PIEZOELECTRIC NANOSCALE ULTRASOUND TRANSDUCERS (PNUTS)

FOR MINIATURIZED INTERNET OF THINGS RECEIVERS

Submitted in partial fulfillment of the requirements for

the degree of

Doctor of Philosophy

in

Electrical and Computer Engineering

Pietro Simeoni

B.S., Physics Engineering, Politecnico di Torino

M.S., Nanotechnologies for the ICTs, Politecnico di Torino

Carnegie Mellon University

Pittsburgh, PA

May 2021
 ACKNOWLEDGMENT

In primis, I would like to thank my defense committee members Gianluca Piazza, Maysam

Chamanzar, Tamal Mukherjee, and Matteo Rinaldi for their valuable feedback and insights

on the work presented in this thesis. In particular, I would like to thank my advisor Gianluca

for his guidance over the last 4 years. Looking back at the progress made since I started I

could not be more grateful for his guidance.

Secondly, a big thank you to my family back in Italy. I have been fortunate enough to

have two parents that supported me in the path I chose, even when it meant being far from

home for most of my adult life. Successfully completing this program is an achievement that

is as much mine as it is theirs.

A thanks goes to the amazing friends and colleagues that helped me in small and big ways

to maintain a balanced perspective on life, especially in moments I was doubting whether I

would be able to complete my Ph.D. A special mention goes to the "pasta club". Antonis,

Marina, Luca, and Gabri, thanks for the precious memories of my years in Pittsburgh.

An equally important thanks goes my colleagues and friends Gabriel, Zach, and James.

Besides the invaluable help you gave me to complete my thesis, our 5 pm discussions definitely

made me a better person. Our conversations kept me sharp, challenged my believes, gave

me perspective, and showed me what civil disagreement looks like.

Thank you to all my friends that were on this journey with me including Harlin, Ayaz,

Shafee, Ashraf and Abhay.

Finally, I would like to acknowledge the sources of funding that made my work possible.

This includes the Carnegie Mellon Electrical and Computer Engineering Department for

supporting my first year and the DARPA SHIELD and NZERO programs for supporting me

ii
during my second and fourth year. I would like to thank Marsha and Philip Dowd for pro-

viding financial support during my third year through the 2019 Dowd Graduate Fellowship.

I am honored to be a Dowd fellow and I am immensely grateful to them for believing in the

project.

iii
PIEZOELECTRIC NANOSCALE ULTRASOUND TRANSDUCERS (PNUTS)

FOR MINIATURIZED INTERNET OF THINGS RECEIVERS

Abstract

Pietro Simeoni
Carnegie Mellon University
February 2021

The landscape of connected devices has both grown in size and changed in nature in the

last few decades. When the internet came along, it represented a first wave of connectivity

that enabled communication between desktop computers. As computers moved to smaller

form factors such as laptops and more recently smartphones, the need for connectivity was

extended to this class of devices. This second wave was wireless in nature, and came with the

additional constraint of lower power consumption as these devices are powered by batteries.

We are now going through a third wave of connectivity, where everyday appliances and sensor

nodes distributed in the environment are equipped with the ability to remotely receive and

report back information. This third wave is commonly referred to as the internet of things

(IoT), and as it rolls out, the constraints on form-factor and power consumption become

increasingly tight and challenging to engineer.

Because of the high density of wireless nodes, radio frequency bands are becoming a

scarce resource and they constitute yet another constraint to account for during the system

design. The number of wireless nodes is increasing exponentially and we expect to have a

trillion sensors deployed by the year 2030. To make the deployment of a trillion sensors

feasible, these nodes must be small and function on limited power budgets. For a subset of
IoT applications, a network of sensors would need to be installed in a localized area, where

the required communication range is less than 10 m and where a central hub can orchestrate

the connection between different nodes.

For such applications, ultrasound between 40 kHz and 100 kHz becomes an attractive

candidate to overcome several of the constraints outlined above. This frequency range offers

two important advantages: 1) The acoustic waves attenuation is low and permits communica-

tion over several meters (loss < 3 dB/m). 2) The node electronics can operate at extremely

low power, potentially extending its lifetime to several years while drawing power from a

miniaturized battery.

If ultrasound is used in place of RF waves, we must replace the node antenna with an

ultrasound transducer. In this work we introduce a novel ultrasound sensor that we dub

the piezoelectric nano-scale ultrasound transducer (pNUT). The pNUTs are characterized

by piezoelectric films that are only 100 nm thick and by a footprint that is 1 to 2 orders of

magnitude smaller than the state of the art, while showing similar performance. A model

for the scaling of ultrasound transducers is presented to offer guidelines for the design of

miniaturized ultrasound sensors. Finally, we design a circuit with accessible off-the-shelf

components to demonstrate a low-power pNUT-based ultrasound wake-up receiver (WuRx).

The WuRx presents a communication range of several meters, confirming the feasibility of

miniaturized ultrasound tags for distributed sensors networks.

TABLE OF CONTENTS

Page

ACKNOWLEDGMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Ultrasound Transducers and State of the Art . . . . . . . . . . . . . . . . 3
1.3 Overview of the pNUT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Motivation and Applications . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Individual pNUTs Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1 Equivalent Circuit Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.1 Airborne waves propagation . . . . . . . . . . . . . . . . . . . . . 13
2.1.2 Acoustic Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.3 Mechanical Domain . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.1.4 Purely Electrical Equivalent Circuit and Scaling Relations . . . . . 23
2.1.5 Quality Factor Scaling . . . . . . . . . . . . . . . . . . . . . . . . 26
2.1.6 The Effect of Scaling on Transducers Performance . . . . . . . . . 29
2.2 Limits of the Analytical Model . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2.1 The Effect of the Undercut from Release . . . . . . . . . . . . . . 35
2.2.2 The Effect of Residual Stress . . . . . . . . . . . . . . . . . . . . . 38

3 pNUTs Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.1 pNUTs Fabrication Process . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2 Fabrication Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

vi
 3.2.1 Device Geometry Motivation . . . . . . . . . . . . . . . . . . . . . 42
3.2.2 Bottom Metal Lift-off . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2.3 Aluminum Nitride Etch Issues . . . . . . . . . . . . . . . . . . . . 47

4 pNUTs Arrays Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.1 Methods of Connection of pNUT Arrays . . . . . . . . . . . . . . . . . . 52
4.1.1 Full Parallel Connection . . . . . . . . . . . . . . . . . . . . . . . . 53
4.1.2 Full Series Connection . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.1.3 Series-Parallel (SP) Connection . . . . . . . . . . . . . . . . . . . 60
4.2 Noise in pNUTs Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5 Devices Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.1 Tx Sensitivity Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.1.1 Equivalent Parameters Extraction . . . . . . . . . . . . . . . . . . 68
5.1.2 Measurements at Low Pressure . . . . . . . . . . . . . . . . . . . . 72
5.1.3 Arrays Tx Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.2 Rx Sensitivity Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.2.1 Rx Sensitivity Angular Dependency . . . . . . . . . . . . . . . . . 79
5.2.2 Single Devices Rx Sensitivity . . . . . . . . . . . . . . . . . . . . . 81
5.3 Arrays Rx Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

6 WuRx System Demonstration and Characterization . . . . . . . . . . . 86

6.1 Electronics Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.1.1 Voltage Amplifier architecture . . . . . . . . . . . . . . . . . . . . 89
6.1.2 Rectifier Architecture . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.2 WuRx System Characterization . . . . . . . . . . . . . . . . . . . . . . . 95
6.3 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . 100

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

APPENDIX

A Open Circuit Voltage vs. Gamma . . . . . . . . . . . . . . . . . . . . . . 113

B Gamma Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

vii
LIST OF TABLES

2.1 Units of components and variables of the equivalent circuit in the acoustic,

mechanical, and electrical domain . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Compiled data used to generate the data in Fig. 2.8 . . . . . . . . . . . . . . 27

4.1 Parameters used in the single cell pNUT used to build the arrays model. . . 53

5.1 Parameters extracted by fitting the individual devices Tx sensitivities. F and

NF refer to the devices with and without the floating metal respectively. The

value of Cel has been measured separately with precision impedance analyzer. 69

5.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.3 Comparison between Rx sensitivity of the individual pNUTs and ultrasound

transducers reported in literature. . . . . . . . . . . . . . . . . . . . . . . . . 83

6.1 Data comparing ultrasound WuRx from literature and the WuRx presented

in this thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

viii
LIST OF FIGURES

1.1 The evolution of computers. This is a qualitative illustration of how the nature

of computing platforms changed in size and nature over the last several decades. 2

1.2 Relation between wavelength and frequency for RF and US, and power con-

sumption of the interfacing electronics. . . . . . . . . . . . . . . . . . . . . . 4

1.3 Depiction of the two most common typologies of MEMS ultrasound transduc-

ers: cMUTs (left) and pMUTs (right). . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Evolution of ultrasound transducers. As piezoelectric thin films synthesis

improved, thinner piezoelectric layers enabled the fabrication of smaller low-

frequency transducers. [5][6][7]. . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.5 Left: Main resonance mode of 4-beams pNUT. Right: SEM images of early

prototypes of the devices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.6 Application scenarios for distributed sensing tags equipped with ultrasound

receivers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.7 Factory floor with a distributed network of sensors. . . . . . . . . . . . . . . 10

1.8 Zero power tags for locating objects in mixed-reality. . . . . . . . . . . . . . 11

2.1 Lumped equivalent circuit of a pNUT. . . . . . . . . . . . . . . . . . . . . . 13

2.2 Delay line analogy for acoustic waves propagating from Tx to pNUT. . . . . 14

ix
2.3 Acoustic pressure generated by an ideal isotropic hemispherical Tx with a

radius of 10 cm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4 Rendering of the transducer portions modeled by Ccavity and Rholes . . . . . . 17

2.5 Acoustic parameters values when scaling up the thickness and area of the

pNUT. The starting point is a device with 300 nm thickness and an area of

100 µm X 100 µm. To estimate Zrad , we assume a frequency of 50 kHz. We

notice that scaling up the total thickness to 3 cm would not be feasible in

practice, and the plots are only meant to illustrate the equivalent parameters

dependence on geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.6 Dependence of Keq , Meq , and η on thickness and area scaling. Keq and Meq

both scale quadratically with the geometrical parameters, indicating that the

resonance frequency remains constant. η increases linearly with the resonator

scaling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.7 Equivalent circuit model of the pNUT once we move all components over to

the electrical domain. In this model we are assuming an open back-cavity is

present, which allows us to remove Ccavity and Rholes from the circuit. . . . . 23

2.8 Linear dependence on plates thickness of the derived coefficient proportional

to the static Rx sensitivity in works from literature. . . . . . . . . . . . . . . 26

2.9 Comparison between the scaling of the measured pNUT acoustic resistance

according to models accounting for viscosity and the theoretical radiation

resistance of a piston with equivalent dimensions. . . . . . . . . . . . . . . . 29

2.10 Complete equivalent circuit model when the transducers operate at resonance. 30

2.11 Value of the theoretical open-circuit Rx sensitivity vs. Γ for the reference

pNUT and pMUT. Both devices have a resonance of 50kHz and an area of

100 µm x 100 µm when SF = 1. . . . . . . . . . . . . . . . . . . . . . . . . . 31

x
2.12 a) Values of Γ expected over a range of device lateral dimensions and frequen-

cies of operation. b) Comparison between the Rx sensitivities of the reference

pNUT and pMUT as they are scaled. . . . . . . . . . . . . . . . . . . . . . . 32

2.13 Left: Resonance frequency of a laminated cantilever simulated in COMSOL

and with the analytical model. Right: Tx sensitivity of the same cantilevers.

In both cases the analytical model agrees well with the results observed in

COMSOL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.14 a) Resonance Mode of a device obtained from an eigenfrequency simulation in

COMSOL. b) Comparison between the device beams mode shape and mode

shapes of a cantilever and a clamped-guided beam. . . . . . . . . . . . . . . 35

2.15 Left: Comparison between the resonance frequency of a pNUT simulated in

COMSOL and in the analytical model. Right: The same comparison for the

static Tx sensitivity. In both cases the discrepancy between the analytical

model and COMSOL is resolved once we use the COMSOL mode shape in

the analytical model. This highlights the role of the central plate in stiffening

the device response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.16 First resonance mode of a device including a 15 µm undercut from the release

process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.17 pNUT first resonance frequency for different levels of undercut. . . . . . . . . 37

2.18 Normalized electrode mode shapes when no undercut and when a 25 µm under-

cut is present. The figure illustrates how relaxing the fully clamped boundary

condition affects the electrodes mode shape and the transduction coefficient η 38

2.19 Comparsion of the effect of residual stress on circular pMUTs and on a 4-

Beams 200nm thick pNUT. The devices dimensions are selected to have an

unstressed resonance frequency of approximately 40 kHz. . . . . . . . . . . . 39

xi
3.1 Fabrication process of the pNUTs: 1) Bottom Pt lift-off, 2) AlN deposition

and patterning, 3) Top Pt lift-off, 4) backside DRIE, 5) topside XeF2 release. 41

3.2 a) Simulated structure characterized by residual stresses of 50 MPa in the AlN

layer and 1 GPa in the top Pt layer. b) SEM picture of a fabricated device. . 42

3.3 Example of broken devices from early pNUTs prototypes. a): Device with a

uniform floating metal. b) Device with segmented floating metal. It is evident

how the influence of the stress gradient is reduced along the direction of the

segmentation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.4 Comparison between the first pNUTs prototypes (a) and latest version (b)

layouts. We moved to the 4-beams anchor topology due to the high sensitivity

to residual stress of the clamped-clamped design. Additionally, all square

corners were eliminated, the top electrode dimensions were reduced by 1 µm

compared to the bottom electrode, and the bottom metal was eliminated from

the floating region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.5 a) Example of effect of lift-off wings in the bottom metal on the devices release.

b) Close-up view of the floating metal. both on the top and bottom metal it

is possible to see the wings along the perimeter of the rectangles. . . . . . . . 45

3.6 Comparison between positive and negative photoresist profiles. . . . . . . . 46

3.7 Alternative process to solve the issue the slots not etching. 1) Bottom metal

lift-off. 2) AlN sputtering. 3) Top metal lift-off. 4) Ion mill to open the slots.

5) CD26 etch to open the vias. 6) Thin metal lift-off to connect the vias. 7)

DRIE. 8) XeF2 release. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.1 Three pNUTs arrays connection options. From left, connection in parallel,

series-parallel (SP), and connection in series. . . . . . . . . . . . . . . . . . . 51

xii
4.2 Equivalent circuit model used in ADS to represent a single pNUT within an

array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.3 Open circuit frequency response of the single pNUT equivalent circuit used

as building block to construct the arrays model. . . . . . . . . . . . . . . . . 53

4.4 Layout of a 2x2 parallel pNUTs array. . . . . . . . . . . . . . . . . . . . . . . 54

4.5 Short-circuit current response of parallel-connected pNUTs arrays. . . . . . . 55

4.6 Parallel arrays Sensitivity at resonance (50 kHz) and capacitance vs. total area. 56

4.7 Series connection of two pNUTs. a) Implementation of the series connection

in ADS. b) layout of two devices connected in series. . . . . . . . . . . . . . 58

4.8 Series arrays Sensitivity at resonance (50 kHz) and capacitance vs. total area. 59

4.9 Layout of a 2X2 SP array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.10 SP arrays Sensitivity at resonance (50 kHz) and capacitance vs. total area. . 62

4.11 Spectral density of a single pNUT, SP, and Series arrays. . . . . . . . . . . . 63

5.1 SEM images of the four measured devices. a) Individual device with floating

metal. b) Individual device without floating metal. c) 2x2 SP array without

floating metal. d) 3x3 SP array without floating metal. . . . . . . . . . . . . 66

5.2 Example on a pNUT imaged under phase view. . . . . . . . . . . . . . . . . 67

5.3 Measured individual pNUTs Tx sensitivity along with the fitted curves. . . . 70

5.4 Experimental setup used to measure the Tx sensitivity at low pressure. . . . 73

5.5 Quality factor of the pNUT measured at different pressures. . . . . . . . . . 74

5.6 Tx sensitivity of the 4 pNUTs in the 2X2 RSCP array. . . . . . . . . . . . . 75

5.7 Comparison between the undercut profiles of the individual pNUT and the

2x2 SP array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

xiii
5.8 Setup used to measure the Rx mode angular sensitivity of the pNUTs. . . . . 79

5.9 Normalized angular Rx sensitivity of the 2X2 SP pNUT array. The slightly

lower response at 15o and 165o angles is likely due to the VA wires on the side

of the chip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.10 Devices measured Rx sensitivity and extracted Rx sensitivity using the pa-

rameters extracted by fitting the displacement curves. . . . . . . . . . . . . . 82

5.11 Open-circuit Rx sensitivity of the NF single pNUT and the two arrays. . . . 84

5.12 Comparison between the peak Rx sensitivity and electrodes capacitance of

the NF devices with respect to the total area. This measurement confirms the

modeled trend for SP arrays as previously shown in Fig. 4.10. . . . . . . . . 85

6.1 Conceptual schematics of a US-based WuRx. . . . . . . . . . . . . . . . . . . 88

6.2 Layout of the PCB designed to demonstrate the concept. The red and green

traces represent the top and bottom layers of the PCB respectively. . . . . . 88

6.3 Circuit Schematic of a single stage of the VA. The resistor Rbias is needed to

provide a path to ground to the base current of the bipolar transistor at the

non-inverting terminal and correctly bias the circuit. The coupling capacitor

filters out low-frequency components from the input of the next stage. . . . . 90

6.4 Gain of the VA with 1, 2, 3, and 4 active stages. It is possible to see that the

first stage is characterized by a pole close to 100 kHz that compensates for

the decline of the gain set by the nominal GBW product. This effect slightly

increase the gain, from 1300 to 1800, between 40 and 80 kHz when all 4 stages

are active. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

6.5 Circuit schematics of the DM included in the PCB layout. . . . . . . . . . . 92

6.6 Measured input-output curve of the DM. . . . . . . . . . . . . . . . . . . . . 93

xiv
6.7 Picture of the wirebonded chip mounted on the PCB. . . . . . . . . . . . . . 95

6.8 Experimental setup to test the complete WuRx system. The Tx generates the

ultrasound, which is picked up on the other side of the room by the WuRx.

