Automated direct patterned wafer inspection

Babak H. Khalaj Hamid K. Aghajan Thomas Kailath

Information Systems Laborator y, Department of Electrical

Engineering Stanford University, Stanford, CA 94305

ABSTRACT
A self-reference technique is developed for detecting the location of defects in repeated pattern wafers and
masks. The application area of the proposed method includes inspection of memory chips, shift registers, switch
capacitors, CCD arrays, and liquid crystal displays (LCD). Using high resolution spectral estimation algorithms,
the proposed technique first extracts the period and structure of repeated patterns from the image to sub-pixel
resolution, and then produces a defect-free reference image for making comparison with the actual image. Since
the technique acquires all its needed information from a single image, there is no need for a database image, an
scaling procedure, or any a-priori knowledge about the repetition period of the patterns. Results of applying the
proposed technique to real images from microlithography are presented.

1 INTRODUCTION

The task of detection and localization of defects in VLSI wafers and masks is an essential but exhausting procedure.
As the complexity of integrated circuits is increasing rapidly, the need to automate the inspection of photomasks and
wafers becomes a more important necessity for maintaining high throughput and yield in the fabrication processes.
Human visual inspection and electrical testing are the most widely used methods for defect detection; however, this
is a time consuming and difficult task for people to do reliably. On the other hand the usage of electrical test is
inherently limited to off-line and overall functional verification of the chip structure, and can only be accomplished
after the fabrication is completed; it cannot be applied to on-line and layer by layer inspection of the wafer during
the fabrication process. In addition to the need for inspecting wafers, the inspection of the mask pattern is critical
because any defect on the mask is transferred to the wafers.
Typical patterns found in wafers and masks can be put into three main classes 1:

• Constant areas

• Straight lines

• Repeating structures

The repeating structure class covers two different cases. The first includes repeated patterns within a single chip
such as memory areas, shift registers, adders, and switch capacitors. The chips themselves considered as repeated
patterns on a wafer can be included in the second case. As another potential example of repeating patterns, one can
mention liquid crystal displays (LCD) and arrays of charge-coupled devices (CCDs) arising in imaging systems and
cameras.
Most inspection techniques fall into one of the following general categories: methods for checking generic properties
and design rules, and methods based on image-to-image comparison. In the first category, the image is tested against
a set of design rules or local properties and violations are reported as defects. An example of this kind of techniques
is the work of Ejiri et al 2 that uses an expansion-contraction method to locate the defects. In image to image
comparison methods, the image taken from the wafer is compared either with an ideal image stored in a database,
or with the image taken from another region of the same wafer that is supposedly identical to the image under the
test. A fairly complete review of the related literature may be found in Kayaalp et a f .

140 I SPIE Vol. 1907 Machine Vision Applications in Industrial Inspection (1993) 0-8194-1 140-X/931$4.00

Downloaded From: http://proceedings.spiedigitallibrary. org/ on 06/27/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOflJse. aspx

 Several optical inspection techniques have been developed for locating and classifying defects on masks and
wafers. In spatial filtering methods, the spectrum of the perfect image in the Fourier transform domain is filtered out
from the image and an image that includes only defective patterns is obtained. This technique can be implemented
through a holographic approach4 to attenuate distortions; however, since it is difficult to filter out only the
frequencies of the acceptable pattern, the signal to noise ratio of the resulting defect image is generally poor 5.
Most commercial inspection systems compare the chip patterns with a pre-stored image in a database. This
requires a large volume of data as a reference. A data conversion step is also needed to make the scaling of the
stored data equal to that of the inspected image 5. As the size of devices decrease, proper adjustment of the scales
for doing the required comparisons becomes more difficult to achieve. As an alternative to this approach that avoids
the need for a large database, images of two adjacent dies can be compared; however, the detection is limited by
step-and-repeat errors and also the errors in synchronizing the location of the two scanner beams over the die.
As was mentioned earlier, an important category of defect inspection applications is the inspection of repeated
pat terns on masks and wafers. This is a field of application for image-to-image comparison methods in which the
repeatedness of the patterns is used. However, most existing systems that perform image to image comparison
face the following difficulties. In order to compare images with each other, or with a reference database, accurate
registration is necessary. This includes both problems of alignment and scaling and introduces a tradeoff between
the minimum detectable defect size and the expense and throughput of the systems that compare the image with
another image or a database image. Moreover, if an image to database comparison method is chosen, there is also
the need to simulate the imaging and development processes in order to produce the database.
A self-reference technique that avoids the mentioned difficulties was developed by Dom et af , in which the com
parison is made using the repeated cells in the image. In this method prior knowledge about the period of repetition
is assumed and scaling of the image is adjusted accordingly; then each pixel is compared with two corresponding
pixels in left and right neighboring patterns.
In this paper, we propose a technique for extracting the structure of repeated patterns, or the building block , from
the acquired image itself; and then detecting the defects by comparing the resulting building block with the image.
Extracting the repeated structure from the image eliminates the need for producing a database and avoids the scaling
problem as well. There is also no need for the image to exactly contain a certain number of pattern blocks. Also
rather than using only pixels from neighboring patterns, the proposed method exploits information contained in the
whole image to decide whether a pixel corresponds to a defect or not. Moreover, the techniques used in the proposed
approach yield sub-pixel resolution for estimating the size of the building block.
The organization of the rest of the paper is as follows. In Section 2, the details of the proposed technique are
presented. Section 3 contains several examples of application of the proposed technique for detection of defects in
real wafer images. Section 4 summarizes the results and offers some concluding remarks. In the proposed algorithm,
the periods of the patterns are estimated by techniques of sensor array processing.

