10.41
27 17.8 160.13 160.27 159.87 37.3 10.5 37.00 10.45 10.34 10.40 35.81 10.36
28 18.0 160.13 160.27 159.87 37.3 10.5 37.36 10.45 10.34 10.45 35.77 10.36
29 18.0 160.13 160.27 159.87 37.3 10.5 37.25 10.45 10.34 10.45 35.74 10.36
30 18.0 160.13 160.27 159.87 37.3 10.5 37.25 10.45 10.45 10.40 36.57 10.47
31 18.0 160.13 160.27 159.87 37.3 10.5 37.36 10.45 10.34 10.45 35.67 10.36
32 18.0 160.13 160.27 159.87 37.3 10.5 37.43 10.51 10.29 10.45 35.49 10.31
33 18.0 160.13 160.27 159.87 37.3 10.5 37.43 10.45 10.29 9.79 35.45 10.31
34 18.0 160.00 160.40 160.00 37.3 10.5 37.47 10.23 10.29 10.45 35.42 10.31
35 18.0 160.00 160.40 160.00 37.3 10.5 37.43 10.45 10.51 10.45 36.67 10.53
36 18.0 160.13 160.40 160.00 37.3 10.5 37.36 10.45 10.56 10.45 36.40 10.59
37 18.0 160.13 160.40 160.00 37.3 10.5 37.29 10.45 10.40 10.45 35.82 10.42
38 18.0 160.13 160.40 160.00 37.3 10.5 37.61 10.45 10.40 10.45 35.79 11.42
39 18.0 160.13 160.40 160.00 37.3 10.5 37.61 10.45 10.45 10.07 36.26 10.48
40 18.0 160.13 160.40 160.13 37.3 10.5 37.65 10.45 10.67 10.45 35.37 10.70
41 18.0 160.13 160.40 160.13 37.3 10.5 36.49 10.45 10.29 10.40 35.17 10.32
42 18.3 160.13 160.40 160.13 37.3 10.5 37.65 10.62 10.34 10.45 35.28 10.37
43 18.0 160.13 160.53 160.13 37.3 10.5 37.79 10.45 10.45 10.45 36.12 10.48
44 18.0 160.13 160.53 160.13 37.3 10.5 37.50 10.45 10.56 10.18 36.12 10.60
45 18.0 160.13 160.40 160.13 37.3 10.5 37.50 10.45 10.40 10.45 35.54 10.43
46 18.0 160.00 160.40 160.27 37.3 10.5 37.25 9.79 10.40 10.45 35.51 10.43

INPUTS ---TARGETS--- OUTPUTS
Run # E R1 R2 R3 Y Z Cntrl Y Cntrl Z1 Cntrl Z2 Cntrl Z3 No-ctrl Y No-ctrl Z1
47 18.0 160.27 160.53 160.27 37.3 10.5 37.21 10.45 10.56 10.45 36.01 10.60
48 18.0 160.27 160.53 160.27 37.3 10.5 37.29 10.73 10.29 10.45 34.93 10.32
49 18.0 160.13 160.40 160.27 37.3 10.5 37.47 10.45 10.73 10.45 34.90 10.77
50 18.0 160.13 160.53 160.27 37.3 10.5 37.54 10.45 10.56 10.45 35.91 10.60
51 18.0 160.13 160.40 160.27 37.3 10.5 37.32 10.45 10.45 10.45 35.84 10.49
52 18.0 160.13 160.40 160.27 37.3 10.5 37.29 10.34 10.07 10.45 34.75 10.11
53 18.0 160.13 160.53 160.27 37.3 10.5 37.14 10.45 10.12 10.45 34.71 10.16
54 18.0 160.13 160.53 160.27 37.3 10.5 37.43 10.51 10.45 10.45 35.73 10.50
55 17.8 160.13 160.53 160.27 37.3 10.5 36.78 10.45 10.56 10.45 35.73 10.61
56 18.0 160.13 160.53 160.27 37.3 10.5 37.54 10.45 10.34 10.23 34.79 10.39
57 18.0 160.13 160.53 160.27 37.3 10.5 37.39 10.45 10.51 10.45 35.90 10.55
58 18.0 160.13 160.53 160.27 37.3 10.5 37.29 10.45 10.45 10.45 35.59 10.50
59 18.0 160.13 160.53 160.27 37.3 10.5 37.32 10.73 10.51 10.40 35.83 10.56
60 18.0 160.00 160.40 160.27 37.3 10.5 36.16 10.45 10.51 10.45 35.79 10.56

14 Process Recipe
Optimization
The operation of a run-to-run system usually takes places in two phases or stages.
In the first stage, a new equipment is “qualified,” which means that experiments are
conducted in order to find a recipe that optimizes the performance of the equipment.
The qualification stage is based on design of experiments techniques and the use of
a set of experimental optimization techniques called response surface methods. Once
the process has been qualified, equipment models and process targets become avail-
able and the goal of an R2R controller is to keep the process responses at the
optimized levels in the presence of drift and disturbances that occur from run to run.
This constitutes the second stage of the operation. Although some optimizing con-
trollers can provide optimization and control capabilities in the same tool set (e.g.,
the OAQC algorithm5), the use of classical response surface methods is much more
widespread and, therefore, these methods are described in this chapter.
14.1 DETERMINING THE OPTIMAL REGION TO RUN

A PROCESS
The optimal region to run a process is usually determined after a sequence of exper-
iments is conducted and a series of empirical models are obtained. In many engi-
neering and science applications, experiments are conducted and empirical models
are developed with the objective of improving the responses of interest. From a
mathematical point of view, the objective is to find the operating conditions (or factor
levels) X1, X2, … , Xk that maximize or minimize the system responses Y1, Y2, … , Yr .
In experimental optimization, different optimization techniques are applied to the
fitted response equations Ŷ1, Ŷ2, … , Ŷr . Provided the fitted equations approximate
adequately the true (unknown) system responses, the optimal conditions of the model
will be “close” to the optimal operating conditions of the true system.
The experimental optimization of response surface models differs from classical
optimization techniques in at least three ways:
1. Experimental optimization is an iterative process, that is, experiments

conducted in one set of experiments result in fitted models that indicate
where to search for improved operating conditions in the next set of
experiments. Thus, the coefficients of the fitted equations (or the form of
the fitted equations) may change during the optimization process. This is

lack of linear fit
detected
"Phase I" "Phase lI"
Line Searches or Canonical Analysis
First-order model Quadratic model
Quadratic effects
detected
FIGURE 14.1
in contrast to classical optimization where the functions to optimize are

supposed to be fixed and given.
2. The response models are fitted from experimental data that usually contain
random variability due to uncontrollable or unknown causes. This implies
that an experiment, if repeated, will result in a different fitted response
surface model that might lead to different optimal operating conditions.
Therefore, sampling variability should be considered in experimental
optimization. In contrast, in classical optimization techniques the func-
tions are deterministic and given.
3. The fitted responses are local approximations, implying that the optimi-
zation process requires the input of the experimenter (a person familiar
with the process). This is in contrast with classical optimization, which
is always automated in the form of some computer algorithm.
The experimental optimization of a single response is usually conducted in two

phases or steps, following the advise of Box and Wilson3 (see Figure 14.1). The first
phase consists of a sequence of line searches in the direction of maximum improve-
ment. Each search in the sequence is continued until there is evidence that the
direction chosen does not result in further improvements. The sequence of line
searches is performed while there is no evidence of lack of fit for a simple first-
order model of the form
Ŷ = b0 + b1 X1 + b2 X 2 + L + bk X k (1)
The second phase is performed when there is lack of linear fit in Phase I and, instead,
a second-order or quadratic polynomial regression model of the form
Yˆ = b0 + b1 X1 + b2 X 2 + L + bk X k + b11 X12 + b22 X 22 + L + bkk X kk2 + b12 X1 X 2
+ b13 X1 X 3 + L + b1k X1 X k + b23 X 2 X 3 + L + b2k X 2 X k + L + bk −1,k X k −1 X k
exhibits adequate fit. Not all responses will exhibit quadratic fit, and in such cases
Phase I is stopped when the response of interest cannot be improved any further.
The direction of the gradient, g, is given by the values of the parameter estimates,
that is, g′ = (b1, b2, … , bk). Since the parameter estimates b1, b2, … , bk depend on
the scaling convention for the factors, the steepest ascent (descent) direction is also
scale-dependent. That is, two experimenters using different scaling conventions will

follow different paths for process improvement. This does not diminish the general
validity of the method, since the region of the search, as given by the signs of the
parameter estimates, does not change with scale. An orthogonal scaling convention,
however, is recommended. The orthogonal coded factors xi in terms of the factors
in the original units of measurement, Xi, are obtained from the relation
xi =
(
Xi − Xlow + Xhigh 2 ) i = 1, 2, …, k
(X high − Xlow 2 )
This coding convention is recommended since it provides better parameter estimates,
and therefore a more reliable search direction. The coordinates of the factor settings
on the direction of steepest ascent separated a distance ρ from the origin are given by
maximize b0 + b1x 1 + b2 x 2 + L + bk x k
k
subject to: ∑x
i= 1
i
2
≤ ρ2
This problem can be solved with the aid of an optimization solver (e.g., like the
solver option of a spreadsheet). However, in this case this is not really needed, as
the solution is a simple equation that yields the coordinates
bi
x i* = ρ i = 1, 2, …, k . (2)
∑
k
2
b j
j=1
An engineer can compute this equation for different increasing values of ρ and get
different factor settings all on the steepest ascent direction.
14.2 OPTIMIZATION OF MULTIPLE

RESPONSE PROCESSES
In the multiple response case, finding process operating conditions that simulta-
neously maximize (or minimize, as desired) all the responses is quite difficult, and
often impossible. Almost inevitably, the process engineer must make some trade-
offs in order to find process operating conditions that are satisfactory for most (and
hopefully all) the responses. Reference 4 explains what to do with multiple responses
during “Phase I” of an RSM study. This chapter focuses on Phase II optimization.
14.2.1 THE DESIRABILITY FUNCTION APPROACH

The desirability function approach is one of the most widely used methods in industry
for dealing with the optimization of multiple response processes. It is based on the

idea that the “quality” of a product or process that has multiple quality characteristics,
with one of them out of some “desired” limits, is completely unacceptable. The
method finds operating conditions x that provide the “most desirable” response values.
For each response Yi(x), a desirability function di(Yi) assigns numbers between
0 and 1 to the possible values of Yi, with di(Yi) = 1 representing a completely desirable
or ideal response value. The individual desirabilities are then combined using the
geometric mean, which gives the overall desirability D:
( ( ) ( ) ( ))
1k
D = d1 Y1 × d2 Y2 × L × dk Yk
where k denotes the number of responses. Notice that if any response i is completely
undesirable (di(Yi) = 0) then the overall desirability is zero. In practice, fitted response
models Ŷi are used in the method.
Depending on whether a particular response Yi is to be maximized, minimized,
or assigned to a target value, different desirability functions di(Yi) can be used. A
useful class of desirability functions was proposed by Derringer and Suich.7 Let Li,
Ui, and Ti be the lower, upper, and target values desired for response i, where Li ≤
Ti ≤ Ui. If a response is of the “target is best” kind, then its individual desirability
function is
0 if Yî ( x ) < Li
 s
 Yî ( x ) − Li 
 T − L  if Li ≤ Yî ( x ) ≤ Ti
()  i
di Yî =  i 
 Yi ( x ) − Ui 
 ˆ
t
 T − U  if Ti ≤ Yî ( x ) ≤ Ui
 i i 
0 if Yî ( x ) > Ui
where the exponents s and t determine how strictly the target value is desired. For
s = t = 1, the desirability function increases linearly toward Ti, for s < 1, t < 1, the
function is convex, and for s > 1, t > 1, the function is concave (see example section
below for an illustration).
If a response is to be maximized instead, the individual desirability is instead
defined as
 s
 Yˆ ( x ) − Li 
()ˆ
di Yi =  i
 Ti − Li 
 if Li ≤ Yî ( x ) ≤ Ti
1.0 if Yî ( x ) > Ti


where in this case Ti is interpreted as a large enough value for the response. Finally,
if we want to minimize a response, we could use

 s
 Yî ( x ) − Ui 
()ˆ
di Yi = 
 Ti − Ui 
 if Ti ≤ Yî ( x ) ≤ Ui
0 if Yî ( x ) > Ui

where Ti represents a small enough value for the response.

The desirability approach consists of the following steps:
1. Conduct experiments and fit response models for all k responses.

2. Define individual desirability functions for each response.
3. Maximize the overall desirability D with respect to the controllable factors.
Example. Derringer and Suich7 present the following multiple response experiment
arising in the development of a tire tread compound. The controllable factors are x1,
hydrated silica level; x2, silane coupling agent level; and x3, sulfur level. The four
responses to be optimized and their desired ranges are as follows:
PICO abrasion index, Y1 120 < Y1

200% modulus, Y2 1000 < Y2
Elongation at break, Y3 400 < Y3 < 600
Hardness, Y4 60 < Y4 < 75
The first two responses are to be maximized, and the value s = 1 was chosen for
their desirability functions. The last two responses are “target is best” with T3 = 500
and T4 = 67.5. The values s = t = 1 were chosen in both cases. The following
experiments were conducted according to a central composite design:
Run no. x1 x2 x3 Y1 Y2 Y3 Y4
1 –1.00 –1.00 –1.00 102 900 470 67.5

2 1.00 –1.00 –1.00 120 860 410 65
3 –1.00 1.00 –1.00 117 800 570 77.5
4 1.00 1.00 –1.00 198 2294 240 74.5
5 –1.00 –1.00 1.00 103 490 640 62.5
6 1.00 –1.00 1.00 132 1289 270 67
7 –1.00 1.00 1.00 132 1270 410 78
8 1.00 1.00 1.00 139 1090 380 70
9 –1.63 0.00 0.00 102 770 590 76
10 1.63 0.00 0.00 154 1690 260 70
11 0.00 –1.63 0.00 96 700 520 63
12 0.00 1.63 0.00 163 1540 380 75
13 0.00 0.00 –1.63 116 2184 520 65
14 0.00 0.00 1.63 153 1784 290 71
15 0.00 0.00 0.00 133 1300 380 70
16 0.00 0.00 0.00 133 1300 380 68.5

Run no. x1 x2 x3 Y1 Y2 Y3 Y4
17 0.00 0.00 0.00 140 1145 430 68

18 0.00 0.00 0.00 142 1090 430 68
19 0.00 0.00 0.00 145 1260 390 69
20 0.00 0.00 0.00 142 1344 390 70
Using ordinary least squares and standard diagnostics, the fitted responses were
the following:
Yˆ1 = 139.12 + 16.49 x1 + 17.88 x 2 + 2.21x3 − 4.01x12 − 3.45 x 22 − 1.57 x32
(
+ 5.12 x1 x 2 − 7.88 x1 x3 − 7.13 x 2 x3 adj. R 2 = 0.6903 ; )
Yˆ2 = 1261.13 + 268.15 x1 + 246.5 x 2 − 102.6 x3 − 83.57 x12 − 124.82 x 22
(
+ 199.2 x32 + 69.37 x1 x 2 − 104.38 x1 x3 − 94.13 x adj. R 2 = 0.4562 ; )
Yˆ3 = 68.91 − 1.41x1 + 4.32 x 2 + 0.21x3 + 1.56 x12 + 0.058 x 22 − 0.32 x32
(
− 1.62 x1 x 2 + 0.25 x1 x3 − 0.12 x 2 x3 adj. R 2 = 0.7466 . )
Note that no interactions were significant for response 3, and that the fit for response
2 is quite poor.
Optimization of D with respect to x was carried out using the Design Expert
software. Figure 14.2 shows the individual desirability functions di(Yˆ i ) for each of
the four responses. The functions are linear since the values of s and t were selected
equal to one. A dot indicates the best solution found by the Design Expert solver.
The best solution is x*′ = (–0.10, 0.15, –1.0) and results in d1(Yˆ 1 ) = 0.34 (Yˆ 1(x*) =
136.4), d2(Yˆ 2 ) = 1.0 (Yˆ 2 (x*) = 1571.1), d3(Yˆ 3 ) = 0.49 (Yˆ 3(x*) = 450.46) and d4(Yˆ 4 ) =
0.76 ( Yˆ 4 (x*) = 69.26). The overall desirability for this solution is 0.596. All
responses are predicted to be within the desired limits.
Figure 14.3 shows a 3-D plot of the overall desirability function D(x) for the
x2 – x3 plane when x1 is fixed at –0.10. The function D(x) is quite “flat” in the vicinity
of the optimal solution, indicating that small variations around x* are not predicted
to change the overall desirability drastically. However, it is quite important to perform
confirmatory runs at the estimated optimal operating conditions. This is particularly
true in this example given the poor fit of the response models (e.g., Ŷ2).
14.2.2 MATHEMATICAL PROGRAMMING APPROACH

The analysis of multiple response systems usually involves some type of optimization
problem. When one response can be chosen as the “primary,” or most important,
response, and bounds or targets can be defined on all other responses, a mathematical
programming approach can be taken. If this is not possible, the desirability approach
should be used instead.

-1.00 1.00 -1.00 1.00
hydrated silica level = -0.57 silane coupling agent = 0.11
170
120
-1.00 1.00 96 198
sulfur level = 1.00 PICO abrasion index = 134.369
1300 500
1000 400 600
490 2294 240 640
200% modulus = 1249.51 Elongation at break = 443.221
67.5
60 75
62.5 78
Hardness = 70.4975
FIGURE 14.2
In the mathematical programming approach the primary response is maximized

or minimized, as desired, subject to appropriate constraints on all other responses. The
case of two responses (“dual” responses) has been studied in more detail by some
authors and is presented first. Then, the case of more than two responses is illustrated.
14.2.2.1 Dual Response Systems
The optimization of dual response systems (DRS) consists of finding operating

conditions x that
optimize Yˆp ( x )
subject to: Yˆs ( x ) = T
x ′x ≤ ρ2
where T is the target value for the secondary response and ρ is the radius of a
spherical constraint that limits the region in the controllable factor space where the
search should be undertaken. The value of ρ should be chosen with the purpose of
avoiding solutions that extrapolate too far outside of the region where the experimental

Actual factors:
X=hydrated silica level

0.996
Y= silane coupling
agent
0.447
Actual constants:
.0298
sulfur level = -1.00
0.149
0.000
Desirability
1.0
1.0
0.0
silane coupling agent 0.0 hydrated sylica level
-1.0 -1.0
FIGURE 14.3
data were obtained. For example, if the experimental design is a central composite
design, choosing ρ = α (axial distance) is a logical choice. Bounds of the form L ≤
xi ≤ U can be used instead if a cuboidal experimental region was used (e.g., when
using a factorial experiment).
In a DRS, the response models Ŷp and Ŷs can be linear, quadratic, or even cubic
polynomials. A nonlinear programming algorithm has to be used for the optimization
of a DRS. For the particular case of quadratic responses, an equality constraint for the
secondary response, and a spherical region of experimentation, specialized optimiza-
tion algorithms exist that guarantee global optimal solutions. In such case, the algo-
rithm DRSALG6 can be used (download from http://www.stat.cmu.edu/jqt/29-3), but
a Fortran compiler is necessary.
In the more general case of inequality constraints or a cuboidal region of
experimentation, a general purpose nonlinear solver must be used and several points
should be tried to avoid local optima. This is illustrated in the next section.
14.2.2.2 More Than Two Responses

Example. Three components (x1, x2, x3) of a propellant need to be selected to
maximize a primary response burning rate (Y1) subject to satisfactory levels of two
secondary responses, namely, the variance of the burning rate (Y2) and the cost (Y3).
The three components must add up to 100% of the mixture. The fitted models were

Yˆ1 = 35.4 x1 + 42.77 x 2 + 70.36 x3 + 16.02 x1 x 2 + 36.33 x1 x3 + 136.8 x 2 x3
+ 854.9 x1 x 2 x3
Yˆ2 = 3.88 x1 + 9.03 x 2 + 13.63 x3 = 0.1904 x1 x 2 − 16.61x1 x3 − 27.67 x 2 x3
Yˆ3 = 23.13 x1 + 19.73 x 2 + 14.73 x3
The optimization problem is therefore
maximize Yˆ1 ( x )
subject to Yˆ2 ( x ) ≤ 4.5
Yˆ3 ( x ) ≤ 20
x1 + x 2 + x3 = 1.0
0 ≤ x1 ≤ 1
0 ≤ x2 ≤ 1
0 ≤ x3 ≤ 1
We can use Microsoft Excel’s “solver” to solve this problem. The table below
shows an Excel spreadsheet that has been set up with the problem above. Cells
B1:B3 contain the decision variables (cells to be changed), cell E1 is to be maxi-
mized, and all the constraints need to be entered appropriately. The figure shows
the spreadsheet after the solver completes the optimization. The solution is x*′ =
(0.212, 0.343, 0.443), which provides Ŷ1 = 106.62, Ŷ2 = 4.17, and Ŷ3 = 18.23.
Therefore, both secondary responses meet the desired bounds. The solver should be
run from a variety of starting points (i.e., try different initial values in cells B1:B3
prior to starting the solver) to avoid local optima. Once again, confirmation exper-
iments should be conducted at the estimated optimal operating conditions.
A B C D E
1 Factors Responses
2 x1 0.21233 Y1(x) 106.6217
3 x2 0.343725 Y2(x) 4.176743
4 x3 0.443946 Y3(x) 18.23221
5 Additional constraint
6 x1 + x2 + x3 1.000001

REFERENCES
1. Box, G.E.P. and Draper, N.R. (1987) Empirical Model Building and Response Sur-
faces, John Wiley & Sons, New York.
2. Box, G.E.P. and Hunter, J.S. (1954) “A Confidence Region for the Solution of a Set
of Simultaneous Equations with an Application to Experimental Design,” Biometrika
41, 190-199.
3. Box, G.E.P. and Wilson, K.B. (1951) “On the Experimental Attainment of Optimum
Conditions,” Journal of the Royal Statistical Society, Series B, 13, 1-45.
4. Del Castillo, E. (1996) “Multiresponse Optimization via Constrained Confidence
Regions,” Journal of Quality Technology, 28, 1, 61-70.
5. Del Castillo, E. and Yeh, J.Y. (1998) “An Adaptive Run-to-Run Optimizing Controller
for Linear and Nonlinear Semiconductor Processes,” IEEE Transactions on Semicon-
ductor Manufacturing, 11, 2, 285-295.
6. Del Castillo, E., Fan, S.K., and Semple, J. (1997) “The Computation of Global Optima
in Dual Response Systems,” Journal of Quality Technology, 29, 3, 347-353.
7. Derringer, G. and Suich, R. (1980) “Simultaneous Optimization of Several Response
Variables,” Journal of Quality Technology, 12, 4, 214-219.
8. Draper, N.R. (1963) “Ridge Analysis of Response Surfaces,” Technometrics, 5, 469-479.
9. Hoerl, A.E. (1959) “Optimum Solution of Many Variables Equations,” Chemical
Engineering Progress, 55, 67-78.
10. Hoerl, A.E. (1964) “Ridge Analysis,” Chemical Engineering Symposium Series, 60,
67-77.
11. Khuri, A.I. and Cornell, J.A. (1987) Response Surfaces, Marcel Dekker, New York.
12. Myers, R.H. and Montgomery, D.C. (1995) Response Surface Methodology: Process
and Product Optimization Using Designed Experiments, John Wiley & Sons, New
York.