During the measurement, two scopes are connected to the system: the UHFLI

scope is used to monitor both the VA output and the incident acoustic pressure

levels, while a separate oscilloscope is used to monitor the digital signal at the

output of the comparator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

6.9 Data collected during the WuRx demonstration. The plots show the mea-

sured MDP and communication range of the WuRx system for the 4 devices

characterized in Chapter 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

6.10 Extrapolated MDP and range for the demonstrated WuRx system vs. trans-

ducer area. The MDP and range are obtained by assuming an ultrasound

source as the one described in Fig. 2.3, and that the Tx and transducers are

frequency-matched. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

6.11 System range vs. transducer area plot. Comparison between ultrasound WuRx.101

6.12 Example of the cMOS rectifier gain curve used in [13]. . . . . . . . . . . . . 103

6.13 Comparison of RF and US WuRx FoM with respect to system area. The data

used to generate the plot is reported in [13]. . . . . . . . . . . . . . . . . . . 104

xv
 Dedication

This dissertation is dedicated to

Daniela, Marco, Luca, and Nicola

xvi
Chapter 1

Introduction

1.1 Background

The landscape of connected devices has both grown in size and changed in nature in the last

few decades. When the internet came along in 1982, there were much fewer nodes mainly

represented by desktop computers. As micro fabrication techniques improved and Moore’s

law unfolded, the number of operations a computer could perform per unit of energy grew

exponentially, which led to a differentiation in the type of devices that were commercially

available. Desktop computers improved in performance, and laptop computers were born

thanks to the increase in efficiency that allowed them to operate on a battery power supply

and within reasonable form factors. This trend continued, and combined with advances in

radio frequency (RF) front ends, sensors miniaturization, and battery chemistry, it produced

a several consumer-electronic products such as cellphones first, smartphones after them, and

a variety of devices like smartwatches, earbuds, home pods etc. As a hobbyist, it is possible

to inexpensively purchase small micro-controller boards equipped with wifi and bluetooth

modules and experiment building personal internet-connected devices. To go even further,

there are a lot of parallel research efforts to miniaturize these wireless modules and ensure

bio-compatibility to implant them in human bodies, where they can monitor a variety of

1
health related variables [1][2]. The exponential growth of nodes connected to the network,

and the breadth of form and scope of these nodes is referred to as the Internet of Things

(IoT) [3].

The advancements in integrated circuit (IC) manufacturing described above enable the

design of extremely miniaturized computing platforms (Fig.1.1) that can accommodate suf-

ficient processing, memory, and sensing in just a few square millimeters area.

Figure 1.1 The evolution of computers. This is a qualitative illustration of how

the nature of computing platforms changed in size and nature over the last several
decades.

These nodes are meant to record a variety of variables from the environment around

them, and report them back to a central hub (star network configuration). The nodes are

set to implement different functions that can go from machinery temperature monitoring, to

indoor position tracking for items in a warehouse, to air quality control in traffic intersections.

Because of the general purpose of these sensing nodes, they are meant to be deployed in high

numbers to collect abundant information from their surroundings. In order to make the

deployment of a high number of these nodes feasible, three requirements must be satisfied.

2
The nodes must:

• Be small

• Secure privacy

• Have long lifetimes

The privacy issue is outside the scope of this thesis. We will instead focus on the chal-

lenges related to miniaturization and power consumption. The power consumption issue is a

direct consequence of making these nodes wireless, which is necessary due to the distributed

nature of these sensor networks. If we are using RF to communicate wirelessly with the

node, it needs to be equipped with an antenna. To receive RF signals efficiently, antennas

need to have lateral dimensions comparable to the wavelength of operation. In contrast, the

electronics interfacing the antenna would benefit to operate at lower frequency (i.e. larger

wavelengths) to maintain a low power consumption. Therefore, a physics-limited trade-off

exists in making a wireless node that is simultaneously small and power efficient. Since the

relationship between wavelength and frequency is set by the propagation speed of the wave,

this thesis explores the possibility of taking advantage of the lower propagation speed of

airborne acoustic waves to build a small receiver that operates on a limited power budget.

This idea is illustrated in Fig. 1.2.

Ultrasound (US) in the 40 - 100 kHz range is especially interesting as it is characterized by

millimeters-long wavelengths, while presenting relatively low attenuation in air (< 3dB/m)

[4]. This guarantees a communication range of 5 to 10 meters, making the approach attractive

for a subset of applications.

1.2 Ultrasound Transducers and State of the Art

If we use ultrasound as a preferred communication approach, we need to substitute the node

antenna with an ultrasound transducer. There are two types of transducers commonly used

3
 Figure 1.2 Relation between wavelength and frequency for RF and US, and power
consumption of the interfacing electronics.

commercially and in research (Fig. 1.3):

• Capacitive Micromachined Ultrasound Transducer (cMUT)

• Piezoelectric Micromachined Ultrasound Transducer (pMUT)

cMUTs are parallel plate capacitors separated by an air gap. The top plate is only an-

chored laterally and is therefore free to bend when an external pressure is applied. As the

plate moves, the value of the capacitance between the two plates changes accordingly. To

measure a net current flow resulting from the displacement, we need to apply a polarization

voltage between the two plates. This requirement implies that cMUTs transduction mecha-

nism is inherently not passive, and therefore not suitable for the low-power applications we

are targeting. pMUTs consist of multi-layer suspended plates with at least one layer made

of a piezoelectric ceramic. As an external pressure bends the plate, the direct piezoelectric

4
 Figure 1.3 Depiction of the two most common typologies of MEMS ultrasound
transducers: cMUTs (left) and pMUTs (right).

effect converts the resulting in-plane strains into a charge polarization. The other layers

in the stack serve two purposes. First, you have metal layers to form the electrodes that

pick up and route the electrical signal, secondly you have an elastic layer responsible for

shifting the neutral plane (zero-strain plane) away from the center of the piezoelectric layer.

Moving the neutral plane is necessary to generate a net polarization across the piezoelectric

thickness and detect a non-zero electrical output. Because the piezoelectric effect is a passive

transduction mechanism, pMUTs are the device of choice for this thesis.

It is then interesting to see how ultrasound transducers, and pMUTs in particular, oper-

ating in the 40-100 kHz band evolved over time. From Fig. 1.4, we can see how advances in

micro-fabrication and thin films deposition lead to a reduction in pMUTs lateral dimensions

from few cm to just a few mm.

This reduction was enabled by thinning down the thickness of the piezoelectric layers

from millimeters down to the µm range without degrading the piezoelectric properties of the

films. The focus of this thesis is to explore the next phase of pMUTs miniaturization. The

objective is using AlN films with thicknesses of only 100-200 nm to deliver an ultrasound

transducer that resonates in the 40 - 100 kHz frequency range, while occupying a footprint

5
 Figure 1.4 Evolution of ultrasound transducers. As piezoelectric thin films syn-
thesis improved, thinner piezoelectric layers enabled the fabrication of smaller low-
frequency transducers. [5][6][7].

of approximately 100 µm x 100 µm, and without losing in performance with respect to its

larger counterparts.

Such device would deliver two main advantages:

• If the design of the node is constrained by the available area, it is now possible to

miniaturize the largest element of the system

• If the design is not constrained by the available area, smaller transducers can be arrayed

together to occupy a larger area, and increase the system sensitivity and range

In the next chapters we will explore the advantages and limitations of thickness scaling as

an approach for miniaturization. We will see that traditional geometries are not suitable for

extremely thin films, and that significant design changes need to be made to build functional

devices. Because of the important design changes developed in this work, we consider these

devices as a separate class from traditional pMUTs, and throughout this document we will

refer to them as piezoelectric nanoscale ultrasound transducers (pNUTs).

6
1.3 Overview of the pNUT

In this section, we take a high-level look at how the pNUT is designed. The motivation

behind the important design changes outlined below is related to the role played by residual

stress in high-aspect ratio flexural resonators. If we tried to scale down the thickness of

a classic circular pMUT, we will find that either its resonance frequency is dramatically

different than the one predicted by its geometry and material properties, or simply that the

device is broken. In both cases, we have that the residual stress in the films used to build the

device introduces a very large tension in the plate. Because of the geometry and boundary

conditions of pMUTs, this tension cannot be relaxed, leading either to a significant change

in the plate stiffness or to mechanical failure. More details on this are presented in Chapter

2 (Section 2.2.2) and Chapter 3 (Section 3.2.1).

The proposed pNUT geometry consists of 4 cantilever beams connected to a common

central plate. Like traditional circular pMUTs, the device is composed by a laminate com-

prising a piezoelectric and an elastic layer. As the ultrasound waves reach the device surface,

the central plate is displaced vertically, forcing the 4 beams to bend. As bending moment is

developed in the beams, the piezoelectric effect converts the acoustic energy into an electrical

signal that can be read out by an electronic circuit. The deformation mode of the transducer

is shown in Fig. 1.5.

From the image we show that the stack is composed by an aluminum nitride piezoelectric

layer of approximately 100 nm thickness, sandwiched between two platinum layers with

thicknesses of around 10 nm and 200 nm. In fact, because of the aggressive scaling in the

piezoelectric layer, we show that the electrodes themselves can play the role of the elastic

layer. The different thickness between top and bottom electrodes is then required to obtain

a net shift in the neutral plane away from the center of the piezoelectric layer. On the

right side of Fig 1.5. we present SEMs images of the early prototypes of the devices that

motivated the research presented in this thesis. We can see that the top metal is patterned

7
 Figure 1.5 Left: Main resonance mode of 4-beams pNUT. Right: SEM images of
early prototypes of the devices.

on the central plate as well. While the details of the design and fabrication process will

be presented in chapter 3, we highlight that only the electrodes on the beams anchors are

required to have a functioning devices, and that the metal patterned on the rest of the

device surface is there to help maintaining the resonance frequency in the desired range by

mass loading the device. In the next section, we comment on some application scenarios

for the pNUTs. An analytical model of the pNUT -along with its limits- is presented in

Chapter 2. The fabrication process, challenges, and recommendations for future fabrications

are presented in Chapter 3. Chapter 4 comments on how to model pNUTs when they are

combined in an array. Finally we show experimental data in Chapter 5 and 6, where we talk

about the experimental setups to characterize the devices and show a demonstration of a

working ultrasound receiver.

8
1.4 Motivation and Applications

As mentioned above, the applications for distributed nodes networks that could benefit from

an ultrasound wake-up receiver (WuRx) are numerous. Typically, use-case scenarios include,

but are not limited to, any indoor settings (Fig. 1.6).

Figure 1.6 Application scenarios for distributed sensing tags equipped with ultra-
sound receivers.

Possible settings that are characterized by a wealth of information that can be gath-

ered through sensors networks are factory floors, warehouses, and healthcare facilities. The

example of what a factory floor populated with distributed sensors is shown in Fig. 1.7.

A functional network is made by two types of objects, a transmitter (Tx) that represents

the central hub of the network, and a receiver (Rx), which in this case is embedded in the

sensing tags distributed across the monitored space. The job of the Tx is to orchestrate the

information recovery from the tags. To do that, it sends out a key that is picked up by the

Rx in the tags. The low-power consumption afforded by an ultrasound-based receiver, makes

it ideal to build a WuRx. WuRxs are useful whenever you have a duty-cycled system that

needs to be active infrequently (e.g. once every hour) and for short amounts of time. When

this conditions are met, the system can be left asleep for most of its lifetime, therefore saving

9
 Figure 1.7 Factory floor with a distributed network of sensors.

power. At the same time, the WuRx is always on while operating on extremely low power

budgets, and it brings the main system back to life whenever a specific signature is detected.

These type of systems have gathered increasing interest in recent years as industrial and

military IoT technology is rolled out, and more computing moves further to the edges of

the network. At the edges, access to the power grid is often not an option and despite the

less demanding nature of the computations, energy remains a scarce resource. The recent

DARPA program NZERO [8][9] is an example of such need. The program produced several

systems tackling the problem in different and creative ways such as those described in [10]

[11] [12]. An example of a WuRx that uses ultrasound can be found in [13].

10
 Another application of interest is the use of ultrasound sensors for indoor navigation. No-

toriously, GPS does not work in indoor spaces, as the frequency bands used by the satellites

are blocked by buildings walls. Interest in the field is highlighted by competitions organized

by Microsoft [14], where our colleagues at Carnegie Mellon ranked 6th worldwide with their

ultrasound time-of-flight approach [15]. Miniaturizing ultrasound transducers while main-

taining high sensitivity would simplify the integration with ICs and enable mass production

of small, low-cost tags for indoor positioning.

Finally, using the acoustic waves themselves to remotely transfer power to small tags is

another area that is being explored [4]. Miniaturizing the transducers and creating arrays

to cover larger areas would offer better coupling to the acoustic waves than a single large

transducer, thus increasing the power conversion efficiency per unit area. This would effec-

tively create zero-power tags that can be turned on remotely when necessary. An example

of an application of such technology is shown in Fig. 1.8.

Figure 1.8 Zero power tags for locating objects in mixed-reality.

11
Chapter 2

Individual pNUTs Modeling

In this chapter we model and study the dynamics of piezoelectric Nanomachined Ultrasonic

Transducer (pNUT). We treat them as flexural resonators operating in the linear regime. An

equivalent circuit model is used to describe the frequency behavior of the devices, similarly

to what has been previously done for microscale devices [16] [17]. Notice that in the 40 - 100

kHz frequency range, airborne acoustic waves have wavelengths between 8.5 and 3.5 mm, 1

to 2 orders of magnitude larger than the pNUTs lateral dimensions. It is then appropriate

to model the devices as lumped-element circuits. We will also point out in what specific

circumstances the pNUT model deviates from more classical microscale counterparts.

2.1 Equivalent Circuit Model

The complete equivalent circuit for an ultrasound transducer operating in receive (Rx) mode

is shown in Fig. 2.1

The circuit is divided in three sections, each representing a distinct physics domain:

acoustic, mechanical, and electrical. Variables in the separate domains relate to each other

through proportionality factors described by transformer elements. Table 2.1 shows the

appropriate units for components and variables in each domain.

12
 Figure 2.1 Lumped equivalent circuit of a pNUT.

Table 2.1 Units of components and variables of the equivalent circuit in the acoustic,
mechanical, and electrical domain

Component/Variable Acoustic Mechanical Electrical

Resistor Ns
m5
Ns
m
Ω
m5
Capacitor N
m
N
F

Inductor kg
m4
kg H

Voltage Pa N V
m3
Current s
m
s
A

We proceed to describe each domain and derive analytical expressions for the elements

associated with each one of them.

2.1.1 Airborne waves propagation

The propagation of acoustic waves from the ultrasound source (Tx) to the pNUT takes

place over several wavelengths. Therefore, while the frequency response of the device can

be modeled as a lumped equivalent circuit, the energy that is transferred from the airborne

incident wave to the device depends on the impedance matching between the medium and

13
the pNUT. To illustrate this concept, we can draw intuition from delay line theory. In a

delay line, the level of matching is typically quantified by the Γ factor [18]:

ZL − Z0
Γ= (2.1)
ZL + Z0

As a forward-propagating wave P + encounters an impedance ZL that is different from

the medium characteristic impedance Z0 , a reflected (i.e. backward-propagating) wave P −

with amplitude ΓP + is generated. The net amplitude of the wave at the location of ZL is

then equal to P + + P − = P + (1 + Γ).

In our case, assuming line-of-sight communication, the equivalent delay line is represented

by the channel formed by projecting the pNUT area on the source as shown in Fig. 2.2.

Figure 2.2 Delay line analogy for acoustic waves propagating from Tx to pNUT.

14
 Z0 is the characteristic acoustic impedance, and its value is set by the properties of the

medium and by the channel cross-sectional area, which is the transducer total area A:

ρair cair
Z0 = (2.2)
A

where ρair is the air density and cair is the sound velocity in air. ZL is equal to the

impedance ZpN U T , the impedance seen from the acoustic input of the equivalent circuit

model, and it is a function of frequency.

Given the small cross-sectional area of the channel, we approximate the pressure wave

in it as a plane wave. As the wave travels the distance between the Tx and the pNUT, its

amplitude decreases due to two main mechanisms:

• Spreading losses. As the wavefront total surface increases, the intensity, measured in

W/m2 decreases with the inverse of r2 , where r is the distance from the Tx.

• Viscous losses. This loss results from heat dissipation as the wave compresses and

releases the medium molecules. This loss is approximately 1 - 2.5 dB/m in in the 40 -

100 kHz band in air [4].

Accounting for these two loss mechanisms, the acoustic pressure amplitude as the wave

propagates away from the Tx is given by:

rT x
Pin = (1 + Γ)γPT x e−αr . (2.3)
r

In equation 2.3, γ is a coefficient that accounts for the directivity of the Tx, PT x is the

pressure at the Tx, r is the distance between the Tx and the pNUT, α is a coefficient that

accounts for viscous losses, and rT x is the radius of the Tx itself. We can get a first order

idea of the pressure amplitudes we can generate at a given distance by plotting the pressure

15
generated by an ideal isotropic (γ = 1) hemispherical Tx with a radius of 10 cm. Assuming

a maximum initial pressure of 350 Pa as mandated by current regulations [4] we can see in

Fig. 2.3 the generated pressure over distance for a signal at 40 kHz and 100 kHz.

Figure 2.3 Acoustic pressure generated by an ideal isotropic hemispherical Tx with

a radius of 10 cm.

For a given distance, we can then obtain the acoustic pressure present on the transducers

top surface by multiplying the propagated acoustic pressure value by (1 + Γ).

2.1.2 Acoustic Domain

The acoustic domain is characterized by three main components: the capacitor Ccavity , the

resistor Rholes , and transducer radiation impedance (Zrad ). We now describe the nature of

these components and describe how to quantify them to a first order.

Ccavity represents the effect of the hollow volume behind the transducer. At rest, the

acoustic pressure on the backside of the device is equal to zero. When the suspended plate

moves vertically, for example when electrically actuated or excited by an incident acoustic

wave, a small change in the volume of the back-cavity takes place. As a result, the pressure

16
in the cavity shifts away from atmospheric pressure in proportion to the relative change of

the volume [19]. Therefore, the back-cavity behaves as a spring element that opposes the

motion of the transducer. The value of the equivalent capacitor is given by

V
Ccavity = (2.4)
ρair c2air

Figure 2.4 Rendering of the transducer portions modeled by Ccavity and Rholes .

The device geometry is generated by etching slots through the AlN layer. This creates

a path for pressure equalization between the top and bottom side of the device. This effect

is represented by the equivalent resistor Rholes . Estimating the value of this component

analytically is not easy; when the device is released, it bends out of plane because of the

stress-gradients across the films stack thickness, complicating the geometry of the slots.