2 THE DEFECT DETECTION ALGORITHM

The proposed defect detection algorithm is composed of three steps. In the first step the repetition periods of the
pat terns in both the horizontal and vertical directions are estimated by a high-resolution method. After obtaining
good estimates of these periods, the building block of the image is extracted by a proper sub-pixel weighted sum of
the repeated patterns throughout the image. In the final step the location of defects is determined by subtracting
shifted versions of the building block from the image. In order to reduce the number of false alarms especially at the
edges of the image, some ideas from fuzzy-logic and median filtering are used in this step. By passing the resulting
difference image through a proper threshold, the location df the defects is obtained.

Estimating t he Period of Repeated ness

The general problem of extracting the spectral components of a signal arises in a wide range of application areas
such as in communications systems, geophysical data processing, and vibration analysis. The objective in time series
analysis is to obtain estimates of the sinusoidal frequenCies in a discrete time signal presumed to be composed of a
superposition of sinusoids added with noise. In a more generic case, one can consider general exponential sinusoids
with decaying or growing envelopes. Mathematically, if the N x 1 vector X N denotes the observed time series, and

SPIE Vol. 1907 Machine Vision Applications in Industrial Inspection (1993) I 141
Downloaded From: http://proceedings.spiedigitallibrary. org/ on 06/27/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse. aspx
 A = [A1, • . . , Ad ] is the unknown vector of exponential terms, the observed signal can be expressed as

(1)

where s; contains the amplitude and phase of the ith exponential Ai = eiw; , and n is the additive noise term.
An efficient technique adopted from the field of sensor array processing, called ESPRIT is used to estimate the
frequencies A/' 8. In our application, we are looking for estimates of the periods of a periodic image in the horizontal
and vertical directions. Therefore, the problem is slightly different from the harmonic retrieval problem in that the
goal here is to find only the fundamental frequency of the signals.
As a matter of background, there are a number of different ways for estimating the period of a two-dimensional
periodic signal. Among these methods one can mention the FFT and the autocorrelation approaches. However,
there are two major drawbacks for these methods. In our problem we are dealing with two-dimensional images and
so the amount of computations will be very high with either of these methods. The second and more important
disadvantage of these standard methods is their limited resolution, which depends on the width of the signal. In
typical images of wafers, the number of periods of the pattern can be as low as 5 and so we want to estimate the
period of a signal by only observing a small number of its periods. Since the resolution of the FFT method for a
given signal frequency is proportional to the number of observed periods of the signal, the period that is estimated
by this method in these situations is not acceptable. Since in general the period of the patterns is not an integer
number of the pixels of the image, it is necessary to use a high resolution (subpixel) algorithm for period estimation.
We shall present such a method below.
First let us note that the estimation of the horizontal and vertical periods of a periodic image are separable prob
lems in nature and by transforming the problem into two one-dimensional problems, large savings in computational
load can be achieved. One way of doing this transformation is described below.
The image is first projected along its horizontal and vertical axes and two one-dimensional vectors are produced.
Then, the aforementioned high-resolution techniques of time series analysis can be applied to each of these vectors
in order to obtain sub-pixel estimates of the horizontal and vertical periods of repeatedness in the image.
Let the image be denoted by the matrix F. We only treat here the estimation of the horizontal period of the
image; an identical procedure is used for estimating the vertical period. The rows of F are 1 x N vectors and are
named fi , i= 1, . . . , N , so that we can write