Part 5
Case Studies
In Parts 1 through 4 of this book the set of tools necessary to develop, deploy, and
customize R2R control solutions has been presented. Specifically, foundational ele-
ments have been presented in Part 1, algorithms in Part 2, integration-enabling
mechanisms in Part 3, and customization methodologies and strategies in Part 4. In
Part 5 we illustrate the application of R2R control tools with control solution
deployment case studies. Note that, while case studies of application of R2R control
solutions have also been presented in earlier chapters (notably Chapters 1 and Chapter
11), they have generally been presented to highlight one aspect of the R2R control
tool set (e.g., the integration technology in Chapter 11). Here, we focus on the
deployment efforts themselves.
Specifically, in Chapter 15 the development of an R2R control solution for a
CMP (chemical mechanical planarization) process is described. In this application
the CMP control solution is developed as the first component of a multistep control
solution in a (frequently occurring) CVD*–CMP–Lithography–Etch sequence. The
major challenge that must be addressed in this application is the modeling and control
of CMP uniformity so as to improve line yield. An innovative approach is described
whereby the uniformity target is adjusted to a nonzero value to focus on yield loss
due to outer “lip” radial nonuniformity, and to “precompensate” for anticipated
downstream etch nonuniformity. This chapter provides insight into the R2R control
solution development and customization process, as well as the Genetic Cell Con-
troller (GCC) R2R control solution integration methodology.
In Chapters 16 and 17 focus is placed on customization of EWMA R2R control
algorithms as a step in the development and deployment process. The EWMA
algorithms, which are discussed in detail in Chapters 1 through 3, are used extensively
* Chemical vapor deposition.

in R2R control. There is, however, a well-recognized need to extend EWMA con-
trollers to address the following two problems: (1) how to choose the EWMA weight
parameters and (2) how to modify the basic EWMA algorithms to account for
unequal times between measurements (i.e., when the sampling period is not always
one run).
The two case studies presented in Chapters 16 and 17 address the two problems
above, respectively, and give a practical demonstration of applying the resulting
techniques in two different process control environments. In Chapter 16 adaptive
control techniques are presented for selecting the tuning parameter of single EWMA
controllers. The resulting adaptive EWMA controller is applied to align a stepper
photolithography tool. The relevance of the alignment problem is carefully detailed,
and two adaptive EWMA controllers are presented. The EWMA controllers are
equipped with special filters that allow the user to obtain the desired performance.
The adaptation mechanism is protected from “bad” measurements by the application
of a spike filter, namely a filter similar to an SPC chart filter.
In Chapter 17 a modification is made to the predictor–corrector double EWMA
controller (see Chapters 2 and 3) to allow the controller to handle metrology obser-
vations obtained at unequally spaced points in time. The resulting “age-based”
controller has the theoretical advantage of being easier to analyze, which produces
the practical advantage of being simpler to tune. An application of the aged-based
EWMA controller to a CMP process is documented in detail. The performance of
the proposed controller is compared, using simulated CMP processes, with that of
the standard predictor–corrector EWMA algorithm.

15 Multizone Uniformity
Control of a CMP Process
Utilizing a Pre- and
Postmeasurement
Strategy
James Moyne, Chadi El Chemali, Kareemullah
Khan, Rock Nadeau, Paul Smith, John Colt,
Jonathan Chapple-Sokol, and Tarun Parikh
15.1 INTRODUCTION
As wafer sizes increase to 300 mm, manufacturers must maintain process capability
and yield and reduce nonproduct wafer (NPW) usage.1 Equipment and process design
improvements were invoked in the past to address these issues. However, it has
become clear that, as noted throughout this book, advanced process control (APC)
has become a critical component of the solution for the future, with R2R control the
most widely pursued form of APC in the semiconductor manufacturing industry.2–4
One process that has repeatedly been shown to benefit from R2R control is chemical
mechanical planarization (CMP). The CMP process is described in the Introduction
to this book, and CMP R2R control solutions are described in Chapter 11. In the
move to 300-mm manufacturing, uniformity control (in conjunction with thickness
control) will be a necessary component of R2R control solutions.2,5
The aim of this chapter is to detail the latest advancements in CMP process
uniformity modeling and R2R control, and also to illustrate the methodology of
developing, deploying, and evaluating an R2R control solution for a semiconductor
process. To achieve these goals, the development and deployment of a multizone
approach to the modeling and control of CMP uniformity is presented in the remainder
of this chapter. The final control solution utilizes both pre- and postprocess metrology
data and provides uniformity control to a multizone optimization metric as part of a
multiprocess control solution. Specifically, following this introduction, background
information is presented in Section 15.2 on a multiprocess control framework that is
being implemented to provide yield improvement of a contact process. This includes
a specific description of the multiprocess control strategy, the CMP process environ-
ment, and the R2R control-enabling technology being utilized. The multizone CMP
process uniformity modeling approach is then presented in Section 15.3 along with

a description of the final uniformity control solution developed. This is followed, in
Section 15.4, with a presentation of results of applying the final uniformity control
solution. Issues associated with the inclusion of the control solution as part of a total
factory solution are then presented in Section 15.5. This chapter concludes with a
summary of the results presented and a discussion of potential future work to extend
the control scheme to include CVD and lithography processes.
15.2 BACKGROUND
15.2.1 CMP Process Uniformity Control
The first CMP R2R uniformity control of CMP was reported on a Strasbaugh CMP
tool and presented in Chapter 11.6 That work shows that significant improvements in
process capability can be achieved through multivariate (thickness and uniformity)
control of a CMP oxide process. Recently, uniformity control reported on other CMP
tool types further illustrated this advantage.7 In all cases the uniformity control focus
has been on radial uniformity with a center-to-edge (CTE) metric utilized to quantify
the radial uniformity. Closer analysis of post-CMP process nonuniformity, however,
reveals significant higher-order radial nonuniformity components such as center “dim-
ple” and outer “doughnut” regions. These and other nonradial nonuniformity charac-
teristics, such as across-wafer gradient nonuniformity, are due in part to upstream
chemical vapor deposition (CVD) processing. Understanding and modeling these
nonuniformity characteristics is a key component to developing an improved unifor-
mity control solution for CMP. Providing for detection and weighted control of these
higher-order nonuniformity characteristics is especially important when developing an
R2R control solution as part of a total factory control strategy and solution.
15.2.2 Processing and Control Environment
The CMP uniformity modeling and control work described in this chapter is part of
a multiprocess control solution being developed to improve yield of a contact process
at the IBM Microelectronics facility in Burlington, Vermont.8,9 The target contact
process line has a typical CVD, CMP, lithography, etch (RIE) sequence. The control
solution is being developed in a number of phases, with the first phase focused CMP
and RIE R2R process control. The initial envisioned control scheme for (Phase I)
measurement and control is illustrated in Figure 15.1. Note that, with this scheme,
R2R control solutions are envisioned for both CMP and etch processes, with pre-
and postprocess measurement utilized along with interprocess feedforward and feed-
back information flow between the two control solutions. For both control solutions,
the process quality metrics being controlled are postprocess thickness and uniformity,
with these metrics indirectly verified at the postetch step through electrical testing.
In developing this multiprocess control scheme, preliminary results have shown
that, while repeatable results on etch process uniformity were observed, satisfactory
models for controlling etch uniformity could not be obtained (through design of
experiments analysis). Specifically, the analysis did not yield a discernable relation-
ship between process uniformity and total power and power ratio of a split coil
reactor. Thus, the control scheme was modified with the RIE process, R2R, and

FIGURE 15.1 Envisioned multiprocess control scheme.
feedforward to RIE control components eliminated. The resulting interprocess con-

trol solution operates in the following manner:
1. Etch process uniformity is determined at infrequent intervals through pre-

and postmeasurement analysis at the etch process.
2. An etch process nonuniformity metric is determined and fed back to the
CMP R2R controller.
3. The CMP R2R controller utilizes pre- and postprocess metrology and pro-
vides for control of rate variation of CMP removal and radial nonuniformity.
4. The CMP R2R control targets are adjusted to precompensate for the etch
process nonuniformity and maximize postetch process yield.
The CMP R2R controller does not necessarily optimize the CMP process, but rather
operates as part of a total factory solution to provide the best CMP process for that
process line.
15.2.3 Control Enabling Solution
The main objective of this project is to improve process yield through reusable
factory-wide integrated control solutions. In order to achieve this objective, the R2R
control solution had to meet a number of integration requirements:
Requirement #1: The solution must be generic, i.e., it can be reconfigured to

control the various processes on the line. In the first phase of the project,
the solution is targeted at CMP and etch processes, but should be sufficiently
generic to also be applicable to CVD and lithography processes in future
phases of the project.
Requirement #2: The solution has to be able to utilize not only postprocess
metrology, but also preprocess metrology and upstream process information
from (potentially) multiple sources.

Requirement #3: The solution should be capable of utilizing control algorithms
that are suited to the control of the target processes.
Requirement #4: The solution should integrate with the currently existing
facility manufacturing execution system (MES), but also provide a migra-
tion path to a future APC framework compliant solution.10
The R2R enabling technology that is being utilized for the project, called the
Generic Cell Controller (GCC), addresses these four requirements.11 (Detailed infor-
mation on the GCC concept and solutions is provided in Chapters 9 through 12.)
Specifically, with respect to requirement #1, the GCC is a flexible control solution
enabler that is fully object-oriented, process-independent, and suitable for factory-
wide distributed implementation. GCC-enabled R2R control solutions have been
demonstrated to provide control of a number of semiconductor manufacturing pro-
cesses including CMP, vapor phase epitaxy, and etch.3 With respect to requirement
#2, the GCC technology has been shown to provide fully integrated process control
solutions that utilize both post- and premetrology.5 As for requirement #3, an EWMA
linear approximation algorithm with nonlinear extensions was chosen; this algorithm
has been utilized effectively for CMP and vapor phase epitaxy process control (see
also Chapters 3 and 13).3,12 Finally, with respect to requirement #4, Figure 15.2
shows the architecture of the GCC solution when enabled for APC framework-
compatible application. Due to the distributed object-oriented nature of the technol-
ogy, it is configurable to existing MES systems, and can be migrated to (future)
APC framework systems as necessary.
The proposed GCC R2R solution integration strategy is shown in Figure 15.2.
A GCC solution is instantiated from a single class for each process to be controlled.
The class has access to upstream and downstream metrology and target information
as necessary to address interprocess control. Both client–server TCP/IP and fully
object-oriented interfaces to the GCC station are provided so that the GCC R2R
solution can operate in the current client–server integration environment, and can
migrate to a (future envisioned) APC framework compliant environment.
FIGURE 15.2 GCC architecture for APC framework integration.

Carrier (head) Slurry Feed
Wafer Slurry
Feed
Holder Carrier
Platen
Polishing Pad
Platen
(a) Side View (b) Top View
FIGURE 15.3 Chemical mechanical polish tool configuration.
15.3 CMP UNIFORMITY MODELING AND CONTROL

The target CMP tool is a Westech 372M.* A schematic of this machine is shown in
Figure 15.3. In this CMP process the wafer is affixed to a wafer carrier via backside
air and pressed face-down on a rotating platen holding a polishing pad. A slurry
with abrasive material (e.g., alkaline slurry of colloidal silica for oxide or silicon
polishing) is dripped onto the rotating platen during polish. The slurry chemically
attacks the wafer surface, converting the silicon top layer to a hydroxylated form,
which is more easily removed by the mechanical abrasive of the pad.
The control of the CMP process is difficult due to variation and degradation of
consumable parts, inconsistency of the slurry, variation in pad physical properties,
and the lack of in situ sensors. The main difficulty arises in achieving a reliable film
thickness due to change in removal rate over time and the within-wafer uniformity
of the polish. Polish rates differ at the center and edge of the wafer due to nonconstant
relative pad velocity from the edge to the center, nonuniform slurry and by-product
transport under the wafer, wafer bowing due to pressure, or machine drift in time
of any of these parameters. In practice, dummy wafers are used to condition and/or
calibrate the tool before or after each lot of wafers. The objective is therefore to use
an R2R process control to reduce or eliminate monitor wafer usage, and to maintain
the performance of the CMP processes by adjusting the removal rate and uniformity
of the film thickness. Achieving this goal requires the identification of appropriate
input parameters to the CMP process, finding suitable metrics for the process outputs
(i.e., removal rate and uniformity), and formulating the appropriate models to be
implemented in an R2R controller.8
15.3.1 CMP UNIFORMITY MODEL DERIVATION AND TESTING

Radial CMP polishers impart consistent radial nonuniformity features on a wafer.
Figure 15.4 shows a map of a typical oxide wafer after undergoing radial polishing.
* SpeedFam — IPEC Corp.

FIGURE 15.4 Wafer map of a radially-polished wafer.
Different regions can be identified with typical radial polishing, largely due to the
fact that polish rates in the center and edge of the wafer are lower than the rates in
the in-between region. The film deposition rate from the CVD process, which
generally shows a radial pattern, can be substantially different in the center of the
wafer because of its singular nature. If the rate of the deposition process in the
outside region of the wafer is faster than the mean rate, the outer edge “lip” region
will be significantly thicker following polishing because of the combined effects of
CVD and CMP. Thus, the film nonuniformity across the wafer can be broken up for
modeling.
An initial effort at modeling the CMP nonuniformity attempted to provide a level
of isolation of these features by breaking the uniformity metric up into concentric
zones, as shown in Figure 15.5. The profile in each zone is approximated to a linear
fit, and the slope of this fit is taken as uniformity metric for that particular zone.
Minimizing each of the slopes contributes to the improvement of the uniformity.
With a multizone uniformity metric defined, a 23 factorial design of experiments
(DOE) was performed to attempt to model process removal rate and uniformity. The
inputs to the process are Platen Speed, Carrier Speed, and Backside Air Pressure.
This DOE design has eight factor-level combinations, each replicated twice, and five
center points. The normalized levels used for each input are shown in Table 15.1.
The wafers were measured before and after processing; measurements were taken at
45 sites on the wafer, as shown in Figure 15.6 (6 mm at the wafer edge are excluded).
In order to develop the models for removal rate and uniformity, standard least-
squares regression techniques were applied to formulate the predictive model.13 The
analysis yielded the following model for removal rate:
RR = −15.66 + 59.68 PS + 29.57 CS − 16.99 PS CS, (1)

FIGURE 15.5 A typical postpolish profile on a wafer after CMP processing.
TABLE 15.1
Normalized DOE Input Levels
Input Low Medium High
Platen Speed (rpm) 0.7 1 1.3

Carrier Speed (rpm) 0.4 1 1.6
Backside Air (psi) 0.3 1 1.7
y
100
80
60
40
20
FIGURE 15.6 Measurement sites.
where RR is the removal rate, PS is the platen speed, and CS is the carrier speed.
The model fits with R2 = 98.7%.* The regression models for the uniformity slopes
* The R2 value is a measure of how well the model is able to predict the variation in the response.

in Zones 1 to 3 also showed good regression fit R2 but low F-ratio* and high
P-value.**
The significance of the effects are therefore subject to a high α risk. No model was
derived for Zone 4 because the F-ratios were close to 1. The lack of model in Zone 4
was unfortunate since, as noted above, control in this outer zone is critical to
improving yield. This provided motivation for adjusting the uniformity modeling
strategy, as described later in this section.
s1 = 11.46 − 9 CS − 6.64 BA + 11.64 PS CS (2)
s2 = −10.65 + 2.78 CS + 8.75 PS + 10.59 BA − 15.01 PS BA (3)
s3 = −3.05 − 21.65 PS − 31.08 CS + 21.64 PS CS + 14.89 PS BA (4)
where si is the slope at zone i, i = 1, 2, 3. The models fit with R2 = 86.5%, R2 =

90.8%, and R2 = 88.7%, respectively.
Process R2R control experiments were run at IBM to test the validity of the
models for thickness and nonuniformity. Two uniformity zones were selected to be
controlled: Zone 1 and Zone 3. Zone 2 was not selected because it was relatively
flat throughout the DOE, and there was a desire to keep the control problem over-
determined and more manageable. The linear approximation algorithm introduced
in Section 15.2 was utilized in the R2R controller. As an example, with this algorithm
applied to thickness control, the removal rate derived from the DOE analysis (Eq. 1)
is approximated to be constant. The removed thickness model used is described by
the following equation:
RmvdT [n] = RR[n] t[n] (5)
where RmvdT is Removed Thickness, t is polish time, RR is Removal Rate constant,

and n refers to current run. This model was implemented in the GCC R2R controller
with the RR constant updated at each run to compensate for drift and noise, according
to an EWMA filtering mechanism:12
RR[n] = α ( RmvdT[n − 1] t[n − 1]) + (1 − α ) RR[n − 1] (6)
where α is an EWMA weighting factor (0 ≤ α ≤ 1), the value of which is selected

based on considerations of noise, drifts, shifts, and model error.14
* F-ratio is the statistic used to evaluate whether the parameters are statistically significant. The lower
the F-ratio for a parameter, the less likely that parameter is statistically significant.
** P-value is the probability that the F-value fails the test and the model parameters are not statistically
significant. A P-value less than or equal to a chosen α risk indicates that the model parameters are
significant, where α risk is the probability of declaring that a model parameter is significant when it is not.

TABLE 15.2
Predicted and Measured Slope Values for
Zones 1 and 3
Slope 1 Slope 1 Slope 3 Slope 3
Run (meas.) (pred.) (pred.) (pred.)
1 4.20 7.4600 –4.990 –19.25

2 5.2974 0.34 1.4760 –3.26
3 4.6302 1.1974 –0.72 –2.534
4 3.8337 4.45 –11.27 –3.96
Note: meas. = measured slopes; pred. = predicted slopes.
The suggested time for the next run n is then calculated as
t[n] = (ST[n] − Target ) RR[n] , (7)
where ST is the pre-CMP film thickness of the wafer to be polished.

The results of applying model-based control to the multivariate control of thick-
ness and (multizone) uniformity revealed a good capability for thickness control,
but an inability to provide uniformity control. As an example, Table 15.2 summarizes
the model predicted vs. measured slopes in Zones 1 and 3 for four control runs.
Clearly, the model does not accurately predict the uniformity in these zones.
As a result of a subsequent analysis of the uniformity modeling problem, it was
hypothesized that the main reason for the poor modeling of the slopes is the existence
of a nonradial cross-wafer gradient, which has been traced to the upstream CVD
process. Figure 15.7 shows the film thickness profile along the x and y axes of a
wafer before and after the CMP process, respectively. The individual measurements
are plotted with error bars. The (nonradial) cross-wafer gradient at the upstream
CVD process is closely correlated with post-CMP process cross-wafer gradient. The
nonradial cross-wafer gradients invalidate the radial uniformity symmetry assump-
tion and add variability to the DOE data, thus hiding the true level of significance
of the input parameters on the slopes’ values.
A second DOE was performed to address the CMP uniformity control problem.
Prior to this DOE, maintenance was performed on the upstream CVD process and
the gradient problem was drastically reduced. Further, a simplified single radial
uniformity metric was used. Specifically, uniformity was measured as the center-to-
edge slope of the thickness profile, where the slope was determined through regres-
sion analysis. This simplified approach to uniformity modeling was taken because
it was felt that satisfactory uniformity control could still be achieved through control
to a nonzero slope that minimizes the yield loss effect due to nonuniformity in the
outer lip region (see Figure 15.12 later in this chapter). Analysis of data from the
second DOE yielded the following models for removal rate and center-to-edge radial
uniformity slope:

FIGURE 15.7 Plots along positive and negative x and y axes illustrating cross-wafer gradient
at the upstream CVD process (pre-CMP thickness) and downstream CMP process (post-CMP
thickness).
RR = 20.2 + 1.91 PS (8)
CTE = −6.550.5 PS + 0.34 CS (9)
where RR is the removal rate and CTE is center-to-edge slope.

Note that the above models are coded to utilize normalized inputs (between +1
and 1). The Removal Rate model has a high value of R2 = 90%, and the PS input
is significant with a P-value less than 0.0001. The CTE model has an R2 = 66.7%,
which is relatively low; however, the effects of Platen Speed and Carrier Speed are
more significant than in with the first DOE, with P-values of 0.0038 and 0.0105,
respectively. Therefore, the two models are statistically valid and accurate enough
to predict the removal rate and uniformity slope of the film oxide.
15.4 RESULTS: MULTIVARIATE CONTROL OF CMP

The models derived from the second DOE analysis, (8) and (9), were utilized to
configure the GCC R2R control solution containing a two-stage linear approximation
EWMA control algorithm. This controller, referred to as the GMt algorithm,12 is an
extension of the EWMA algorithm described in Chapter 3. It provides more accurate
control of systems that cannot be accurately approximated as linear functions of the
process inputs. In the CMP process, for example, the removed thickness metric is
a function of the removal rate multiplied by the process variable time, i.e., t, as

Primary Primary Secondary Secondary
Inputs Outputs Inputs Output
RR RR
PS
Primary Tt Secondary RmvdT
stage stage
CS
CTE
FIGURE 15.8 Gmt two-stage controller and its application to CMP multivariate process control.
shown in Eq. (5). We see that, in this case, the process quality parameter, amount
removed (RmvdT), cannot be approximated by a linear function of the CMP machine
parameters, PS and CS, because these parameters impact the true process variable,
i.e., the RR. The GMt algorithm is a suitable control solution in this case because
it models the relationship between the input parameters, PS and CS, and the primary
output, RR, and then models the multiplicative relationship between this primary
output and the secondary output, the RmvdT.
The GMt provides a control solution for our models by breaking the system
outputs down into two sets, namely primary output(s) and secondary inputs, as shown
in Figure 15.8. Therefore, the GMt implements a two-step linear solution process
that approximates a nonlinear solver. In the first step, the controller uses the GCC
R2R EWMA method to compensate fully for the primary outputs that do not have
corresponding secondary outputs, and to partially compensate (in a weighted fash-
ion) for those primary outputs that also have corresponding secondary outputs. The
GMt then completes the compensation on the secondary outputs by adjusting sec-
ondary inputs.
For the CMP control, the removal rate thickness model given in Eq. (8) and the
center-to-edge uniformity model given in Eq. (9) are used in the primary stage with
PS and CS as primary inputs and RR and CTE as primary outputs, as shown in
Figure 15.8. In the first stage of the controller, the GMt compensates for RR drift
and for CTE. In the second stage, a secondary input of time is adjusted to compensate
for the secondary output, the amount removed.
The results of application of this control solution at the IBM Microelectronics
facility are shown in Figures 15.9 and 15.10. In each figure the controlled output
metrics of remaining thickness and nonuniformity slope, respectively, are plotted
along with the desired target output and an estimation of the uncontrolled output.
The uncontrolled output value for each metric is estimated through applying the
difference between the current controlled recipe and the starting recipe to the process
model for the metric. Specifically, the uncontrolled thickness value is estimated as
ThicknessUncontrolled = Actualrem + ∆rem (10)
where Actualrem is the actual amount of oxide removed, i.e., the difference between
premetology measurement and postmetrology measurement of oxide thickness.

FIGURE 15.9 Illustration of CMP thickness control and actuation of the primary thickness
control input of time.
∆rem is the amount of thickness to be added or removed if no controller exists.