However, an upper bound on the value of Rholes can be obtained by modeling the slots as a

rectangular duct [19]:

17
 12tslot µair
Rholes = 3
(2.5)
lslot wslot

The final element in the acoustic domain is the radiation impedance Zrad . This is a

complex impedance that represents the energy transferred to the medium surrounding the

transducer in the form of radiated acoustic waves. This means that, in the equivalent circuit,

the energy dissipated by the real part of Zrad is not actually lost, but rather radiated away.

A good radiator has the value of Re{Zrad } as close as possible to the air acoustic impedance

Z0 . The imaginary part of Zrad models the portion acoustic energy that is transferred back

and forth between the medium and the transducer through the inertia of the mass of the

medium. In a denser medium, like water, the effect can be quite important, and Im{Zrad }

can significantly shift the resonance frequency of the transducer. Generating an analytical

formulation of Zrad is not easy and often not possible. Generally, for a flexural transducer

the value of Zrad is approximated by the one of a piston in an infinite baffle. The piston is

characterized by an effective radius aef f , which in our case is given by Aef f /π.
p

The expression of Zrad of the equivalent piston in air, measured in N s/m5 , is given by:

ρair cair J1 (2kaef f ) S1 (2ka)

Zrad = Re{Zrad } + Im{ZRad } = 2
[1 − +j ], (2.6)
πaef f kaef f kaef f

where J1 is the first order Bessel function of the first kind, and S1 is the first order Struve

function.

In the next sections, we will show that as long as the plate thickness and area are scaled

together, in the electrical domain the reactive parameters of the pNUT -and of flexural

resonators in general- remain constant. However, the same scaling dependence does not hold

for the parameters in the acoustic domain. The dependence of these parameters with respect

to the device total thickness is presented in Fig. 2.5.

18
 Figure 2.5 Acoustic parameters values when scaling up the thickness and area of
the pNUT. The starting point is a device with 300 nm thickness and an area of 100
µm X 100 µm. To estimate Zrad , we assume a frequency of 50 kHz. We notice that
scaling up the total thickness to 3 cm would not be feasible in practice, and the plots
are only meant to illustrate the equivalent parameters dependence on geometry.

From the figures, we see that for a small radiator as the case of the pNUT, there is a

large mismatch between the radiation impedance and the acoustic impedance of air Z0 . As

the device dimensions are increased, they get closer to the acoustic wavelength at 50 kHz (

the reference frequency used to generate the plots in Fig. 2.5), and the real part of Zrad ends

up converging to the value of Z0 . The value of Im(Zrad ), which is negligible compared to

the mass of the transducer at all frequencies because of the small mass density of air, ends

up converging to zero as the device is scaled up. When the device operates at resonance,

its equivalent circuit looks purely resistive. If Re(Zrad ) was the only resistive component

when the device is 300 nm thick, we would observe very high quality factors and a great

mismatch with the impedance of air Z0 . As shown in Fig. 2.12, and experimentally in

Chapters 5 and 6, the pNUTs present values of quality factors similar to those reported for

much larger pMUTs operating at similar frequencies. The reason is that the way Zrad is

calculated does not take into account the viscosity of the medium ([20]), which is the main

19
energy loss mechanism for highly scaled micro-structures [21][22].

As mentioned above, the value of Rholes represents an upper bound on the range of

possible values. For Ccavity we assume that the undercut necessary to release the devices

remains constant across the scaled geometries at 30 µm. This means that the depth of the

back-cavity stays constant, and the total volume is increased only by the area scaling up with

the total thickness of the film stack. For both Ccavity and Rholes , higher values are desirable.
5
Because the value of Ccavity is only 3e − 18 mN for the 300 nm thickness case, the device

response to ultrasound will be considerably stiffened, reducing the sensitivity and shifting

the resonance frequency above the target range of 30-100 kHz. As explained in Chapter 3,

this issue is solved by adding a back-etch step to the fabrication process to open the cavity.

For simplicity, and within the limits of the lumped equivalent circuit model, opening the

cavity (i.e. the value of Ccavity goes to infinity) we remove Rholes from the equivalent circuit

since its presence would not affect the electrical response of the pNUT.

2.1.3 Mechanical Domain

We now look at the variables that govern the frequency response dictated by geometrical

and material properties. We derive the equations for a 4-Beams pNUT, and show that the

values of the reactive parameters are preserved when thickness and area of the devices are

scaled simultaneously.

Due to the large number of variables in the following equations, the variables description

can be found in the nomenclature section, along with the variables used throughout the

document.

4-Beam pNUT Equivalent Parameters

The lumped equivalent model of the 4-beam pNUT can be thought of as 4 parallel springs

connected to a common central mass. The value of the individual springs is here approxi-

20
mated as the one of a beam with clamped-free boundary conditions (i.e. a cantilever).

Since we are dealing with a laminate beam, the first step of the derivation is to obtain the

flexural rigidity D and the effective surface µef f mass density of the stack. The expressions

for these two quantities can be found in [23]. Since we are approximating the beams as

cantilevers, we take their normalized mode shape ([24], pp.139) as:

πx
YCF (x) = 1 − cos( ) (2.7)
2

where x is the normalized coordinate along the length of the beam. From the mode

shape, it is possible to obtain the equivalent parameters Meq , Keq , and η:

Z 1
Meq = 4µef f Wb Lb YCF (x)2 dx + µef f (Lb − Wb )2 (2.8)
0

1 2
d2 YCF (x)
Z 
DWb
Keq = 4 3 dx (2.9)
Lb 0 dx2

d2 YCF (x)
Z
Wb
η = 4e31,ef f (zn − zpiezo ) dx (2.10)
2Lb xel dx2

Meq is an inertial term that measure the device ability to store kinetic energy. Similarly

Keq represents the pNUT ability to store potential energy when the beams are deformed.

Together, Meq and Keq define the dynamics of a 1-dimensional second order system that

matches the displacement experienced at the tip of the beams and over the central plate.

The role of η is to provide a proportionality factor to link the displacement set by the

mechanical parameters with the voltage produced across the electrodes through the inverse

piezoelectric effect. The value used to model e31,ef f for AlN is −0.75C/m2 ([25] pp.442).

21
 In the 4-beams pNUT geometry, for a given A, the values of Lb and Wb are not inde-

pendent since once we fix the length of a beam the width will automatically occupy the

remaining portion of the device side. For example, in a 100 µm x 100 µm pNUT, if we fix

the beam length to be 70 µm, the width will automatically be set to be approximately 30 µm

(as we want to keep the holes between beams to a minimum). Once we fix the value of A and
√
the relative length of the beams we can see that both Lb and Wb scale with A. Therefore,

we can extract how the parameters derived above vary as we scale the device thickness and

area simultaneously (Fig. 2.6).

Figure 2.6 Dependence of Keq , Meq , and η on thickness and area scaling. Keq
and Meq both scale quadratically with the geometrical parameters, indicating that
the resonance frequency remains constant. η increases linearly with the resonator
scaling.

We see that as we scale down thickness and area, the value of η decreases proportionally.

This is because of η dependence on the distance between the center of the piezoelectric

layer and the laminate neutral axis. This quantity is represented by (zn − zpiezo ), and is

proportional to the total stack thickness. As shown in the next section, the fact that η

decreases with scaling does not reduce the out-of-resonance sensitivity of the devices, as it

22
results in the equivalent circuit reactive parameters to remain constant once moved over to

the electrical domain. In other words, the dependence of Meq , Keq , and η on the total stack

thickness cancels out when we move all parameters in the electrical domain.

2.1.4 Purely Electrical Equivalent Circuit and Scaling Relations

The electrodes capacitance can be written as

Ael
Cel = 0 r (2.11)
t

Starting from the equations derived above we can obtain an expression of the components

in the acoustic and mechanical domain once they are moved over to the the electrical domain,

allowing us to describe the behaviour of the system purely in terms of electrical quantities.

The transformed, purely electrical equivalent circuit is shown in Fig. 2.7.

Figure 2.7 Equivalent circuit model of the pNUT once we move all components
over to the electrical domain. In this model we are assuming an open back-cavity is
present, which allows us to remove Ccavity and Rholes from the circuit.

To move elements from one domain to another we use the following relations:

M η2
L = 2, C= (2.12)
η K

23
 Therefore, the proportionality relation of the components in the electrical equivalent

model with respect to the device thickness and area are

η ∝ t, Aef f ∝ A (2.13)

Aef f A
VP in = Pin ∝ (2.14)
η t

Meq tA A
Lm = 2
∝ 2 = (2.15)
η t t

η2 At2 A
Cm = ∝ 3 = (2.16)
Keq t t

A
Cel ∝ (2.17)
t

t
f0 ∝ (2.18)
A

The value of Rm is given by:

r
1 Lm
Rm = (2.19)
Qair Cm

From these proportionality relations it is possible to see that as long as area and thickness

of the device are scaled together, the out-of-resonance frequency response governed by the

structural parameters of the device remains constant. At resonance, the circuit is purely

resistive and the response is set by Rm . Since Cm and Lm remain constant with scaling, the

value of Rm is determined by the quality factor in air Qair . The role played by Qair and how

24
scaling affects its value will be discussed in the next section. Notice that the relations hold

for both the circular diaphragm [16] and 4-beam pNUT geometries, and are applicable to

flexural resonators in general.

As discussed in [26], the first step to observe this scaling trend in literature consists in

normalizing the reported sensitivities by the quality factor of the main resonance mode.

This normalization accounts for the fact that transducers operating at different frequencies

present significant differences in how air damping affects their response at resonance, there-

fore normalizing for differences in Rm . Next, we observe that most published work presents

the Tx sensitivity of the transducers, measured in nm/V , rather than the Rx sensitivity, as

it is easier to measure. For this reason, we take advantage of the proportionality relations

2.20 and 2.21 to obtain a coefficient that is proportional to the Rx sensitivity starting from

the Tx sensitivity figures reported in literature.

d Feq η At A
T xSensitivity = ∝ ∝ 3 ∝ 2 (2.20)
V Keq Feq t t

Vout Feq A A
RxSensitivity = ∝ ∝ ∝ (2.21)
Pin ηPin η t

From these relations, a coefficient proportional to the Rx sensitivity is obtained by taking

the reported Tx sensitivities and multiplying them by the piezoelectric layer thickness. We

finally normalize the coefficient by the transducers area in order to obtain a coefficient that

depends on only one geometrical parameter. Fig. 2.8 shows a survey of AlN pMUTs from

published works, and it is possible to observe the inverse linear dependence of the derived

coefficient with the thickness of the piezoelectric layer.

The works referenced in Fig. 2.8 with the respective data is presented in Table 2.2.

The fact that this trend emerges from literature data serves as a confirmation that the

proportionality relationships outlined above are correct, and are equally valid for classic

25
pMUTs, pNUTs, and flexural resonators in general.

Figure 2.8 Linear dependence on plates thickness of the derived coefficient propor-
tional to the static Rx sensitivity in works from literature.

2.1.5 Quality Factor Scaling

In the previous section we showed that all values of the components in the purely electrical

circuit are independent from scaling with the exception of Rm . The dependence of Rm value

on scaling depends on the quality factor of the transducer. In flexural resonators operating in

air, air-damping is typically the main loss-mechanism. As the plates move in the fluid, part

of the energy in the plate is passed to the medium either in form of radiation (represented

by Re(ZRad )), or in the the form of viscous losses. In fact, the expression of the radiation

impedance that was shown in Section 2.1.2 was derived assuming a continuum non-viscous

medium. When making this assumption we can neglect the tangential component of the

26
 Table 2.2 Compiled data used to generate the data in Fig. 2.8

TxS Q fres Radius Area Piezo/Total Comments Ref

[nm/V] [Hz] [µm] [mm2 ] Thickness

30 60 2.5e6 40 5e-9 0.7/1.4 [27]

20 100 5.4e6 29 2.6e-9 0.7/1.4 [27]

430 25 200e3 230 1.7e-7 2*0.8/2.4 Double piezo [28]

452 42 350e3 170 9.1e-8 2*0.8/2.4 Double piezo [28]

45 40 2.2e6 95 2.8e-8 2/3.3 Curved plate [29]

400 50 220e3 175 9.7e-8 1/2.1 [30]

20 140 19e6 25 2e-9 0.8/3.3 [16]

medium velocity. As discussed in [20] (pp. 440), when the medium is considered to be

viscous, the tangential components of the fluid velocity cause a disturbance in the pressure

field, but they do not extend to the far field. In other words, this energy transfer from the

transducer to the medium results in heat dissipation. An overview of various models used

to estimate air damping in cantilever beams that account for the medium viscosity through

the Navier-Stokes equations can be found in [31]. In the derivation presented in the previous

section, the quality factor normalization is applied in order to compare transducers operating

at different frequencies. However, if we fix the operational frequency, the quality factor of an

ultrasound transducer is affected by the mass and geometry of the device as well. Although

the particular geometry of the transducer has an effect on it experiences air-damping, we can

gain insights on the quality factor scaling by looking at the expression of losses in cantilevers,

which has been extensively characterized [32]:

r
APatm M
φair ≈ (2.22)
mω RT

27
 in Eq. 2.22, φair = Q−1
air is the loss due to air damping, A is the cantilever area, Patm is the

atmospheric pressure in the gas, m is the total mass, and ω is the frequency of vibration. The

terms under the square root are the gas constant, the gas temperature, and the gas molar

mass (R,T , and M respectively). It is worth noting that this expression does not make a

distinction between the damping resulting from heat dissipation and acoustic radiation. We

can then use this expression to see how the losses we observed experimentally (presented

in Chapter 5) would scale with the geometry. In general, we can expect the impedance of

a radiator to be close the matching condition with the surrounding medium provided the

dimensions are comparable to the wavelength of the operational frequency. Interestingly, we

see that as the transducer dimensions are scaled up using the proportionality dependence of

Eq. 2.22, the pNUT resistance ends up following closely the theoretical value of the radiation

resistance calculated in Section 2.1.2 for a circular piston in an infinite baffle (Fig. 2.9).

A possible interpretation of this convergence is that as the transducer dimensions are

increased, there is a transition from a region where viscous losses dominate to a region

where losses are dominated by radiation to the far field, where the device resistance is

dominated by Re(Zrad ). Eq. 2.22 does not distinguish between the two loss mechanisms as

it is derived directly by means of Navier-Stokes equations -which account for the medium

viscosity-, while the derivation of Zrad explicitly neglects the role played by viscous losses.

As shown in Chapter 5, the pNUTs show quality factors between 5 and 10, which are typical

for pMUTs with thicknesses and areas around 10 to 100 times larger.

This points to an interesting design insight. Because of the pNUT use of the Pt electrodes

as elastic layers, as well as having the central plate, the pNUTs are characterized by a much

larger equivalent mass than an equivalently scaled pMUT. In theory, additional material

can be added on the central plate in a separate lithographic step, further increasing the

equivalent mass. From Eq. 2.22 we see that as long as we remain in the desired frequency

range, the mass adjustment can be exploited to reduce the losses to maintain a high quality

factor.

28
 Figure 2.9 Comparison between the scaling of the measured pNUT acoustic re-
sistance according to models accounting for viscosity and the theoretical radiation
resistance of a piston with equivalent dimensions.

It is important to notice that the use of the electrodes metal to increase the equivalent

mass of the transducers is feasible only in highly scaled films, in the order of few hundreds

of nm. This is because it is typically impractical to deposit and pattern much thicker metal

layers through sputtering or evaporation.

2.1.6 The Effect of Scaling on Transducers Performance

The analysis shown at the end of Section 2.1.4 shows that the scaling relations derived for the

reactive parameters is confirmed by the experimental data presented in literature. We can

now combine these relations with the theory presented in the previous sections to obtain a

complete analysis of the pNUT equivalent circuit response and better understand the impact

of highly scaled geometries on the receive sensitivity of an ultrasonic transducer.

29
 When the transducers operate at resonance, their impedance is purely resistive. The

value of the equivalent resistive component quantifies the losses in the resonator, and its

resistance value sets the value of Γ. Therefore, for a fixed area, varying Γ over a range of

values between -1 and +1 is equivalent to varying the losses in the resonator in a range

between zero and infinity.

The complete equivalent circuit model at resonance is shown in Fig. 2.10

Figure 2.10 Complete equivalent circuit model when the transducers operate at
resonance.

For our scaling analysis we select a reference geometry and assign the corresponding

values to Z0 , η, Aef f , and Cel according to the equations derived in the previous sections.

The reference geometry we choose for the pNUT is a 100 µm x 100 µm area with an AlN

thickness of 100 nm and a Pt thickness of 200 nm. This geometry sets the resonance frequency

to 50 kHz. Since we do not know Rm , which is set by the quality factor, we sweep its value

over a range that generates values of Γ ranging from -1 to +1. We can now estimate the Rx

sensitivity by setting P + equal to 1 Pa, and calculating the output voltage with respect to

Γ.

This procedure can be repeated for larger transducers and it will give us an idea of how

scaling affects the devices performance. To do that, we define a scaling factor SF . SF is

30
a coefficient that multiplies the area and thickness of the reference geometry. Interestingly,

the only parameter that changes as we vary SF is Z0 , since we know that both the turn

ratio η : Aef f and Cel -as well as the resonance frequency- remain constant with respect to

scaling.

We can repeat the same analysis for any flexural resonator geometry (assuming it is

possible to overcome some of the issues highlighted in section 2.2 for other geometries). For

example, we can use the equivalent circuit data reported in [33] to generate a pMUT with

a resonance frequency of 50 kHz and an area of 100 µm x 100 µm, and observe how its

Rx sensitivity changes with respect to SF and Γ. More details on this model, including a

MATLAB script to perform the analysis, are presented in Appendix A. The Rx sensitivity

for the reference pNUT and the reference pMUT with respect to scaling is presented in Fig.

2.11.

Figure 2.11 Value of the theoretical open-circuit Rx sensitivity vs. Γ for the
reference pNUT and pMUT. Both devices have a resonance of 50kHz and an area
of 100 µm x 100 µm when SF = 1.

The first insight that emerges from this analysis is that scaling is detrimental to the Rx

sensitivity regardless of the transducer of choice. This is in agreement with the fact that as

we reduce the transducer area, the total available acoustic energy decreases. In this model

there are two main mechanisms that determine how efficiently we convert the acoustic energy

31
into an electrical signal across the electrodes. The two mechanisms are the level of matching

between Z0 and Rm and the amount of losses represented by Rm . In Fig. 2.11 we see that,

for the values of SF under consideration, as Γ becomes more negative the Rx sensitivity

does not change significantly, while as it becomes more positive it quickly decreases. In the

first case these two mechanisms compensate for each other, which means that despite the

mismatch between Z0 and Rm increases (Γ is more distant from 0), the losses introduced by

Rm decrease. In the second case these two mechanisms both contribute to waste energy: the

transducer is both mismatched to the medium and lossy.

