Improved Non-parametric Subtraction for Detection of Wafer Defect Hye Won Kim, Suk In Yoo Artificial Intelligence & Computer Vision Lab, Seoul National University Email:
[email protected],
[email protected]
Automated defect inspection for wafer has been developed since 1990’s to replace defect detection by human eye for low-cost and high-quality. Defects are detected by comparing an inspected die with a reference die in application of wafer defect inspection. Referential methods compare with reference image by computing the intensity difference pixel by pixel between a reference image and an inspected image or measuring the similarity between two images using normalized cross correlation or eigen value. These methods are problematic for defect detection due to illumination change, noise and alignment error. To reduce the sensitivity of illumination change and noise, the new image subtraction called non-parametric subtraction was proposed. Non-parametric subtraction can solve problem about illumination change and noise, but sensitivity of alignment remains unsolved. This paper introduces new approach less sensitive to alignment using non-parametric subtraction for wafer defect inspection.
subtraction technique called non-parametric subtraction based on a scattergram of the gray levels in two images. Non-parametric subtraction based on a scattergram computes the difference between two images by using frequency of gray-level pairs, thus determining if two image are similar or not. Two images are similar if gray levels of corresponding pixels lie along the y=x (called main distribution). Likewise, two images are different if there is a distribution away from the main distribution in the scattergram or the distribution forms a non linear shape. By using statistical information, non-parametric subtraction for wafer inspection can avoid the strict criteria needed in image subtraction or methods based on NCC or eigen value. Still, the sensitivity of alignment remains to be solved. In this regard, this paper introduces a new approach using non-parametric method for wafer defect inspection which is less sensitive to alignment. In section 2, this paper reviews the prior referential methods for defect detection. A new approach is described in section 4, and detection results are shown in section 5.
1. Introduction
2. Previous works
Wafer defect detection is an essential part of the manufacturing process for IC (Integrated Circuit). Since the 1990’s automated defect inspection of wafers has replaced detection by the human eye, bringing lower costs and higher quality to the defect detection process. Wafer defect detection is performed using referential methods such as comparing an image of and inspected wafer against a defect-free die image. These methods compute the intensity difference pixel by pixel between a reference image and an inspected image, or measure similarity based on NCC (Normalized Cross Correlation) or eigen value. Although image subtraction is quite simple, fast and efficient for defect detection and has been widely adopted for wafer inspection, this method is problematic due to issues of distortion and precise alignment. The methods based on NCC or eigen value are robust against changes in illumination but are sensitive to noise and alignment. These methods, therefore, require uniformity of illumination, noise free and perfect matching between a referential image and an inspected image in order to be used effectively for defect detection. To reduce the sensitivity of illumination change and noise, P.A. Bromiley [4] introduced a new image
Image subtraction as shown in Figure 1 computes the intensity difference between two images. Wu [1] used image subtraction in binary mode for defect detection, and they applied an elimination process in order to distinguish true defects. Ibrahim [2] and AlAttas [3] applied image subtraction in the wavelet-domain image instead of a binary image. This method is well known as a wafer defect detection method since it is very simple and fast. However, this method requires a uniformity of illumination, noise free and precisely alignment in order to be used for defect detection.
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| R(x,y) – T(x,y)|
Figure 1. Image subtraction NCC (Normalized Cross Correlation) has been used to evaluate the similarity of two images. Du-Ming [7-8] proposed a method for defect detection based on correlation. This method detects defect by measuring
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the similarity of a sub-image between two images as shown Figure 2. Each NCC for the sub-images is calculated by a sliding window size of m×n and will be in the range [-1, 1]. A reference sub-image and an inspected sub-image are similar if NCC is close to 1, whereas a defect is in the sub-image if the NCC is less than one or close to -1. Although this method is robust to illumination change, NCC is sensitive to noise and alignment. For example, a histogram of computed NCC values can be flat due to noise and alignment issues although defect exists in a given image, producing a false result. In this case, NCC can not be used as a criterion of detection.