∆rem is given by
∆rem = ( Actual RR + ∆RR ) × (t N − t S ) (11)
where tN is the nominal time recipe and tS is the actual time recipe suggested by the
controller. ∆RR is the amount to be added or removed to the removal rate if no
controller exists. From Eq. (8), ∆RR is calculated as
∆RR = 1.01 ∆PS (12)
The uncontrolled uniformity value is estimated as
UniformityUncontrolled = ActualCTE + ∆CTE (13)
where ActualCTE is the actual amount of the slope uniformity, i.e., the difference
between premetrology measurement and postmetrology measurement of center-to-
edge-metric. ∆CTE is the amount of slope uniformity to be added or removed if no
controller exists. From Eq. (9), ∆CTE is calculated as:
∆CTE = 0.34 ∆CS − 0.5 ∆PS (14)

FIGURE 15.10 Illustration of radial uniformity control and actuation of the uniformity con-
trol inputs of Platen Speed (Pspeed) and Carrier Speed (Cspeed).
where ∆CS is the difference between the controlled and nominal carrier speed recipe
and ∆PS is the difference between the controlled and nominal platen speed recipe.
The results presented in Figures 15.9 and 15.10 indicate the multivariate control
of both thickness and uniformity. This is further illustrated by comparing the post-
process wafer map of the final control experiment, Figure 15.11, with that of a typical
uncontrolled process run (Figure 15.4).
15.5 ISSUES: A CMP CONTROL SOLUTION AS PART

OF A TOTAL FACTORY CONTROL SOLUTION
To date, run-to-run control research has been focused for the most part on the control
of single processes. A key goal of the control development effort presented in this
chapter, however, is that the control solution be part of a total factory control solution.
While this goal imparts requirements of configurability, reusability, etc., on the
control solution enabler (as presented in Section 15.2), it also raises other issues
with respect to design of the factory control solution. A discussion of the more
prominent issues is provided in this section.
15.5.1 CMP UNIFORMITY CONTROL FOR YIELD MAXIMIZATION

As shown in Section 15.2, CMP radial process nonuniformity is characterized by a
number of zonal features. The efforts in CMP uniformity control to date have been

FIGURE 15.11 Postprocess wafer map of last control experiment presented in Figure 15.10.
focused on minimizing a single CTE metric.6,7 While this approach has been shown
to provide increased process capability, the effort described in this chapter has been
focused on establishing a relationship between nonuniformity targets and yield, and
configuring the CMP controller to those targets. Of the four uniformity zones
described in Section 15.3 and illustrated in Figure 15.5, IBM researchers have qual-
itatively determined that nonuniformity in the outer lip region is the largest source
of yield loss. Thus, in providing a uniformity control solution, the target must be
weighted to the minimization of nonuniformity due to this outer lip region. Consid-
ering that the uniformity control solution developed is limited to controlling one
uniformity parameter, namely the slope of radial nonuniformity, it is this target that
must be adjusted. Luckily, the outer lip region is characterized consistently by an
upward sloping profile; thus, the impact of this region on the entire process can be
minimized by targeting a slightly downward sloping radial uniformity gradient as
shown in Figure 15.12.
15.5.2 CMP UNIFORMITY CONTROL FOR PRECOMPENSATION

OF ETCH NONUNIFORMITY
Establishing controller performance metrics at the factory level rather than the
process-centric level impacts the formulation of the control solution. Specifically,
by attending to overall yield, particular control solutions at a process may be con-
figured to control “nonoptimal” process-centric targets so that they may provide
“precompensation” for downstream processes. This precompensation method from
CMP to etch is illustrated graphically in Figure 15.13. The etch process does not
have a developed R2R control capability. However, through pre- and postetch metrol-
ogy, the etch process uniformity is characterized. This information is fed back to the
CMP process and the CMP R2R process control targets are adjusted to precompensate

FIGURE 15.12 CMP uniformity targeting for yield maximization.
FIGURE 15.13 Applying precompensation at CMP for postetch uniformity.
for etch nonuniformity. In the current control solution described in this chapter, the
precompensation feedback is static, i.e., the CMP R2R controller targets are adjusted
manually as necessary to provide precompensation. Further, the precompensation
assumes that a specific etch tool is chosen for wafers processed on a particular CMP
tool. Providing a dynamic configurable precompensation capability, and addressing
precompensation as a component of chamber matching with banks of tools, are
topics of future work (see Section 15.6).
15.5.3 CMP UNIFORMITY ANALYSIS FOR CVD GRADIENT

NONUNIFORMITY LIMITS MONITORING
Analysis of the first CMP process DOE (see Section 15.3) revealed that the pre-
CMP process nonuniformity contains two distinct components: (1) a radial nonuni-
formity component, and (2) an across-wafer gradient component. While straightfor-
ward techniques can be used in many cases to deconvolute these two components,
the choice of metrology strategy in the first DOE (see Figure 15.6) and lack of

knowledge of wafer alignment resulted in insufficient data to carry out the decon-
volution. This issue was addressed in the second DOE with a focus on minimizing
across wafer nonuniformity at CVD, and a new pre-CMP metrology measurement
pattern to better detect the axis of across-wafer nonuniformity. However, the results
of the DOE experiments also revealed another use for pre-CMP measurement,
namely control and/or limits monitoring of uniformity imparted at the upstream
CVD process. Specifically, across-wafer gradient nonuniformity at CVD is largely
due to nonuniform spacing between the reactant source (a showerhead) and the
wafer. The factors affecting this type of nonuniformity cannot be “tuned” on an R2R
control base. However, the equipment can be taken off line and the problem can be
mechanically corrected. Therefore, while pre-CMP measurements of gradient non-
uniformity cannot be used as feedback for a CVD R2R control solution, they can
be used in a limits-monitoring capacity to initiate process maintenance activities at
the CVD.
Radial nonuniformity at CVD is due to a number of factors, including the
distance between the deposition source and the wafer. It is hypothesized that this
type of nonuniformity is controllable to a degree, and thus pre-CMP radial nonuni-
formity data could be utilized as part of a CVD radial uniformity R2R control
scheme. Development of such an R2R controller is being considered as a future
effort in this project (see Section 15.6).
15.6 CONCLUSIONS AND FUTURE WORK

In this chapter we have presented a multizone approach to the modeling and control
of CMP radial nonuniformity. The work focuses on CMP control as part of a total
factory control solution rather than a process-centric solution. While the analysis
does not reveal a capability for control of the individual radial zones, it does provide
data for the development of uniformity metrics and control solutions that are tied
to maximization of yield in the process line rather than minimization of nonunifor-
mity at the CMP process. The solution has been applied to a Contact process at
IBM’s Microelectronics facility. This solution is configurable and process-indepen-
dent, is capable of accommodating pre- and postmetrology information, and is
designed to be utilized as an integral part of a total factory (interprocess and
multiprocess) control solution. The results of application of the CMP controller
indicate a capability for simultaneous control of both CMP process thickness and
uniformity. The results also indicate that (1) the CMP nonuniformity target for the
controller should be set to a nonzero value to compensate for weighting of the outer
lip area, which is a major contributor to yield loss; (2) in order to maximize line
yield, the CMP nonuniformity target should also be adjusted to precompensate for
radial nonuniformity characterized at the downstream etch process; and (3) with the
appropriate measurement scheme in place, CMP pre- or postmetrology could be
utilized to determine contributions to radial and gradient nonuniformity from the
upstream CVD process. This information could be fed back to the CVD process as
part of a process maintenance system and R2R control scheme for CVD.
Future efforts should be focused on further development of the total factory
control solution. CVD process maintenance alarming and R2R process control

elements could be used to reduce yield loss due to CVD misprocessing, and to
provide a more consistent uniformity profile for CMP processing. Further, depending
on the level of controllability of CVD radial process uniformity, CVD R2R control
could be used as a radial uniformity precompensation tool for both CMP and etch.
Other efforts should be focused on continuing to provide generic and configurable
control solution enablers. Specifically, it is proposed that the current GCC generic
R2R process control solution enabler (which currently supports pre- and postme-
trology input) be enhanced to provide dynamic adjustment to the control process
due to any number of upstream advices, and any number of downstream precom-
pensation requests. Development of such an enabler would provide an avenue for
rapid implementation, configuration, and test of multiprocess, factory-wide control
schemes.
ACKNOWLEDGMENT
Portions reprinted with permission from the proceedings of the 46th International
Symposium of the American Vacuum Society.15 The authors would like to thank
Victor Solakhian of the University of Michigan for controller software development,
Jason Silbergleit of IBM Microelectronics for RIE process support, and John Taylor
of Compugenesis for providing a GCC-to-CMP tool SECS interface solution.
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Journal of the American Vacuum Society (accepted December 1999).

16 Control of
Photolithography
Alignment
Nital S. Patel and Robert A. Soper
16.1 INTRODUCTION
A modern semiconductor device exists in three dimensions; throughout the course
of its manufacture, a chip experiences the patterning of approximately two dozen
different layers, each of which must be precisely positioned with respect to the one
beneath.1 This positioning (or alignment) is necessary in order to ensure the correct
operation of the final device. Sufficiently large alignment errors can result in many
different types of failures; the exact nature depends on the specific levels involved.
As an example, if the misalignment of the contact layer to the implanted substrate
(the well) is too great, shorts or diode leakage can result (see Figure 16.1).
The rapid pace of advancement in consumer electronics has been driven in large
part by the rapid increase in computing power available from computer chips of
ever-decreasing size. These two driving forces have required that computer chips
become both more complex and more compact simultaneously. Together, such
demands place stringent requirements on alignment accuracy.
Until very recently, alignment requirements could be met using statistical process
control (SPC) techniques, wherein the alignment input settings were held more or
less fixed, and the sources of alignment variation were identified and removed.*
Unfortunately, as alignment requirements have become tighter and the known
sources of variation have been removed, the quality of alignment control afforded
by SPC has ceased to be sufficient. SPC is particularly unsuited to the task of
controlling alignment in the face of unexplained disturbances because of its inability
to take corrective action. Combating disturbances has become a significant drain on
the photolithography process engineers who are responsible for alignment. The
engineers, in effect, are the controllers in informal feedback loops around the align-
ment process.
A need is thus identified to provide automated control of the alignment process.
This chapter describes a methodology for run-to-run control of photolithography
alignment. By replacing the engineers in these feedback loops with run-to-run
controllers, a number of benefits can be realized. First and foremost, the engineers’
* SPC techniques were introduced in Chapter 1.

Source Drain Gate Isolation Corrast
FIGURE 16.1 Cross-sectional view of a MOS transistor illustrating perfect contact-to-well

alignment (a), contact shorting to gate (b), and contact impinging on isolation (c).
time is freed to pursue more important activities. Alignment is essentially a non-

value-added process, and the less effort expended on it, the better. In some cases
the quality of the alignment can be improved by continual corrective action. A
collateral benefit is uniformity of control action. When faced with an alignment
failure, individual engineers will use their own personal experience as a guide in
determining the type and magnitude of the correction to make. As the levels of
experience of process engineers vary widely within a company, even within a single
process engineering group, the style of alignment correction will vary correspond-
ingly. With a run-to-run controller in place, all corrections are completely predictable
and repeatable. This predictability also makes the manufacturing process for a device
more transferable from one facility to another.
This chapter is structured as follows. In the remainder of this introduction
section, the alignment process is introduced, including discussions of misalignment
measurement and compensation, and sources of measurement error. This is followed
in Section 16.2 by a detailed discussion of the metrology technique, and in
Section 16.3 by a presentation of the R2R control solution. This chapter concludes
with a brief summary and some final thoughts.
16.1.1 ALIGNMENT PROCESS

Before actually exposing the photoresist on a pattern level that requires alignment,
the stepper takes a series of actions intended to provide accurate alignment — in
effect, performing internal feedforward control. There are three separate actions:
measuring existing misalignment in the layer to which the current layer is being
aligned, modeling the raw misalignment data to determine the optimum corrections
to make to match the current layer as closely as possible to the existing layer, and
applying alignment corrections during exposure.
16.1.2 MISALIGNMENT MEASUREMENT

Alignment quality is generally defined in a relative sense; i.e., the alignment of one
layer to the next is expressed as the difference between their positions. The stepper
is the only piece of photolithography equipment that uses an absolute coordinate
system and is therefore able to measure the misalignment of a single layer without
another layer to use as a reference. This capability (provided by the extremely
accurate interferometer-controlled stepper stage) is used to good effect in controlling
alignment.

+ +
+ + + +
+ +
+ + + +
+ +
+ + + +
+ +
+ + + +
FIGURE 16.2 Example of alignment mark locations read by the stepper.
Each pattern level to which another level is to be aligned contains a set of

structures that the stepper uses to determine absolute position. Several (typically one
to four) of these structures are measured in each of a number of fields (approximately
six to ten) around the wafer (Figure 16.2). These measured locations are compared
to the desired locations defined by the device layout. The differences between the
actual and desired locations are recorded as raw X and Y alignment errors.
16.1.3 STEPPER COMPENSATION

Once measured, the alignment errors are modeled by a set of linear stage- and wafer-
level parameters.2 These model parameters correspond to the stepper input variables
that can be manipulated to control the ultimate layer-to-layer alignment.
After measuring the incoming wafer alignment errors and modeling them into
correctable components, the stepper combines the calculated optimum input values
with any offsets specified by the user to arrive at the final input settings. These
settings are then used in exposing the current wafer. The process of alignment
measurement, modeling, and compensation is repeated for each wafer independently.
A run-to-run controller would interact with the stepper by determining the values
of these user-specified offsets. Typically, they would be sent to the stepper automat-
ically through some sort of network connection, but they could also be entered
manually.
16.1.4 PROCESS BIASES

In theory, the feedforward action afforded by measuring the inherent alignment errors
on the wafers before exposure should result in perfect alignment; however, this is
not the case for several reasons. The stepper’s alignment measurement system relies
on optical technology (broad- or narrow-band visible light); the alignment mark is
covered by, and is itself made up of, optically transparent materials that have a
thickness on the order of the illuminating wavelength. As a result, diffraction and
interference phenomena can bias the alignment readings. In addition, the stepper’s

alignment metrology system is subject to changes in behavior over time due to
mechanical wear, miscalibration, maintenance, etc. Finally, the input settings are
defined relative to arbitrary baselines, which can be changed in order to optimize
other aspects of stepper operation.
16.2 ALIGNMENT METROLOGY

16.2.1 METROLOGY TECHNIQUE
Measuring the alignment of one layer to another after patterning is accomplished
with a separate piece of equipment that reads a composite mark containing two
elements, one patterned in each layer. A typical mark comprises two nested boxes —
the outer box is etched in the substrate and the smaller, inner box is patterned in
photoresist at the current step.
Multiple copies of these box-in-box structures are printed in each stepper field;
a common arrangement is to have a box-in-box structure in each corner of the field,
with a number of fields measured around the wafer. The choice of number of fields
(and number of wafers per lot) to measure is driven by many, sometimes competing,
factors, e.g., desired throughput, measurement noise, desired precision, etc.
An alignment metrology tool uses pattern recognition techniques to locate the
edges of each box and calculate the amount by which the inner box is off center
with respect to the outer box, in both the X and Y directions.
The alignment metrology tool fits the same alignment model that was used
previously in the stepper to the raw misalignment data. The values of the modeled
parameters (averaged across the wafers measured) are the process measurements
that are sent to the run-to-run controller for feedback to the stepper.
16.2.2 SOURCES OF ERROR

As in the stepper, final alignment measurement is also optical and, therefore, sensitive
to variation in material properties such as refractive index and thickness. Since the
technique depends on detecting the edges of the box-in-box structure, it is also
influenced strongly by edge contrast, roughness, etc., which can be changed by
process variations in other areas. It is not uncommon for metal pattern levels to
cause measurement difficulties; the grainy substrate scatters light, confusing the edge
detection algorithm, and the etched outer boxes are frequently deformed (refer to
Figure 16.3). The run-to-run control system must be designed with these challenges
in mind, and must be able to reject “fliers” that do not represent the true state of
the process. This is a nontrivial requirement that plays a significant role in deter-
mining the ultimate utility of the controller in a real manufacturing environment.
16.3 CONTROLLER DESIGN

The previous sections presented the principles by which the stepper and alignment
metrology tools operate. In this section, the impact of these on controller design is
first considered. Having done so, two designs are presented that are currently being

FIGURE 16.3 Distorted (left) and normal (right) box-in-box alignment metrology structures.
employed in multiple fabs within Texas Instruments (TI). The first is based on
integral (EWMA-based) control, and the second design adds additional filtering to
better trade off noise attenuation and response times. The effect of stepper lens
distortion, and varying die sizes, is seen in the appearance of device dependencies.
Specifically, it is observed that certain devices exhibit different markshift behavior
from others. At present, these dependencies are relatively small (<20%) compared
to the specs, and given the need to make the system manufacturing-friendly, such
dependencies are ignored. Note that trying to weed out and correct for such depen-
dencies, especially in an environment where multiple new devices are introduced
each week, is both cumbersome and results in large data sets. The latter results in
software performance issues that impact lot login and logout times (cycle times) in
the fab. However, such device dependencies do impact the noise characteristics seen
by the controller. This noise is now driven by product mix. In addition, there are
metrology issues dealing with recipe maintenance and spikes (e.g., due to the
metrology structures being affected by other processes). An incorrectly written recipe
will cause a device to fall out, and the recipe will be corrected. However, multiple
lots of such a device could have run prior to the recipe error being detected. This
results in a temporary increase in noise magnitude. Figure 16.4 shows the effect of
device dependencies on process noise. At the same time, a stepper could run any
one of a multitude of pattern levels. These different levels see different drift rates
by virtue of nonuniform sampling. For example, a level that has multiple runs a day
would generally require less aggressive correction than one that has a run every
other day. Also, the same pattern level could exhibit different noise characteristics
across different steppers (Figure 16.5).
Given the fact that there could be thousands of overlay loops (one for each
variable, per pattern level, per stepper), it is virtually impossible to manually reopti-
mize these controllers in order to cope with such variations in noise and disturbance
characteristics. Instead, adaptive controllers are employed to effectively deal with this
problem (as well as fan-out). The designs presented will focus primarily on the loop
for x-markshift. Control loop design for the other variables is done similarly. The
design of the controllers is based on the algorithm presented in Reference 3. This
reference also provides an example of applying the algorithm developed for controlling

Device A
Device B
X-Markshift
11
1
3
5
7
9
13
15
17
19
21
23
25
27
29
Run No.
FIGURE 16.4 Example of device dependencies resulting in perceived process noise.
overlay. Here, a simplified version of the tuning algorithm is presented. This sim-
plification is made noting that the typical disturbance encountered in overlay control
is that of a shift vs. drift (especially after stepper maintenance). Most of the sophis-
tication required for the algorithm in Reference 3 was due to the need to optimally
deal with drifts. In case of shifts, the scheme can be simplified considerably by
noting that the asymptotically optimal value of the controller gain is 0. The markshift
loop can be modeled as follows:
yk +1 = θ uk + dk + wk , k = 0, 1, 2, … (1)
where yk+1 is the offset measured at metrology, uk is the offset input to the stepper,
dk is the disturbance that the controller is required to compensate for, wk is (high-
frequency) noise, and θ ≈ 1 is the stepper gain. An EWMA-based controller is
considered first. The results are then extended to second-order controllers due to
their ability to provide better noise attenuation while preserving the response times.
16.3.1 THE EWMA CASE

For the EWMA case, the controller is given by
( )
xk +1 = xk − λ k yk +2− τk − uk − τk + xk , x0 x , k = 0, 1, 2, …
(2)
1 
uk = y ⋅ round xk 
γ 
where τk ≥ 0 is the (variable) delay to metrology, γ is the precision of the stepper

input, xk ∈ is the controller state, and λk is the controller gain. The value of λk is
determined by the following recursion:
(
µ k +1 = µ k + ε yk +1− τk + uk − µ k ) (3)

X-Markshift Magnification
x-Mark
Mag
A
106
106
1
8
15
22
29
36
43
50
57
64
71
78
85
92
99
15
22
29
36
43
50
57
64
71
78
85
92
99
Run No. Run No.
x-Mark
Mag
106
106
8
1
15
22
29
36
43
50
57
64
71
78
85
92
99
15
22
29
36
43
50
57
64
71
78
85
92
99
Run No. Run No.
FIGURE 16.5 Example of interstepper differences. The same pattern level exhibits different noise characteristics on
steppers A and B.
(
ξ k +1 = ξ k + ε yk +1− τk − uk − τk _ uk ) − ε  , µ
2
2
≤ ξ0
 k 0
δ 2 + 2µ 2k
λk = λ , k = 0, 1, 2, …
δ + µ 2k + ξ k
–
with 1 > ε, δ > 0 with ε, δ ≈ 0 and 0 < λ ≤ 2. Equations (2) and (3) have been
written in a form that essentially takes the delay out of the loop,4 and minimizes its
impact on stability. Equation (3) is similar to the one derived in Reference –
3, except
that– in this case the value of λk is forced to lie in the open interval (0, λ). The value
of λ is chosen to satisfy gain margin requirements in order to ensure closed-loop
stability. In addition to this, a spike filter is employed to prevent the controller (2)
from updating on data from maverick lots. This filter works by looking at the
measurements from consecutive lots and allows the controller state xk to update only
if this difference is less than some given value. One way to implement this is as
follows (4), where the controller Eq. (2) is modified with the addition of an extra
~
state ( x k ) to reject spikes having a magnitude greater than ∆ > 0.
 
(
xk +1 = xk − λ k yk +1− τk − uk − τk + xk ⋅ round
∆
)
 ∆ + abs yk +1− τ − x˜ k ( )


 k 
x˜ k +1 = yk +1− τk (4)
1 
uk = γ ⋅ round xk  .
γ 
Figure 16.6 shows an example of an EWMA-based x-markshift controller for a

mix-and-match (previous layer was patterned on a different stepper) implant level.
Mix-and-match levels see additional noise due to stepper mismatch (both in lens
60%
40%
20%
% X-mark Error
0%
-20%
-40%
-60%
Controlled
Simulated offset: no control
-80%
0 5 10 15 20 25 30 35 40
Run No.
FIGURE 16.6 Behavior of x-markshift for a mix-and-match implant level.

distortions and reference baselines). In the example, the controller rejects a shift that
occurs at approximately run 20. The dashed line shows a simulation of what the
output would have been without the input correction (refer to (1)).
16.3.2 SECOND-ORDER CONTROLLER

In certain situations (i.e., for certain pattern levels), one is unable to achieve the
required amount of high-frequency noise attenuation while still preserving the
response speed by using an EWMA-based controller alone. To this end, the EWMA-
based controller is augmented with a low-pass filter to yield the following controller
equations (the spike filter is retained):
 λk λk   λk  
 − 2 −   2 
xk +1 = xk +  
1 − e −2 λ k e
2
−2 λ k  xk −  −2 λ k
− 1 e
(
 y
− 1  k +1− τk
− uk − τk )

.
 3 
  4 4   4  
 
∆
round 
( )
(5)
 ∆ + abs yk +1− τ − x˜ k 
 k 
x˜ k +1 = yk +1− τk
1 
uk = γ ⋅ round [1 1]xk 
γ 
~
where [xy xk ]T ∈ 3 are the controller states (the base controller is second order),
and once again the delay is taken out of the loop. Equation (5) is the discretized
(assuming a zero-order hold) form5 of a critically damped continuous time controller
having the following Laplace transform:
λ 2k
C( s ) = , λk > 0 . (6)
s (s + 2λ k )
The additional high-frequency attenuation achieved by this controller (5) is apparent

from the Bode plot shown in Figure 16.7, as is the extra phase lag. As seen in
Figure 16.8, the controller exhibits the noise attenuation properties of a low-gain
EWMA-based controller, while achieving response times equivalent to a high-gain
EWMA. Stability for the closed-loop system (assuming unity stepper gain) is guar-
anteed provided that the roots of the following (characteristic) equation are less than
1 in magnitude:
( )
4 z 2 + 2λ k − 3e −2 λ k − 5 z + 3e −2 λ k − 2λ k e −2 λ k + 1 = 0 (7)

Crossover Additional
frequency (CF) EWMA; λ=0.1 high-frequency
50 attenuation
Phase (deg), Magnitude (dB)

-50
-100
-50
-100
-150
-200
-250 -2 -1 0 1
10 10 10 10
Frequency (rad/sec)
λ = 0.2
FIGURE 16.7 Bode plot comparing frequency responses of EWMA-based (dashed) and
second-order controllers (solid).
This is true provided 0 < λk < 5. However, the maximum allowable value of λk is
typically chosen to be much smaller than this to achieve sufficient gain and phase
margins. For example, setting λk = 0.4 yields gain and phase margins of 21 dB and
71°, respectively. Increasing this to 0.8 results in a phase margin of 65° and the
introduction of undesirable underdamped behavior. This underdamping is the result
of discretization.
In this case also, the gain λk is allowed to vary according to Eq. (3). Furthermore,
due to the phase lag, large adaptation rates can be chosen (i.e., the gain is allowed
to fluctuate more) since the controller response is less sensitive to fluctuations in
the gain (as compared to the EWMA case). Figure 16.9 shows the performance of
this controller for control of x-markshift (arbitrarily scaled) at metal-1 pattern.
Figure 16.9 (top) also shows simulated data obtained by backing out the controller
corrections from the measured misalignment employing the model (1). The corre-
sponding controller gain (λk) is shown in Figure 16.9 (bottom). It is seen that the
controller gain remains high when the stepper experiences a shift/drift disturbance.
After this disturbance is compensated for, the controller gain returns to a lower
value. The maximum controller gain allowed was 0.4, and at no instance is this
value exceeded (as predicted by theory).
The adaptive scheme proves very useful in fan-out and maintenance of the
controllers. In addition to allowing identical controllers to be employed across
multiple pattern levels and steppers, the system also results in zero maintenance.

Response to a step of 5
5
4.5
4 2nd Order; λ=0.2
3.5
Error from Target 2.5
1.5
EWMA; λ=0.1
1
0.5
EWMA; λ=0.2
0
0 5 10 15 20 25 30 35 40
k
FIGURE 16.8 Step response comparison of EWMA-based and second-order controllers.
20
0
% X-mark Error
-20 Controlled
-40
-60
-80 Simulated offset: no control
-100
0 10 20 30 40 50 60 70 80 90 100
Run No.
0.4
0.3
0.2
λ
0.1
0
0 10 20 30 40 50 60 70 80 90 100
Run No.
FIGURE 16.9 Behavior of x-markshift for metal-1 pattern: % error (top), and controller gain
(bottom).