This model offers a straightforward way to compare the performance of different ultra-

sound sensors geometries and topologies. Once we fix the transducer area and its resonance

frequency, all the other properties are automatically set. This includes the layers stack

thickness, Z0 , the equivalent transformer ratio η : Aef f , and Cel .

This idea is presented in Fig. 2.12.

Figure 2.12 a) Values of Γ expected over a range of device lateral dimensions and
frequencies of operation. b) Comparison between the Rx sensitivities of the reference
pNUT and pMUT as they are scaled.

In Fig. 2.12a we take the value of Rm we measured (presented in Chapter 5) as a

reference point, and we scale its value according to the theoretical scaling of Qair presented

in Section 2.1.5 (code included in Appendix B). This allows us to define a reasonable interval

32
of values for Γ. We see that Γ is always larger than -0.4 as we scale up the transducer. We

can also reasonably assume that as the transducer dimensions are increased its impedance at

resonance will match the one of air, corresponding to Γ = 0. Therefore we consider an interval

of values for Γ between -0.4 and 0. Fig. 2.12b shows the corresponding Rx sensitivities in this

Γ interval as we scale the reference pNUT and pMUT. Clearly, the pNUT geometry offers

approximately an order of magnitude better performance compared to traditional pMUTs.

This property makes the pNUTs ideal for building miniaturized ultrasound receivers, as the

significantly higher performance per unit area compensates for the lower acoustic energy

available for smaller footprints.

2.2 Limits of the Analytical Model

To verify the analytical model formulated in the previous section, we can check the values of

the first mode resonance frequency and of the equivalent parameters through finite element

analysis (FEA) in COMSOL. The first step is verifying that the analytical models apply to

a single cantilever. We consider a laminate beam formed by an AlN and a Pt layer with

equal thickness. The beam has fixed length of 70 µm and width of 30 µm, while we vary the

thickness of the two layers to observe how its properties scale. In particular, we can observe

the resonance frequency of the beam, which ties the relation between Keq and M eq, and the

static tip displacement per unit voltage, which ties the relationship between Keq and η (for

1 V actuation the displacement is equal to η/Keq ). The comparison between the analytical

model and COMSOL for a single cantilever beam is shown in Fig. 2.13.

Now that we know the analytical model predicts well the parameters for a single beam,

we can move to a complete device. We keep the beams geometry with a width of 30 µm and

length of 70 µm, while we vary the thickness of the layers in the laminate. These are dimen-

sions close to the ones used in the fabricated devices and that will be discussed in Chapter

5. For simplicity, we neglect the bottom electrode, only 20 nm in the fabricated devices, and

33
 Figure 2.13 Left: Resonance frequency of a laminated cantilever simulated in
COMSOL and with the analytical model. Right: Tx sensitivity of the same can-
tilevers. In both cases the analytical model agrees well with the results observed in
COMSOL.

assume its absence would not affect dramatically the devices mechanical dynamic response.

The first resonance mode of the device obtained from an eigenfrequency simulation in

COMSOL is shown in Fig. 2.14a.

We can see that because of the common central plate, the beams are subject to a partial

constraint on the angle they can have at the tip. In Fig. 2.14b we can see the mode shape

obtained directly from COMSOL on the plate side of the beam, and how it compares to the

mode shapes of an ideal cantilever and clamped-guided beam. The mode shape of the real

device is in between the two ideal boundary conditions examples, although closer to that of

a cantilever. By repeating the same analysis as above, we can see in Fig.2.15 (left) that the

resonance frequency of the device observed in COMSOL is higher than the one obtained by

assuming clamped-free boundary conditions on the beams. The analytical model matches

the results obtained through FEA after the COMSOL mode shape is used in the analytical

model. Similar results are shown on the right side of Fig.2.15. The analytical model that

uses the COMSOL mode shape to obtain η and Keq follows closely the static Tx sensitivity

directly observed in COMSOL. On the other hand, the displacement of the pNUT obtained

34
 Figure 2.14 a) Resonance Mode of a device obtained from an eigenfrequency sim-
ulation in COMSOL. b) Comparison between the device beams mode shape and
mode shapes of a cantilever and a clamped-guided beam.

with the cantilever mode shape, being more compliant, is much higher than the one from

the FEA model.

During the design phase, the analytical model is a useful tool to quickly establish the

device parameters and get a sense of how those scale as we vary the geometry. However,

as outlined in the next sub-sections, we will see that as more non-idealities are taken into

account, the analysis through FEA becomes inevitable to understand how a real fabricated

device will respond to ultrasound.

2.2.1 The Effect of the Undercut from Release

The devices fabrication process, presented in Chapter 3, uses an isotropic release step. Be-

cause of this, a certain amount of undercut will always be present, and it measures typically

between 20 µm and 30 µm once the devices are completely released. When accounting for

the effect of the undercut on the device, the COMSOL model must be modified as shown in

Fig. 2.16.

Adding the undercut to the geometry does not change significantly the equivalent mass

35
 Figure 2.15 Left: Comparison between the resonance frequency of a pNUT simu-
lated in COMSOL and in the analytical model. Right: The same comparison for the
static Tx sensitivity. In both cases the discrepancy between the analytical model
and COMSOL is resolved once we use the COMSOL mode shape in the analytical
model. This highlights the role of the central plate in stiffening the device response.

of the device, but it decreases Keq by relaxing the clamped constraint previously imposed

on the anchored side of the beam. This change modifies the beams mode shape around

the clamped region, reducing the amount of bending that occurs. The natural frequency

of the modified structure is shown in Fig. 2.17. The model suggests that a small amount

of undercut is responsible for most of the softening, while expanding the release further

accounts for progressively minor changes in the resonance frequency of the device.

Another important consequence from the presence of the undercut is its effect on the

transduction coefficient η. Just like Keq , the value of η is determined by the amount of

bending that occurs in the beams clamped region (see Eq. 2.9 and 2.10), where the electrodes

are located. Relaxing the ideal zero-angle constraint significantly reduces the amount of

bending, reducing how effectively we convert the beam in-plane strain into an electric field.

This change can be visualize in Fig. 2.18, where we show the normalized electrodes mode

shapes when no undercut is present and when we have a 25 µm undercut respectively.

We can see that in the 25 µm undercut case significantly less bending occurs. In theory,

36
 Figure 2.16 First resonance mode of a device including a 15 µm undercut from the
release process.

Figure 2.17 pNUT first resonance frequency for different levels of undercut.

this reduction causes an important reduction in the transduction coefficient of about 20x.

This analysis highlights the importance of developing a fabrication process that allows for

37
 Figure 2.18 Normalized electrode mode shapes when no undercut and when a 25
µm undercut is present. The figure illustrates how relaxing the fully clamped bound-
ary condition affects the electrodes mode shape and the transduction coefficient η

precise control of the devices release.

2.2.2 The Effect of Residual Stress

Another important non-ideality that must be taken into account is the effect of the residual

stress on the devices frequency response. A certain amount of residual stress from the films

deposition process is inevitable. In a similar way as the undercut, the stress does not affect

the equivalent mass of the resonators, but it can increase or decrease the equivalent stiffness

depending on the stress being tensile or compressive, respectively. The in-plane residual

38
stress influence becomes increasingly dominant as the aspect ratio of the suspended plate

increases. An analogy that describes this effect is that of a drum head pelt. The pelt is a

high aspect ratio flexural resonator, and the pitch of the drum is not just determined by

geometric and material parameters, but by the tension in the pelt as well. On the other

hand, a short steel rod is a low-aspect ratio resonator, and adding tension to it does not

significantly change its resonance frequency. Classic pMUTs are characterized by a circular

geometry that is clamped all around. This geometry, like in the drum case, is extremely

susceptible to residual stress. In fact, the fully clamped boundary condition does not allow

the structure to deform to relax the stress once it is released. An analytical model that

describes the dynamics of a circular plate accounting for the residual stress is described in

[34]. The geometry of the 4-Beams pNUT permits to the structure to release some of the

tension by deforming. The effect of residual stress on circular plates of different thicknesses

and radii compared to a 200 nm thick 4-Beams pNUT is shown in Fig. 2.19.

Figure 2.19 Comparsion of the effect of residual stress on circular pMUTs and
on a 4-Beams 200nm thick pNUT. The devices dimensions are selected to have an
unstressed resonance frequency of approximately 40 kHz.

Besides having a reduced sensitivity to residual stress, the pNUT also has more tolerance

to buckling when the residual stress is negative. While less sensitive, the pNUT resonance

39
frequency is still shifted by residual stress. In the case of positive residual stress, the reso-

nance frequency is increased, partially counteracting the effect of the undercut seen in the

previous sub-section.

Ideally we would prefer a zero dependence of the stiffness on residual stress. This would

be achieved by a cantilever-like structure, which is clamped on only one side and can deform

along all other directions to relax the stress to 0 MPa. Unfortunately, the in-plane stress

distribution along the stack thickness is not uniform, especially because the structure is

a laminate. This means that stress gradients along the thickness are present, which will

cause the structure to bend out of plane when released. While a circular pMUT, being

fully clamped, would not deform vertically, a cantilever would be completely free to curl,

potentially even folding on itself. The pNUT geometry offers a compromise between these

two scenarios. By only allowing partial relaxation of the residual stress we can reduce the

resonance frequency shift while limiting the out-of-plane bending. This effect is evident in

Fig. 3.2.

40
Chapter 3

pNUTs Fabrication

3.1 pNUTs Fabrication Process

The pNUTs were built in the Carnegie Mellon nano-fabrication facility with a four-masks

process as shown in Fig. 3.1.

Figure 3.1 Fabrication process of the pNUTs: 1) Bottom Pt lift-off, 2) AlN depo-
sition and patterning, 3) Top Pt lift-off, 4) backside DRIE, 5) topside XeF2 release.

In step 1) the 20 nm Pt bottom electrode is deposited and patterned through lift-off.

In step 2) a 100nm thick AlN layer is sputtered in a Tegal AMS system and subsequently

wet-etched in a heated CD26 developer solution. The Pt top electrode is then sputtered and

lifted-off in step 3). The device release is performed through a combination of back-side and

41
front-side etch. First (step 4), the area of the device back-cavity is defined by a back-side

Bosch etch process carried out in a STS DRIE System. The depth of the back-etch was

characterized to leave about 5 to 10 µm of silicon below the device and prevent damaging it

during the removal from the holder. The device release is completed in step 5) by removing

the remaining silicon with a XeF2 etch from the front-side.

An example of a fabricated pNUT is shown in Fig. 3.2 b, side by side with a simulated

structure characterized by residual stresses of 50 MPa in the AlN layer and 1 GPa in the top

Pt layer.

Figure 3.2 a) Simulated structure characterized by residual stresses of 50 MPa in

the AlN layer and 1 GPa in the top Pt layer. b) SEM picture of a fabricated device.

3.2 Fabrication Challenges

During the fabrication process several challenges were encountered. In this section we sum-

marize them and describe possible solutions for future pNUTs fabrications.

3.2.1 Device Geometry Motivation

Initial prototypes of the pNUT were simple square clamped-clamped beams. An example

of the layout of these devices is shown in Fig. 3.3a. Upon release, most of these devices

broke due to the difficulty in controlling residual stress in extremely thin sputtered films.

Additionally, even if the stress in the single layers could be controlled within ± 100 MPa, the

42
small thickness of the layers in the laminate produces stress gradients along the thickness of

the device in the order of GPa/µm. As shown in Fig. 3.3a, the floating metal in this device

variation was patterned as a continuous patch over suspended portion of the device that was

not covered by the electrodes. Because of the high stress gradients in the laminate (positive

in this case), the structure bent upwards, and tore along the side of the metal sheet. In

the same layout we included a variation where the electrodes were split and connected in

series with each other and the floating metal was segmented along the same width as the

individual beams electrodes as shown in Fig. 3.3b.

Figure 3.3 Example of broken devices from early pNUTs prototypes. a): Device
with a uniform floating metal. b) Device with segmented floating metal. It is
evident how the influence of the stress gradient is reduced along the direction of the
segmentation.

In the image, it is evident how the segmentation helps mitigating the bending moment

along the width of the device, preventing mechanical failure along that direction. At the same

time we see that along the length of the beams we still see some tearing in the plate. This

observation prompted a change in the design to make sure there are always discontinuities

in the patterned metal by segmenting it along both the in-plane directions to limit the

influence of the bending moments resulting from the stress gradients in the stack. Another

43
observation is that the mechanical failure always originated at the angle of the patterned

metal, that was originally designed with sharp 90 degrees angles. A sample layout of the

first pNUTs prototypes is presented in Fig. 3.4a. Fig. 3.4b showcases the layout of the last

generation of devices. In the image, we can see that besides being segmented, the floating

metal is also characterized by rounded corners with 1 µm radius. In doing so, we prevent

stress concentration points where tears typically are originated. In a similar way, we round

individual beams where they attach to the substrate on the anchor side.

Figure 3.4 Comparison between the first pNUTs prototypes (a) and latest version
(b) layouts. We moved to the 4-beams anchor topology due to the high sensitivity
to residual stress of the clamped-clamped design. Additionally, all square corners
were eliminated, the top electrode dimensions were reduced by 1 µm compared to
the bottom electrode, and the bottom metal was eliminated from the floating region.

In the first devices, the bottom metal was patterned even in the floating metal region.

The reasoning for that choice was that it would increase the equivalent mass of the device

and maintain the resonance frequency in the desired range of operation. In our last design,

we kept only the top metal for the floating region, since the shift in resonance frequency was

not significant, especially if compared to the variance in the equivalent stiffness introduced

44
by the residual stress alone. Finally, the lateral dimensions of the top electrodes were reduced

by 1.5 µm compared to the bottom electrodes to limit the overlap of the two metals on the

regions where the AlN is sloped along the side of the bottom metal. Since the AlN are only

100 nm to 200 nm thick, it is possible to not have perfect coverage of the bottom electrodes

along its perimeter. By making the top metal electrodes slightly smaller we minimize the

chance of creating a short circuit between the two electrodes. This design change is especially

relevant for the following section.

3.2.2 Bottom Metal Lift-off

This issue is present during the first step of the fabrication process, where the bottom

electrode metal is deposited and lifted-off. During a lift-off process it is common to have so

called "wings" on the perimeter of the patterned metal [35]. An example of this phenomenon

is shown in Fig. 3.5. Lift-off wings are problematic when working with very thin piezoelectric

films as it results in device shorting.

Figure 3.5 a) Example of effect of lift-off wings in the bottom metal on the devices
release. b) Close-up view of the floating metal. both on the top and bottom metal
it is possible to see the wings along the perimeter of the rectangles.

This occurrence is especially common if positive photoresist is used, as it is characterized

45
by a positive slope angle along the sides of the developed pattern (Fig. 3.6). On the

other hand, negative photoresist is expected to be more resilient to wings formation, as the

negative-angled slope helps creating a sharp discontinuity in the metal film, easing access to

the solvent to etch the photoresist during the lift-off [36].

Figure 3.6 Comparison between positive and negative photoresist profiles.

In the first round of fabricated devices, we used positive photoresist for the bottom

electrode step. When we tested the finished devices, we found that almost all of them were

presenting a low resistance (between 100Ω and 2kΩ) between the top and bottom electrode.

While normally the wings would be covered by the dielectric between the two electrodes,

because of the extremely thin piezoelectric layer that characterizes the pNUTs, they were

not completely passivated by the AlN, and formed a low resistance path to the top electrode

as a result. We identified the problem in the chrome (Cr) adhesion layer used for the bottom

electrode. Both the chrome deposited in the CVC and in the 5-Target sputtering system were

found to be extremely conformal. In fact, after further testing, even switching to negative

46
photoresist did not completely eliminate the wings issue. As a temporary solution, after the

lift-off, we resorted to breaking the wings with a gentle swab cleaning followed by a 40 kHz

sonication in acetone and a step in the spin washer. After repeating these step 3 to 4 times

almost all wings were eliminated. For future fabrications, we recommend characterizing the

bottom layer lithography with a lift-off photoresist, or possibly switching to the bi-layer

method [36]. Another possibility might be switching to a different adhesion metal, such as

titanium (Ti), although we did not verify if it is less conformal than Cr.

3.2.3 Aluminum Nitride Etch Issues

Issue #1

Multiple issues were encountered during this fabrication step. The device geometry is pat-

terned in the AlN through a wet etch. The used etchant is a solution of CD26 developer

heated to approximately 70C. The wafer is immersed in the solution for approximately 25

seconds before being rinsed in de-ionized water. During this etch step both the slots that

define the beams profile and the vias to access the bottom electrode are patterned. The first

issue encountered on this step is that once the wafer is removed from the CD26 and after

stripping the photoresist mask, only the vias were thoroughly patterned, while the AlN on

the slots seemed completely unaffected. Since the vias consist in 5 µm x 5 µm squares, while

the slots are only 1 µm wide lines, we initially thought the issue was that the photoresist on

the slots was underdeveloped, leaving the AlN underneath unexposed. However, in a sepa-

rate test, we observed that overdeveloping the photoresist did not change the results. It is

worth noting that this issue was not experienced in the first generation of devices. The only

difference between the first round of devices and the later fabrications is that the Carnegie

Mellon cleanroom was moved to a new facility and the shape of the container where the

etch was taking place. Of course these changes should not have affected the process, and the

reasons for the different outcome are still unclear.

47
Issue #2

The solution to the problem outlined above consisted in a modification to the initial fabri-

cation process that is presented in Fig. 3.7. In this variation, we switch the order of step

#2 and #3. In this way we pattern the top metal before etching the vias and the slots

in the AlN, momentarily leaving the bottom electrode disconnected from the pads. Next,

we do the lithography to pattern the vias and slots, and we run an etch step in the ion

mill. At this point, the AlN on the slots location is exposed, while the AlN on the vias is

masked by the top metal sputtered previously. Now, we time the milling to make sure we

etch completely the slots AlN, and etched completely top metal on the vias location, while

still leaving some AlN to mask the bottom metal under the vias. At this point we are left

with the slots completely patterned, while the vias are yet to be opened. After the milling

is complete. Since the vias where correctly etched in the CD26, we now place the wafer

in the heated solution to etch the remaining AlN and gain access to the bottom electrode.

The fabrication is finished by repeating the top metal deposition step, lifting-off a thin Pt

layer (around 30 nm) to connect the pads to the bottom electrode. The modified fabrication

process is showed in Fig. 3.7.