(2)
The simple horizontal projection of the image produces an N x 1 vector x whose elements are
N

Xj = L(f;)j ' i= 1, . . . ' N (3)

j=l

Then, the goal is to estimate the fundamental frequency of the signal x. In matrix formulation, the entire time series
can be written as

(4)

For applying eigenstructure methods of sensor array processing we need to compute the sample covariance matrix
of the measurements. The above formulation views the data as one snapshot of a uniform linear array. This defines
only a one-dimensional signal subspace. To obtain a subspace of dimension d , we divide x into P vectors of length
m by sliding a window of size m over the data. The value of m should satisfy d < m :S N - d + 1. Then, P plays the
role of the number of snapshots here as compared with array processing formulation. Thus, the data is rearranged

142 I SPIE Vol. 1907 Machine Vision Applications in Industrial Inspection (1993)
Downloaded From: http://proceedings.spiedigitallibrary. org/ on 06/27/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse. aspx
 as follows

X1 X N -m+l
nl nN -m+l
X2 X N -m+2 n2 nN -m+2

l
] = Am(A) [ ' s
= [ ;i;N-m , ] +
Xm XN

Am (A) =
[ nm nN
] (5)

where

(6)

1 1

]
>11 Ad

Am-1 Am-1
1 d

and = diag [ Al Ad ] . The vector s cont ains the amplitudes of different frequency components and is not
important in our analysis.
With the above formulation, the signal subspace techniques of sensor array processing can be applied to estimate
the significant frequencies of the signal X N . A computationally efficient technique for estimating the frequency
components in the above problem is the ESPRIT algorit hm 7' 8. ESPRIT assumes the availability of measurements
from two identical subarrays that are displaced from each other by a displacement vector A. In the time series
analysis, the measurements come from equally spaced time instants. So this problem possesses the structure required
by ESPRIT and the frequencies of the sinusoids in the time series signal can be estimated by t his method.
In our application, the signal X N is a periodic signal and has a set of harmonically related frequency components.
In other words, we only need to estimate the frequency of the first harmonic of t he signal. If the signal obtained by
projection has a large component in its principle frequency (which is true for square waveforms), then by choosing
the number of components equal to 4 (corresponding to the first and second harmonics in positive and negative
frequencies), one can directly obtain the period of the signal using a subspace method. However, in general, there
may be a relatively large amount of energy in higher harmonics, and in these cases one can estimate the value of
these higher harmonics of the signal and since the frequencies of these harmonics should be multiples of the principle
frequency, this frequency can be extracted by a simple linear least-squares method.
As mentioned before one of the most important characteristics of these subspace fitting methods is t heir ability to
provide high resolution estimates of the parameters. In our application, this leads to subpixel resolution in estimating
the periods. The estimated periods of row and column projections determine the size of the building block of the
image. The procedure of extracting the building block is described in the next section.

2.2 Ext racting the Building Block

Given estimates of the period of the patterns in both horizontal and vertical directions, the building block is con structed
by simply shifting a window of proper size through the image and adding the corresponding pixel values together. Since
in general the size of the building block is not an integer number of pixels, it is necessary to shift the window by
subpixel values and use interpolation to find the values of subpixel points. A simple linear interpolation proves to be
sufficient and is used for this purpose.
If the estimated horizontal and vertical periods of the image are T,, and Ty respectively, the size of the building
block BB( k , l ) will be
1< k ::; int( T,,) +1
1< ::; int( Ty ) + 1
Denoting the value of the N x N image at location ( k , l ) by F ( k , l ), the following equations are used to const
ruct the building block n , n2

B B( k , l ) = L L (1 - ri )( l - Sj ) F ( ki + k , lj + l)
i=l j=l

+ ri ( l - sj ) F( k; + k + l , lj + l )
+ (1 - r;)s j F ( k; + k , lj + l + l)
Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/27/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse. aspx
 + ri Sj F ( ki + k + l , lj + l + l ) (7)

SPIE Vol. 1907 Machine Vision Applications in Industrial Inspection (1993) I 143

Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/27/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse. aspx

 where

n1 = int( N /Tx
) n2 = int( N
/Ty ) ki =
int(T.r: * i) li
= int( Ty * j) r;
= Tx * i- k;
Sj = Ty * j - lj

By averaging among all of the blocks in image, the amount of noise and the effect of the defects are reduced
considerably and a good estimate of building block is obtained in this way. It should also be mentioned that if the
sizes of defects in an image are so large that the computed building block is no longer a good estimate of the true
value, then although the defect can not be localized exactly, the algorit hm will still give an alarm and will reject the
sample.