The EWMA-based and second-order controllers are both being employed to control
lithography overlay in TI, with different fabs preferring one controller structure over
the other. Based on experience, it appears that the EWMA case works best for fabs
with low volume and low product mix, which have less device and metrology recipe-
induced noise, and need very aggressive control. For a high-mix, high-volume
environment, the second-order controllers prove superior due to their additional
filtering capability. The initial lag in the controller response is inconsequential in
such a setting, and in fact helps prevent spurious control action.
16.4 CONCLUSIONS
Two examples of adaptive feedback controllers being employed to control lithogra-
phy overlay in TI fabs have been presented in this chapter. The first example was
that of an EWMA-based controller, and the second example built on this by incor-
porating additional low-pass filtering. It is expected that with scaling device geom-
etries and tightening alignment requirements, lens distortion will contribute signif-
icantly to the overall alignment error budget. This will prompt a move toward device-
dependent overlay control. Efficient software will be required to implement such
control schemes in a manufacturing-friendly fashion, particularly in high-mix ASIC
(application-specific integrated circuits) fabs. Other issues that will arise is the need
to ensure adequate sampling across various pattern levels in order to further enhance
system performance.
ACKNOWLEDGMENTS
The authors would like to acknowledge the following people who have contributed
to development and deployment of overlay feedback control in TI: Stephanie Hilbun,
Eddie Brooks, Doug Ballard, Adriana Sanchez, and Steve Jenkins.
REFERENCES
1. Maly, W., Atlas of IC Technologies: An Introduction to VLSI Processes, Ben-
jamin/Cummings, Menlo Park, NJ, 1987.
2. Armitage, J.D., Analysis of overlay distortion patterns, in Integrated Circuit Metrol-
ogy, Inspection, and Process Control II, Monahan, K.M., Ed., 921, SPIE, Bellingham,
1988, 207.
3. Patel, N.S. and Jenkins, S.T., Adaptive optimization of run-to-run controllers: The
EWMA example, IEEE Transactions on Semiconductor Manufacturing, to appear.
4. Smith, O.J.M., Feedback Control Systems, McGraw-Hill, New York, 1958.
5. Kuo, B.C., Automatic Control Systems, (7th ed.), Prentice-Hall, Englewood Cliffs, NJ,
1995.

17 Age-Based Double
EWMA Controller
and Its Application
to a CMP Process
Argon Chen and Ruey-Shan Guo
17.1 INTRODUCTION
The basic R2R control algorithm solutions presented in Chapter 1, and especially
Chapter 3, are based on the R2R control scheme originally proposed by Sachs et al.1
In this scheme, the EWMA statistic is used as an estimate of the process deviation
from its target. However, the controller based on the EWMA statistic is not sufficient
for controlling a wearing out process. The predictor–corrector controller (PCC)
algorithm, also described in Chapter 3, was developed to enhance the EWMA R2R
controller’s capability.2,3 In this chapter, we first reexamine the fundamentals of the
PCC formulations and propose an adjustment that is cleaner and more pervasive in
controlling processes subject to both random shifts and drifts, and takes into account
process age. We then study the application of this adjusted algorithm to the control
of the CMP process. We refer to this adjusted PCC scheme as an age-based double
EWMA (d-EWMA) scheme. As shown throughout this book (see, for example the
Introduction), the CMP process is an ideal candidate for R2R control and therefore
represents an ideal candidate for demonstrating the benefits of the d-EWMA scheme.
This chapter is organized as follows. In the remainder of this section we provide
background information on the EWMA statistic. In Section 17.2 we examine the
fundamentals in the PCC formula and propose an adjustment that is cleaner and
more pervasive. The adjusted PCC formula is then further refined in Section 17.3
to take the process age into consideration. The methodology is illustrated in
Section 17.4 using the CMP process as a case study.
17.1.1 BACKGROUND: THE EWMA STATISTIC

The use of exponentially weighted moving average (EWMA) statistic for estimating
process deviations has been widely studied and adopted in practice. Box and Jenkins4
show that a controller based on the EWMA statistic is a minimum mean square error
(MMSE) controller when the underlying process disturbance follows the IMA(1,1)
(first-order integrated moving average) process. In practice, the EWMA statistic has

been shown to be quite effective, even for processes subject to disturbances other
than the IMA process. In particular, applications in the semiconductor process
industry, known as R2R process control, have shown that the EWMA statistic is
also capable of bringing processes with linear drift under control.1,5-7 Suppose that
the process output Yt can be controlled linearly by an input variable Xt and is subject
to a natural process disturbance εt (~N(0, σ2)) and a systematic disturbance δt. The
process model can be written as:
Yt = α + βXt + ε t + δ t
(1)
= (α + δ t ) + βXt + ε t
where α is the linear process model’s intercept term and β is the system gain that
translates the input variable’s size to the process output’s responded size. The EWMA
statistic is then used to estimate the size of the process’s intercept (α) plus its
systematic deviation at time t + 1 (δt+1):
at = w(Yt − βXt ) + (1 − w)at −1
(2)
∑[ )]
t
= w(1 − w)
t− j
(
Yj − βX j
j =1
where the weight w is usually set between 0 and 1 and at is an exponentially weighted
average of the historic deviations α + δj’s. Therefore, the process output at time t +
1 is estimated to be
Yˆt +1 = at + βXt +1 . (3)
In order to keep the process output at a predetermined target level (T), we obtain
the process recipe at time t + 1:
T − at
Xt +1 = . (4)
β
Such a controller is insufficient for processes subject to systematic wear-out.

Several authors2,3 have addressed this problem and propose using two EWMA
formulas: one for estimating “step-change” deviation and the other for estimating
the process “drift” speed.
at = w1 (Yt − βXt ) + (1 − w1 )at −1

(5)
pt = w2 (Yt − βXt − at −1 ) + (1 − w2 ) pt −1

where w1 and w2 are the weights for the first and second EWMA equations, respec-
tively, and pt is to estimate the size of the process drift from t to t + 1. Thus, the
process recipe at t + 1 should be
T − (at + pt )
Xt +1 = (6)
β
Such a control scheme is referred to as predictor corrector control (PCC) scheme,

termed by Butler and Stefani.2
17.2 PCC AND DOUBLE EWMA FORMULA

The PCC formula in (5) has two purposes: one is to estimate the intercept plus the
systematic deviation (at) and the other is to estimate the process drift speed (pt).
Suppose that the process is subject to a linear drift only. That is,
Yt = α + βXt + ε t + cσt
(7)
= (α + cσt ) + βXt + ε t
where the process output is systematically drifting away by a size of cσ per unit
time. To see how the estimates at and pt work, we can examine the process’s steady
state as time approaches infinity (Appendix A):
cσ
lim E(at ) = α − + cσ(t + 1)
t→∞ w1
(8)
 cσ 
lim E  pt = 
t→∞  w1 
This result somehow surprises us, since in this PCC formula at is not really an
estimate for α + δt+1 and pt is not really the estimate for the drifting speed.
The steady-state recipe becomes
 cσ cσ 
T − α − + cσ(t + 1) + 
 w1 w1  T − [α + cσ(t + 1)]
lim Xt +1 = = (9)
t→∞ β β
The expected process output at time t + 1 is then
lim E(Yt ) = T (10)

t→∞

1
0.8
0.6
=
0.4
0.2
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
FIGURE 17.1 I-II controller’s control space.
Here, we show that the system with PCC controller is a stable system and the
expected process output converges to the desired target.
The estimate for α + δt in the PCC formula can be further rewritten as (Appendix B)
t t i
at + pt = (w1 + w2 − w1w2 ) ∑
i =1
ei + w1w2 ∑∑e + a
i =1 j =1
j 0
(11)
t t i
= wI ∑e + w ∑∑e + a
i =1
i Π
i =1 j =1
j 0
where ej = Yj – T. This is, in effect, an integral-double-integral (I-II) controller, in

contrast to the proportional integral derivative (PID) controller. In this I-II controller,
the control action is proportional to the summation of the output errors and to the
summation of summations of the output errors. The I-II controller can shown to be
an MMSE controller for processes subject to IMA(2,2) disturbances.4 In (11) we
can observe that the controller’s integral constant is wI = w1 + w2 – w1w2 and the
double-integral constant is wII = w1w2. We define a control space of the I-II controller
as the space filled up by all possible settings of control constants (wI, wII), as shown
in Figure 17.1. In Figure 17.1, the controller allows both wI and wII to be set between
0 and 1. For PCC controller, we usually set w1 and w2 between 0 and 1 as well. This,
however, leads to a limited control region in the (wI, wII) control space, as in the
shaded area shown in Figure 17.1.
Now we would like to propose an adjustment of the PCC formula such that the
control region can be extended to the entire space and the steady-state estimates are
cleaner. We refer to this adjusted PCC formula as double EWMA (d-EWMA)
formula as distinct from the original PCC formula. This d-EWMA formula is
at = w1 (Yt − βXt ) + (1 − w1 )(at −1 + pt −1 )

(12)
pt = w2 (Yt − βXt − at −1 ) + (1 − w2 ) pt −1

As can be observed in (12), the only difference from the original PCC formula is
that in the first EWMA formula for at, we add pt-1 into the formula. As a result, the
I-II controller becomes (Appendix C)
t t i
at + pt = w1 ∑
i =1
ei + w2 ∑ ∑ e + (t + 1) p + a
i =1 j =1
j 0 0 (13)
That is, wI = w1 and wII = w2 and with 0 < w1 < 1 and 0 < w2 < 1 we will have an
I-II controller that fills up the entire control space.
With this d-EWMA formula, we can also obtain a cleaner steady state:
lim E(at ) = α + cσt

t→∞
(14)
lim E( pt ) = cσ
t→∞
This result is much cleaner than the original PCC formula. Moreover, the two
estimates at and pt here have very clearly defined meanings. In this d-EWMA
formula, at represents an estimate for α + δt and pt an estimate for the size of the
process drift from t to t + 1. Together at + pt is the estimate for α + δt+1. The steady-
state recipe at time t + 1 becomes
T − (at + pt ) T − α − cσ(t + 1)
lim Xt +1 = =
t→∞ β β
This is exactly the same as (9) and thus the process output with d-EWMA control
will also converge to the desired target T. Though both controllers (PCC and d-
EWMA) are “unbiased” controllers, the advantages of d-EWMA controller over the
PCC controller are twofold:
1. The d-EWMA controller is a direct form of I-II controller and its control
space fills up the entire I-II control space.
2. Unlike the PCC controller, at and pt in the d-EWMA formula have clear
definitions.
To illustrate these two advantages, we simulate a random drift process where

T = 3500, a0 = α = 3000, β = 10, and p0 = 0. The process drift speed c is a random
number over time, i.e.,
ct −1 with p = 0.99

ct = 
~ N (0.02, 0.05) with p = 0.01
A typical process with such random drift disturbances is shown in Figure 17.2.

1200
1000
800
600
δ
400
200
0
-200
0 200 400 600 800 1000
(a) Systematic Deviations - random drifts
5000
4500
4000
3500
3000
0 200 400 600 800 1000
(b) Process Output
FIGURE 17.2 A typical random drift process.
To evaluate the control efficiency, we use a normalized mean squared error

(MSE/σ2) as the performance measure. MSE is defined as
∑ (Y − T )
2
t
t =1
MSE = .
n
And MSE/σ2 is a measure normalized against the variance (σ2) of the natural
disturbance (εt). Figure 17.3 shows the contour plot for the control efficiency over
the control space. As can be seen, the optimal I-II control setting (wI ≅ 0.115 and
wII ≅ 0.005) falls outside the control region (shaded area) of the original PCC
controller. That is, if we use the PCC controller and restrict the values of w1 and w2
in the interval of (0, 1), the PCC controller would never be as effective as an optimal
I-II controller (or d-EWMA controller).

MSE/σ2
DDl
DDDT
Wn
DDD-
DDDl
W1
1.113 Wn
W1
FIGURE 17.3 Contour plots for the I-II control efficiency over the control space.
17.3 AGE-BASED DOUBLE EWMA CONTROLLER

In many applications, the data sampling time is not equally spaced. This leads to an
invalid result in the d-EWMA formula. However, the data collected often comes
with the process’s age at the time of sampling. In this section we will develop an
age-based d-EWMA formula in which the unequally spaced data can be accommo-
dated along with the age data.
First, let ti denote the process age at the ith sampling. In Eq. (12), the two EWMA
equations need to be modified to take the age into consideration. The term ai now
becomes the estimate for the intercept (α) plus the systematic deviation at the ith
sample (δi). The first EWMA equation in (12) should be modified to
[
ai = w1 (Yi − βXi ) + (1 − w1 ) ai −1 + (ti − ti −1 ) pi −1 ] (15)

where pi–1 is an estimate for the drifting size per unit time at the (i – 1)th sample.
From sample i – 1 to sample i the process has grown (ti – ti-1) older. Since the process
continues to drift away at a rate of pi-1 between the two samples, by the ith sample
the process has further deviated for an amount of (ti – ti-1)pi-1. This explains the
second term of the EWMA formula in (15). We also need to modify the second
EWMA formula for estimating the drifting speed at the ith sample (pi):
 Y − βXi − ai −1 
pi = w2  i
ti −1 − ti  + (1 − w2 ) pi −1 (16)
 
where Yi – βXi – ai-1 represents the amount the process drifts away between sample
i – 1 and sample i. The recipe at the (i + 1)th run should be therefore set at
Xi +1 =
[
T − ai + (ti +1 − ti ) pi ] (17)
β
to keep the process output on target.

It should be noted that such a modification to accommodate the process age is
only possible for the d-EWMA formula. For the original PCC formula, the modifi-
cation becomes almost impossible because of its unclear definitions of at and pt.
17.4 APPLICATION TO CMP PROCESS WITH AGING

PAD AND DISC
A simple strategy for controlling the CMP process is to predict the R2R process
removal rate and then adjust the polishing time based on the prediction.5,8,9 EWMA
and PCC (or double EWMA) techniques are the two most often used prediction
techniques. Based on the age-based d-EWMA controller presented earlier, we will
design an age-based R2R prediction technique that takes into account the ages of
the abrasive pad and brushing disc. We will show how this proposed technique could
improve the prediction capability and, thus, the control efficiency through actual
CMP production data. Figure 17.4 shows a typical CMP process.
In a CMP process, both the abrasive pad and the brushing disc are wearing out
quickly. Because of the combination of chemical and mechanical processes during
polishing, the wear-out process becomes quite irregular. Simple EWMA prediction
of the removal rate is not sufficient. d-EWMA is therefore needed to capture the
changes of the removal rate. The d-EWMA prediction of removal rate at (i + 1)th
observation ( Rˆ i+1) can be expressed as
ai = w1 Ri + (1 − w1 ) Rî (18)
pi = w2 ( Ri − ai −1 ) + (1 − w2 ) pi −1 (19)

Top View
Side View
Wafer
Brushing disc Carrier
Carrier
Holder Abrasive
Pad Brushing disc
Platen
Abrasive Pad
Platen
FIGURE 17.4 CMP process.
R̂i +1 = ai + pi (20)
These are d-EWMA prediction equations corresponding to Eq. (12) without consid-
ering the process age. Similar to the d-EWMA controller, the first EWMA Eq. (18)
is to estimate the level of the removal rate (ai) and the second EWMA Eq. (19) is
to capture its changing speed (pi). In Eq. (20), the removal rate at observation i + 1
is then predicted by adding together the level estimate ai and the anticipated change
(pi) from observation i to i + 1.
In practice, the age of the abrasive pad and the brushing disc can be acquired
along with the removal rate data. Figure 17.5 shows the trend of the removal rate
4 13
0.131.251.923.33 6.4 16.317.769.090.092.434.0235.1 62.563.464.465.53
26.327.328.359.380.4431.432.343.385.46 37.350.451.442.543.544.445.446.447.15 47.608.549.351.451.84
9.049.9712.212.89 54.455.456.11 58.068.7.3
Disc life (hr)
FIGURE 17.5 Trend of removal rate over a disc’s lifetime.

over an entire lifetime of one disc. During the lifetime of a disc, preventive main-
tenance (PM) was performed seven times. Each time the abrasive pad was replaced
with a new one.
It can be observed that the removal rate is changing in different speeds during
a disc’s lifetime. In the beginning of a disc (e.g., the first pad), the removal rate
seems to fall drastically. However, the drop of the removal rate becomes less as the
disc gets older. Observing the last two pads in Figure 17.5, the removal rate becomes
a constant during these two pads. This observation helps us understand how the ages
of pad and disc affect the removal rate. The removal rate basically falls as the pad
gets older. And the falling speed of the removal rate during each pad is again affected
by the disc’s age. The older the disc, the less the removal rate falls. Based on this
observation, we can design an age-based d-EWMA prediction scheme, similar to
Eqs. (15) to (17), that takes into consideration the age of the pad and the age of the
disc.
First, the initial changing speed of the removal rate (p0) for each abrasive pad
is estimated based on the age (τ) of the disc:
p0 ( τ) = d + bτ , (21)
where d is the changing speed of the removal rate for a brand-new disc (τ = 0) and
b represents how the changing speed changes as the disc ages.
Second, given the initial changing speed of the removal rate for each new pad,
the formula in Eqs. (18) to (20) is then revised to accommodate the age (t) of the
pad. Let ti denote the age of the pad at the ith observation. We propose the following
age-based d-EWMA prediction scheme:
ai = w1 Ri + (1 − w1 ) Rî (22)
R −a 
pi = w2  i i −1  + (1 − w2 ) pi −1 (23)
 ti − ti −1 
R̂i +1 = ai + (ti +1 − ti ) pi (24)
The data shown in Figure 17.5 is then used to estimate the model parameters (d, b,
w1, and w2) in Eqs. (21) to (24). Figure 17.6 shows this estimated model. The model
estimated using data in Figure 17.5 can be now be used to predict the removal rate
for other discs. Figure 17.7 shows the raw removal rate data for four discs.
Figure 17.8 shows the prediction for Disc 3 using the model estimated from Disc 1.
We summarize the performance of EWMA, d-EWMA, and age-based d-EWMA
prediction schemes by comparing their prediction mean squared error (MSE) in
Table 17.1.
It is recommended that when the age data for the abrasive pad and the brushing
disc are available, the proposed age-based d-EWMA scheme should be used to

Actual removal rate
Removal rate model
4 24
0.13 1.92 9.97 12.9 17.8 20.1 27.3 29.4 31.4 33.4 40.5 42.5 44.4 46.5 48.6 51.4 54.4 56.1 58.1 62.5 64.5 66.5
FIGURE 17.6 Estimated removal rate model vs. actual removal rate.
4 12 16 20 53
0.13 9.97 20.1 29.433.440.544.4 51.456.162.566.5 2.339.19 20.624.128.833.637.8 49.855.658.4 1.02 9.8716.920.827.531.340.345.854.2 61.367.5 1.025.049.1314.3 23.929.232.440.544.648.5
FIGURE 17.7 Trend of removal rate over four discs.
predict the removal rate. The prediction improvement is about 17% better than the
EWMA scheme, and 11% better than the d-EWMA scheme.
17.5 CONCLUSIONS
In this chapter we presented an adjustment of the original PCC controller. This
adjustment has a cleaner form and was shown to be more pervasive in the form of

Actual removal rate
Predicted removal rate
12 16 40
0.33 2.33 6.29 9.19 11.4 14.2 18.9 20.6 22.9 24.1 26.5 28.8 33.6 34.7 37.8 46.4 49.8 53.6 55.6
FIGURE 17.8 Removal rate prediction for Disc 2.
TABLE 17.1
Comparison among EWMA, PCC, and Time-Based PCC
Improvement (%)
Prediction MSE over EWMA
EWMA 191.683 —
d-EWMA 178.484 6.88%
Age-based d-EWMA 158.163 17.48%
the I-II controller. We refer to this adjusted PCC controller as a d-EWMA controller.
This cleaner form of d-EWMA controller enabled us to accommodate the process
age into the formula. An age-based d-EWMA controller was therefore developed.
The performance of this age-based d-EWMA controller was then illustrated through
the example of CMP removal rate prediction. The results show that the age-based
d-EWMA controller is indeed the most effective.
ACKNOWLEDGMENTS
We would like to thank Mr. J.-J. Chen, Mr. C.-P. Tung, Mr. Y.-L. Chou, and Ms.
C.-L. Lin for their help in preparing the figures. We also like to thank Dr. Jowei
Dun and Mr. S.-A. Wu of TSMC who provided the precious CMP data for this study.

REFERENCES
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and Feedback Control,” IEEE Transactions Semiconductor Manufacturing, vol. 8,
no. 1, February 1995.
2. Bulter, S. and Stefani, J., “Supervisory Run-to-Run Control of Polysilicon Gate Etch
Using In Situ Ellipsometry,” IEEE Transactions Semiconductor Manufacturing, vol.
7, no. 2, May 1994.
3. Smith, T., Boning, D., Stefani, J., and Butler, S., “Run by Run Advanced Process
Control of Metal Sputter Deposition,” IEEE Transactions on Semiconductor Manu-
facturing, vol. 11, no. 2, May 1998.
4. Box, G. and Jenkins, M., Time Series Analysis — Forecasting and Control, Oakland,
CA: Holden-Day, 1974.
S., and Taylor, J., “Run by Run Control of Chemical-Mechanical Polishing,” IEEE
Transactions on Components, Packaging, and Manufacturing Technology — Part C,
vol. 19, no. 4, October 1996.
6. Smith, T. and Boning, D., “A Self-Tuning EWMA Controller Utilizing Artificial
Neural Network Function Approximation Techniques,” IEEE Transactions on Com-
ponents, Packaging, and Manufacturing Technology, March 1997.
7. Castillo, E.D. and Hurwitz, A., “Run-to-Run Process Control: Literature Review and
Extensions.” Journal of Quality Technology, vol. 29, no. 2, April 1997.
8. Chiou, H.W. and Chen, L.J., “PID Run to Run Control of CMP Removal Rate,” Proc.
CMP-MIC Conference, pp. 375-382, 1997.
9. Ning, Z., Moyne, J., Smith, T., Boning, D., Castillo, E.D., Yeh, J., and Hurwitz, A.,
“A Comparative Analysis of Run-to-Run Control Algorithms in the Semiconductor
Manufacturing Industry,” Advanced Semiconductor Manufacturing Conference, Cam-
bridge, MA, 1996.