In principle this variation should have solved the problem of the slots not being correctly

patterned. Once the photoresist was completely stripped, the slots were clearly visible under

the optical microscope. Under higher magnification it was also possible to observe the gray

color of the silicon substrate under the AlN, indicating the AlN was completely removed.

However, after the DRIE step, the devices exposed to XeF2 did not release. The reason for

this is still unclear. Unless the issue is related to the XeF2 step itself, the best explanation

is that during the AlN wet etch step some residues from the etched film re-deposit in the

slots, creating a passive layer on the exposed silicon. These issues are still being investigated

and will be the subject of future work. To avoid these problems in future pNUTs designs,

we recommend splitting the AlN etch step in two separate masks, to etch the AlN to open

48
 Figure 3.7 Alternative process to solve the issue the slots not etching. 1) Bottom
metal lift-off. 2) AlN sputtering. 3) Top metal lift-off. 4) Ion mill to open the slots.
5) CD26 etch to open the vias. 6) Thin metal lift-off to connect the vias. 7) DRIE.
8) XeF2 release.

the vias first, and to separately mill the slots after that.

In the end, the devices were released directly from the DRIE step by etching the silicon all

the way to the device layer. The issue with this approach is that the devices are extremely

thin, and during the DRIE step they are in contact with an adhesive meant to keep the

chip attached to a holder wafer. When the chip is removed after the etch, many devices are

damaged in the process, reducing the yield significantly. Because of time constraints due to

the global pandemic, we did not start a new fab aiming at increasing yields. However, we

were able to find enough functional devices to validate the models presented in chapter 2

and chapter 4.

49
Chapter 4

pNUTs Arrays Modeling

The pNUTs offer an opportunity to reduce the total area of the transducer to a small fraction

of current devices operating in the same frequency range. This makes the integration with

electronics more practical and reduces the total size of the IoT nodes to the sub-mm range,

with a consequent costs reduction. In our single device design we targeted an area of 100

µm x 100 µm. However, it is possible that for a given node specifications more real estate is

available. To take full advantage of the available area we can either scale up the single device

area and thickness by the same factor (to maintain a constant operational frequency), or we

can build arrays of devices. If we choose to build pNUTs arrays, we must select a method to

connect the devices electrodes together. Depending on the selected connection method, the

electrical output of the array will vary, as well as the equivalent impedance seen from the

input of the interfacing circuitry. The use of an array of devices results in greater flexibility

than simply using a larger area device in setting the overall system impedance or the output

voltage/current in a given form factor. This is a unique advantage of starting out from a

smaller device and synthesizing arrays of pNUTs.

While a large number of connection methods are possible (depending on the size of

the array), we describe here three possible scenarios, which serve different implementations

and offer different advantages depending on the conditioning electronics used to detect the

50
electrical signal generated by the pNUTs. In the spectrum of possible methods, at the

extremes we have all the devices connected in series on one side, and all the devices connected

in parallel on the other one. The third scenario we consider is in the middle of the spectrum,

which we call series-parallel (SP). This scenario represents a compromise between the two

extremes. In a square array with a SP connection, all the devices in the same row are

connected in series with each other, and the rows are connected in parallel. Schematics of

the three connection methods are shown in Fig. 4.1.

Figure 4.1 Three pNUTs arrays connection options. From left, connection in par-
allel, series-parallel (SP), and connection in series.

To observe how the array properties change by varying the connection method, we build

a model in the circuit simulation software ADS. The first step to build the model is to

generate a cell that describes the individual device response. The cell is represented by a

2-port system, with an acoustic port input and an electrical port output as described in

Chapter 2. A picture of the single pNUT cell is shown in Fig. 4.2. For simplicity, we neglect

the effects of Rholes and Ccavity , which is appropriate since in the fabrication process we

51
included the backside etch step to have an open cavity.

Figure 4.2 Equivalent circuit model used in ADS to represent a single pNUT within
an array.

Once we have functioning single cells, we can use them as instances (building blocks)

in ADS, and start connecting them together with the desired connection method. We note

that we only have control over the way we connect the electrical port of the cell (i.e. the

terminals of Cel ). When incident ultrasound is present, all the devices in the array are

experiencing the same acoustic pressure regardless of the connection method. Therefore, in

the model, all the acoustic ports are connected to the same acoustic pressure source (see Fig.

4.7a for an example). We can now take a look at the possible connection topologies and the

corresponding electrical responses.

4.1 Methods of Connection of pNUT Arrays

As a sample individual pNUT, we use the equivalent parameters listed in Table 4.1, which

deliver a resonance frequency of 50 kHz.

To study the device response, we run an AC simulation, while applying an acoustic

pressure of 1 Pa at the single cell input and sweeping it between 40 kHz and 60 kHz. The

52
 Table 4.1 Parameters used in the single cell pNUT used to build the arrays model.

Keq Meq Q η Aef f Cel Pin Rholes Ccavity

9[ N
m
] 9e − 11[kg] 11[.] 8e − 8[ N
V
] 7e − 9[m2 ] 2.4[pF ] 1[P a] Open Short

single device open-circuit voltage response is shown in Fig. 4.3.

Figure 4.3 Open circuit frequency response of the single pNUT equivalent circuit
used as building block to construct the arrays model.

4.1.1 Full Parallel Connection

In the fabricated devices, to connect them in a parallel topology we would run a metal

trace to connect all the top electrodes to one pad, and a separate trace to connect all the

bottom electrodes to the other pad. In the ADS model this is represented by grounding all

53
 Figure 4.4 Layout of a 2x2 parallel pNUTs array.

the bottom terminals of the electrical port and wiring all the top terminals together. As

an example of how a parallel array is implemented, the layout of a 2x2 array connected in

parallel configuration is shown in Fig. 4.4. To study how the response scales with size, we

build a 2x2 and a 3x3 parallel array, characterized by 4 and 9 individual cells respectively.

Then, we run an AC simulation the same way as the individual pNUT cell example shown

above. When probing the open-circuit voltage, the response is identical as the one shown in

Fig. 4.3 since all the cells terminal are connected together. When probing the short-circuit

current, we observe the response shown in Fig. 4.5.

From the device response, it follows that a parallel connection topology is more suitable

for a receiver based on a current sensing amplifier, as the sensitivity (measured in current

54
 Figure 4.5 Short-circuit current response of parallel-connected pNUTs arrays.

per unit of pressure in this case) increases linearly with the number of devices. In other

words, the sensitivity has a linear dependence to the total transducer area. In case a voltage

amplifier is used to recover the response, the parallel array does not offer a boost in sensitivity.

However, connecting the devices electrodes together changes the output impedance of the

array by increasing the total capacitance, making the parasitic capacitance through the

substrate and at the amplifier input less relevant (Fig. 4.6). It is worth noting that when

a current sensing circuit is used, like a trans-impedance amplifier (TIA), the increase in

capacitance must be taken into account when analyzing the total system performance, as it

can introduce instabilities or reduce the bandwidth of the circuit [37]. Additionally, a current

sensing approach makes sense as long as the input impedance of the current amplifier remains

lower than the array output impedance. If we take an operational amplifier-based TIA as

an example, the input impedance of the circuit is set by the gain of the system. In turn, the

55
system gain is set by the operational amplifier gain-bandwidth product, which is typically

correlated with the circuit power consumption. Therefore, the number of devices we can add

in parallel to increase the system performance is set by the available power budget.

Figure 4.6 Parallel arrays Sensitivity at resonance (50 kHz) and capacitance vs.
total area.

For example, if we build a TIA with the operational amplifier used to build the circuit

in Chapter 6 (MIC861 by Microchip), we have a power consumption of about 7 µW for a

gain-BW product (GBW ) of 400 kHz. The formula for the −3dB bandwidth of the TIA is

given by:

s
GBW
f−3dB = (4.1)
2πRf Cel

56
 where Cel is the array capacitance and Rf is the feedback resistor that sets the tran-

simpedance gain. For our implementation, the capacitance of a 2x2 parallel array is 10 pF

and we can set the minimum value of Rf to 1M Ω. We also need to add a capacitor Cf in

the feedback loop in parallel to Rf in order to compensate for the instability introduced by

Cel :

s
Cel
Cf = (4.2)
2πGBW Rf

At 50 kHz these numbers deliver a bandwidth of 80 kHz and a transimpedance gain of

600kΩ. A 2x2 array should generate about 1.8 nA/Pa, which means approximately 1 mV/Pa

at the TIA output. Obviously, for larger parallel arrays the system gain needs to be further

reduced to meet the bandwidth and stability requirements. Even accounting for the parasitic

capacitance at the VA input shown in Chapter 6, we have a sensitivity close to 1 mV/Pa at

the output of the first amplification stage for just a single device. Therefore, we decided to

select a voltage sensing approach for our full system demo.

4.1.2 Full Series Connection

To connect the devices in a series configuration, we need to link the bottom electrode of

the first device to the array terminal, and the top electrode to the bottom electrode of the

next device. We repeat this connection for the subsequent devices. The last pNUT top

electrode will be connected to the other terminal. An example of the implementation of this

configuration in ADS for two pNUTs in series is shown in Fig. 4.7a, while the corresponding

layout is shown in Fig. 4.7b.

The way the sensitivity scales in a series configuration occurs in an inverse way compared

to the parallel configuration. We have that the total current of the array remains identical

to the one of the single pNUT cell, represented by the red curve in Fig.4.5. The open-circuit

57
 Figure 4.7 Series connection of two pNUTs. a) Implementation of the series con-
nection in ADS. b) layout of two devices connected in series.

voltage sensitivity on the other hand, scales linearly with the number of devices connected

in series. Therefore, the output voltage per unit of pressure grows proportionally with the

total array area (Fig. 4.8).

Since we are connecting the parallel plate capacitor across the pNUTs the electrodes in

series, the total output impedance of the array is increased proportionally by dividing the

single device electrical capacitance by the number of devices we place in series in the array.

Since the current remains unchanged, it is more convenient to recover the array output

electrical signal with a voltage sensing circuit. Just as the parallel array, we will incur in

diminishing return in the total system sensitivity once we start taking into account the

amplifier input impedance. If we do voltage sensing, ideally we would want a circuit input

impedance as close to an open circuit as possible. However, realistically there will always

be some parasitic capacitance between the amplifier input terminal and ground. Using an

operational amplifier-based voltage amplifier or buffer, a typical value of capacitance between

the positive and negative terminal stands at a few pF, which can be brought down to a few

hundreds fF with an IC. Considering that the single pNUT electrical capacitance is also at a

few pF (2.4 pF in our example), we will already observe a saturation of the system sensitivity

even for small sizes of the array. This effect is shown in Fig. 4.8, where by adding a load

58
 Figure 4.8 Series arrays Sensitivity at resonance (50 kHz) and capacitance vs. total
area.

of 1 pF to the array terminals we can already observe diminishing returns in the system

sensitivity as we add more devices connected in series. In the voltage amplifier used in the

WuRx demo (Chapter 6) the VA is built with off-the-shelf components soldered on a printed

circuit board. The measured input capacitance for this VA was 6.7 pF, clearly making a

series array implementation impractical. However, in a scenario in which the pNUT and an

IC are monolithically integrated, the expected value of parasitic capacitance can be as low as

100 fF. At this capacitance values, the array can be formed by 20 devices connected in series

before matching the parasitic capacitance and observing significant diminishing returns in

the Rx Sensitivity. Such system would be characterized by approximately a 20x increase in

Rx sensitivity compared to an individual device.

59
4.1.3 Series-Parallel (SP) Connection

The final connection topology we take into consideration is the SP. To implement this topol-

ogy we build a linear series array as described in the previous section with the desired number

of pNUTs. We then connect the same number of series array in parallel with each other as

we did for the single devices in a parallel array. The layout implementation of a 2x2 SP

array is presented in Fig. 4.9.

Figure 4.9 Layout of a 2X2 SP array.

Being a balanced compromise between the series and parallel array connection approaches,

the SP configuration can be used both in current sensing and in voltage sensing mode. The

array open-circuit voltage sensitivity scales linearly with the number of devices in series.

Each row has the same current contribution of a single pNUT. Since in a SP configura-

60
tion the number of parallel rows is the same as the number of devices in each row, the total

short-circuit current sensitivity scales by the same amount as the voltage sensitivity. Finally,

the total array electrical capacitance remains identical to the one of the individual pNUT

cell. The voltage sensitivity and the array capacitance of SP arrays are shown in Fig. 4.10.

We can see that in this case the array sensitivity grows with the square root of the total

array area. In fact, in the SP configuration, we are trading off sensitivity for maintaining a

constant output impedance. As outlined above, the series and parallel connection topologies

are ultimately limited in scaling by the input impedance of the interfacing electronics. This

is not the case for the SP array. While, for a given size, the theoretical sensitivity is lower

than the other two configurations, once we interface it with a sensing circuit the array size

can be increased arbitrarily to increase the total system sensitivity.

It is interesting to notice that, for a given array area, and in absence of a load impedance

on the arrays, the total output power for a given input pressure is constant across all con-

nection schemes. This is consistent with the conservation of energy since the same amount

of acoustic power is provided to the arrays regardless of their configuration. While this is

not the focus of this work, in case we are interested in recovering and converting the acoustic

power from the ultrasound, the pNUTs offer the flexibility to vary the connection topology

to better match the impedance of the interfacing circuit, and optimize the power transfer

efficiency.

4.2 Noise in pNUTs Arrays

In an ultrasound receiver system, the most useful metric to quantify the minimum detectable

pressure is the signal-to-noise ratio (SNR). Therefore, it is interesting to get an idea of the

noise contribution of the pNUTs and how that noise scales once we form an array with differ-

ent connection methods. The main noise source expected from the devices comes from the

thermal dissipation caused by the friction between the device surface and the air molecules

61
 Figure 4.10 SP arrays Sensitivity at resonance (50 kHz) and capacitance vs. total
area.

surrounding it. In the purely electrical equivalent circuit (2.7), we represent this phenomenon

through the equivalent resistor Rm . The noise spectral density source associated with this

resistive element, also called Johnson noise, is given by Eq. 4.3 [38].

p
vn = 4kb T Rm (4.3)

where kb is the Boltzmann constant. The noise at the device terminals is shaped by Cm ,

Lm , and the electrodes capacitance Cel . We can obtain the RMS amplitude of the noise

by integrating the spectral density over the device resonance peak frequency range (i.e. the

device spot noise [39])

62
 s Z
Vn = 4kb T Zout (f )df (4.4)
BW

where Zout is the impedance of the pNUT as seen from the electrical port. We obtain

the device noise spectral density from the AC simulation in ADS. As an example, we can

see the spectral density for a SP and Series arrays in Fig. 4.11 compared to that of a single

device. We see that the spectral density of the SP array remains identical to the one of

the individual pNUT cell. This is expected since the overall impedance of a SP array stays

constant regardless of the size of the array. By integrating over a 20 kHz bandwidth around

the resonance frequency, for the SP arrays the total RMS noise Vn stands at around 1 µV. In

a similar way, in the series array the total impedance increases linearly, while the equivalent

noise source between the array terminals increases sub-linearly (follows square root law).

The equivalent noise source at the terminals is obtained by taking the square root of the

squared sum of the noise sources. The corresponding increase in noise is shown in Fig. 4.11

on the right.

Figure 4.11 Spectral density of a single pNUT, SP, and Series arrays.

As shown in Chapter 5 in the WuRx system demonstration, the noise from the pNUTs is

not the limiting factor for the system sensitivity, and we will see that these noise levels are

negligible compared to the ones measured from the electronics. These findings are critical

63
in pointing out that arrays of pNUTs can be used to effectively enhance the overall system

sensitivity.

64
Chapter 5

Devices Characterization

In this chapter we describe the methodologies and experimental setups used to characterize

the fabricated pNUTs. The devices discussed here and in chapter 6 are part of the last

batch of fabricated devices. As described in chapter 3, these devices were released directly

during the DRIE step. Because of this, the devices yield was much lower than it would

normally be. However, from the few devices that survived the release process, we are able

to obtain enough information to validate the models presented in the previous chapters and

show a demonstration of a long-range miniaturized ultrasound WuRx. We consider 4 classes

of devices:

• Individual pNUT with floating metal

• Individual pNUT without floating metal

• 2x2 SP array without floating metal

• 3x3 SP array without floating metal

These devices were obtained from two chips that were released separately. The individual

pNUTs were obtained from the first chip, while the arrays were obtained from the second chip.

As discussed in the following sections, this will lead to slight differences in the frequency of

65
operation between the single device and the two arrays despite having identical geometries

and having the same equivalent mass. The laminate layers thicknesses measured in this

fabrication were 30 nm, 130 nm, and 230 nm for the bottom Pt, AlN, and top Pt respectively.

SEM pictures of the devices are presented in Fig. 5.1.

Figure 5.1 SEM images of the four measured devices. a) Individual device with
floating metal. b) Individual device without floating metal. c) 2x2 SP array without
floating metal. d) 3x3 SP array without floating metal.

5.1 Tx Sensitivity Measurements

The first step to characterize the devices is to measure their Tx sensitivity. The Tx sensitivity

is measured by applying an external voltage between the pNUTs electrodes and recording the

resulting out-of-plane displacement. We measure the Tx sensitivity in nm per unit voltage

(nm/V). The Tx sensitivity is obtained through digital holographic microscopy (DHM). We

66
use the R-2100 Series microscope by Lyncèe Tec [40]. DHM reconstructs a 3-dimensional

representation of the observed sample by measuring both the intensity of a laser reflected by

the sample surface - called object beam - and the interference pattern between the object

beam and an internal reference. When generated, the reference beam is coherent with the

object beam. By adjusting the optical length of the reference beam to be identical to the

path of the object beam, we can obtain an interference pattern resulting from the phase

differences between the two lasers. The phase differences are related to height variations on

the sample surface. The interference pattern effectively converts the information carried by

the phase of the object beam into an intensity pattern that can be measured with a camera.

An example of a pNUT observed in phase mode is shown in Fig. 5.2.

Figure 5.2 Example on a pNUT imaged under phase view.