2.3 Detecting t he Defects

When the building block is constructed, one might simply compare each point of the original image with the corre
sponding point in the building block, and if the difference is larger than a threshold, that point may be identified as
a defect. However, because of the quantization effects at the edges of the image, in practice each point should also
be compared with the eight neighboring points of its corresponding point in the building block. Having compu ted
the difference between each point of the image and all 9 points in the neighborhood of its corresponding point in
the building block , that point of the image is assigned a value equal to the minimum of the absolu te value of these
differences. It is this value that gives a measure of the probability that the point is a defect.
Mathematically, the above procedure can be stated by the relation

min I F ( m, n) - BB( k + i, l + J (8)

) I
-l:S:i,j:'O 1

where

k m - int( m/T.r ) *
Tx n - int( n /Ty )
* Ty

By t ransforming all the points of the image to such a difference image, and using a proper threshold value, one
can classify the points of image as either defects or nondefects. The value of the threshold generally depends on the
contrast of the image and the amount of the difference in intensity which is supposed to be interpreted as a defect
and can be chosen accordingly.

3 EXPERIMENTAL RESULTS
In this section we apply the developed techniques to the detection of defects in images that have repeated pat tern
blocks.
In these examples, real images taken by an optical microscope are considered. In this case the period in either
of the two directions is not an exact number of pixels and the sub-pixel algorithm is necessary to obtain a good
estimate of these non-integer numbers. In Figs. 1 and 2 the image and its projection along the horizontal axis are
shown. In fact the signal in Fig. 2 is the signal whose period is to be estimated. The spatial frequencies of t his signal
as estimated by the ESPRIT algorit hm are shown in Fig. 3. Finally the estimated building block of this image and
the location of the defects are shown in Figs. 4 and 5 respectively.
Fig. 6 shows the image of another pat terned wafer, and Figs. 7 and 8 show the extracted building block and the
location of the defects in this example.
The third example considers another real image, which consists of two interlaced subimages that are shifted with
respect to each other ( Fig. 9). As a result , there are some rows of the image that are similar but shifted versions
of each other ( Fig. 10), and by simple projection of the image along t he horizontal axis we obtain a signal that has
Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/27/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse. aspx
 144 I SPIE Vol. 1907 Machine Vision Applications in Industr ial Inspection (1993)

Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/27/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse. aspx

 almost twice the true frequency of the patterns. In such cases by a proper preprocessing of the image (see below), we
obtain another signal that has the correct pattern frequency (Fig. 12). By estimating the period of this signal, the
building block and the location of defects are obtained accordingly ( Figs. 13 and 14). To handle these cases a simple
preprocessing step can be applied to the image as follows. First each row is centered by removing its mean. Let the
new rows be denoted by z; , i = 1, . . . , N . The average vector of all rows is calculated and called a. Then each row
of the image is projected onto the plane orthogonal to a. By this transformation the two vectors that were shifted
versions of each other will be transformed to vectors 180 degrees apart. In Fig. 11, a simple diagram is shown to
visualize this situation. Vectors z1 and z2 represent the two similar and shifted rows and their projections onto the
space orthogonal to a are along directions qi and q2 , respectively. After this preprocessing step, the inner product
of each of the two kinds of rows wit h a selected row vector will have opposite signs to each other. An example of such
cases is presented in Fig. 9. In Fig. lO(a) and (b), the two similar and shifted rows of the image are shown. Simple
projection of these rows results in similar values in the projection vector x which is shown in Fig. 12(a). However,
by implementing the preprocessing step and multiplying the transformed image by one of these typical vectors, the
two shifted vectors will be transformed to two opposite numbers and so the period of the projection will be equal
to the true period of the patterns. In the above example, the resulting projection vector x has the form shown in
Fig. 12(b) in which the effects of similar rows have been converted to opposite values.