APPENDIX A
PCC controller:
at = w1 (Yt − bXt ) + (1 − w1 )at −1 = w1 (α + cσt + ε t ) + (1 − w1 )at −1
pt = w2 (Yt − bXt − at −1 ) + (1 − w2 ) pt −1 = w2 (α + cσt + ε t − at −1 ) + (1 − w2 ) pt −1
Using matrix expression, we obtain
 at  1 − w1 0   at −1   w1α + w1ε t + w1cσt 

 p  =  −w +
1 − w2   pt −1  w2α + w2 ε t + w2cσt 
.
 t  2
 at  1 − w1 0   w1α + w1ε t + w1cσt 

Let U (t ) =   A= B(t ) =  .
 pt   − w2 1 − w2  w2α + w2 ε t + w2cσt 
α   1 0 1 − w
 0   w1 0
Then, U (0) =   A =  − w2 1  0  1
1
1 − w2   w − w
2
0 w − w  
 2 1   2 1 
We obtain
 1
At =  − w2
( 1)
0  1 − w t 0  1 0
1  t
 w2 1
w − w
 2 1
  0
 (1 − w2 )   w2 − w1 

 (1 − w1 ) 
t
0
 
=  w2
 w2 − w1((1 − w2 ) − (1 − w1 )
t t
) ( 2 ) 
1 − w
t
and, thus
U (t ) = AU (t − 1) + B(t )
= A[ AU (t − 2) + B(t − 1)] + B(t )
t
= A t U (0) + ∑A
i =1
t −i
B(i )
 (1 − w1 ) 
t
0
  α 
=  w2
 w2 − w1
( (
1 − w2 ) − (1 − w1 )
t t
) (1 − w2 )
t
 0
  

(1 − w1 )
t −i
t  0 
+ ∑ 
 w2
(
(1 − w2 ) − (1 − w1 )
t −i t −i
) (1 − w2 ) 
t −i

i =1  w2 − w1 
 w1α + w1ε i + w1cσi 
w α + w ε + w cσi 
 2 2 i 2 
Finally,
at = α(1 − w1 ) + ∑ (1 − w ) (w1α + w1ε i + w1cσi)

t t −i
1
i =1
pt =
αw2
w2 − w1
t
(
(1 − w2 ) − (1 − w1 )
t
)
+ ∑
t  w2
 2 1
( t −i 
 w − w (1 − w2 ) − (1 − w1 ) (w1α + w1ε i + w1cσi )
t −i

)
i =1 + (1 − w )t −i (w α + w ε + w cσi ) 
 2 2 2 i 2 
As t approaches infinity,
cσ
lim E(at ) = α − + c σ (t + 1)
t→∞ w1
cσ
lim E( pt ) =
t→∞ w1
APPENDIX B
t t −1
at = w1 (et + pt −1 ) + at −1 = w1 ∑e + w ∑ p + a
1
i 1
0
i 0
pt = w2 et + pt −1 = w2 ∑e + p
1
i 0
t t −1
at + pt = (w1 + w2 ) ∑e + w ∑ p + a
1
i 1
0
i 0 + p0
t −1
t
 i

= (w1 + w2 ) ∑ 1
ei + w1 ∑ ∑ e + p  + a
0
 w2
 1
j 0 0 + p0

t t −1 i
= (w1 + w2 ) ∑1
ei + w1w2 ∑ ∑ e + (w t + 1) p
0 1
j 1 0 + a0
t t i
= (w1 + w2 − w1w2 ) ∑ 1
ei + w1w2 ∑ ∑ e + (w t + 1) p
1 1
j 1 0 + a0
APPENDIX C
t t −1
at = w1et + pt −1 + at −1 = w1 ∑ ∑p +a
1
ei +
0
i 0
pt = w2 et + pt −1 = w2 ∑e + p
1
i 0
t t −1
at + pt = (w1 + w2 ) ∑ ∑p + p
1
ei +
0
i 0 + a0
t −1
t t
 
= (w1 + w2 ) ∑ ∑ ∑ e + p  + a
1
ei +
1
 w2
 0
j 0 0 + p0
t t −1 i
= (w1 + w2 ) ∑1
ei + w2 ∑ ∑ e + (t + 1) p
0 1
j 0 + a0
t t i
= w1 ∑1
ei + w2 ∑ ∑ e + (t + 1) p
1 1
j 0 + a0

Part 6
Advanced Topics
In the Introduction section of this book we provided a chronology of the development
of R2R control. The information presented in Parts 1 through 5 provides a snapshot
of the current state of the art of the many aspects of R2R control. While the case
studies and results of deployment presented throughout the book (notably
Chapters 11, 13, and 15 to 17) confirm that R2R control technology is indeed a
mature capability that is ready for industry-wide deployment, there are numerous
areas where additional research and development could lead to new and better
solutions. Part 6 of this book is devoted to selected advanced topics in R2R control.
As is illustrated in many of the examples in this book, the CMP process appears
to have benefited the most from R2R control. In Chapter 18, advances in R2R control
of the CMP (chemical mechanical planarization) process are described; these
enhancements to R2R control tools will pave the way to more effective and eco-
nomical CMP R2R control solutions. Solutions that are described in Chapter 18
include (1) a “New Pad” feature that provides for the enhancement of the R2R
control algorithm to accommodate process shifts due to pad replacement, (2) a
methodology for utilizing in situ endpoint data for R2R process uniformity control,
and (3) a solution for utilizing CMP R2R control as part of a multiprocess control
strategy.
The enhancements to the EWMA algorithms that are described in Chapters 16
and 17 illustrate the benefit that can still be achieved from improving algorithms to
address practical issues. This concept is extended in Chapter 19, where an enhanced
EWMA controller is presented that has the capability of choosing the control param-
eter dynamically in response to the underlying process disturbances. There are two
modules in this controller, namely the dynamic-tuning loop trigger module and the
run-by-run feedback control module. In the dynamic-tuning loop trigger module,
two EWMA control charts are used sequentially to determine if there is a large or
medium shift in the process output, and to trigger a new dynamic-tuning loop
accordingly. In the run-by-run feedback control module, the control parameter and
control model are retuned sequentially and a new process recipe is generated to
compensate for the process output’s deviation from the target. Simulation results
validate that the enhanced EWMA controller is superior to the traditional EWMA
controller with fixed control parameters.
In the Introduction section, and again in Chapter 7, we noted that R2R control
is really just one (and the first) component in an envisioned multilevel hierarchical
control strategy. In Chapter 20 this idea is explored in detail and an interprocess
control solution is presented that incorporates R2R control at the lower control levels
to provide a factory-wide strategy for control. The solution, called the “active
controller,” has the required properties of being generic, portable, and configurable.
Many of these qualities arose from adapting design requirements and solutions that
have been utilized for R2R control (see Chapters 8 and 9). Chapter 20 thus provides
a vision for a multilevel, total factory control solution.

18 Advancements in
Chemical Mechanical
Planarization Process
Automation and Control
James Moyne
18.1 INTRODUCTION
Maintaining acceptable yields in the semiconductor manufacturing and display
industries requires constant attention to the state of the art in process tools, process
chemistries and physics, and techniques for processing and process improvement.
As feature sizes shrink and wafer sizes increase, the industry must continually
innovate to maintain acceptable product yield, throughput, and overall equipment
effectiveness (OEE). Some manufacturing capability attributes, such as nonproduct
(NP) wafer usage and wafer scrap, must actually be improved in the transition to
larger wafer sizes because of the increased cost of 300-mm wafers. As an example,
one user reported that a processed 300-mm wafer costs approximately $5000 USD,
while a raw wafer cost $2500 to $2000.1
A number of techniques, including improved equipment design and process
innovation, continue to aid in this cost-effective transition to 300-mm wafers and
smaller linewidth technologies. However, as detailed in the Introduction of this book,
traditional avenues within this industry are no longer sufficient with the focus turning
to process and equipment parameter sensing, process identifying, and dynamic
process tuning to complement equipment and process improvements.1,2
The CMP process is an excellent case study of this movement toward process
automation and control (as demonstrated throughout this book). CMP was a rela-
tively late arrival to semiconductor and display device processing, but its use is
highly motivated through its “requirement” for .35 mm and below processing.1,3,4
Since the advent of the first CMP control solutions (see Introduction and
Chapter 1), process automation and control of CMP has advanced in a number of
directions, including (1) automated control, (2) multivariate control, (3) enhanced
control techniques to address practical process limitations and to address specific
cost issues such as NP wafer requirements, (4) control solutions that combine R2R
control with endpoint techniques, and (5) R2R control solutions that are incorporated
as part of a total factory solution. This chapter provides a summary of the recent
advancements in process automation and control for CMP, focusing on model-based

R2R control solutions. Specifically, in the next section, a background of advance-
ments in CMP process automation and control up to the current year is presented.
While many of these advancements are considered mature and are available on some
CMP tools today, it is important to note that research and development efforts may
still be needed to apply these capabilities to other CMP tools. This background
section is followed by a discussion of current efforts in CMP process automation
and control. This chapter concludes with a brief summary and a discussion of
potential future directions in CMP process automation and control.
18.2 BACKGROUND
As mentioned above, CMP became an ideal process candidate for enhancement
through process automation and control because (1) it is clearly an important com-
ponent of .35 mm and below processing; (2) the process is relatively new and not
well understood, and process engineers are generally open to process improvement
through automation and control; (3) in-line and (later) in situ metrology technology
became available. Because of the generally prohibitive in situ sensing environment
of CMP, many early sensing results in CMP were in ex situ (multipoint) thickness
measurement.5 Thus, in attempting to “close the loop” and provide process control
of CMP, R2R control solutions were pursued.
The typical application of R2R control to CMP is described in the Introduction
as well as Chapter 11 and Chapter 15 of this text. The first reported results in CMP
R2R control came out of a three-year project sponsored by SEMATECH, whose
goal was to provide reusuable solutions for CMP R2R control.6 Significant results
that came out of that work for a CMP process include (1) thickness control, (2)
thickness plus uniformity (multivariate) control strategies, (3) demonstration of
process capability (Cpk*) improvement, and (4) demonstration of pad-life extension.7
Other significant results that came out of that work for process control solutions
include (1) a configurable R2R process control solution; (2) a multivariate, first-
order, nonlinear R2R control algorithm solution with exponential weighted moving
average (EWMA) noise filtering;8,9 (3) R2R control algorithm enhancements to
support process input weighting (based on tunability), output weighting (to achieve
multi-parameter optimization functions), and input boundary and discretization con-
ditions;10 (4) a comparative analysis of R2R control algorithms;11 and (5) mecha-
nisms for R2R process control automation.12–14
Building on the results of the SEMATECH effort, a tool supplier** and control
systems supplier*** continued the R2R control research effort and produced signif-
icant results of (1) thickness + uniformity (multivariate) control and Cpk improve-
ments of over 50%, and (2) a fully automated R2R process control solution for
CMP.7,14 The solution developed as well as results achieved are described in detail
in Chapter 11. Other, more recent results have reported uniformity control of other
CMP tool types.15,16 In each case, different parameters were identified and utilized
* Cpk, or “process capability,” is described in Chapter 11.

** Strasbaugh, San Luis Obispo, California — www.strasbaugh.com.
*** MiTeX Solutions, Inc., Canton, Michigan — www.mitexsolutions.com.

TABLE 18.1
Comparison of CMP Uniformity Solutions Reported
Location Tool Type Parameters Used to Control Uniformity Date Reference
Micron Strasbaugh Time and backpressure 1997 [7,14]

Technologies 6DS-SP
AMD Speedfam Arm oscillation length and conditioning 1999 [15]

position
IBM IPEC Platen speed and carrier speed 1999 [16]

372M
to control uniformity (see Table 18.1), suggesting that uniformity control solutions
vary significantly between tool types.
Two fronts along which CMP R2R control development has been achieving
significant milestones are automation and integration. The capabilities and charac-
teristics of R2R systems that facilitate automation and ease of integration are
described in detail in Part 3 of this book.
18.3 CURRENT EFFORTS IN CMP PROCESS

AUTOMATION AND CONTROL
The results of development and deployment of R2R automation and control solutions
for CMP over the past few years have demonstrated their effectiveness in reducing
process variability, increasing process capability (Cpk), increasing life of consum-
ables and decreasing process maintenance events, and reducing operator error
through automation. These results combined with advancements in sensing, integra-
tion, and control technologies have allowed the CMP process automation and control
field to branch out into a number of new directions. While the full benefit of these
pioneering efforts has not yet been realized, they do provide insight into the further
potential benefits of CMP process automation and control. In this section a few of
these efforts are described and prospects for process benefit are discussed.
18.3.1 ALGORITHM ENHANCEMENT: “NEW PAD” FEATURE

Recently, significant results have been achieved in advancing the state of the art of
practical R2R control algorithms solutions for semiconductor and display manufac-
turing. For example, higher-order modeling and control algorithms have been devel-
oped that incorporate a learning capability, thus reducing the need for process
identification ahead of control system deployment.17 Solutions have been demon-
strated that support changing metrology strategies with both pre- and postmetrology.7
Stability analysis of EWMA algorithms has allowed for better determination of range
of operation.9,18 A multialgorithm approach to control has been developed to provide
a wider range of controllability of systems.19 Interprocess feedforward and feedback
techniques have been proposed to reduce R2R variability (see also Chapter 15).16,20,21

FIGURE 18.1 The “new pad” enhancement to CMP R2R control. (Note: Uncontrolled plot
does not “spike” at run number 280, but rather spikes earlier at run 242 because pad replace-
ment is required more often without control; note also that the uncontrolled spike is lower
than the controlled spike because modeled removal rate just before pad replacement is lower
than the nominal removal rate used to calculate the uncontrolled polish time.)
Some of the recent algorithm enhancements reported have been focused on

tailoring the control capability to the CMP process. For example, the R2R control
solutions have recently been developed to be more robust to specific process shifts
in CMP processing. Figure 18.1 provides an illustration of the benefit of this type of
improvement. The “new pad” feature shown increases equipment effectiveness by
quickly bringing the process within acceptable limits after a pad replacement event,
thereby reducing the number of required NP wafers. The operation of an EWMA
R2R controller in adjusting for pad replacement can be understood by examining the
basic equation for R2R adjustment of CMP process time for the current run tn+1, based
on results for the previous run n and starting thickness measured for the current run,
STn+1 (see also Chapter 2). The removal rate, RRn+1, is modeled as
RR n +1 = α( RmvdTn tn ) + (1 − α )RR n , (1)
where RmvdTn is the thickness of the material removed with the previous polish,
and α is an EWMA weighting factor (0 ≤ α ≤ 1), the value of which is selected
based on considerations of noise, drifts, shifts, and model error.8 The suggested time
for the next run t is then calculated as
tn +1 = (STn +1 − Target ) RR n +1. (2)
In adjusting the control parameters to a new pad event, it is important to note

that the removal rate of a new pad on the first wafer, RRnp+1, cannot be accurately
estimated from the removal rate from the previous run as shown in (1), because the
main process trend of pad wear modeled with the old pad does not apply to the new

pad. The best statistical estimate of RRnp0 is some function (e.g., moving average)
of RRnp+1 determined from previous calculations of actual removal rate on first wafer
after a pad replacement. Then, assuming that the difference between RRnp+1 for the
current pad and RRnp0 is much larger than the measurement and process noise factors,
the removal rate estimate can be quickly adjusted to the new pad by setting the
EWMA coefficient α to 1 for the first run. Thus, from (1), we have
RR np+2 = RmvdTnp+1 tnp+1. (3)
Utilizing this strategy, the improvement in thickness control over a strategy that
does not utilize pad change event knowledge is shown in Figure 18.1. Note that the
new pad thickness removed “spike” is reduced. The magnitude of the spike that
remains is a function of the difference between RRnp for the current pad and RRnp0.
Note also that a significant transient exists for a number of runs as the removal rate
model settles to the actual removal rate. This transient can be significantly reduced
through adjustment of the removal rate model estimate by a factor that captures the
exponential-like decay of removal rate over the first few wafers after a pad replace-
ment event. For example, the following equation set could be utilized in place of
(1) and (3) to model removal rate for the first i wafers after a pad replacement:
RR np+1 = RR np 0
[
RR np+2 = e − x RmvdTnp+1 tnp+1 ] (4)
{[ ( )] [( ) ]}
RR np+i = e − x α np RmvdTnp+i −1 tnp+i −1 + 1 − α np RR np+i −1 , for i ≥ 3,
where αnp is an EWMA weighting factor (which may differ from α in (1)) and x is
associated with the decay constant (in wafers) of the removal rate profile for a new pad.
The benefits of employing an effective new pad strategy are numerous, including
reduction of NP (test) wafer requirements, reduction of length of PMs associated
with new pad replacement and tool qualification, and increased overall equipment
effectiveness (OEE). Key issues are repeatability of removal rate decay after pad
replacement, determination of end of pad decay profile (e.g., appropriate run in
which to switch from (4) to (1) for removal rate model). Note also that the “new
pad” model enhancement feature may also be applicable to other semiconductor and
display process modeling scenarios such as etch modeling after a clean operation,
or sputter deposition modeling after replacement of a deposition source.
18.3.2 COMBINING IN SITU ENDPOINTING WITH R2R

UNIFORMITY CONTROL
A common misconception in semiconductor and display process control is that in situ
control is a replacement for R2R control. The truth is that in situ control and R2R
control are complementary and will coexist in the factory of the future.10,22 One
example of the complementary nature of this hierarchical control structure is the

FIGURE 18.2 Combining in situ endpoint with R2R uniformity control.
combination of endpointing and R2R control in CMP to better achieve process

thickness and uniformity targets. The apparatus, shown in Figure 18.2, is applicable
to both oxide and metal polishing, and can utilize motor current or optical endpoint-
ing along with R2R control to achieve both thickness and uniformity control. The
system operates by utilizing the optical or motor current endpointing to achieve
thickness targets. The R2R control system provides accurate estimates of endpoint
times, thereby reducing the need for endpoint monitoring until very near endpoint,
and reducing the chance for misreading endpoint traces (e.g., stopping on the wrong
cycle of an optical interference endpoint signal).
More importantly, the R2R controller can be adapted to utilize endpoint trace
data to determine uniformity characteristics of the polished wafer. For example, the
slope of a motor current trace is related to the uniformity of the wafer. With respect
to optical endpointing, if the laser monitors the wafer through a hole in the platen,
it can be set to monitor a track across the wafer, thereby providing endpoint infor-
mation at different points on the wafer; this data can then be used to determine a
uniformity profile. Utilizing this uniformity information, the R2R controller can then
suggest process input adjustments on a run-to-run basis to achieve uniformity targets.
In many cases it may also be used to suggest optimal endpointing algorithms.
18.4 MULTIZONE UNIFORMITY YIELD MODELING

AND CONTROL
Previous results in CMP uniformity control focus on controlling center-to-edge
(CTE) nonuniformity to an “optimal” target of zero.7,15 Recent efforts in CMP
process uniformity analysis and modeling, however, suggest that a model of CMP
process uniformity can be broken into radial zones, and an optimal yield target is
generally not a CTE value of zero.21 The analysis of the multizone uniformity yield
problem and derivation of optimal yield targets is detailed in Chapter 15. Process
modeling for control to yield targets as opposed to process targets is expected to be
a future direction of semiconductor manufacturing R2R control.
18.5 CMP R2R CONTROL AS

PRECOMPENSATION STRATEGY
Previous advancements in CMP process control have focused strictly on the CMP
process and optimizing the CMP tool to remove evenly across the entire wafer to a

FIGURE 18.3 CMP precompensation interprocess control solution.
desired thickness. Recently, efforts have been focused on incorporating CMP process
control as part of a factory-wide scheme to improve yield of the process at the
postetch step.16,21 The target contact process line has a typical CVD, CMP, lithog-
raphy, etch (RIE) sequence. The control solution is being developed in a number of
phases, with the first phase focused on the development of CMP and RIE R2R
process control solutions, with pre- and postprocess measurement utilized along with
interprocess feedforward and feedback information flow between the two control
solutions. For both control solutions, the process quality metrics being controlled
are postprocess thickness and uniformity, with these metrics indirectly verified at
postetch process through electrical testing.
In developing this multiprocess control scheme, preliminary results have shown
that, while repeatable results on etch process uniformity were observed, satisfactory
models for controlling etch uniformity could not be obtained (through design of
experiments analysis). Thus the control scheme was modified with the RIE process
R2R and feedforward to RIE control components eliminated. The resulting inter-
process control solution operates in the following manner (see also Figure 18.3 and
Reference 22):
1. Etch process uniformity is determined at infrequent intervals through pre-

and postmeasurement analysis at the etch process.
2. An etch process nonuniformity metric is determined and fed back to the
CMP R2R controller.
3. The CMP R2R controller utilizes pre- and postprocess metrology and
provides for control of CMP process removal thickness and radial
nonuniformity.
4. The CMP R2R control targets are adjusted to precompensate for the etch
process nonuniformity and maximize postetch process yield.
The CMP R2R controller thus does not necessarily optimize the CMP process,
but rather operates as part of a total factory solution to provide the best CMP process
for that process line. Note that the impact of CMP process targets on overall line
yield must be taken into consideration in determining CMP uniformity targets that
produce the optimal overall line yield.

18.6 CONCLUSIONS AND FUTURE DIRECTIONS
The CMP process industry has benefited from significant advancements in CMP
process automation and control over the past seven years. Conversly, CMP has served
as an excellent case study and showcase for the development and demonstration of
the capabilities of process automation and control in semiconductor and display
manufacturing. Significant achievements in CMP process automation and control
include thickness R2R control, thickness plus uniformity R2R strategies and (later)
control, demonstration of process capability (Cpk) improvement, demonstration of
pad-life extension, and R2R control with post- and premetrology capabilities. Results
applicable to generic R2R control that resulted from efforts utilizing CMP as a process
research vehicle include a configurable R2R process control solution; a multivariate,
first-order, nonlinear R2R control algorithm solution with exponential weighted mov-
ing average (EWMA) noise filtering; R2R control algorithm enhancements to sup-
port process input weighting (based on tunability); output weighting (to achieve
multiparameter optimization functions), and input boundary and discretization con-
ditions; and mechanisms and solutions for R2R process control automation.
Over the past year CMP process automation and control research has yielded
results and potential advancements in a number of new areas, including algorithm
enhancements such as the “new pad” feature (to minimize NP wafer useage after
PMs), solution designs that combine R2R uniformity control with endpoint technol-
ogy (reducing the need for ex situ measurement), multizone uniformity modeling
and yield control, and precompensation (interprocess) control targeting strategies
for CMP for improved line yield.
Future process automation and control directions for CMP will be increasingly
focused on CMP processing as part of a multilevel total factory solution. Thus the
emphasis will be on optimizing the factory output as opposed to the CMP process
output, and the choice of process control targets and metrology strategies will be
made based on these factory-level directives. The CMP process control solution will
have to be automated to meet increasing demands on throughput and to reduce
operator error. The automated control solution will be multilevel with in situ control
providing for endpointing and in situ parameter adjustment. The R2R controller will
provide input to the in situ control system, especially to provide adjustment param-
eters for process shift events such as PMs and product shifts. The R2R controller
will also control parameters that cannot (yet) be controlled at an in situ level, and
will accommodate and utilize interprocess feedforward and feedback information to
achieve factory-level control targets. R2R control solutions will also be enhanced
accordingly to provide R2R plus interprocess control configurable algorithm solu-
tions and enablers that can be integrated at the CMP equipment level or distributed
over the factory computer integrated manufacturing system.
ACKNOWLEDGMENT
Portions reprinted with permission from proceedings of the Third International
Symposium on Chemical Mechanical Polishing in IC Device Manufacturing: 196th
Meeting of the Electrochemical Society.23

REFERENCES
1. Rozich, W., SEMATECH AEC/APC Symposium XI, Vail, CO (1999).
2. Baliga, J., Semiconductor International, Vol. 22, No. 8, (1999).
3. National Technology Roadmap for Semiconductors, Semiconductor Industry Associ-
ation (1999).
4. Jairath, R. et al., Solid State Technology (May 1994).
5. Nova Measuring Instruments, Rehovoth, Israel.
S., and Taylor, J., IEEE Trans. Components, Packaging, Mfg. Tech. Part C, Vol. 19,
No. 4 (1996).
7. Moyne, J., SEMATECH AEC Workshop VIII, Santa Fe, NM (1996).
8. Moyne, W., M.S. Thesis, Electrical Engineering and Computer Science, MIT (1996).
9. Smith, T., M.S. Thesis, Electrical Engineering and Computer Science, MIT (1996).
10. D. Boning et al., Proc. 6th Ann. SEMI/IEEE ASMC, Boston, MA (1995).
11. Ning, Z. et al., Proc. 7th Ann. SEMI/IEEE ASMC, Boston, MA (1996).
12. Moyne, J., U.S. Patent No. 5,469,361 (1995).
13. Telfeyan, R. et al., J. Vac. Sci. Technol. A, Vol. 14, No. 3 (1996).
14. Moyne J., and Curry, J., Fifteenth International VLSI Multilevel Interconnection
Conference, Santa Clara, CA (1998).
15. Campbell, J.W., SEMATECH AEC/APC Symposium XI, Vail, CO (1999).
16. Moyne, J., SEMATECH AEC/APC Symposium XI, Vail, CO (1999).
17. Del Castillo, E., IIE Transactions, Vol. 28, No. 12 (1996).
18. Ingolfsson, A. and Sachs, E., J. Quality Technol., Vol. 25, No. 4 (1993).
19. Moyne, J., Chaudhry, N., and Telfeyan, R., J. Vac. Sci. Technol. A, Vol. 13, No. 3
(1995).
20. Ruegsegger, S., Wagner, A., Freudenberg, J., and Grimard, D., IEEE Trans. Semic.
Mfg. (November 1999).
21. Moyne, J. et al., 46th International Symposium of the American Vacuum Society,
Seattle, WA (1999).
22. Rashap, B. et al., IEEE Trans. Semiconductor Mfg. (August 1995).
23. Moyne, J., “Advancements in CMP Process Automation and Control,” (Invited) Third

19 An Enhanced EWMA
Controller for
Processes Subject to
Random Disturbances
Ruey-Shan Guo, Argon Chen, and
Jin-Jung Chen
19.1 INTRODUCTION
As explained throughout this book, semiconductor manufacturing processes are
subject to small and large special disturbances such as process drifts or shifts. In
many cases the causes of disturbances are known, but it is either impossible or too
expensive to remove them. For example, variations of raw material quality may be
difficult to reduce. Another example is the disturbance caused by the machine
maintenance or changes in process settings. In such cases, when the resulting output
deviations can be compensated by adjusting the processing recipe, process control
techniques such as R2R control will be useful. Since the feedback control action is
exercised after observing the process output on a run-by-run* basis, there is no
input–output transient (dynamics) effect involved, as seen in the real-time control
problems. Usually, a “continuous” run-by-run feedback control strategy is often
adopted if the following conditions apply:
• The causes of variation are difficult to remove

• The adjustment of the process recipe is easy and fast
• The adjustment cost is relatively inexpensive
• The quality loss due to the output deviation from the target is significant.
The use of the exponentially weighted moving average process controller

(EWMA controller, see Parts 1 and 2 of this book) for processes subject to small
disturbances has been widely studied and adopted in practice. Box and Jenkins2
proved that the EWMA controller is a minimum mean square error (MMSE) con-
troller when the underlying process disturbance is an IMA(0,1) (first-order integrated
moving average) process. In the semiconductor process industry, several applications
* “Run-by-run” and “run-to-run” (R2R) are used interchangeably in this chapter.

of the EWMA R2R controller are shown to be effective, even when the underlying
disturbances don’t follow the IMA pattern but follow an approximately linear drift
pattern.1,10,12 For example, the chemical mechanical polishing (CMP) process usually
suffers from a drift in the removal rate due to the wear of the polishing pad. Such
a phenomenon is also seen in the deposition rate of the metal sputtering process due
to the consumption of the metal target. Other R2R control work can be found in
References 8, 9, and 13–15.
Although effective in many applications, the EWMA controller still has some
deficiencies. To be more specific:
• It is mostly used to compensate for small disturbances, and there is no

control strategy focusing on random disturbances with different shift sizes.
• The control efficiency strongly depends on the choice of the control
parameter, and in many cases it is determined empirically.
• There is no capability to change the control parameter dynamically in
response to the change of the process disturbances.
To overcome these deficiencies, several approaches have been proposed in recent

years. Sachs et al.10 proposed a Bayesian-based algorithm instead of the EWMA
algorithm to compensate for large disturbances. Ingolfsson and Sachs6 analyzed the
stability of the EWMA controller and provided a guideline for choosing the control
parameter under different process drifts. Smith and Boning11 proposed a self-tuning
EWMA controller for processes with drift. Del Castillo3,4 also presented a self-tuning
controller that uses recursive least squares to continuously estimate the process
parameters. He showed that the self-tuning controllers have many advantages over
controllers with fixed control parameters. The controllers he proposed are based on
a process model that follows linear stochastic processes.
In this chapter we focus on processes subject to random disturbances of different
shift sizes, and propose an enhanced EWMA-based control algorithm to address the
control of this class of processes. Specifically, the goals of this chapter are to
1. Present a straightforward control strategy for practical applications.