In the figure, gradients in height manifest as fringe patterns like the ones present along

the beams length. We can also see that we observe the fringe pattern only in some locations

over the device surface. This is due to the thickness of the layers that make up the pNUT

plate. Since the layers are extremely thin, depending on the angle of incidence of the object

laser with the pNUT surface, different portions of light go through the plate instead of being

reflected back into the microscope. Those regions manifest as noise in the phase image and

67
we cannot get height information from them, like the tip of the beams. For this reason,

we recommend that the thickness of the layers should be at least 130 nm for for AlN and

200 nm for the top Pt in order to have a strong enough signal on the central plate. This

recommendation is based on what has worked in this implementation, but other combinations

of layer thicknesses might also work. To take the measurement, we take advantage of the

stroboscopic unit that comes with the DHM. In stroboscopic mode, we can generate a voltage

at a given frequency and synchronize it with the DHM image sampling. While taking and

processing a single frame can take several periods, thanks to the stroboscopic module we

can reconstruct the pNUT displacement over a single period by sampling the holograms

at precise phases within different periods. This process is repeated for several excitation

frequencies. Finally, we take a discrete Fourier transform (DFT) of the samples from each

excitation frequency to generate the pNUTs Tx sensitivity in the frequency domain.

5.1.1 Equivalent Parameters Extraction

From the Tx sensitivity measurement it is possible to extract the equivalent parameters of

the devices. Since we modeled the resonator as an RLC circuit, we extract the parameters

by fitting a second order response to the measured curve. To perform the fitting we use a

least-mean-squares approach. We present the fitted function both in terms of the variables

(η, Keq , ω0 , Q) and in terms of (η, Keq , Meq , Q):

η/Keq η
d= q 2 =q (5.1)
1 ω2 ω 2
( ωω2 − 1)2 + Q ω02
(Meq ω 2 − Keq )2 + Meq Keq ( Q )
0

In the first form, it is evident that we have 4 variables but only 3 are independent. For

example, if we fix ω0 and Q, we can produce infinite valid values of η and Keq as long as their

ratio remains constant. To solve this problem we can take an educated guess on the value

of one of the variables and select the others by fitting the measured displacement curves.

68
We will see that this approach is reasonably validated by the Rx sensitivity measurements,

presented in Section 5.2.2. The variable that makes the most sense to select is Meq . We

know from Section 2.2 that Keq is subject to significant uncertainty from the undercut

and residual stress, whereas a quick COMSOL simulation confirms that Meq is not affected

significantly by these two phenomena. Similarly it is difficult to accurately predict the losses

due to air damping. The value of η is affected both by the non-ideally-clamped boundary

condition at the beam anchors and the quality of piezoelectric layer. As verified through

FEA simulations, Meq has little dependence on the exact beams mode shape as its value

is largely determined by the mass of the central plate. Therefore, we use the value of Meq

predicted by the analytical model and we obtain the rest of the parameters through least-

mean-square fitting. The Tx sensitivity of the individual pNUTs is shown in Fig.5.3 and the

equivalent parameters obtained from fitting equation 5.1 are shown in Table 5.1 along with

the theoretical values from the analytical model.

Table 5.1 Parameters extracted by fitting the individual devices Tx sensitivities. F

and NF refer to the devices with and without the floating metal respectively. The
value of Cel has been measured separately with precision impedance analyzer.

Keq [ N
m
] Meq [kg] Q[.] η[ N
V
] ζ[ Nms ] Rm [M Ω] Cm [f F ] Lm [H] Cel [pF ]

F 2.6 2e − 11 8.9 3.4e − 8 0.8e − 6 708 0.5 17e3 2.5

NF 2.7 1.3e − 11 5.7 4.3e − 8 1.15e − 6 602 0.7 6.8e3 2.5

*F 2.1 2e − 11 − 1.2e − 7 − − 6.9 1.4e3 2.3

*NF 2.1 1.3e − 11 − 1.2e − 7 − − 6.9 0.9e3 2.3

*Analytical model, not accounting for undercut and residual stress (see Section 2.2)

Looking at the extracted parameters, we can see that the devices have similar values of

Keq . This does not follow automatically by the imposed values of Meq , since the correspond-

ing values of Keq are determined by the measured positions of the resonant frequencies. The

fact that the values of Keq in the two devices are almost identical confirms the intuitive

69
 Figure 5.3 Measured individual pNUTs Tx sensitivity along with the fitted curves.

observation (verified in COMSOL) that most of the stiffness is defined by the mode shape

in the clamped region of the beams where the electrodes are located, which is identical for

the two measured pNUTs designs. Additionally, we expect the two devices to have very

similar levels of stress in their layers as they were positioned very close to each other, and

consequently have similar levels of stress-induced stiffening. Therefore, whether the floating

metal is present or not is the main reason the two devices have different center frequencies.

It is interesting to see that the extracted values of Keq are not too far off from the ones

predicted by the purely analytical model. This effect was shown in Sections 2.2.1 and 2.2.2,

where we see that the undercut softens the transducer considered in the purely analytical

model, while adding positive residual stress in the Pt layer has the opposite effect, bringing

the resonance frequency back up. From the undercut study we see that for levels of undercut

70
of 15 µm or larger - as is the case for the fabricated devices - there is not significant additional

softening. We also see that the softening lowers the devices resonance frequency by the same

factor for both the presented layer thickness cases. This observation allows us to estimate

the drop in stiffness caused by the undercut in the fabricated devices, which changes from

2.1 N/m down to 0.85 N/m. Then, we can estimate the value of the residual stress that

causes the stiffness to increase to 2.6-2.7 N/m. The stress level in the AlN layer is both

more controllable and repeatable than the stress measured in the Pt during the deposition

recipe characterization, and was estimated to be between 20 and 50 MPa. Therefore we can

expect the majority of the stress-induced stiffening to be caused by the top Pt layer. During

the Pt sputtering characterization, for the same deposition parameters, we measured stress

levels ranging around ±100 MPa the expected value. In the Pt deposition run during the

devices fabrication we tuned the argon pressure to make sure we would get a positive residual

stress in the 100-200 MPa range. In order to increase the devices stiffness from 2.1 N/m up

to 2.7 N/m a residual stress of approximately 200 MPa is necessary, which is in agreement

with the Pt recipe we characterized. Another interesting insight comes from the scaling of

the quality factor between the two pNUTs design. Looking at the scaling from air damping

losses reported in equation 2.22, we have that Qair is expected to scale as ∝ Meq f . Using the

resonance frequencies of 57 kHz and 72 kHz, and the respective values of Meq , we should ob-

tain a theoretical value of Qair that is 1.54 times higher in the pNUT with the floating metal

compared to the variation without it. This value is quite close to the factor of 1.74 obtained

from the ratio of quality factors obtained from the curves fitting. Finally, we can compare

the values of η and Cel with respect the one expected from theory. Using equation 2.10, we

obtain a theoretical value of 1.2e − 7 N

V
. The measured η of around 0.4e − 7 N
V
is on the same

order of magnitude but around 60% lower than the ideal value. This should be expected

because of non-idealities such as the undercut from the devices release, which affects the

device mode shape around the clamped region as pointed out in Section 2.2.1. According to

the analysis in Section 2.2.1 the expected reduction was actually more important than 60%,

71
at around 95% for a 25 µm undercut. A possible explanation for the difference between the

extracted experimental value and the model is that the geometry used in the FEA model

does not account for the effect of the metal traces connecting to the electrode. These traces

significantly stiffen the beam anchor, partially compensating for the softening caused by the

release undercut. Using equation 2.11 we have a theoretical capacitance value of 2.3pF . The

experimental values of 2.5pF were obtained in a separate measurement with a high precision

impedance analyzer. To take the measurement we use two DC probes and landed them on

the device terminals to access the device electrodes. We did not have the calibration kit for

the impedance analyzer at hand, therefore only the open circuit calibration was performed.

The calibration was done over a frequency range between 30 kHz and 100 kHz while only

one of the two probes was in contact with the pads. After the calibration was finished the

other probe was landed to take the impedance measurement. We observed a value of around

2.5pF over the entire frequency range. The difference of a few hundreds of fF’s between the

theoretical and the measured values can be attributed to parasitic capacitance between the

pads through the substrate.

5.1.2 Measurements at Low Pressure

We also performed the Tx measurements at low pressure on the pNUT with floating metal.

Because of the limited availability of the vacuum chamber and the complexity of the ex-

perimental setup, the measurement was done only on one device. The first step to set up

the experiment is to secure the chip on a printed circuit board (PCB) with double adhesive

tape, and to connect the device pads to two signal and ground metal traces via wirebonding.

Then, the PCB is itself secured to a platform with tape and two jumper wires are soldered to

the traces. The vacuum chamber has an opening on the topside that can be covered by a 1

cm thick glass cover and several wires that go through a sealed passage to provide electrical

access to the inside of the chamber from the outside. The platform with the PCB on top is

72
placed inside the vacuum chamber, and the jumper wires are secured to the chamber wires

with a set of screws.

Figure 5.4 Experimental setup used to measure the Tx sensitivity at low pressure.

It is important to adjust the height of the platform to make sure that when the glass

cover is placed on the chamber opening the PCB is right below it. Having a few SMA

connectors soldered around the PCB provides enough spacing from chip to make sure the

devices are not damaged by being touched by the glass cover. This step is important for two

reasons. 1) the pump-down process generates quite strong vibrations, and having the PCB

stuck between the platform and the glass makes sure that nothing in the chamber moves.

2) We need the devices to be extremely close to the glass to be able to re-calibrate the

tool to compensate for the glass diffraction and image them with the Lyncee Tec. Finally,

we connect the chamber wires to the Lyncee Tec stroboscopic unit, and the chamber to a

roughing pump. The complete setup is shown in Fig. 5.4.

Because of the vibration, it was not possible to image the devices while the pump was

active. Therefore, the minimum stable pressure that the chamber was able to hold after

turning the pump off was 0.1T orr. This pressure is not low enough to make the losses from

73
 Figure 5.5 Quality factor of the pNUT measured at different pressures.

air damping negligible compared to the anchor losses through the substrate, which should

occur at around 0.1mT orr. In this measurement, presented in Fig. 5.5, we see a discrepancy

between the theoretical scaling of the quality factor with respect to the chamber pressure.

From the theory, we expect the air-damping losses in flexural resonators to scale with the air

pressure. From the data presented in Fig. 5.5, we see that this is the case only in going from

atmospheric pressure (760T orr) down to 100T orr. Below this pressure we approximately

have a doubling in quality factor for every decade of pressure. To confirm whether this trend

is correct or not more measurement are needed. However, this measurement serves as a

confirmation that air damping is the loss mechanism that dominates in setting the device

frequency response in air.

74
5.1.3 Arrays Tx Sensitivity

As mentioned at the beginning of the chapter, the measured arrays were part of a separate

chip. Because of the fabrication challenges explained in Chapter 3, the release process was

not readily controllable. This means that, compared to the individual devices, the devices

that compose the arrays experienced slightly different undercut levels and profiles. Because

of these reasons, the center frequency of the devices in the array (without the floating metal)

has increased from 72 kHz to 90 kHz. The frequency response of the every device in the 2x2

SP array was measured in the Lyncee Tec and is displayed in Fig. 5.6.

Figure 5.6 Tx sensitivity of the 4 pNUTs in the 2X2 RSCP array.

These curves were obtained by applying a 2 V actuation at the array electrodes, with the

assumption that the devices are characterized by similar electrical capacitances. With this

assumption, observed displacement on every single device should equal the the displacement

per unit voltage. We obtain the equivalent parameters with a similar fitting approach as in

Section 5.1.1. The 4 curves fitted parameters are shown in Table 5.2.

Clearly, since we assigned a Meq value identical to the one of the single pNUT with a

75
 Table 5.2 .

Keq [ N
m
] Meq [kg] Q[.] η[ N
V
] ζ[ Nms ] Rm [M Ω] Cm [f F ] Lm [H]

R1C1 4.4 1.3e − 11 6.8 7.7e − 8 1.1e − 6 186 1.3 2.2e3

R1C2 4.1 1.3e − 11 4.9 8.6e − 8 1.5e − 6 202 1.8 1.8e3

R2C1 4.2 1.3e − 11 5 9.5e − 8 1.5e − 6 163 2.1 1.4e3

R2C2 4.3 1.3e − 11 6.9 5.3e − 8 1.1e − 6 382 0.7 4.6e3

resonance at 72 kHz, the devices in the array presented a higher value of Keq to obtain a

fitted curve with a 90 kHz resonance. A clue as of why the devices in the array present

a higher resonance frequency can be found by inspecting the devices SEM images. We re-

propose the SEM images of the individual pNUT and the 2x2 array shown in Fig. 5.1 below,

in Fig. 5.7, highlighting the likely source for the discrepancy in Keq values.

Figure 5.7 Comparison between the undercut profiles of the individual pNUT and
the 2x2 SP array.

In Fig. 5.7 it becomes evident that, unlike the individual device, the array experienced an

uneven release profile. We see that all devices part of the 2x2 array present limited undercut

in 2 out of 4 beams. In all devices the 2 beams are on the same side, and the same effect can

be observed on the 3x3 array SEM picture in Fig.5.1. The consistency of this effect suggests

that the source of the uneven undercut is a small offset in the back-side etch lithography

76
alignment. The reduced undercut at the base of the beams explains why we observe both

an increase in Keq and η when extracting the equivalent parameters of the devices in the

array. As pointed out in Section 2.2.1, the presence of the undercut at the base of the beams

modifies the beams mode shape by relaxing the ideal zero-angle constraint and reducing the

amount of bending experienced at the beams anchors. From equations 2.9 and 2.10, we know

that the value of both Keq and η is set by the amount of bending experienced by the beam

(i.e. the mode shape second derivative). Therefore, we can expect that variations in the

undercut at the beams base will translate in corresponding variations for both Keq and η.

At resonance, the pNUTs in the array show quality factors and displacements similar

to that of the single device. A likely source of the small difference in displacement is that,

because of the uneven release, some parts of the plate experience higher displacement am-

plitudes than others. To a lesser extent, this effect should also be expected in an evenly

released device, since the analytical model assumption that the plate is perfectly rigid is

an ideality. Unfortunately, it is not easy to characterize the displacement over the pNUT

surface. Because of the small thickness of the layers, when we measure the displacement the

data often present artifacts. These errors in the data are easy to spot and the corresponding

measurement is discarded, but they make the measurement process slow and based on trial

and error when selecting different regions on the center plate. Because of this, we expect

that the equivalent displacement of all devices should be in the region found in between the

lowest and the highest curves.

Because of the reciprocity of the system, we can expect the resonance Rx sensitivity

response to be similar for the devices in the array as the single pNUT despite having different

resonance frequencies (90 kHz and 72 kHz respectively). An interesting insight from the

response in Fig. 5.6 is that because of air damping, the devices have enough frequency

bandwidth for their frequency response to overlap, and subsequently increase the overall

array sensitivity when used in Rx mode. From Fig. 5.6 we see that the peak frequencies

range between 88 kHz and 92 kHz. These frequencies cover a range of 4 kHz, while the 3

77
dB bandwidth of all devices is approximately 20 kHz. Although quite small, the differences

in resonance frequency between devices within the same array can be easily explained by

slightly different release profiles, as shown in Fig. 5.7.

5.2 Rx Sensitivity Measurements

The Tx sensitivity measurements presented in the previous section were necessary to de-

termine the device equivalent parameters and to locate their frequency of operation on the

30 to 100 kHz range we are interested in. Since the devices are meant to be used as part

of a WuRx, we can now proceed to characterize their electrical response when exposed to

airborne ultrasound. To generate the airborne ultrasound we use commercial ultrasound

sources purchased from ProWave [5]. The available sources center frequencies are at 25 kHz,

32 kHz, 40 kHz, 50 kHz, and 82 kHz, respectively corresponding to the transducer model

numbers 250ST160, 328ST160, 400ST100, 500MB120, and 080SR365. Exciting the ultra-

sound sources off-band still generates ultrasound at lower pressures. At those frequencies,

the distance between the ultrasound transmitter (Tx) and the pNUT must be reduced in

order to obtain a readable electrical output. To read the pNUT output, we need to amplify

the output voltage between the electrodes and detect it with an oscilloscope. The voltage

amplifier (VA) we used is described in Chapter 6 as part of the complete WuRx system demo.

To measure the signal amplitude, we feed the amplifier output to a UHF Lock-In amplifier

by Zurich Instrument (ZI) [41]. Through the ZI software interface LabOne we can use the

UHFLI as an oscilloscope and monitor the signal at the VA output in frequency domain.

As the UHFLI is equipped with two channels, we can simultaneously observe the pressure

amplitude that is present at the pNUTs location, and use it to quantify the Rx sensitivity

in mV/Pa. To measure the pressure we use the Type 4939 calibrated microphone rated up

to 100 kHz [42], along with its conditioning amplifier.

78
5.2.1 Rx Sensitivity Angular Dependency

The first step to characterize the devices in Rx mode is to verify whether their response

has an angular dependence on the direction the ultrasound is coming from. To perform

this measurement, we taped the VA and the devices on a metal stage. The metal stage is

connected to a pole through a slider that allows for adjusting its vertical position. The pole

is positioned on a table with the devices right at the edge. Next, we take the position on

the table border as the angular center. On the floor under the table, we use this position to

arrange tape lines in a semicircle at 15o intervals. All tapes are 1m long. On a separate cart,

we position the Tx and the arbitrary wave generator (AWG). The Tx holder is also attached

to a pole and we can adjust its vertical position. The set up is shown in Fig. 5.8.

Figure 5.8 Setup used to measure the Rx mode angular sensitivity of the pNUTs.

79
 To perform the measurement, we make sure that the cart is aligned with the tape line. We

generate the ultrasound and record the output voltage at the VA output. Additionally the

pressure at the pNUTs location is monitored to make sure it is consistent across angles. This

procedure is repeated for all lines in the angular range between 15o and 165o . The normalized

Rx sensitivity for this measurement is shown in Fig. 5.9. As expected, no major nodes were

observed during this experiment. In the frequency range of interest, the wavelength of the

ultrasound in air is several mm long, while the biggest array we are considering (the 3x3 SP)

is only 400 µm in lateral dimensions, around 1 order of magnitude smaller. In a similar way

as observed in antennas, small radiators tend to be isotropic. In the measurement presented

in Fig. 5.9, the normalized response remains very close to 1 at all angles. It seems to be

slightly lower at the limit angles of 15o and 165o , although we think it can be attributed to

the VA wires that partially covered the sides of the chip.

Figure 5.9 Normalized angular Rx sensitivity of the 2X2 SP pNUT array. The
slightly lower response at 15o and 165o angles is likely due to the VA wires on the
side of the chip.