step
scan
preprocessing
alignment inspected image
detection
reference die image
result of defect information
inspected die images
Figure 4. Wafer defect inspection Figure 2. The method based on NCC Eigen value-based method has the advantage of being less sensitive to illumination changes. An eigen value-based similarity measure proposed by DuMing[8] uses the shape of distribution on a scattergram for defect detection. This method calculates minor-axis, and defect is then detected by applying threshold value to this minor-axis. The minor-axis will be close to zero if the two images are identical, and likewise, it will be a large value if there is defect is in the inspected image. For defect detection, the degree of major-axis of distribution has to be close to 45°. A degree of majoraxis is larger than 45° when an inspected image is distorted by noise or a reference image and an inspected image are not perfectly aligned. To use an eigen valuebased method for defect detection, noise free and perfect alignment are required. major-axis minor -axis a
b
Figure 3. Scattergram : a. two images are identical, b. two images are different
3. Problem
Figure 4 shows application for wafer defect inspection. A wafer containing scores of dies is scanned, and inspected images are generated. Next, the ‘Alignment’ locates the position of the die in an inspected image, followed by the ‘detection’ step which detects defect in the inspected die image. Due to variance in the shapes of each wafer, it is difficult to detect defect using some fixed features of wafer. For this reason, wafer defects are detected using a referential method which compares a reference die with an inspected die. For comparison with a reference die, precise alignment between the reference die and the inspected die is necessary. Dies in an inspected image are aligned by pattern matching, such as the mean of absolute difference, phase only method [9], and normalized cross-correlation. Two dies, however, cannot be aligned precisely as the die in an inspected image is distorted by noise, rotation, scale, and nonuniformity while it is scanned. Through alignment error, false defect is detected as defect, or true defect is not detected in the process. Non-parametric subtraction based on a scattergram, one of the referential methods, requires precise Figure 5-(a), the distribution alignment. As shown in of two images in the scattergram forms a linear shape with perfect alignment between a reference image and an inspected image. Through alignment error, the shape of distribution in the scattergram is transformed into a non linear shape.
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described in Figure 7 using non-parametric subtraction based on a new method of generating a scattergram.
inspected die image
region partition
produce scattergrams reference die image
a
b
c
inspected die image
d
Figure 5. a : perfect matching, b: 0.1 geometric shift, c: 0.2 geometric shift, d: 0.4 geometric shift False alarm is major problem caused from alignment error. Inspected images of (b)-(d) are generated with sub-pixel alignment errors. Figure 5 (b)-(d) shows the detection results using non-parametric subtraction and scattergram when a reference die image and an inspected die image are not precisely aligned. As shown Figure 5, false defects are in the results of (b)-(d) in detected due to an alignment error. Alignment error also reduces the chance of lowcontrast defect being detected. Low-contrast defect is invisible to human eye because the intensity difference between the low-contrast defect and its surrounding area is low. In this case, the distribution of low contrast defect is located in the main distribution as shown in Figure 6, with the result that the defect is not detected in detection process.
Figure 6. Low-contrast defect: a. inspected image, b. scattergram
produce difference image
thresholding & postprocessing
Figure 7. New approach
4.1. Partitioning regions As shown in Figure 8, the incorrect detection of defects occurs in the regions with significant local change, such as edges. Region with significant local change is excluded when the scattergram of (b) in Figure 9 is constructed. The scattergram of (b) shows that alignment error on a region with abrupt change in intensity results in a transformation of the shape of the distribution in scattergram between two images.
Figure 8. An inspected die image and detection result
4. New approach Non-parametric subtraction proposed in [4] uses a scattergram which is generated as follows: 1. Take gray level. i = IR(x, y) : gray level of a reference image j = II(x, y) : gray level of an inspected image 2. Increase S(i, j) The scattergram is constructed pixel by pixel for the entire image, so alignment error results from the problems mentioned in section 3. Proposed approach
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a
b
Figure 9. scattergram : a. scattergram for entire image, b. scattergram for region excluding region with significant local change
In the intensity difference image of the reference and inspected image, the region in which incorrect detection of a defect occurs has a high value. The proposed method in this paper is based on this property. To partition an image into two regions, region mask is generated using intensity difference. Instead of calculating intensity difference pixel by pixel, vertical or horizontal projection is used. Each projection for a reference image and an inspected image are calculated, and then the difference of projection is computed. Figure 11 presents the intensity difference of the horizontal projection between a reference die image and an inspected die image. Alignment accuracy of (a) is low and that of (b) is high. As shown in each profile in Figure 11, the difference is high when an alignment error occurs on regions having significant local change. By applying threshold value to difference, an image is partitioned into two regions. One region is a set of pixels that have a high difference of intensity between a reference die image and an inspected die image, and another region is a set of pixels corresponding to low difference. A scattergram for the each of the two regions is constructed. An image is not partitioned if the reference image and the inspected image are matched with high alignment accuracy. In this case, intensity differences for all pixels are less than 1.