2. Extend the EWMA controller to compensate for process disturbances with
different shift sizes.
3. Provide the capability to dynamically change control parameters in
response to disturbance changes.
In the following sections, we first overview the system architectures for both
the EWMA controller and the enhanced EWMA controller. The two main modules
of the enhanced controller, the Dynamic-Tuning Loop Trigger module and the R2R
Feedback Control module, are then detailed in Sections 19.3 and 19.4, respectively.
We then use simulations to validate the advantage of the enhanced EWMA controller
over the conventional EWMA controller in Section 19.5. Conclusions are presented
in Section 19.6.

19.2 SYSTEM ARCHITECTURE
19.2.1 EWMA CONTROLLER
To better explain the enhanced EWMA controller, we need to review the control
algorithm of the current EWMA controller first (see Chapter 3 for an in-depth
discussion). Assume that a typical process during production stage is already opti-
mized through design of experiments. In this case, the input–output process behavior
can be approximated by a linear model as
Yt = α + βXt + ε t (1)
where Yt = output measurement (t is the current run no.)

α = process model’s constant term
β = process model’s slope term
Xt = equipment settings
εt = white noise ε t ~ N(0, σ 2)
If there are special process disturbances such as process drifts and process shifts
(in addition to the underlying white noises) superimposed onto the process, the
process model will become
Yt = α + βXt + ε t + δ t
(2)
= (α + δ t ) + βXt + ε t
where δ t are the special process disturbances.

To reduce the impact of these special process disturbances on the output value,
an EWMA controller is used. Figure 19.1 illustrates the system architecture of a
current EWMA controller,10 and its main concepts are briefly explained below.
1. Assume that the underlying process model in (1) is estimated by a control

model with the following form:
Ŷt = at −1 + bXt (3)
where Yˆ t = predicted output value

at–1 = control model’s constant term
b = control model’s slope term (assumed = β and is fixed for all runs)
If we compare (2) with (3), we have a ≅ α +δt providing that β is correctly

estimated by b through design of experiments. This means that the special
process disturbances result in the changes of the constant term of the
control model.

Output Output
measurement measurements
station Yt
Residual Model prediction

^
et = Y t _ Y t Y^t = at _1 + bXt
Equipment
Model tuning
at = Wet + at _1
= W (Yt _ bX t ) + (1 _ W )at _1
Equipment Recipe generation

settings
Xt+1 = (T _ at) /b
Xt
FIGURE 19.1 System architecture of the EWMA controller.
2. Collect the output measurement Yt after one run and calculate the residual
between the measured output value and the predicted value:
et = Yt − Yˆt (4)
3. Fine-tune the constant term of the control model using the calculated
residual. To estimate its value more accurately, the constant term of the
control model is updated using the EWMA algorithm. Notice that W is
the control parameter to decide the weighting schemes on the historical
data and a0 = α.
at = Wet + at −1
= W (Yt − bXt ) + (1 − W )at −1 (5)
∑[W (1 − W ) (Y − bX )] + (1 − W ) α
t
t− j t
= j j
j =1
4. Obtain the new control model for the next run.
Ŷt +1 = at + bXt +1 (6)

5. Obtain the equipment settings (recipe) for the next run.
T − at
Xt +1 = , where T is the target value (7)
b
6. Repeat steps 2 to 5 on a run-by-run basis.
19.2.2 ENHANCED EWMA CONTROLLER

Figure 19.2 illustrates the system architecture of the enhanced EWMA controller.
As can be seen, there are two modules: the Dynamic-Tuning Loop Trigger module
Output Output
measurement measurements
station Yf
Residual Model prediction

ef = Yf - Yf Yf = af-1 + bXf
EWMA control chart Dynamic-Tuning Loop

El,f = Wlef + ( 1 - Wl ) El,f-1
Trigger Module
Large shift Yes, d=2

El,f > glσl
No
EWMA control chart
Em,f = Wmef + ( 1 - Wm ) Em,f-1
Yes, d=4 No
Medium shift? Controllable Stop
Em,f > gmσm
No Yes
Equipment
Dynamic-tuning Dynamic-tuning loop begins

loop completed f* = k - d + 1, k = current f
Yes No
Run-by-Run
Wf = 1 / ( f - f *+ 1) Feedback
No Control Module
W = Wb Wf > W b ?
Yes
W = Wb W = Wb
Dynamic-tuning Dynamic-tuning
loop completed loop completed
Model tuning & recipe generation

af = W (Yf - bXf ) + (1 - W) af-1
Xf+1 = ( T - af ) /b
Equipment Yes No
settings Recipe in spec ? Stop
Xf
FIGURE 19.2 System architecture of the enhanced EWMA controller.

and the Run-by-Run Feedback Control module. In the Dynamic-Tuning Loop Trig-
ger module, control charts are first used to determine if there is a large or medium
process shift. If there is a large or medium process shift and the error is controllable,
then the control parameter (W) must be reset to a higher value and starts a new
dynamic-tuning loop. In the Run-by-Run Feedback Control module, the control
parameter is tuned based on the current run’s sequence in the dynamic-tuning loop.
Once the control parameter is retuned, the control model will be retuned accordingly.
A new recipe is then generated so that the observed deviation can be compensated
for in the next run of the process. If the generated recipe is not feasible in practice,
we have to stop the process.
19.3 DYNAMIC-TUNING LOOP TRIGGER MODULE

In our proposed enhanced EWMA controller, a baseline EWMA controller will be
always utilized to compensate for smaller disturbances. In addition, large and
medium disturbances will be dealt with through the controller’s dynamic-tuning
mechanism. Thus, in the Dynamic-Tuning Trigger module, the goals are to detect
if there is a large or medium process shift and to reset the value of the control
parameter. Here, two EWMA control charts are used as the detection tools. As shown
in Figure 19.2, the residual for the current run is first calculated and plotted on the
EWMA control charts. If there is an out-of-control signal and the error is control-
lable, a dynamic-tuning loop is triggered.
In general, control charts are designed to detect a change as fast as possible
while minimizing the false alarm rate. We will use the following criteria to judge
the performance of the control charts:
• Robustness: long average run length (ARL0) between false alarms. The
larger the ARL0, the better the robustness.
• Sensitivity: short average run length (ARL1) between the shift and the
alarm. The smaller the ARL1, the better the sensitivity.
Typically, there are four types of control charts, and their difference can be charac-
terized by the weighting scheme on the historical data (Figure 19.3).5
• Shewhart control chart: each control point uses only the current measure-
ments, so a 100% weight is assigned to the current data.
• CUSUM control chart: each control point uses all the historical data by
assigning equal weights to all historical data.
• Moving average control chart: each control point uses the latest n (n = 4
in the example) data points by assigning equal weights to the latest n
points.
• EWMA control chart: each control point uses all the historical data, but
the more recent the data, the higher the weight. As shown in (8), the
weight is exponentially decreased as the data point ages.

Shewhart CUSUM
Weight % Weight %
100 100
50 50
0 0
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
Run Number Run Number
Moving Average EMMA W=0.6

Weight % Weight %
100 100
50 50
0 0
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
Run Number Run Number
FIGURE 19.3 Weighting schemes of different control charts.
Et = Wet + (1 − W ) Et −1
t (8)
= ∑ W (1 − W )
j =1
t− j
ej
For each of various control chart designs, tradeoffs have to be made between
robustness and sensitivity. Since the Shewhart control chart is usually more sensitive
to a large disturbance, but at the cost of a higher false alarm rate,7 we need to design
our two EWMA control charts with better sensitivity and robustness. Table 19.1
shows the ARL0 (the average run length when the shift size = 0) and ARL1 (the
average run length when the shift size > 0) for the Shewhart control chart and two
EWMA control charts. Here the EWMA results are calculated by using the Mark-
ovian approximation.7 As can be seen, the EWMA large control chart with Wl = 0.6
and control limit (CL) = 3.285σl (here, W 1 ⁄ ( 2 – W t )) is as good as the Shewhart
control chart at detecting a large shift (3σ), but at a better robustness. The EWMA
medium control chart with Wm = 0.33 and CL = 3.25sm (here, Wm ⁄ ( 2 – W m )) is better
than the Shewhart control chart at detecting a medium shift (2σ) in terms of sensi-
tivity and robustness. Here the average run length for the EWMA large control chart
is roughly equal to 2 after a 3σ shift (d = 2 in Figure 19.2). The average run length
for the EWMA_medium control chart is roughly equal to 3.9 after a 2σ shift (d =
4 in Figure 19.2).
19.4 RUN-BY-RUN FEEDBACK CONTROL MODULE

The control parameter (W) also determines the controller’s sensitivity and robustness.
It is known that a larger value of W will increase the controller’s sensitivity to the
process deviation and is able to capture the size of the deviation more quickly,

TABLE 19.1
Average Run Length for Shewhart and Two EWMA
Control Charts
Shewhart: EWMA large: EWMA medium:
W=1 Wl = 0.6 Wm = 0.33
Shift size ARL CL = 3σ CL = 3.285σl CL = 3.25σm
0σ ARL0 370.40 1003.44 1007.44

1σ ARL1 43.89 31.55 15.87
2σ ARL1 6.30 4.55 3.90
3σ ARL1 2.00 2.06 2.27
4σ ARL1 1.19 1.36 1.67
whereas a smaller W helps stabilize the controller’s response to white noises. It

seems reasonable to use a large value of the control parameter right after the detection
of a large shift (for sensitivity purposes), and to decrease the values gradually
afterward (for robustness purposes).
Now, suppose that a sudden shift (or a step change) occurs in the process (δt =
S∆t–t* in (2)). That is,
Yt = α + βXt + S∆ t −t* + ε t (9)
where S = size of the process shift
= 1 when t ≥ t *
∆ t −t* 
= 0 when T < t *
Assume for now that the change point t* is known. In order to compensate for the
sudden shift (S) quickly, W of the EWMA controller in Eq. (5) should be set larger
immediately after the change point to capture the shift size. However, the step change
occurs only once and the process mean remains unchanged after t*. If the value of
W remains large, the controller becomes oversensitive to the white noises. To over-
come the trade-off between large and small W and to design a more effective
controller for processes subject to sudden shifts, we propose a controller with a
dynamically adjusted control parameter:
at = Wt (Yt − bXt ) + (1 − Wt ) at −1 (10)
In Eq. (10), the value of the control parameter (Wt) is dynamically adjusted over
time. The task now is to derive a method for adjusting Wt.
Here, we first consider the case where the change point is known and we do not
have prior knowledge of how the process will be shifting away. In this case, we rely
only on the sample data presently obtained from the process to estimate the shift

size. In the appendix to this chapter, a theorem is provided to determine the optimum
control parameter Wt, which minimizes the mean squared deviation (MSDt+1) at run
t + 1. MSDt+1 is defined as follows:
[
MSDt +1 = E(Yt +1 − T )
2
] (11)
The following results for are is obtained:
1
Wt opt = (12)
t − t * +1
 1 + 1 σ 2
+1 = 
MSDtopt (13)
 t − t * +1 
In Eq. (12), Wt decreases over time and diminishes to zero. This, however, is
not desirable, since very often the process is subject not only to shifts, but also to
drifts and other smaller disturbances. Therefore, a minimum value of Wt is required
to keep the baseline EWMA controller working for compensating for such distur-
bances. The control equation becomes
at = W (Yt − bXt ) + (1 − W )at −1 for t ≥ t * (14)
max (Wt , Wb ) if dynamic − tuning loop is not completed

W= (15)
Wb if dynamic − tuning loop is completed
where Wb is the required minimum value of the control parameter.

In reality, the change point t* is unknown. EWMA charts are therefore installed
to detect the shifts. As mentioned earlier, two EWMA control charts are used in our
approach: one for detecting a larger shift and the other for detecting a medium shift.
However, the signaling of either control chart only takes place some time after the
actual change point. The time delay can be roughly estimated by the average run
length (d) of the control chart. Suppose now the control chart detects the shift at the
kth run (Figure 19.4). Then, the change point can be estimated to be
tˆ* = k − d + 1 (16)
change point detection point

X X
t* k
control chart run length ~ d
FIGURE 19.4 The run length for the control chart to detect a process shift.

0.6
dynamic parameter
0.5 minimum control parameter
Dynamic-tuning loop begins
0.4 under a large process shift
Dynamic-tuning loop begins
Wt
0.3 under a medium process shift
Dynamic-tuning
0.2 loop stops
0.1
Run
FIGURE 19.5 Dynamic-tuning feature of the control parameters.
Equations (12), (14), and (15) can be then applied, followed by the recipe
generation and model prediction as presented in Eqs. (6) and (7). The complete Run-
by-Run Feedback Control module is shown in Figure 19.2.
From Eqs. (12) and (16), the control parameter of the enhanced EWMA con-
troller has a starting value:
1 1
Wk = = (17)
k − tˆ * +1 d
That is, the controller will take into consideration d data points prior to the detection
point k while estimating at. The control parameter continues to diminish over time
until it reaches Wb (Figure 19.5) and is fixed at that minimum required level (0.1 in
Figure 19.5) afterward. This control cycle holds on until one of the EWMA charts
signals again. The alarm given by the control chart indicates the occurrence of a
shift (large or medium) and triggers the need of adjusting the control parameter
again to capture the step change. The dynamically adjusting scheme of the control
parameter as described above is thus restarted, and Eqs. (4) and (12) are recalculated
starting from the estimated change point t̂*.
Figure 19.5 shows the changes of the control parameter over time. As can be
seen, the value of W starts with 1/2 (triggered by the first EWMA chart for detecting
a large shift) and decreases until it reaches a minimum value of 0.1. The cycle lasts
until a new signal is given by the second control chart. The new signal triggers a
new cycle of the dynamically adjusting W. This time, it starts with 1/4 and again
diminishes to 0.1.
19.5 SIMULATION VALIDATION

19.5.1 PROCESS DISTURBANCE MODELS
To validate the superior performance of the enhanced EWMA controller over the
traditional EWMA controller with fixed control parameter, simulations are performed.

First we need to define the special process disturbances. Two types of disturbances
are simulated, namely, process drifts and shifts, and modeled in Eq. (18):
δ t = cσt + τt (18)
where cσt is the process drift and τt is the process shift. Assume, also, that the drift
follows a linear drift pattern and deviates from the target at the speed of cσ (c is a
constant and σ is the standard deviation of white noise) per unit time. As for the
shift, it is modeled as a random shift with the following pattern:
τt −1 with probability 1 − p

τt =  (19)
τt −1 + S with probability p
where p is the probability of the shift occurrence. The shift size S is a random
variable and follows a normal distribution with mean µ S and variance σS2, i.e., S ~
N(µ S,σS2). To simplify the simulation, we further assume that σS = σ, so S ~ N(µ S,σ 2).
19.5.2 A SIMPLE EXAMPLE

Next, a simple example is used to illustrate the dynamic-tuning feature in the
presense of random disturbances. In this simulation example, a process is assumed
to have the following model form:
Yt = α + βXt + ε t + δ t = 3000 + 10 Xt + ε t + δ t (20)
( ) (
ε t ~ N 0, σ 2 ~ N 0, 50 2 ) (21)
δ t = cσt + τt = 0.02(50)t + τt (22)
τt −1 with probability 1 − p

τt =  (23)
τt −1 + S with probability p
p = 0.05, ( ) (
S ~ N 3σ, σ 2 ~ N 150, 50 2 ) (24)
Let’s further assume the target output is 3500. Now the simulation is performed
with the above parameters for 2000 runs in one simulation cycle. With different
random numbers, the simulation is repeated 200 cycles. Results of the first 71 runs
in one cycle are shown in Figure 19.6a,b,c,d. Notice that there are three shifts
occurring during the first 71 runs. The shift sizes and the locations are 3.3σ at run
17, 3.1σ at run 45, and 2.2σ at run 62. In Figure 19.6b, the alarms given by the first
EWMA control chart at the 18th run and the 46th run indicate the occurrence of
large shifts and trigger the need to increase the value of the control parameter in

4000
3900
3800
3700
Yt
3600
3500
3400 dynamic control parameter
3300 fixed control parameter
without control
3200
1 11 21 31 41 51 61 71
Run
150
100
50
E l,t
0
-50
-100
-150
1 11 21 31 41 51 61 71
Run
FIGURE 19.6 (a) A simple example to show the effectiveness of the enhanced EWMA
controller. (b) The first EWMA chart detects large shifts at the 18th run and 46th run. (c) The
second EWMA chart detects a medium shift at the 65th run. (d) The changes of control
parameters over time.
order to capture the step changes. In Figure 19.6c, the alarm given by the second
EWMA control chart at the 65th run also indicates the occurrence of a medium
shift. Figure 19.6d shows the changes of the control parameter over time. As can be
seen, the values of W reset with 1/2 at the 18th run and 46th run and reset with 1/4
at the 65th run. Then W decreases until it reaches a minimum value 0.15 (Wb = 0.15
in this case). As shown in Figure 19.6a, when a shift occurs the enhanced EWMA
controller can estimate the change of the process mean value and compensate for
the deviation more quickly than the EWMA controller with fixed control parameter.
19 .6 MONTE CARLO SIMULATIONS

To validate the performance of the enhanced EWMA controller, Monte Carlo sim-
ulations are performed under various random disturbances. In these Monte Carlo
simulations process models are assumed to be the same as in (20), (21), and (22).
The superimposed random shifts in (23) are simulated in four cases, and their
occurrence probability (p) and magnitude (S) are summarized in Table 19.2. For
example, in the first case the random shift has a low probability of occurrence and
smaller shift magnitude. In the fourth case, the random shift has a high probability
of occurrence and larger shift magnitude.

150
100
50
E m,t
0
-50
-100
-150
1 11 21 31 41 51 61 71
Run
0.6
0.5
0.4
Wt
0.3
0.2
0.1
0
1 11 21 31 41 51 61 71
Run
FIGURE 19.6 (continued)
TABLE 19.2
Four Simulated Cases in the Monte Carlo Simulations
Case Case 1 Case 2 Case 3 Case 4
p 0.005 0.005 0.05 0.05

S N (0, σ 2) N (3σ, σ 2) N (0, σ 2) N (3σ, σ 2)
In these simulations, we compare the performance of the enhanced EWMA

controller with the EWMA controller with fixed control parameter under the four
cases of disturbances. As for the control performance characterization, the normal-
ized mean squared error is used as the performance index. The smaller the value,
the better the performance. The normalized mean squared error is denoted as MSE/σ 2
and is defined as
 1 n 
∑ (Yt − T ) 
2
MSE σ 2 =  σ2 (25)
n
 t =1 
Here the MSE/σ 2 index is calculated based on the simulation results of 2000 runs
and 200 simulation cycles. Results of the study (MSE/σ 2 index against Wb) are

shown in Figures 19.7a,b,c,d. We also plot the average of Figures 19.7a,b,c,d in
Figure 19.7e. Figure 19.7e represents the situation where the disturbance information
is unknown and all types of disturbances are possible.
Based on these simulation results, we have the following conclusions:
• When there are only small process drifts or small shifts, as happened in
Cases 1 and 3, the baseline EWMA controller is very effective in con-
trolling these small disturbances. As a result, the enhanced EWMA con-
troller doesn’t trigger the dynamic-tuning capability and uses the
minimum control parameter in most of the runs. Therefore, a similar
control performance in Figures 19.7a and 19.7c is observed.
• When there are large process shifts, as happened in Cases 2 and 4, the
enhanced EWMA controller is much better than the EWMA controller
with fixed control parameter. As shown in Figures 19.7b and 19.7d, the
performance of the EWMA controller with fixed control parameter highly
depends on the choice of the control parameter. The range of the optimal
control parameter is quite large, ranging from 0.3 in Case 2 to 0.6 in
Case 4. The performance of the enhanced EWMA controller, on the other
hand, is less dependent on the minimum control parameter.
• The superiority of the enhanced EWMA controller is validated by the
better average performance as shown in Figure 19.7e.
19.7 CONCLUSIONS
In this chapter, an enhanced EWMA controller for processes subject to small and
large random disturbances has been presented. The controller uses two EWMA
control charts to trigger a dynamic-tuning loop and adjusts the control parameter in
response to the disturbances. Through the simulation study, we reach the following
conclusion:
• The enhanced EWMA controller is very effective in controlling processes

subject to small and large random disturbances.
• The enhanced EWMA controller adjusts its control parameter dynamically
in response to the process changes.
• The enhanced EWMA controller is better than the EWMA controller with
fixed control parameters.
The enhanced controller presented thus represents an ideal extension to the

EWMA solutions presented in Chapter 3 and utilized throughout this book (e.g., in
Chapters 1, 6, 11, 13, and 15). Utilizing this extension, the domain of applicability
of the EWMA solutions can be expanded and control can be provided for systems
that are subject not only to well-behaved drift, but also larger random disturbances.

2
dynamic control parameter
1.8
fixed control parameter
MSE/ σ2
1.6
1.4
1.2
1
0 0.2 0.4 0.6 0.8 1
Wb
2
1.8
MSE/ σ2
1.6
1.4
1.2
1
0 0.2 0.4 0.6 0.8 1
Wb
2
1.8
MSE/ σ2
1.6
1.4
1.2
1
0 0.2 0.4 0.6 0.8 1
Wb
FIGURE 19.7 (a) Simulation results of Case 1. (b) Simulation results of Case 2. (c) Simu-
lation results of Case 3. (d) Simulation results of Case 4. (e) Average results of Cases 1, 2,
3, and 4.