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5.2.2 Single Devices Rx Sensitivity

Once we established that the devices receive pattern was isotropic, we moved on to measure

the Rx sensitivity over frequency. The measured Rx sensitivity profile for the two single

pNUTs is presented in Fig. 5.10. The process to take one data point begins by generating

the ultrasound at the desired frequency, and to align the Tx with the pNUTs. This step is

necessary because as we vary the frequency, the emission pattern of the ultrasound source

also shifts. Next, the VA output voltage is observed. The output voltage does not remain

constant over time because of the noise in the VA and because of the natural fluctuation in the

pressure field generated by the Tx. While recording the voltage, the LabOne software allows

to keep track of the standard deviation of the voltage at a given frequency. Empirically, we

noticed that the standard deviation was always contained within a 10% range of the average

VA output. We added the error bars on the plot in Fig. 5.10 to reflect this observation.

After recording the VA output voltage, the UHFLI scope was switched to the second

channel connected to the calibrated microphone. While making sure that the Tx and the

platform holding the pNUTs were not moved, the microphone was held right above the

platform, and slightly tilted to make sure the microphone head was on the line of sight

between the Tx and the devices, just at a few inches away from the pNUTs. The microphone

was also moved in that region to make sure the highest possible pressure was recorded.

Typically, once the microphone head is in the spot of maximum pressure, the recorded

pressure is quite stable. We then obtain the voltage at the device electrodes by taking

the VA output voltage, dividing it by the VA gain (approximately equal to 1800), and de-

embedding the input capacitance of the VA. Because the devices capacitance is about 2.4

pF, and the measured capacitance at the VA input is 6.7 pF, the de-embedding process

consists of multiplying the voltage at the VA input by a factor of 3.7. Finally, we take this

voltage value and we divide it by the measured pressure to obtain the open circuit (OC)

voltage sensitivity of the device. This process is repeated for several frequencies around the

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 Figure 5.10 Devices measured Rx sensitivity and extracted Rx sensitivity using
the parameters extracted by fitting the displacement curves.

device resonance with 2 kHz intervals. From Fig. 5.10, we see that both devices relative

position of the resonance peaks and their relative heights match the profile obtained from

the Tx sensitivity measurements. We also superimpose the theoretical OC Rx sensitivities

expected from the equivalent circuit model when the circuit elements are selected according

to the fitted parameters. In both cases the theoretical response is slightly lower than the one

expected from the fitted parameters even assuming Γ = 0 (i.e. Pef f = 1), and the resonance

frequencies are slightly higher than what observed during the displacement measurements.

Overall, the values of the measured Rx sensitivities are quite close to those expected from the

equivalent model. More measurements are needed to establish whether the minor differences

82
can be eliminated with a more rigorous Rx sensitivity testing setup -aimed at reducing the

uncertainty intervals- or if the equivalent circuit model itself needs to be expanded.

Comparison with pMUTs/cMUTs Rx Sensitivity

Now that we quantified the Rx Sensitivity of the individual pNUTs, it is interesting to

compare their performance against other ultrasound transducers reported in the literature.

As mentioned in Section 2.1.4, the open-circuit Rx sensitivity is not frequently reported. The

instances we found where the device Rx sensitivity was included -either directly or indirectly-

are presented in Table 5.3.

Table 5.3 Comparison between Rx sensitivity of the individual pNUTs and ultra-
sound transducers reported in literature.

Type RxS[ mV
Pa
] Area [mm2 ] f[kHz] mV
N RxS[ P amm2] Q Reference

pMUT (PZT) 0.26 1.22 40 0.21 25 [43]

pMUT (AlN) 0.64 0.12 214 5.33 20 [33]

cMUT 41 16 50 2.5 50 [4] [6]

pNUT F 0.4 0.022 55 18.2 9 This Thesis

pNUT NF 0.3 0.022 72 13.6 6 This Thesis

*Obtained from reported equivalent circuit values

**Estimated

The data presented in Table 5.3 shows that despite the pNUTs are orders of magnitude

smaller than transducers operating at similar frequencies, they show high Rx sensitivities in

compact form factors. When normalizing the Rx sensitivity (NRxS) by the transducer area,

the pNUTs fair better than classical pMUTs by 1 to 2 orders of magnitude (keeping in mind

that [33] is operating at 4x the pNUTs frequency, with the consequent reduction in losses

and a smaller area). These results are in agreement with the analysis presented in Section

2.1.6, and open up the possibility for truly miniaturized (sub-mm) long-range ultrasound

83
receivers. A demonstration of such receiver is presented in the next chapter.

5.3 Arrays Rx Sensitivity

A similar measurement procedure was implemented to obtain the open-circuit Rx sensitivity

of the 2x2 and 3x3 SP arrays. The measured curves are presented in Fig. 5.11.

Figure 5.11 Open-circuit Rx sensitivity of the NF single pNUT and the two arrays.

As expected from the displacement curve from Fig. 5.6, the two arrays fabricated on

a separate chip present Rx sensitivity peaks at higher resonance and at around 90 kHz.

In the measurements of the individual devices in the 2x2 SP array with the Lyncee Tec

instrument, we observed displacements per unit voltage similar to those of the single pNUT,

but we see that the Rx sensitivity of the arrays grows with the size of the array. The

electrical capacitance of the individual pNUT and of the array was measured with a precision

84
impedance analyzer (4294a by Agilent). Both the Rx sensitivities and the capacitance at

the devices electrodes vs. area are presented in Fig. 5.12.

Figure 5.12 Comparison between the peak Rx sensitivity and electrodes capaci-
tance of the NF devices with respect to the total area. This measurement confirms
the modeled trend for SP arrays as previously shown in Fig. 4.10.

We can see that, as expected from the theory of array scaling presented in Chapter 4, Rx

sensitivity increases with the number of devices placed in series in each row of the SP array,

while the electrodes capacitance remains constant as the array is scaled.

85
Chapter 6

WuRx System Demonstration and

Characterization

The development of the IoT comes with mass deployment of wireless nodes. Typically, these

nodes are expected to operate on a small battery, and the distributed nature of these networks

makes it impractical to perform frequent battery swaps. From a power consumption point of

view, the most demanding task for the nodes is communicating with their base-station [44].

A WuRx is a class of receivers that became popular during the last decade and that emerged

as the best approach to address the issue of power consumption required to communicate

asynchronously with wireless nodes.

A wireless receiver is typically formed by a transduction element and the read-out elec-

tronics interfacing with it. In RF receivers the transduction element is an antenna that

converts RF waves into an electrical signal. The read-out electronics is generally divided in

three parts:

1. A front-end that interfaces the antenna with the next block. This block generally

provides matching to the next block and some initial amplification.

2. A mixing block that takes advantage of non-linear elements to demodulate the detected

86
 signal.

3. A base-band block that post-processes the demodulated signal. Generally this means

that the signal is further amplified and rectified.

At a high level, the system design implemented in our demonstration follows the same

template outlined above, with the difference that the antenna is substituted for the pNUT

and the communication takes place over acoustic waves instead of radio waves.

6.1 Electronics Description

To demonstrate the system, the three blocks described in the introduction are implemented

respectively using:

• A voltage amplifier

• A diodes-based rectifier

• A comparator

The amplification block increases the amplitude of the electrical signal at the output of

the device to ensure that it is beyond the voltage threshold necessary to trigger the rectifier.

The voltage amplifier also acts as a buffer to impedance-match the pNUTs to the mixing

block. The rectifier block takes the amplified modulated signal as input, and outputs its

envelope, i.e. the portion of the signal that contains the information we want to retrieve.

The signal envelope is then fed to the input of a comparator. The comparator acts as an

analog-to-digital converter by comparing the envelope analog signal to an arbitrary threshold,

and outputting either a HIGH or LOW signal. Effectively, the comparator is also a base-

band amplifier matching the mixing block to the processing unit of the IoT tag. If the string

of HIGHs and LOWs matches a specific signature, the main electronics is awaken.

87
 A conceptual schematic of the complete WuRx system is shown in Fig. 6.1, while the

layout of the printed circuit board (PCB) is shown in Fig. 6.2.

Figure 6.1 Conceptual schematics of a US-based WuRx.

Figure 6.2 Layout of the PCB designed to demonstrate the concept. The red and
green traces represent the top and bottom layers of the PCB respectively.

The technical specification that guided the electronics design were the system range, the

data rate, and the total power consumption. The system range depends on the devices

Rx sensitivity, the VA and rectifier gains, and the noise levels at the comparator input.

In general, we aim to be able to detect around 1 Pa pressure as it corresponds to several

meters distance while complying with regulations (Fig 2.3). The system data rate depends

on the modulation technique and on the time constants the rectifier is able to achieve.

For simplicity, we selected an OOK modulation, and therefore the data rate is set by the

88
maximum modulation frequency we can achieve. We aim to achieve a modulation frequency

of 1 kHz. Although this data rate is not very high compared to typical RF communication,

it should be sufficient to transmit small amount of data such as a numeric key that serves

as a node identifier. Finally, we target a power budget of 50 µW. The architecture of the

demonstrated system is presented in the following sub-sections.

6.1.1 Voltage Amplifier architecture

The amplification block was implemented with a classic operational amplifier (OpAmp) non-

inverting architecture. The voltage amplifier (VA) is the main source of power consumption

in the system, therefore, the main metric used to select the OpAmp was the supply current.

Naturally, an OpAmp characterized by a lower supply current comes with a lower gain-

bandwidth (GBW) product, resulting in a smaller bandwidth for a chosen overall system

gain. This trade-off can be relaxed by choosing to reduce the gain of a single OpAmp stage,

hence increasing the bandwidth, and add multiple OpAmp stages in series with each other

to obtain an overall gain equal to the product of the individual stages. This choice must be

weighted against the increment of power consumption (proportional to the number of stages),

and the additional noise introduced by every OpAmp that gets amplified at all subsequent

stages. The circuit schematic of an individual OpAmp stage is shown in Fig. 6.3.

The OpAmp MIC861 by Microchip was selected because of the extremely low supply

current (4 µA). According to the datasheet the MIC861 has a GBW product between 400

kHz and 650 kHz. The gain of the single stage is given by G1 = R2
R1
+ 1, so the gain Gn of n

consecutive stages is given by

R2
Gn = ( + 1)n . (6.1)
R1

In the demonstrated system we included 4 stages with R1 = 30kΩ and R2 = 150kΩ,

89
 Figure 6.3 Circuit Schematic of a single stage of the VA. The resistor Rbias is
needed to provide a path to ground to the base current of the bipolar transistor at
the non-inverting terminal and correctly bias the circuit. The coupling capacitor
filters out low-frequency components from the input of the next stage.

for a theoretical total gain of 1300 and a bandwidth between 70 and 110 kHz. These gain

levels were selected based on the expected Rx sensitivity of the pNUTs, the desired mini-

mum pressure detection level, and the voltage amplitude required at the voltage amplifier

output to trigger the comparator. For simplicity, the benchmark values used for these three

requirements were 0.1 mV/Pa, 1 Pa, and 150 mV respectively, which brings the required VA

gain from 1000 to 2000 V/V.

In the layout, pins to bypass R2 are included in every stage in order to remove the gain

contribution of one or more stages (i.e transforming the stage into a voltage buffer). This

feature was included to characterize the performance of the system in terms of operational

range vs. power consumption. Fig. 6.4 shows the gain over frequency of the VA when the

single stages are progressively eliminated.

When all 4 stages are active and no input is provided, the noise at the output of the VA

has a standard deviation of 70 mV, with peaks of up to 200 mV amplitude. The noise was

measured on the UHFLI oscilloscope by observing the histogram of the noise amplitude over

time, as well as the noise spectral density in the frequency domain. The total current drawn

90
 Figure 6.4 Gain of the VA with 1, 2, 3, and 4 active stages. It is possible to see
that the first stage is characterized by a pole close to 100 kHz that compensates
for the decline of the gain set by the nominal GBW product. This effect slightly
increase the gain, from 1300 to 1800, between 40 and 80 kHz when all 4 stages are
active.

by the 4 OpAmps is 15 µA when the positive and negative supply voltages are 0.9 V and -0.9

V respectively, setting the VA total power consumption to 27 µW. On the first stage, we used

the high precision impedance analyzer to measure an input capacitance of 6.7 pF. Since all

devices have an electrode capacitance of approximately 2.5 pF, the input impedance of the

VA will reduce the Rx sensitivity of the system compared to the open-circuit Rx sensitivity

of the devices characterized in Chapter 5 by a factor of 3.7.

6.1.2 Rectifier Architecture

The rectifier job is to take the modulated signal as input, and output a signal with a voltage

that profiles the modulation envelope. Since the harmonic components of the envelope are

not present in the desired rectified signal, the rectifier needs to be composed of non-linear

91
elements. There are several possible architectures for the rectifier, as shown in chapter 2 of

[45]. We choose a Dickson multiplier (DM) architecture for this demonstration due to its

simplicity and the possibility of building it with off-the-shelf commercial components. The

architecture of the DM is presented in Fig. 6.5.

Figure 6.5 Circuit schematics of the DM included in the PCB layout.

In the DM, an individual cell is composed by 2 diodes and 2 capacitors that alterna-

tively connect the diodes outputs to the input line and to the ground line respectively (this

configuration is also called "voltage doubler"). As the name suggests, in principle, adding

more cells in series multiplies the magnitude of the output. However, the time constant

of the system is increased for every additional cell, which ends up limiting the maximum

modulation frequency of the system. This issue can be partially compensated by adding

another diode in parallel to the ones in the topology. Adding a second diode is equivalent to

having a single diode with the same threshold voltage but double reverse saturation current,

resulting in faster discharge times and higher modulation frequency. Adding more diodes in

parallel increases the total diode capacitance. For the DM to function as a voltage multiplier

we need the diodes capacitance to be much smaller than the DM capacitances, which in turn

sets the modulation frequency and the gain of the system. We use this technique (see Fig.

6.2) to increase the modulation frequency of the system and meet the target of 1 kHz. The

92
number of cells has been kept to 2 for simplicity, as adding more cells would require adding

more diodes in parallel in each cell to maintain an appropriate time constant. The value of

CDM is 39 pF, a value that was selected to compromise between modulation frequency and

gain of the system. The selected diode model is NSR0140P2T5G by ON Semiconductor, a

Schottky barrier diode characterized by a low forward threshold voltage. This diode model

is characterized by a junction capacitance of 2 pF, therefore having two parallel diodes per

cell ensures that the diode capacitance stands at about 10 % of the DM capacitances. The

typical parabolic gain curve [46] is shown in Fig 6.6 for an amplitude-modulated (AM) 75

kHz signal with a modulation frequency of 1 kHz.

Figure 6.6 Measured input-output curve of the DM.

The gain curve stays the same for all carrier frequencies in the desired 30-100 kHz range,

93
while the gain slightly increases for modulation frequencies lower than 1 kHz.

The bit error rate (BER) is the metric we use to establish whether a signal is detected

or not.

We cannot assign a value to the BER of a system, but only establish whether the BER

of a signal is above or below a certain threshold [47]. We choose a BER of 10−3 as threshold

to consider a certain pressure signal detectable or not. The formula we use to establish that

a system has a BER below a threshold with 95% confidence is [47]

3
BER ≈ (6.2)
fmod T ime

From equation 6.2 we find that we need to correctly rectify the signal for approximately

2.5 seconds to have a BER below 10−3 .

The gain curve in Fig. 6.6 was produced by providing an amplitude-modulated input

through the SMA connector at the VA output. The DM gain starts to degrade incrementally

beyond 1 kHz. However, modulation frequencies higher than 1 kHz would not work in the

actual WuRx when the signal was fed from the VA. Because of the noise at the VA output,

the system BER quickly rises beyond the threshold of 10−3 for modulation frequencies higher

than 1 kHz, as the phase jitter amplitude introduced by the VA noise becomes comparable

to the modulation period. As mentioned before, the white noise introduced by the VA

presented spikes as high as 200 mV. Using an RMS noise of 140 mV, and following the gain

in Fig. 6.6, this translates in a noise amplitude of approximately 25 mV at the rectifier

output. When the VA is powered but no signal is present, noise is still present and could

trigger the comparator. To avoid triggering the comparator we adjust the threshold terminal

voltage. A threshold of 40 mV is selected when all four VA stages are used. The noise at

the DM output is significantly reduced when three or less VA stages are used. In these cases

the comparator threshold is reduced to 10 mV.

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6.2 WuRx System Characterization

In this section we describe the experimental setup used to characterize the WuRx system

and show the WuRx performance for the devices described in Chapter 5. The first step is

the system assembly. In Fig. 6.2 we showed that a portion of the PCB was left empty to

accommodate the chip with the fabricated devices. An opening is cut out of that region

to guarantee that the devices have an open back-cavity. We placed bi-adhesive tape on the

sides of the cut-out, we position the chip on top of it, and we press on the chip corners to

make sure the chip is soundly connected to the PCB. It is important to have the chip firmly

attached to the PCB as we will need to wirebond the pNUTs to the metal traces connected

to the VA input and the system ground. If the chip moves during the wirebonding process

the bond will fail, with the risk of having the wire hitting the device and breaking it. An

example of the assembled system is presented in Fig. 6.7.

Figure 6.7 Picture of the wirebonded chip mounted on the PCB.

The assembled system is then attached to a metal stage and mounted on a pole with

adjustable height as described previously in Section 5.2.1. Unlike the experimental setup

used to characterize the angular sensitivity of the devices, we position the adjustable pole

on a moving cart in order to test the WuRx over various positions both for the Tx and the

95
Rx.

To test the the WuRx, we generate ultrasound with the source with the center frequency

closest to the resonance, and we on-ff-key the signal at 1 kHz. For example, to test the single

pNUT with the floating metal, which resonates at 57 kHz, we use our 50 kHz source. For the

other 3 devices, with resonance frequencies of 72 and 90 kHz, we use our 80 kHz source. This

means that in the actual distance measurement we are losing some performance because of

the Tx-Rx frequency mismatch. We can then use the Rx sensitivity curves showed in Section

5.2.2 to infer the approximate minimum detectable pressure (MDP) in the scenario where

the Tx and Rx have the same center frequency. What we consider the MDP is determined

by the bit error rate (BER) observed in the output signal at the output of the comparator

as explained in the previous section. To probe the signal, we monitor the VA output with

the UHFLI scope, and we use a separate oscilloscope to observe the digital signal at the

output of the comparator. In the way the experiment was setup, we tried to replicate as

accurately as possible a free-space condition. Having a movable setup allows for positioning

the Tx and Rx in a way that minimizes reflections from the surrounding and their effect on

the measurement. An example of the complete experimental setup is presented in Fig. 6.8.

The measurement is performed by aligning the Tx and Rx beginning with a short distance.