4 CONCLUSION

An automatic self-reference technique has been developed for detecting defects on repeated pattern wafers and masks.
The technique uses information from the image to extract the building block of the repeated struct ure and locates
the defects by subtracting a regenerated defect-free image from the acquired image. There is no need in t his method
for a reference database image or a scaling procedure. Potential application areas for the proposed method include
inspection of memory chips, shift registers, switch capacitors, liquid crystal displays ( LCD) and CCD arrays. Since
the proposed algorithm extracts the required information from a single image, it may be applied for automatic
detection of any defect or non-regularities in a repeating two-dimensional signal. In the current paper its application
to images from the area of wafer and mask defect inspection has been considered , but the ideas of the proposed
approach may also be extended to other areas that deal with repeated structures such as crystallography.

5 ACK NOWLEDGEMENTS
This work was supported by the Advanced Research Projects Agency of the Department of Defense and was
monitored by the Air Force Office of Scientific Research under contract F49620-90-C-0014.

6 RE:FERENCES
1. F. Babian, Optical Defect Detection Limits in Semiconductor Wafers and Mc1sks, PhD thesis, Stanford University, Stanford,
CA 94305, 1986.
2. M. Ejiri, T. Uno, M. Mese, and S. Ikeda, "A Process for Detecting Defects in Complicated Patterns", Computer Graphics
and Image Processing, 2:326-339, 1973.
3. A. E. Kayaalp and R. Jain, "A Knowledge Based Automatic On-Line Wafer (IC) Inspection System", In Proc. of VISION
85, pages 117-130, 1985.
4. L. H. Lin, D. L. Cavan, R. B. Howe, and R. E. Graves, "A Holographic Photomask Defect Inspection System", In Proc.
of SPIE, Optical Microlithograph y IV, pages 110-116, 1985.
5. S. Chae, Defect Detection and Classification in VLSI Pattern Inspection, PhD t hesis, Stanford University, Stanford, CA
94305, 1987.
6. B. E. Dom, V. H. Brecher, R. Bonner, J. S. Batchelder, and R. S. Jaffe, "The P300: A System for Automatic Patterned
Wafer Inspection", M achine Vision and Applications, 1(3):205-221, 1988.
7. A. Paulraj, R. Roy, and T. K ailath, " Estimation of Signal Parameters by Rotational Invariance Techniques (ESPRIT)",
In Proc. of 19th Asilomar Conference on Circuits, Syste ms and Comp., 1985.
8. R. Roy and T. Ka.ilath, "ESPRIT: Estimation of Signal Parameters via Rotational Invariance Techniques", IEEE Trans.
on ASSP, 37(7):984-995, July 1989.

SPIE Vol. 1907 Machine Vision Applications in Industrial Inspection (1993) I 145
Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/27/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOftJse. aspx
1.5

Figure 4: The building block of the image in Fig. 1.

Figure 1: An image from a repeated pattern chip.

1
x104
.,..,,,. ,,,.._ ,> -
Horizontal Projection •
"""" r"""
0.5 """" """"'
0

-0.5

-1

-1.5 Figure 5: Defects of the image in Fig. 1 extracted by the

proposed technique.
-2 \.I

-2.5
w ., v '-

0 50 100 150 200 250 300

Figure 2: Projection vector along the horizontal axis of

the image in Fig. 1.

-1.5

-2 - - - ---'----'
-2 -1.5 -1 -0.5 0.5 1.5 2

Figure 3: Horizontal spatial frequencies of the image in

Fig. 1 estimated by the ESPRIT algorithm. The funda-
mental period corresponds to the lowest frequency. Figure 6: Another image from a repeated pattern chip.

146 I SPIE Vol. 1907 Machine Vision Applications in Industrial Inspection (1993)

Downloaded From: http://proceedings.spiedigitallibrary. org/ on 06/27/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOflJse. aspx

 Figure 7: The building block of the image in Fig. 6.
Figure 11: A diagram showing how two similar and
shifted rows of the image are mapped to vectors with
opposite directions .

....,.
• al

(7

Figure 12: (a) Result of simple projection of the image of

Fig. 9 along horizontal axis. (b) Result of applying the
projection after preprocessing the image (see text).

Figure 8: Extracted defects in Fig. 6.

Figure 13: The building block of the image in Fig. 9.

Figure 14: Defects of the image in Fig. 9 extracted by the

proposed technique.

Figure 9: Image of a chip with similar and shifted rows.

Figure 10: Plots of two rows of the image of Fig. 9 that ..

are similar but shifted versions of each other.

SPIE Vol. 1907 Machine Vision Applications in Industrial Inspection (1993) I 147
Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/27/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOftJse. aspx