3
2.8
MSE/ σ2
2.6
2.4
2.2
2
0 0.2 0.4 0.6 0.8 1
Wb
2.4
2.2
MSE/ σ2
2
1.8
1.6
1.4
0 0.2 0.4 0.6 0.8 1
Wb

APPENDIX
Theorem: Given a process model in Eq. (9), an EWMA controller with a dynami-
1
cally adjusted control parameter in Eq. (10) minimizes MSDt if Wt = for
t − t * +1
all t ≥ t* and the observation at the time t* is known.
1
Proof: Given the control parameter Wt = for any t* ≤ t < τ and assuming
t − t * +1
b = β:
aτ = Wτ (Yτ − bXτ ) + (1 − Wτ ) aτ−1
[
= Wτ (α + S + ε τ ) + (1 − Wτ ) Wτ−1 (Yτ−1 − bXτ−1 ) + (1 − Wτ−1 ) aτ−2 . ]
1
Substituting Wτ–1 = into the above equation, we obtain:
τ−t*
τ − t * −1
aτ = Wτ (α + S + ε τ ) + (1 − Wτ )  ( α + S + ε τ−1 ) + aτ−2 
1
 τ − t * τ − t * 
= Wτ (α + S + ε τ ) + (1 − Wτ )
τ − t * −1
 1 α+S+ε

τ − t *
( τ −1 ) +
τ−t*
[
Wτ−2 (Yτ−2 − bXτ−2 ) + (1 − Wτ−2 )aτ−3 ] .
1
Again, substituting Wτ–2 = into the above equation, we obtain
τ − t * −1
aτ = Wτ (α + S + ε τ ) + (1 − Wτ ) (α + S + ε τ−1 )
1
τ
 t*−
τ − t * −1 
+
1
(Y − bXτ−2 ) + ττ −− tt ** −−21 aτ−3 
τ − t *  τ − t * −1 τ−2 
 1
= Wτ (α + S + ε τ ) + (1 − Wτ )  (α + S + ε τ−1 ) + τ τ−−t *t *−1  τ − t1* −1
τ − t *
(α + S + ε ) + ττ −− tt ** −−21 (W (Y
τ−2 τ −3 τ −3 )

− bXτ−3 ) + (1 − Wτ−3 ) aτ− 4  
τ −1
= Wτ (α + S) + (1 − Wτ ) (α + S) + Wτ ε τ + (1 − Wτ ) ∑
2 1
ε
τ−t* τ − t * i = τ−2 i
τ − t * −2
+
τ−t*
[
Wτ−3 (Yτ−3 − bXτ−3 ) + (1 − Wτ−3 ) aτ− 4 . ]

By recursively substituting Wτ–3 = 1 , …, Wt* = 1 into the equation, we finally
have τ − t * −2
τ −1
aτ = α + S + Wτ ε τ + (1 − Wτ )
1
τ−t* ∑ε .
i = t*
i
The recipe at τ + 1 becomes
T − aτ
Xτ +1 =
b
τ −1
t − α − S − Wτ ε τ − (1 − Wτ )
1
τ−t* ∑ε
i = t*
i
= .
b
The process output and its MSD at τ + 1 are
τ −1
Yτ +1 = α + bXτ +1 + S + ε τ +1 = T + ε τ +1 − Wτ ε τ − (1 − Wτ )
1
τ−t* ∑ε
i = t*
i
and
[
MSDτ +1 = E (Yτ +1 − T )
2
]
= σ 2 + Wτ2 σ 2 + (1 − Wτ )
2 1
σ 2.
τ−t*
By minimizing MSDτ+1 with respect to Wτ, we obtain the optimal control parameter
at τ,
1
Wτopt =
τ − t * +1
and the optimal MSD,
 1
+ 1 σ 2 .
+1 = 
MSDτopt
 τ − t * +1 
1 1
We have shown that given Wt = for t* ≤ t < τ, Wτopt = . That is,
t − t * +1 τ − t * +1
1 1
if Wt*opt = , then recursively we can obtain Wt opt = for ∀ t ≥ t*.
t * −t * +1 t − t * +1
opt
Now, we show that Wt* = 1. Since

at* = Wt* (Yt* − bXt* ) + (1 − Wt* ) at* − 1
(
= Wt* (α + S + ε t* ) + (1 − Wt* ) Yˆt* − bXt* )
= Wt* (α + S + ε t* ) + (1 − Wt* ) (T − Yt* + α + S + ε t* )
= α + S + (1 − Wt* ) (T − Yt* ) + ε t* ,
the new recipe for the next run is
T − at*
Xt*+1 =
b
T − α − S − (1 − Wt* ) (T − Yt* ) − ε t*
=
b
and the next run’s output is
Yt*+1 = α + bXt*+1 + S + ε t*+1
= T − (1 − Wt* ) (T − Yt* ) − ε t* + ε t*+1 .
Given the output at time t* is observed to be yt*, MSD for the next run becomes:
[
MSDt*+1 = E (Yt*+1 − T ) Yt* = yt*
2
]
{[
= E (1 − Wt* ) (T − yt* ) − ε t* + ε*+1t ]
2
Yt* = yt* }
= (1 − Wt* ) (T − yt* ) + σ 2 + σ 2
2 2
Minimizing MSDt*+1 with respect to Wt* , we obtain optimal control parameter:
Wt*opt = 1 and MSDt*opt+1 = [1 + 1] σ 2 .
Therefore,
Wt opt =
1  1 + 1 σ 2 for ∀ t ≥ t *.
+1 = 
and MSDtopt
t − t * +1  t − t * +1 

REFERENCES
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20 Enabling Generic
Interprocess
Multistep Control:
the Active Controller
Nauman Chaudhry, James Moyne, and
Elke A. Rundensteiner
20.1 INTRODUCTION
Control of a semiconductor manufacturing facility can take place at various levels
throughout the facility and can take different forms. As shown in Figures 7 and 8
in the Introduction to this book, there are various levels of control that can be
configured in a hierarchical complementary fashion to better achieve process goals.
As R2R control becomes more mature and widely accepted, attention will become
more focused on the integration of layers of control above (interprocess) and below
(in situ) the R2R control level. The implementation of generic, configurable R2R
control solutions, as defined in Part 3 of this book, will simplify the integration task.
Similarly, development of generic and configurable solutions at other control layers
will facilitate their complementary and incremental utilization in the factory, thereby
easing the migration to a multilevel control scheme depicted in Figure 8 of the
Introduction.1
This chapter addresses the migration to multilevel control in the semiconductor
industry by presenting a methodology for implementing generic and configurable
interprocess multistep control.2,3 Multistep (also called interprocess) control can be
carried out whenever the fabrication process consists of several steps. In multistep
feedforward control, deviations in the processing of a wafer in one step are com-
pensated for by adjusting the processing in some/all of the steps that are yet to be
carried out on that particular wafer. In multistep feedback control, a cell which has
already processed a wafer receives advice from a “downstream” cell so as to adjust
its model for “better” processing in future runs. In other words, for multistep
feedforward control, a cell carrying out a step on a wafer gives advice to cells which
are “downstream” for the processing of this wafer, whereas in multistep feedback
control the direction of flow of advice is “upstream” with respect to the processing
of the present wafer, as shown in Figure 20.1.
Control of semiconductor processes over multiple steps has been identified as
an important feature of the semiconductor manufacturing facilities of the future,4

FIGURE 20.1 Conceptual flow of information and product for multistep feedback/feedfor-
ward control.
and research has been conducted for developing control algorithms for carrying out
such control.5,6 However, the development of generic enabling mechanisms, which
can be used to implement multistep feedback and feedforward control, has not been
adequately addressed (see Section 20.4 for further discussion). To fill this gap, we
present in this chapter an adaptable, portable, and generic software enabler for
multistep control in manufacturing. This enabler, called the Active Controller, uses
an active database system to carry out multistep control, and provides the capability
of defining control rules that serve to provide an adaptable and portable mechanism
for multistep control.
The remainder of this chapter is organized as follows. In Section 20.2, the require-
ments for implementing a generic multistep controller are described. An introduction
to some of the basic concepts in active databases and an in-depth description of the
Active Controller is contained in Section 20.3, and in Section 20.4 the issue of inte-
grating the Active Controller with computer integrated manufacturing (CIM) environ-
ments is discussed. In Section 20.5 the current research in multistep control and CIM
environments is summarized, while conclusions are presented in Section 20.6.
20.2 PROVIDING MULTISTEP CONTROL

Factory computer integrated manufacturing (CIM) systems are comprised of several
applications that provide the various CIM functions.7 In this section we discuss those
applications whose functionality is relevant for providing multistep control. We will
use this discussion to derive requirements for a generic multistep controller.
20.2.1 SEMICONDUCTOR CIM ENVIRONMENT

In a typical CIM implementation,8 the processing of wafers requires interaction
between various applications, the following of which are important for providing
multistep control:
• The processing to be carried out to fabricate wafers is specified using an

application termed Process Flow Specification Manager (PFM).8 PFM

provides a computer-aided specification environment for defining process
flows. A process flow for a particular product specifies the process steps
to be carried out on the wafer, and the sequence in which these steps are
to be executed to achieve the desired processing of the wafer.
• The process flow is given as an input to a scheduler. The scheduler decides
when a wafer is to be processed by a piece of equipment and directs the
factory resources to effect these decisions.
• Processing and control at individual pieces of equipment is carried out
by equipment controllers. An equipment controller provides mechanisms
for the specification and manipulation of recipes which are used for
carrying out processing at an equipment when instructed by the scheduler.
An equipment controller has information about required equipment con-
trollables (settings/recipe) to achieve specified goals (effects) in the pro-
cess flow.
20.2.2 REQUIREMENTS FOR A MULTISTEP CONTROLLER

For any wafer undergoing processing in the facility, the multistep controller needs
to be able to detect when and if multistep control is required, and carry out the
appropriate compensating action. To provide this functionality, the multistep con-
troller needs to be informed of the result of each processing step completed by an
equipment controller. Depending upon this result and relevant previous result data,
the multistep controller may suggest changes to the existing process flow for the
wafer so as to compensate for any processing errors. In addition, the multistep
controller may also respond to temporal and other events (e.g., machine shutdowns,
etc.) to carry out appropriate actions as needed. To provide these functions, the
multistep controller should be able to
• Understand the process flow specification,

• Monitor events of interest in the facility,
• Retain or access information about the processing carried out on individual
wafers,
• Keep historical information necessary to make control decisions about
equipment in the facility.
In addition to the functional requirements listed above, the following design goals
are identified for the multistep controller:
• Since modification of control knowledge is an ongoing necessity in a

semiconductor manufacturing environment,9 the multistep control mech-
anism should be adaptable to allow easy extension/adaptation to handle
new control situations.
• The controller should be portable so that it can be easily reused for
different fabrication processes.
• The controller should be generic in that it is not tied to a particular CIM
implementation and can be integrated with various CIM environments.

20.3 ACTIVE CONTROLLER FOR
MULTISTEP CONTROL
The Active Controller, a multistep controller developed to fulfill the requirements
for multistep control (as discussed in the previous section), is described in this
section. Since active database technology is at the core of the Active Controller, we
first give an introduction to relevant basic concepts of active database systems. We
then discuss the design and implementation of the Active Controller, and research
toward extending active database technology to provide advanced features for the
general domain of process automation and control.
20.3.1 ACTIVE DATABASE TECHNOLOGY

Conventional database systems are passive: they only execute queries or transactions
explicitly submitted by a user or an application program. Recent trends in database
technology have attempted to extend this conventional functionality to accommodate
advanced applications. Active database systems represent one of the important
enhancements of conventional database systems, where the database system is trans-
formed to be active, i.e., to provide the ability to monitor the database state and to
react to predefined situations without explicit user action or application requests.10
Situations to be observed and actions to be initiated are managed by the database
system. Active database systems thus provide common application-independent func-
tionality for complex dynamic control structures. Instead of having each application
survey events and conditions individually and schedule the appropriate reactions (i.e.,
consistency checks, notification procedures, etc.), both the monitoring of events and
the scheduling of the actions is incorporated into the database system.10
The desired behavior of active database systems is expressed in terms of
event–condition–action (ECA) rules. The rule syntax can be described as
ON event IF condition DO action,
with the following semantics: when the event occurs, if the condition is true, then
carry out the action. Events signal situations inside or outside the database system.
Conditions are Boolean expressions that are checked as preconditions of actions.
Actions are executable routines within or outside the database system.
The basic behavior of an active database system is illustrated in the following
example:
Example: Consider a simple rule defined to keep track of the value of temperature of
an oven and raise an alarm if the value exceeds a limit.
ON current temperature updated for oven

IF current temperature > high temperature limit
DO signal high temperature alarm.
Now, whenever an application updates the temperature value in the database, the active
database system will check if the temperature value exceeds the specified limit, and if
so will raise a high temperature alarm. Notice that if the policy is to be changed (e.g.,
the high temperature limit is to be modified), this will require only modifying the rule.

20.3.2 USING ACTIVE DATABASES FOR MULTISTEP CONTROL
Multistep control is performed using ECA rules as follows: rules encoding the
desired control algorithms are defined on the process specification. Execution of a
process step at a machine or a composition of several such process steps constitutes
the (composite) event for the Active Controller rules. The conditions of these rules
are the scenarios in which multistep control can be used to improve the processing
of the product, i.e., the situations in which processing at certain machines can be
adjusted to compensate for errors in processing at certain other machines. These
conditions are defined in terms of relevant process parameters, such as predicted
process mean, specification limits, etc., and parameters of the manufacturing process,
e.g., acceptable yield loss, etc. Firing of the rules causes appropriate actions to be
taken to change the processing to be carried out in the future, and thus compensate
past processing errors.
A suitable active rule mechanism which allows expression of a range of condi-
tions for multistep control provides for a portable implementation of multistep
control, since the specification of the control behavior via active rules means that
same controller can be reused for a different process by defining a suitable rule base.
This mechanism is easily adaptable, since by adding appropriate rules the controller
can be adapted to handle new situations. This is in contrast with the use of an
application program written for event detection and condition checking, because in
this case moving from one process to another may require significant modification
of the application program.
It should be noted that since expert systems provide the capability of rule
definition and execution, a multistep control enabler could be developed using expert
systems technology instead of using active database systems. Use of expert systems,
though, would require the overhead of coupling the expert system to the (passive)
CIM database. Additionally, active database systems are more powerful than expert
systems. Expert systems typically have condition–action rules, which are evaluated
and executed in recognize–act (“if–then”) cycles. Active databases have event–con-
dition–action rules, which are a superset of the expert system condition–action rules
and can provide more efficient processing of rules.11 Other advantages of active
database systems over expert systems stem from the fact that active database systems
provide all the capabilities of passive database systems. Database mechanisms such
as indexing can be utilized for condition checking, making rule execution more
efficient than in expert systems. Active database systems have in fact been suggested
as suitable platforms for building large and efficient expert systems.12
20.3.3 ACTIVE CONTROLLER DESIGN AND

SAMPLE IMPLEMENTATION
An Active Controller solution has been implemented using the Ode active object-
oriented database system developed by AT&T.13,14 The implementation has been
carried out using O++, Ode’s programming language, and comprises about 10K
lines of O++ source code. A graphical user interface (GUI) has been developed for

FIGURE 20.2 Process flow structure.
the Active Controller using Tcl/Tk15 and daVinci, a graph visualization system
developed at the University of Bremen, Germany.16
20.3.3.1 Modeling the Process Flow
In current semiconductor manufacturing CIM systems, process flows to fabricate a

wafer are specified by a hierarchical object-oriented data structure.17,18 Process flows
are composed from flows, processes, steps, and equipment, as shown in Figure 20.2,
using the object modeling technique (OMT).19 In this model, a step is the basic unit
of processing and is defined as what can be accomplished in one chamber. A step
is carried out on one piece of equipment. However, the same equipment may be
used by more than one step. The next higher processing abstraction is a process. A
process is defined as a sequence of other processes or steps. The highest processing
abstraction is a flow, which is defined as a sequence of processes.
Each flow, process, and step may have a set of effects, which describe the
expected impact of the flow, process, or step on the wafer. The effects associated
with a step are used to create settings/recipe for the equipment on which the step is
being carried out. However, these effects can be overridden by a process that contains
this step. Similarly, a flow may use its set of effects to override effects associated
with its processes.
The current software implementation of the process-flow schema in the Active
Controller includes classes corresponding to flow, process, step, and effect (and
subclasses of these classes). Equipment is simulated by asking the user of the Active
Controller to input the results of process-flow execution.
Example #1: A screen shot of daVinci’s representation of a process-flow in the Active

Controller database appears in Figure 20.3. In the Active Controller GUI, a flow is
represented by an oval, a process by a rhombus, and a step by a rectangle. The effects
of a step are shown in the rectangle under the name of the step. The figure shows a

FIGURE 20.3 Screen-shot of an example process flow in the active controller.
flow instance cmos_3 which is composed of one process mosfet_n1. mosfet_n1 is

composed of a process gate_definition4, which in turn in composed of various steps
and processes, such as deposit1, photolitho20, measure4, and etch3.
20.3.3.2 Defining Rules for Multistep Control
When a wafer is to be fabricated, an instance of the corresponding flow is selected

from the database and the resultant process-flow is executed. The execution of the
process-flow results in the execution of the processes of which the flow is composed.
Similarly, the execution of a process, in turn, causes the execution of the processes
and steps of which this process is composed. The fabrication of a wafer thus results
in the execution of a number of processes and steps at different levels of nesting in
the process-flow.
As the execution of a process-flow proceeds, the need to control the wafer
fabrication frequently requires changes to the original processing sequence specified
in the process-flow. To provide this capability we need the ability to specify control
actions for the process specification. We use the rule definition facilities of Ode to
specify the multistep control knowledge in terms of active rules defined on the
process flow structure. These control rules can trigger appropriate control actions
during process execution whenever the need arises, and can modify processing by,
for example, requiring reexecution of a part of the process-flow. Simpler modifica-
tions consist of tuning the process by changing just the effects associated with one
or more steps in the processing sequence. Such modifications can be easily accom-
modated by causing the appropriate attributes of the relevant step objects (e.g.,
settings) to be changed.

Example #2: Consider that a photolithography sequence (see Figure 20.3) is being
executed and a statistically significant error violating the control limit is observed in
the photoresist linewidth. The rule encoding to detect this condition, photoresist_error
defined on class measure is shown in Figure 20.4a and the controller operation to
verify this condition is illustrated in Figure 20.4b. The event associated with the rule
is after measure_execute and hence will be raised after the execution of the complete
(postlithography) measure step. When an out-of-limits condition is detected
(Figure 20.4c), the appropriate rule fires (Figure 20.4d) and a new recipe is generated
for the (downstream) etch step by modifying the etch target (Figure 20.4e).
Example #3: Consider that a photolithography sequence is being executed and a

statistically significant error violating the control limit is observed in the reflectance
of the wafer after the spin-coat and bake step. A new recipe is generated for the exposure
step by modifying the exposure time to compensate for the reflectance error; the
formulation for recipe adjustment for example is given in Reference 20. In the active
controller implementation, a rule spin_cb_error is defined on the class spin_coat.
The event associated with the rule is after spin_cb_execute and hence will be raised
after the execution of the spin-coat and bake step. To check for alarm condition a
function error_check is called, and if it returns TRUE, indicating an alarm has been
raised, the spin-coat step informs the photolitho step of this error. In case this error
has been reported, the rule spin_cb_error defined on the expose_resist class is fired
before the execution of the expose step. This results in modifying the exposure time.
This modification is achieved by calling the modify method for effects, which can
query the database to determine the results of the spin-coat step and call an external
function to find out the new recipe.
In addition to the simple modification of changing only the recipe associated

with a particular step (as in the previous two examples), the Active Controller can
also implement more complex control actions such as rework, repair, etc. Actions
such as rework require modification to the actual sequence of steps that were to be
carried out. The Active Controller can be used to implement such control actions.3
20.3.3.3 Active Controller Features
Ode provides powerful rule definition capabilities. The condition part allows calling
functions in addition to querying the database, while the action part can contain
programming language statements and allow for interaction with foreign functions.
This capability can be used to integrate third-party analysis software with the Active
Controller implementation.
Ode also provides a rich event language with multiple operators (e.g., conjunc-
tion, negation, ordering, etc.) for composing events. Events can be defined to be
raised either before or after the execution of a method. Events can also be defined
to be raised with respect to transactions. When defining a class, the user specifies
the events that need to be monitored for instances of this class. Ode keeps a history
of these events of interest. This capability, in conjunction with the event composition
operators, means that the Active Controller implementation provides an extremely
powerful control rule definition capability. It is thus possible, for example, to use
the Active Controller to define rules that fire based on historical trends or on events
that occur at different points in the processing of a particular wafer. Note that the

FIGURE 20.4 (a) Rules Defined (on “gate_definition”, “measure”, and “etch”) for correcting
for photoresist linewith error. (b) Mechanism for evaluating photoresist linewith error.
(c) Detecting linewith error and rule firing. (d) Figure 20.4d. Active Control: action associated
with rule firing; adjustment of etch recipe. (e) Active Control: correcting for linewith error
by adjustment of etch recipe.


Active Controller implementation provides all the functional capabilities identified

in Section 20.2. In addition, the use of active database technology in the Active
Controller helps achieve the design goals of adaptability and portability. The third
design goal of genericity of the Active Controller implementation is linked to
emerging trends in CIM environments and software technology, and is further
discussed in Section 20.4.
20.3.4 EXTENDING ACTIVE DATABASE TECHNOLOGY

FOR PROCESS CONTROL
Active database technology is still in the process of maturing. In particular, unlike

traditional (passive) database systems for which well-defined methodologies for
building database applications exist, a key difficulty in developing applications using
active databases is the lack of methodological support for active rule definition.21 It
has also been noted that another hindrance in the employment of active database
technology is the difficulty in defining and maintaining rule sets.10 Therefore, for
active database technology to be an attractive vehicle for the implementation of
advanced applications, the implementor needs to be guided toward defining rules
that are easy to analyze and have predictable behavior.
To make active database technology suitable for developing control applications,
solutions have been developed for these different problems for the domain of process
control by exploiting particular characteristics of the process specification model
(i.e., Figure 20.2). A detailed description of this research is given in Reference 3.
Here we give a brief summary of some of the salient features.

To overcome the absence of design methodologies for defining active rules,
specific guidelines for rule definition are developed. Programming and maintaining
rules that arbitrarily span many classes can be an extremely difficult task, since the
rule programmer has to ensure that a newly defined rule does not cause unforeseen
interaction with other rules already defined for other classes. In addition, such rule
definition violates the object-oriented principle of encapsulation. Guidelines have
been developed that require each rule to have a well-defined scope of influence.2,22
To limit the scope of interaction of rules, each rule has to be defined on a particular
process (or flow or step) class. The rule can only refer to properties (i.e., attributes,
methods, or other rules) that are directly accessible from the process class it is
defined on. Since we remain within the scope of the process on which the rule is
defined, the resulting definition of process classes respects the principle of encap-
sulation, and this leads to rules whose interaction is easier to analyze. We have
applied these design guidelines in defining control rules for the Active Controller,
and have found the resulting rule sets to have the aforementioned properties of
maintainability and predictability.
20.4 INTEGRATING THE ACTIVE CONTROLLER

WITH CIM ENVIRONMENTS
Having described the design and implementation of the Active Controller, we now
look at the issue of integration of this controller in CIM environments. In this area,
the SEMATECH CIM Framework7 provides a comprehensive specification for an
application framework for CIM in semiconductor facilities. The heart of the CIM
framework is a set of semiconductor manufacturing abstractions and services that
are typically embodied as applications. The CIM Framework can be viewed as a set
of integrated frameworks, providing functionalities at different levels in the factory.
These frameworks include Enterprise Framework, MES Framework, APC Frame-
work, and Equipment Integration Framework (see Figure 7.2 of Chapter 7).
The Active Controller can be envisaged as an additional application in the APC
Framework providing multistep control while drawing upon the services provided
by several applications, such as the Specification/PFM application in the MES
Framework, the Process History application in Equipment Integration Framework,
etc. Object technology is at the core of the design and implementation of the Active
Controller. Hence, as the CIM framework matures, it should be possible to tailor
the Active Controller implementation to fit in as an application drawing upon and
providing services to the CIM Framework.
The Active Controller needs to interact closely with the PFM. To modify the
processing of the wafer, the Active Controller has to act on the process flow speci-
fication and thus requires knowledge of this specification. This information is main-
tained by the PFM. One possible design alternative is to add the functionality of the
Active Controller to the PFM. However, to keep the Active Controller as a pluggable
application, the Active Controller has been designed to duplicate the needed process-
flow information in the Active Controller database, and then the Active Controller
as an advisory application to the PFM.