Once the rectified signal is observed on the oscilloscope the Tx is pulled farther away from

the Rx while maintaining the alignment. Once we find the approximate distance over which

the signal starts disappearing we begin fine-tuning the Tx position to determine the system

range more accurately. As mentioned in Section 6.1.2, we need to monitor the signal for

at least 2.5 seconds to ensure we have a BER below 10−3 . To do that, we switch the time

scale of the oscilloscope to at least 1 second, and monitor the signal for a few seconds. A

visual inspection is sufficient to spot possible errors in the rectification. The communication

range is measured once we find the maximum distance that shows no rectification errors

over a few seconds measurement. Generally, we repeated the measurement varying the

relative angle position of the Tx and no significant change in the communication range was

96
 Figure 6.8 Experimental setup to test the complete WuRx system. The Tx gen-
erates the ultrasound, which is picked up on the other side of the room by the
WuRx. During the measurement, two scopes are connected to the system: the UH-
FLI scope is used to monitor both the VA output and the incident acoustic pressure
levels, while a separate oscilloscope is used to monitor the digital signal at the output
of the comparator.

observed, confirming the results of the angular sensitivity presented in Section 5.2.1. Finally,

we maintain the Tx position and we switch to the second channel of the UHFLI scope to

measure the pressure corresponding to the maximum range. This pressure corresponds to

the MDP. For a given transducer, the procedure is repeated while reducing by 1 the number

of amplification stages in the VA. We virtually remove 1 stage by connecting a jumper wire

between the stage gain resistor terminals. Fig. 6.7 shows an example of what the VA looks

like when two stages are bypassed, converting those stages in voltage buffers. In this way, we

can characterize the system range with respect to its power consumption. This process has

been repeated for the four devices characterized in Chapter 5. The devices demonstrated

MDP and communication range with respect to power consumption are shown in Fig. 6.9.

The data presented in Fig. 6.9 reflects the actual measurements performed with available

97
 Figure 6.9 Data collected during the WuRx demonstration. The plots show the
measured MDP and communication range of the WuRx system for the 4 devices
characterized in Chapter 5.

equipment, and does not reflect the full potential of the pNUTs-based system. We did not

have ultrasound sources that exactly matched the resonance frequency of the devices, and

therefore the measured MDP and the corresponding range can be improved under the Rx-

Tx frequency match condition. Another non-ideality is that we were not able to produce

pressures higher than 100 Pa with the 82 kHz Tx. To actuate it, we used a power amplifier

to interface the AWG and the Tx, increasing the actuation voltage amplitude from 10 V

to 25 V. For higher voltages, the source would quickly heat up, affecting the ultrasound

source response curve mid-measurement. The maximum pressure limit of 100 Pa does not

impact the reported MDP, and only reduces the communication range. As we reduce the

98
system power consumption by removing the amplification stages we have a corresponding

reduction in the WuRx working range, and an increase in the MDP. As the range is reduced,

we need to get the ultrasound source closer to the pNUTs to generate a pressure sufficiently

high to trigger the comparator. However, below a 0.1 m distance the rectified signal did

not satisfy the BER<10−3 requirement despite the high value of the generated pressure.

The likely reason for this is that as the Tx gets too close to the Rx, the effect of reflected

acoustic waves is not negligible anymore, and the assumed free-field condition is no longer

valid. When the single devices were used, the system range is above 0.1 m when at least 3

amplification stages are used. For this reason, only the range data points corresponding to

3 and 4 amplification stages are used. Similarly, the arrays needed at least 2 amplification

stages to present a range equal or above 0.1 m. Therefore, the array plots in Fig. 6.9 present

3 data points, corresponding to when 2, 3, and 4 amplification stages are used.

Figure 6.10 Extrapolated MDP and range for the demonstrated WuRx system vs.
transducer area. The MDP and range are obtained by assuming an ultrasound source
as the one described in Fig. 2.3, and that the Tx and transducers are frequency-
matched.

To get an idea of the full performance of the demonstrated WuRx, we must imagine having

1) a Tx that produces 350 Pa at the source, and 2) a Tx that is frequency-matched to the

resonance frequency of the pNUTs. We can extrapolate such scenario by scaling the measured

99
MDP as if it was at resonance. To do that, we take a look at the Rx sensitivity curves of the

devices presented in the previous chapter in Fig. 2.21. Then, we can relate the newly found

MDP to a range by using the plot for an hemispherical isotropic ultrasound source as in

Fig. 2.3. The extracted MDPs and the corresponding range for the 4 transducers are shown

in Fig. 6.10. Fig. 6.10 clearly shows the effect of higher propagation losses experienced by

acoustic waves at higher frequency. While we see that the MDP decreases as we increase the

total transducer area, we can see that the 57 kHz individual pNUT present a larger range

than the 2x2 SP array operating at 90 kHz.

6.3 Conclusion and Future Work

In this thesis we demonstrated the use of pNUTs in a working ultrasound-based WuRx. We

can now compare the performance of the system with other WuRx reported in literature that

use ultrasound as mean of communication. A comparison in terms of range vs. transducer

area is presented in Fig. 6.11, while more detailed data is compiled in Table 6.1.

From Fig. 6.11 we see a trend outlining a trade-off between the transducer area and

the MDP of the system, which in turn sets the system range. However, Fig. 6.11 does

not show explicitly the role of the interfacing electronics in determining the overall system

performance. In this demonstration we used off-the-shelf commercial components. Switching

to an IC would bring the following improvements to the system range:

• Reduced parasitic capacitance: the VA input capacitance would decrease from 6.7 pF

to a value significantly lower than the 2.5 pF across the pNUT electrodes, lowering the

system MDP by a factor of 3.7. This change alone would bring the system range above

10 m.

• Reduced VA noise. The system has an input-referred rms noise of approximately 80

µV. This noise is the cause of the phase jitter at the comparator input that increases

100
Figure 6.11 System range vs. transducer area plot. Comparison between ultra-
sound WuRx.

the the BER above 10−3 . It is possible to reduce it by a factor of 2 by reducing the

VA bandwidth from 100 kHz down to 50 kHz.

• Improved rectifier gain. Even maintaining an identical architecture, switching to a

CMOS-based DM would improve significantly the block gain. In conjunction with the

previous point, this upgrade would further increase the system MDP. As an example,

the rectifier gain curve from [13] is shown in Fig. 6.12. In this example the threshold

for unity gain stands at 40 mV at the VA output, as opposed to several hundreds mV

as in the current implementation.

101
 Table 6.1 Data comparing ultrasound WuRx from literature and the WuRx pre-
sented in this thesis.

MDP [P a] Area [mm2 ] Range [m] Power [µW ] f [kHz] IC Reference

0.004* 178 35 4.4 40.6 Yes Yadav [48]

0.005* 201 30 1 41 Yes Fuketa [49]

0.25* 14.5 13 8e-3 50 Yes Rekhi [13]

0.9 0.014 7.5 27 57 No This Thesis

1.1 0.014 6.5 27 72 No This Thesis

0.5 0.09 7 27 90 No This Thesis

0.3 0.2 8 27 90 No This Thesis

* Obtained from [13]. The formula to obtain the minimum detectable pressure from the Rx
q
dBm
power sensitivity in dBm is M DP = 2ρair cair 10 10 1mW
Area .

Assuming the rectifier in Fig.6.12 is used in place of our diodes implementation, the

system MDP would further improve with negligible additional power consumption (≈ 10

nW).

For example, we can imagine to reduce the system bandwidth to 50 kHz, and obtain

a VA gain of 100 with two amplification stages (i.e. a gain of 10 per stage). With the

reduced BW, the peak input-referred noise is now 60 µV, and the corresponding peak noise

at the comparator input is 2 mV. Since the comparator has a hysteresis of 4 mV, we set

the threshold at 6 mV. Targeting a 7 mV signal to trigger the comparator, we would need a

voltage at the input of the comparator of about 0.15 mV. In the scenario where the parasitic

capacitance is reduced to the point that it is negligible compared to Cel , we have lowered the

MDP of the individual device (assuming a 50 kHz center frequency) to 0.3 Pa. This would

extend the range to 10-12 m while reducing the power consumption to 14 µW.

On top of the improvement enabled by IC technology, different architectures are possible.

For example, the circuit used in [10] presents orders of magnitude lower power consumption

102
 Figure 6.12 Example of the cMOS rectifier gain curve used in [13].

for a comparable bandwidth, however it is unclear if there would be matching issues between

the pNUT and this specific topology.

On the transducer side, further improvement can be achieved by making the release

process more controllable. From the analysis shown in Section 2.2.1, we know that the value

of η is significantly reduced by not having a completely fixed anchor at the beams base. Once

the release process is better characterized, this issue can be fixed by either minimizing the

amount of undercut around the beams base, or by increasing the electrodes area further out

to cover the part of the undercut area where most of the bending moment occurs. Finally,

as discussed in Section 4.1.2, the lower parasitic capacitance offered by an IC, would allow

to use series-connected arrays and allow for a linear improvement of the transducers Rx

sensitivity, further extending the WuRx communication range.

Comparison between Ultrasound and Radio Frequency WuRx

As mentioned in the introduction, the use of WuRxs to extend the lifetime of wireless tags

gathered a lot of attention as the number of deployed sensing nodes is increasingly exponen-

tially, and several WuRx architectures were developed, mostly relying on RF as a mean of

communication. Given the multitude of applications for the nodes, the respective require-

103
ments in terms of power consumption, range and system area can vary significantly. Depend-

ing on the application, we will determine what carrier frequency and select the transmission

medium to be either US or RF. With this in mind, we can try to contextualize the perfor-

mance of the demonstrated pNUT-based system in the broader landscape of WuRxs. By

following the example reported in [13], we define a figure of merit (FoM) for WuRx in general,

and visualize it versus the total system area. In order to compare US and RF receivers, the

FoM accounts for the minimum detectable input radiation power and for the total squared

system power consumption. A lower FoM indicates a better performing transducer. The

resulting FoM versus system area is shown in Fig. 6.13.

Figure 6.13 Comparison of RF and US WuRx FoM with respect to system area.
The data used to generate the plot is reported in [13].

Fig. 6.13 shows the compromise between the system performance and its area. The

104
system we demonstrated in this work clearly fits in the expected trade-off between FoM and

area, although we notice that with the improvements to the system electronics listed above

we should expect a pNUT-based WuRx to break through the trade-off line shown in Fig.

6.13.

Future Research Directions

Besides optimizing the performance of the system demonstrated in this work, there are other

research avenues where pNUTs could be useful and that are worth exploring.

The first one is related to the use of the devices higher electrical output per unit area to

harvest acoustic energy and directly power standalone nodes. To do this, a large array of

devices would be necessary to collect enough input power. An application scenario of such

implementation was shown in Chapter 1 and a concept was shown in Fig. 1.8.

The second direction would explore an analogy in the acoustic domain for the research

published on optical metasurfaces (OM) in recent years [50][51]. In the case of OM, deep

sub-wavelength structures are patterned over large areas to manipulate the electromagnetic

waves amplitude, phase, and frequency. In doing so, there is a higher degree of control in

manipulating light compare to traditional techniques that use convex or Fresnel lenses due

to the flexibility in designing surface micro-machined structures. In the acoustic domain

it would be interesting to verify the feasibility of implementing ultrasound pNUT-based

metasurfaces to manipulate acoustic waves in a similar fashion. A possible obstacle could

be the high viscous losses we measured in the devices presented in Chapter 5, and further

analysis is necessary to verify the feasibility of the project.

105
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111
APPENDIX
Appendix A

Open Circuit Voltage vs. Gamma

Below we present the matlab script used to derive the OC Rx sensitivity of the devices in

Chapter 2.

% Reference Transformer Ratios, Electrodes Capacitance and Scaling Factor

SF = 1; %Scaling Factor, pMUT has the same area as pNUT with SF=0.2

eta_pNUT = 1e-7;

% eta for a pNUT with 100 µm X 100 µm area and 100/200 nm AlN/Pt (fs 50 kHz)

A_eff_pNUT = 7e-9;

% effective area of a 100 µm X 100 µm pNUT

Area_pNUT = 1e-8;

% total area of a 100 µm X 100 µm pNUT

cap_pNUT = 2.4e-12;

% reference capacitance pNUT

eta_pMUT = 6.4e-6/50;

% Data estimated from [1].

% eta of a pMUT with diameter 120 µm and 100/100 nm AlN/SiO2

113
A_eff_pMUT = 0.3*pi*(60e-6)^2

% effective area of a pMUT with 60 µm radius

Area_pMUT = pi*(60e-6)^2;

% total area of a 60 µm radius pMUT

cap_pMUT = 4*14.6e-12;

% reference capacitance pMUT

%Choose pNUT or pMUT by commenting out the other

% area = Area_pNUT*SF;

% A_eff = A_eff_pNUT*SF;

% eta = eta_pNUT*SF;

% Cel = cap_pNUT;

area = Area_pMUT*SF;

A_eff = A_eff_pMUT*SF;

eta = eta_pMUT*SF;

Cel = cap_pMUT;

%Acoustic Domain

p_plus = 1; %Incident Pressure

rho_air = 1.293;

c_air = 331.5;

Z0 = rho_air*c_air./area; %Air Acoustic Impedance

114
ZpNUT = linspace(Z0/30,Z0*30,10000); %pNUT Acoustic Resistance

Gamma = (ZpNUT-Z0)./(ZpNUT+Z0);

p_eff = (1+Gamma)*p_plus; %Effective Pressure on pNUT

power = p_eff.^2./ZpNUT; %Power on pNUT

efficiency = power./(p_plus^2./Z0)/2; %Efficiency from air to pNUT

%Electrical Domain

%eta = SF*1e-7;

%Cel = 2.4e-12; %Capacitance

f = 50e3;%Frequency

Z_el = 1/(2*pi*f*Cel); %Electrodes Impedance

ZpNUT_el = ZpNUT.*A_eff^2./eta^2; %pNUT resistance in electrical domain

V_eff = p_eff.*A_eff./eta; %Effective pressure in electrical domain

V_el = V_eff.*Z_el./(Z_el+ZpNUT_el); %Voltage across electrodes

power_el = V_el.^2./Z_el; %Electrical power actross electrodes

total_efficiency = power_el./(p_plus^2./Z0)/8;

%[1] Richard J. Przybyla et al., In-Air Rangefinding With an AlN

Piezoelectric Micromachined Ultrasound Transducer, 2011

%Plotting

plot(Gamma,1e3*V_el,’LineWidth’,2)

xlabel(’\Gamma’, ’FontSize’, 16, ’FontWeight’, ’bold’)

ylabel(’Open Circuit Voltage [mV]’,’FontName’,’Helvetica’, ’FontSize’, 16)

115
Appendix B

Gamma Scaling
As pointed out in Chapter 2, Keq and Meq are proportional to t3 /A and tA respectively. In

the code below, we are assuming that t and A are scaled together. Therefore, we can reduce

the scaling to A2 for both parameters. As a result, ζ, is scaled proportionally to A through

the factor "(side/side_ref)2̂". We assume in the code that the frequency of operation can

be treated as an independent variable.

f0 = 1e3*[30:5:100];

sides = 1e-6*[100:10:300];

Pin_eff = zeros(length(f0),length(sides));

Gam = zeros(length(f0),length(sides));

i = 1;

for side = sides

side_ref = 100e-6;

rho_air = 1.293;

c_air = 331.5;

area = side.^2;

Z0 = rho_air*c_air./area;

Effective_Radius = sqrt(0.65.*area/pi);

Zpnut = (side/side_ref)^2*1.75e-6./area.^2;

k_air = 2*pi.*f0/c_air;

Z_rad_air = rho_air*c_air/pi./Effective_Radius.^2 .*...

(1 - besselj(1,2.*k_air.*Effective_Radius)./k_air./Effective_Radius ...

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 + 1i*StruveH1(2*k_air.*Effective_Radius)./k_air./Effective_Radius);

Zrad = abs(Z_rad_air);

Zl = Zrad + Zpnut;

Gamma = (Zl-Z0)./(Zl+Z0);

Gam(:,i) = Gamma;

%Pin = 1;

%Pin_eff(:,i) = (1+Gamma)*Pin;

i = i+1;

end

surf(sides, f0, Gam)

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Nomenclature

α Coefficient accounting for viscous losses during acoustic waves propagation

η Electro-mechanical coupling coefficient

Γ Reflection coefficient at impedance boundaries

γ Coefficient accounting for ultrasound source directivity

µ Surface mass density

µair Air viscosity (1.8e − 5 ms

kg
)

νef f Effective Poisson ratio

φelastic Fraction of the total thickness occupied by the elastic layer

φpiezo Fraction of the total thickness occupied by the piezoelectric layer

ρair Air density

ρef f Effective volume mass density

ζ Transducer equivalent damper

A Transducer total area

a Circular pMUT radius

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Aef f Effective transducer area

aef f Effective radius of the piston that best approximate the radiation impedance of the

transducer

Ael Area covered by electrodes

C0 Device electrical capacitance

Cm Device motional capacitance

cair Sound velocity in air

Ccavity Equivalent capacitor in the acoustic domain describing the effect of of the back-cavity

volume

D Flexural rigidity of the films stack

d pNUT vertical displacement

e31,ef f Effective piezoelectric coefficient

Eef f Effective Young modulus

f0 Resonance frequency of the plate

Feq Equivalent force in the mechanical domain induced by the incident pressure

2
Gn Boltzmann constant approximately equal to 1.38e − 23[ ms2 Kkg ]

Gn Total gain of n consecutive voltage amplifier stages

J1 Bessel function of the first kind, order 1

J1 Struve function of order 1

Keq Transducer equivalent stiffness

119
Lm Device motional inductance

Lb pNUT beams length

lslot total length of the slots etched in the piezoelectric layer

Meq Transducer equivalent mass

P + /P − Amplitude of a forward/backward-propagating acoustic wave in a delay line

Pin Effective acoustic pressure at the device acoustic port

PT x Acoustic pressure at the ultrasound source location

r Distance from the ultrasound source

R1 , R2 Gain resistances in an individual stage of the voltage amplifier

Rm Device motional resistance

rT x Radius of the ultrasound source

t Transducer thickness

tslot Thickness of the slot etched in the piezoelectric layer

V Volume of the back-cavity

Vout Voltage across the device terminals

VP in Equivalent input voltage generated by the incident pressure

Wb pNUT beams width

wslot width of the slots etched in the piezoelectric layer

x Normalized position along pMUT radius / pNUT beams length

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xel Portion of the device covered by electrodes

Y (x) Device mode shape

Z0 Characteristic impedance in a delay line

ZL Load impedance in a delay line

zneutral Relative position of the neutral plane along the stack thickness

ZpN U T Acoustic impedance of the device seen from the acoustic port

Zrad Radiation impedance of the transducer

121