20.5 RELATED RESEARCH
20.5.1 RESEARCH IN MULTISTEP CONTROL
Recently, research has also been carried out to provide control of sequences of
interrelated processes. A control system for photolithography sequences is described
in Reference 5. Two process control methodologies are used for multistep control.
In one of these, a local controller corrects the shortcomings of the present machine
by generating customized recipes at the next process step. In the other control
methodology, a global controller finds optimum specification for the upstream pro-
cesses to ensure that the outputs of the final process can meet their specifications.
Results indicate a significant improvement in the overall capability of the process
sequence.
Another research effort in multistep control is reported in Reference 6. Feed-
forward and feedback techniques are applied to a processing sequence involving the
four basic steps of silicon oxidation, aluminum metallization, lithography, and alu-
minum etch. Feedforward control is carried out at two points. The stepper focus in
the exposure substep of the photolithography step is varied depending upon the result
of the oxide thickness of the oxidation step. Adjustments are also made in the etching
step, depending upon the oxide thickness and the size of the resist pattern. The study
demonstrated the potential of using multistep control by achieving the stated goal
of keeping the capacitance of a fabricated capacitor fairly constant (within 1%). A
recent research effort in feedforward control is described in Reference 23, where a
feedforward controller adjusts the recipe of an etch step to compensate the deviations
in a photolithography process.
The control strategies described in Reference 6, as well as the strategies
described in References 5 and 23, can be implemented by using the Active Controller.
In fact, the control rules shown in the examples in Section 20.3 implement some of
the control strategies described in these papers. Since the Active Controller provides
an adaptable vehicle for implementation of control strategies, results obtained from
future research in the area of multistep control could also be easily incorporated in
the Active Controller via the definition of appropriate active rules.
20.5.2 RESEARCH IN CIM ENVIRONMENTS

Among research efforts devoted to developing semiconductor manufacturing sys-
tems, the Berkeley Computer Aided Manufacturing (BCAM) system developed at
the University of California, Berkeley, is to our knowledge the only system that
provides multistep control functionality.24 BCAM software utilizes equipment mod-
els for supervisory control. The models are used by the software for process simu-
lation and recipe generation. This recipe generation is used to accommodate product
specifications. BCAM stores and retrieves equipment recipes and models in a recipe
database. Research within BCAM has also focused on the provision of multistep
control as described in References 5 and 20, and discussed in the previous section.
The Active Controller solution can be considered to be complementary to this
research effort since the Active Controller provides a clean and easy platform for
implementing these various control algorithms.

20.6 CONCLUSIONS
In this chapter an interprocess control-enabling mechanism called the Active Con-
troller was described. The solution is a generic, adaptable, and portable software
enabler for multistep control in manufacturing facilities. The Active Controller
provides multistep control through the use of active database technology. It keeps
track of relevant processing events and data, and when the conditions for multistep
control hold, executes appropriate actions to compensate for the errors in processing.
The Active Controller implementation, with its capability for the definition of
complex rules over a history of processing events and ability to invoke user-provided
analysis routines, provides for a generic and adaptable implementation that can be
used to implement various algorithms for multistep control. The same controller can
be reused for a different process by defining suitable rules for the new process and
adding these rules to the active database. This mechanism is flexible and adaptable
since, by adding appropriate rules, it may be extended to handle new situations.
Active Controller research had its foundations in R2R control and extended
concepts of reusability and flexibility to higher levels in the factory control hierarchy.
Similarly, research is also being conducted in developing real-time control solutions
for specific processes (see, for example, Reference 25), thereby addressing levels of
below R2R control. If these control solutions at all levels continue to be developed
with forethought to multilevel integration, a true multilevel generic control solution
for semiconductor manufacturing will soon be realized.
ACKNOWLEDGMENTS
Portions reprinted with permission from IEEE Transactions on Components, Pack-
aging, and Manufacturing Technology — Part C, Vol. 21, No. 3, pp. 217-224.2 © 1998
IEEE.
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Part 7
Summary and Conclusions
This text has served to provide a detailed look into the many aspects of R2R control
in semiconductor manufacturing from an historical perspective through a description
of basic foundational tools, algorithms, enabling technologies, and customization
methodologies, to case studies and advanced topics. In this final part of the book
we provide a high-level summary of the material presented in the book, give a
snapshot of the current status of R2R control development and deployment in the
industry, and identify general future directions for R2R control. As part of the
discussion of future directions we will highlight a few new research and development
efforts that came into fruition near the final stages of editing this text; these efforts
serve to illustrate that the level of activity in both R2R control research and devel-
opment continues to grow. We also identify particular conferences and publications
that could serve as avenues for further research, and provide some final thoughts on
this book and its role in facilitating R2R control understanding and deployment.
1 SUMMARY
The R2R control field is expansive and involves many dimensions of research and
development. In organizing this book, we quickly came to realize that the wealth of
research results in each of these dimensions could support its own complete text.
Thus, in providing a text that addresses the entire semiconductor manufacturing R2R
control field, we chose to provide the reader with a foundation of information in
each dimension, along with more in-depth treatises of important aspects of each
dimension. In this way the reader is provided with a foundation to further investigate
the aspects of R2R control in which he/she is most interested.
Although the R2R control field could be partitioned in a number of ways, we
chose a partitioning that seems to reflect a natural grouping of research efforts and
researchers. These partitions roughly correspond to the “Parts” of this book. In the
remainder of this section we provide a brief summary for each of these parts.
1.1 FOUNDATION
In Part 1 of the book, practical and theoretical components that comprise the foun-
dation for R2R control were presented. R2R control in the semiconductor manufac-
turing industry arose from both the successes and limitations of SPC. SPC provided
the first solution that utilized process observation to affect the process. R2R control
emerged as a new alternative to SPC in the early 1990s.
A number of issues hindered early widespread acceptance of R2R control. These
included lack of commercial solutions, no infrastructure for integration or automa-
tion, few on-line metrology and in situ sensors, and possibly inadequate algorithms.
All of these issues were addressed as part of the maturation process of R2R control,
resulting in increasing acceptance of this technology.
The benefits of this technology in the semiconductor industry are seen as
increased throughput, reduced non-product wafers, improved wafer-to-wafer and
lot-to-lot variability, reduced within-wafer and within-die variability, and reduced
operator error. Possible future directions in the R2R control field include increased
use of complex, adaptive, self-tuning controllers, tool- and process-specific mod-
els/controllers, and multistep or full-flow process controllers. Better understanding
of the properties of existing R2R control solutions (along the lines described in
Chapter 2) will lead to improved tuning methods and better performance.
1.2 R2R CONTROL ALGORITHMS

A wide range of R2R control algorithms were described in Part 2. Two basic
algorithms, called the “gradual mode” and “predictor–corrector,” utilize linear
approximation modeling combined with EWMA data filtering. These algorithms are
widely utilized in the semiconductor manufacturing R2R control industry, and have
been proven effective in a number of process control scenarios. The OAQC algorithm
provides a quadratic modeling capability and can be utilized either as a process
optimizer or a process controller. This capability all but eliminates the need for a
DOE preceding the deployment of the controller.
These algorithms represent just a few of the R2R control algorithm alternatives
available; however, these approaches represent the majority of R2R control imple-
mentations in the industry. A comparison of these algorithms reveals that, in most
relatively well-behaved scenarios, the basic linear approximation algorithms perform
as well or nearly as well as the quadratic solutions. A quadratic (or other nonlinear)
control solution proves necessary, however, if the system is highly nonlinear.
1.3 INTEGRATING CONTROL

The existence of methodologies and technologies for effective integration and auto-
mation of R2R control represents a major hurdle to its acceptance. This topic was
addressed in Part 3 with a detailed description of methods and solutions for inte-
grating control. Three major entities facilitating the development of solutions for

R2R control integration are the Semiconductor Industry Association, which provides
a roadmap for APC development, acceptance, and adoption; SEMATECH, which
has defined a Control Systems Requirements Specification for the industry; and
SEMI, which continues to support development of standards for communications
and integration.
A detailed requirements analysis for integrated R2R control solutions has been
conducted for the industry, and an R2R control enabling technology, called the
Generic Cell Controller (GCC), has been developed that addresses these require-
ments. The GCC has been effectively utilized as an enabling solution for a large
number of applications, including CMP, vapor phase epitaxy, and etch. In providing
a migration path for the integration of R2R control into existing and next generation
systems, a “piggyback” R2R control design has been developed that provides for
the addition of a R2R control capability to an existing system with minimal change
to that system (i.e., virtually nonintrusive at the equipment and factory level).
Utilizing a technology such as the GCC to implement this design, the piggyback
solution can be ported to a fully integrated solution for next generation tools. An
example of this process illustrates the cost and technology leverage that can be
obtained in the migration from piggyback to fully integrated solutions.
1.4 CUSTOMIZATION METHODOLOGY

In Part 4 a methodology for deployment of R2R control is presented. The components
of the methodology include (1) quantifying the problem with process engineers, (2)
DOE for process characterization and R2R control model development, (3) DOE
execution, (4) subsequent data analysis, (5) R2R controller specification, (6) cus-
tomization and delivery of R2R system, and (7) testing, training, and technical
support.
Customization of R2R control solutions is almost always required; this motivates
the need for an open and flexible solution-enabling technology such as that described
in Part 3. A key part of the methodology is the development and qualification of
response surface models of the process. Classical methods are available that can be
applied. If control solutions that include an optimization component are used, such
as the OAQC solution described in Part 2, several of the response-surface quantifi-
cation steps may be omitted from this deployment methodology.
1.5 CASE STUDIES

A number of case studies of R2R control are included throughout this book as
vehicles to illustrate a particular feature of the R2R control field that is the topic of
that part. In Part 5 the focus is on the case studies themselves. Here we illustrate
the effectiveness of R2R control, and provide insight into possible future directions
of R2R control research and development.
For example, an R2R control solution being deployed at IBM* is a multiprocess
solution that includes a CMP component and possibly a CVD component, along
with feedback from the upstream etch process. This multiprocess solution is providing
* IBM Microelectronics, Burlington, Vermont.

R2R control as a total factory solution rather than a process-centric solution, with
the control solution quality parameters including total line yield rather than just
individual process quality parameters.
Other case studies illustrate how practical application of R2R control can moti-
vate and guide algorithm enhancement. In a photolithography application, an adap-
tive version of the basic EWMA control solution was used to provide effective
control in an environment where there are both small and larger process shifts and
drifts. In addressing a CMP process control scenario with both aging pad and disc,
a predictor–corrector EWMA algorithm was enhanced to provide control in an
environment where metrology observations are obtained at unequally spaced points
in time.
1.6 ADVANCED TOPICS

The R2R control field is rapidly expanding in a number of directions. A few of these
directions are explored in Part 6. One clear future direction is the movement from
process-centric R2R control to a total factory solution. R2R control solutions must
be flexible so that targets are set based on factory goals rather than process goals.
Facilitating flexible solutions at this interprocess level requires an assessment
of factory level integration and enabling requirements, and utilizing the sequential
control and integration techniques that are suitable for factory-wide systems. The
Active Controller represents such a solution for the interprocess control arena; this
event-driven control solution utilizes active database technology to provide a flexible
and portable sequential control environment.
Another future direction in the R2R control field is the enhancement of R2R
control solutions to include process-specific modeling features. For example, a
control solution that models a pad replacement process shift in a CMP process will
produce a solution that provides for reduced test wafer requirements and increased
OEE through reduced process (re)qualification time.
2 CURRENT STATUS OF R2R CONTROL IN

SEMICONDUCTOR MANUFACTURING
At the time of this writing, R2R control solutions are being widely reported, origi-
nating from users, metrology suppliers, and integrated control solution suppliers.1–3
As noted throughout this book, success is being reported in control of all front-end
process types. Thus, to some extent, the focus with respect to R2R has shifted from
demonstrating viability of R2R control, to demonstrating R2R control as an integral
part of total factory solutions.4 In this regard, enabling technologies such as the
Generic Cell Controller and framework specifications will remain in the spotlight
as tools to facilitate factory-wide deployment of R2R control.* Examples of these
are provided in Chapters 15 and 20.
Although research into enhancement of control algorithms has produced a number
of alternatives, the dominant algorithm types being utilized in the industry continue
* See Part 3 and Chapter 1 of this book, respectively.

to be variants of the first linear approximation algorithms with EWMA filtering as
described in Chapter 3. This will probably continue to be the case because, as noted
in Chapter 1, the “keep-it-simple” approach seems to be effective, and other aspects
of R2R control acceptance, such as integration, are lagging behind algorithm devel-
opment. It is important that the research in algorithm development and refinement
continue, however, because, as integration issues are rapidly being solved, algorithm
refinement could move back toward the top of a priority list. In this regard, it is
critical that integrated control enabling solutions support a level of “plug-and-play”
of algorithms for rapid and cost effective upgrade of control solutions.*
A dominant enabling technology for R2R control as a third-party solution con-
tinues to be the Generic Cell Control.** While a large number of solutions have
been reported in the user community that don’t utilize the GCC approach, much of
the GCC literature base for R2R control focuses on integrated and portable solu-
tions.*** The GCC compatibility with the APC framework (see Chapters 9 and 10)
should allow this technology to continue as an enabler for R2R and other APC
solutions well into the future.5 The APC framework will continue to play an increas-
ingly important roll in R2R control deployment, due in part to the increasing
acceptance of R2R control as part of a total factory solution (see above), and the
fact that the APC Framework is being specified as a SEMI standard.6****
The research and development arena for a large majority of activity in R2R
process control continues to be front-end processing. This focus has arisen for both
technical and historical reasons. As noted in the Introduction to this book, the CMP
process was an early target for R2R control investigation because at the time it was
a new technology that suffered from process drift and shift as well as a lack of in situ
sensory capability. CMP continues to be an ideal candidate for R2R control; however,
application has quickly spread to other processes in the front-end community. This
is due mainly to the relative similarity between CMP and other front-end processes,
and the fact that the front-end community shares the same literature base. At the
time of this writing there was no known effort dedicated to deploying R2R control
for back-end processes such as assembly and test; however, it is reasonable to assume
that these processes also have drift and shift characteristics that could make them
ideal candidates for R2R control. Thus, movement of R2R control into this area is
a probable future direction in the industry, as described below.
3 THE FUTURE OF R2R CONTROL IN

SEMICONDUCTOR MANUFACTURING
Although R2R control solutions are being deployed throughout the industry, the
field of R2R control in semiconductor manufacturing, which is only about 10 years
old, could yet be considered in its infancy. Results reported to this point have served
* See, for example, Chapters 9 to 11.

** The GCC is described in Part 3.
*** See, for example, Chapter 11.
**** SEMI is an acronym for Semiconductor Equipment and Materials International, and is described
in Chapter 7.

to provide effective control solutions for various processes in the industry, and they
have also opened new doors, showing us that we have only begun to realize the
potential of APC. In the remainder of this section a few of the new opportunities
for expansion of R2R control and APC are discussed.
3.1 R2R CONTROL AS PART OF A FACTORY-WIDE APC SOLUTION

The case study presented in Chapter 15 illustrated a trend toward viewing R2R
control as part of a factory-wide solution. Factory-wide deployment of R2R control
and, more importantly, factory-wide access to control data, will serve to open up
new research and development areas that will extend the reach and capability of
advanced process control. One such area is enabled by the (electronic) publishing
of metrology data for a process at the factory level. This allows upstream and/or
downstream process control solutions to utilize this data in their control strategies.
As an example, CMP pre-metrology data can be used as part of the CMP control
scheme to control CMP thickness and radial nonuniformity. However, through the
use of deconvolution techniques, it can further be used in the upstream CVD control
scheme to identify the magnitude of cross wafer gradient or “wedge” nonuniformity
contributed by the deposition process.7
Another research and development area opened up by factory-wide data access
results from the accessibility of control algorithms and parameters. This allows the
development of factory-wide, rather than process-centric, control algorithms that
focus on process line yield optimality, rather than process optimality.8,9 It also allows
for the incorporation of higher level control loops as part of a multilevel hierarchical
control scheme.10 Further, it allows for the use of factory level control enabling
solutions that support incremental improvements to the factory-wide control
scheme.11
3.2 INTEGRATION OF APC COMPONENTS

R2R control is clearly a mature APC technology; however, other APC technologies
are emerging in the industry. For example, fault detection and classification (FDC)
is receiving an increasing level of attention and could become a critical component
of some process solutions.5,12 A high-level schematic representation of an FDC system
is given in Figure 1. A typical FDC system utilizes in situ process data along with
possibly ex situ metrology data to identify and classify tool and process faults. Tools
such as time series analysis or neural networks can be utilized to establish and qualify
the relationships between the data collected and the fault classes.13 Other APC
technologies such as maintenance scheduling and automated process modeling are
also receiving attentions as components of an open APC solution suite.5
As these individual APC components mature, it is becoming more and more
evident that they can be utilized in a complementary fashion if the underlying
enabling technologies and frameworks facilitate the structured exchange of process
and control information among the components. While the enabling technology and
frameworks described in Chapters 9 and 1, respectively, do address this issue, it is

Tool Status
Fault Classification
FDC
In-Situ Monitoring
- Particle Monitoring In-Line
- RF Metrology
- Optical
- Residual Gas Analyzer
-...
Tool Metrology
FIGURE 1 High-level depiction of a fault detection and classification (FDC) system.
expected that future APC efforts will be devoted to further specifying and evaluating
the interaction of the various APC technologies via these enablers and frameworks.
4 FURTHER READING
The references found throughout this book list the primary conferences and publi-
cations that present the latest results and innovations in R2R control for semicon-
ductor manufacturing. A summary of these conferences and publications, and the
probable content of material presented, is provided in Table 1.
The single most important conference associated with APC in the semiconductor
manufacturing industry is the SEMATECH Advanced Equipment Control Sympo-
sium.14 As the name implies, this workshop has served as a forum for presentation
TABLE 1
Summary of Sources of Further Reading
Resource Internet Reference Comment
American Vacuum Society www.vacuum.org Symposiums and Journal

CMP for Multilevel Interconnection Conference www.imic.org Conference
(CMP-MIC)
Electrochemical Society www.electrochem.org Symposiums and Journal
IEEE Transactions on Semiconductor www.ieee.org Journal
Manfuacturing
IEEE Transactions on Components, Packaging, www.ieee.org Journal
and Manufacturing Technology — Part C
SEMATECH Advanced Equipment Control www.sematech.org Workshop
Workshop
SEMI Standards www.semi.org Equipment Automation
and Software Standards
SEMI/IEEE Advanced Semiconductor www.semi.org Conference
Manufacturing Conference (ASMC)

of innovative, though oftentimes preliminary, APC results, and obtaining feedback
and direction.
The American Vacuum Society and the Electrochemical Society also regularly
sponsor symposiums that contain a wealth of submissions devoted to semiconductor
manufacturing process control. Examples of other conferences where papers devoted
to semiconductor manufacturing process control regularly appear include the
SEMI/IEEE Advanced Semiconductor Manufacturing Conference (ASMC), and the
CMP for Multilevel Interconnection Conference (CMP-MIC).
Journals that regularly contain papers devoted to aspects of semiconductor man-
ufacturing process control include IEEE Transactions on Semiconductor Manufac-
turing and IEEE Transactions on Components, Packaging, and Manufacturing Tech-
nology — Part C. Journals of the American Vacuum Society and the Electrochemical
Society also occasionally contain papers devoted to APC topics.
Another important source of APC innovation is the SEMI standards meetings.6,15
As noted in Chapter 7, many aspects of integrated R2R control such as “piggyback”
communications and the APC Framework are being pursued as standards within
SEMI. Many of the task forces within SEMI devoted to the development of these
standards have defined solutions to integrated process control and, more importantly,
are shaping the path for APC integration and acceptance.* Thus, any developer
interested in any aspect of APC for semiconductor manufacturing should include
research into the latest relevant SEMI standards as part of any literature survey.
5 FINAL THOUGHTS
R2R control continues to be an exciting field for research and development in
semiconductor manufacturing. The benefits that have been experienced to this point
represent the tip of the iceberg. The road to total acceptance and utilization of R2R
control in aspects of semiconductor manufacturing is necessarily long; however, as
researchers have paid attention to generic, portable, and expandable solutions, a
clear migration path to integrated factory-wide R2R control has been opened up.
Any research effort, though, is only effective if the results are communicated to the
industry in a timely and organized fashion. In this book, we put a level of organization
around this rich research pool of R2R control and presented the results in a fashion
that would allow a developer to understand and take advantage of the many facets
of R2R control research. In doing so, it is our hope that this book is a step on the
path toward R2R control being fully accepted as an integral component of a total
factory solution for semiconductor manufacturing.
* The primary group addressing APC within SEMI is the Information and Control Committee; various
subcommittees and task forces are under its leadership. Further information can be found at
www.semi.org.

REFERENCES
1. Campbell, W.J., SEMATECH AEC/APC Symposium XI, Vail, CO (1999).
2. Dishon, G., D. Eylon, M. Finarov, and A. Shulman, “Dielectric CMP Advanced
Process Control Based on Integrated Thickness Monitoring,” Proc. of 1998 CMP-
MIC, 1998.
3. Moyne, J. and J. Curry, “A Fully Automated Chemical-Mechanical Polishing Pla-
narization Process,” Proc. 1998 VLSI Multilevel Interconnect Conf., pp. 515-517, June
1998.
4. SEMATECH AEC Workshop XI, Vail, CO (October 1999).
5. Moyne, J., R. Gwizdak, and M. Hanssmann, “An Integrated Framework Solution for
APC Component Development and Deployment,” International SEMATECH
Advanced Equipment Control/Advanced Process Control Workshop, Dresden, Ger-
many (March 2000).
6. www.semi.org.
7. Moyne, J., C. El Chemali, J. Kim, T. Parikh, J. Chapple-Sokol, J. Colt, R. Nadeau,
and P. Smith, “Gradient and Radial Uniformity of a CMP Process Utilizing a Pre-
and Post- Measurement Strategy,” Proc. CMP-MIC, Santa Clara, CA (March 2000).
8. El Chemali, C., J. Moyne, K. Khan, J. Colt, J. Chapple-Sokol, R. Nadeau, P. Smith,
T. Parikh “Multizone Uniformity Control of a CMP Process Utilizing a Pre and Post-
Measurement Strategy,” 46th International Symposium of the American Vacuum Soci-
ety, Seattle, WA (October 1999); also accepted for publication in the Journal of the
American Vacuum Society (accepted December 1999).
9. Moyne, J., “Advancements in CMP Process Automation and Control,” (Invited) Third
11. Chaudhry, N., J. Moyne, and E. Rundensteiner, “Active Controller: Utilizing Active
Databases for Implementing Multi-Step Control of Semiconductor Manufacturing,”
IEEE Trans. Components, Packaging, Manufacturing Technol. — Part C (July 1998),
pp. 217-224.
Association (1997-2000), available at www.sematech.org.
13. A number of articles on Fault Detection and Classification can be found in IEEE
Transactions on Control Systems Technology.
14. www.sematech.org.

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Run-to-Run Control in

© 2001 by CRC Press LLC

No claim to original U.S. Government works

WHO SHOULD USE THIS BOOK

• A corporate-level technical strategist would utilize the book as a resource

© 2001 by CRC Press LLC

HOW TO READ THIS BOOK

* Excerpt for Part 6: Advanced Topics.

© 2001 by CRC Press LLC

Arnon Max Hurwitz, Ph.D., is Managing Director of Qualtech Productivity

© 2001 by CRC Press LLC

© 2001 by CRC Press LLC

James Moyne, Enrique Del Castillo, and Arnon Max Hurwitz

© 2001 by CRC Press LLC

© 2001 by CRC Press LLC

Nital S. Patel Joe White

© 2001 by CRC Press LLC

© 2001 by CRC Press LLC

© 2001 by CRC Press LLC

PART 1: FOUNDATION FOR CONTROL

PART 2: R2R CONTROL ALGORITHMS

© 2001 by CRC Press LLC

PART 4: CUSTOMIZATION METHODOLOGY

© 2001 by CRC Press LLC

PART 6: ADVANCED TOPICS

PART 7: SUMMARY AND CONCLUSIONS

© 2001 by CRC Press LLC

This book is dedicated to our wives,

© 2001 by CRC Press LLC

© 2001 by CRC Press LLC

© 2001 by CRC Press LLC

The semiconductor manufacturing industry is arguably the fastest evolving major

* W. Rozich, IBM, SEMATECH AEC/APC Symposium XI, Vail, CO (1999).

© 2001 by CRC Press LLC

FIGURE 1 Input/output structure of a typical R2R control solution.

FIGURE 2 Typical R2R control application — R2R control of a CMP process.

© 2001 by CRC Press LLC

2 VLSI TOOLS: THE EXAMPLE OF CMP

Focal plane (clear)

Enlarging lithography system

FIGURE 3 Enlarging lithography system.

© 2001 by CRC Press LLC

FIGURE 4 Comparison between nonplanar and planar processes.

Carrier (head) Slurry Feed

(a) Side View (b) Top View

FIGURE 5 Schematic of a CMP machine.

© 2001 by CRC Press LLC

Wafer measurement sites

FIGURE 6 Wafer measurement sites.

Uniformity between wafers is measured by comparing the average thickness

3 CHARACTERISTICS OF R2R CONTROL SYSTEMS

• Some form of postprocess quality measurement data is available. This

A typical R2R control solution was shown in Figure 2. Here, a wafer-to-wafer

© 2001 by CRC Press LLC

* SEMATECH has since changed its name to International SEMATECH.

© 2001 by CRC Press LLC

© 2001 by CRC Press LLC

FIGURE 8 Hierarchical partitioning of control problem.

© 2001 by CRC Press LLC

1. Sensor and Actuator Innovation: Progress along this front provides