Figure 12. Scattergram applying averaging
4.3. Production of the difference image In this paper, log-likelihood, one of the non-parametric subtraction techniques produced by P.A. Bromiley[4] x−µ z=
σ that means distance was used. Using z-score of x from the mean, difference image is produced as : F ( I 1 ( x, y), I 2 ( x, y )) D( x, y ) = −2 ln ∑ F ( I 1 ( x, y ), c) c
where D(x,y) : difference image, F(I1 (x,y), I2(x,y)) : frequency of gray level The resulting difference image indicates the distance of gray-level for pixels in an inspected die image from the mean of distribution in each vertical cut. Therefore, a set of pixels having a large value indicates a defect in an inspected die image.
5. Experiment Figure 10. Region partition mask
a
For this experiment, we generated test samples. Test images are generated using real die images as shown Figure 13. Each image as shown in the figure is distorted by additive Gaussian noise of the variance 1, 2, 3, and non uniformity which is in a quadratic form. Eight test sets were generated per die. 20 percent of all dies are defect-free dies, with defects accounting for 80 percent. The shape of defect is a circle, with a radius is 5~50 pixels, and a contrast of 2~5.0. Each image is generated by 1.1 times reference die image in order to create a sub-pixel alignment error.
b
Figure 11. Difference of horizontal projection
4.2. Averaging
To reduce sensitivity to regions having significant local change, a scattergram is constructed by averaging gray levels. When a scattergram is constructed the mean of gray levels in a 5×5 window is taken instead of a single gray level. This process brings the distribution close to the linear shape.
Figure 13. Die images and an inspected image Table 1 and Figure 14 show result from nonparametric subtraction proposed [4] and proposed method in this paper. ‘False’ is the rate of incorrect
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detection of a defect. ‘True’ is the rate of correct detection of a defect. False = number of die with incorrect detection / total number of dies True = number of die with correct detection / total number of dies with defect By alignment error occurred when test images are generated, success rate of an original non-parametric subtraction is low. However, the proposed method in this paper shows better result. Each the rate of die with incorrect detection for two methods is similar because number of die is counted instead of number of incorrect defects. Incorrect defects reduced in the result from the proposed method as shown in Figure 14. Table 1 . Result from two methods Distortion
Original method (Log-likelihood)
Proposed approach
alignment on region with significant local change can reduce. As shown in experimental results, the proposed method brings better result than original method. The experiment reveals that the proposed method is less sensitive to alignment than other methods. To reduce incorrect defects as shown in Figure 14, application may require identifying which is real defect and which is not real defect such as dust on the die may be required.
7. References [1] W.Y. Wu, M.J. Wang, and C.M. Liu, “Automated inspection of printed circuit board through machine vision”, Computers in Industry 28, 1996, pp103-11 [2] Z. Ibrahim, S.A.R.A1-Attas, and Z.Aspar, “Analysis for the wavelet based image difference algorithm for PCB inspection”, Proceedings of the 41th SICE Annual Conference, Osaka 2002
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5
0.22
0.71
0.13
0.93
[3] Z.Ibrahim, S.A.R.A1-Attas, “Wavelet-based printed circuit board inspection algorithm”, Integrated Computer-Aided Engineering 12, 2005, 201-213
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10 5 10
0.15 0.15 0.21
0.28 0.07 0.71
0.10 0.09 0.11
0.92 0.90 0.93
[4] P.A.Bromily, N.A.Thacker, P.Courtney, “Non-parametric image subtraction using gray level scattergrams”, Image and Vision Computing, 2002
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0.29 0.08
0.10 0.09
0.93 0.91
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[5] Shang-Hong Lai and Ming Fang, “An Accurate and Fast Pattern Localization Algorithm for Automated Visual Inspection”, Real-Time Imaging, 1999 [6] Du-Ming Tasi, Chien-Ta Lin, Jeng-Fung Chen, “The evaluation of normalized cross correlations for defect detection”, Pattern Recognition Letters, 2003 [7] Du-Ming Tasi, Chien-Ta Lin, “Fast normalized cross correlation for defect detection”, Pattern Recognition Letters, 2003
a . Log-likelihood
b. New approach
Figure 14. Result image
6. Conclusion For defect detection, referential methods such as subtraction, method based on NCC, and eigen value have been proposed. Although an image subtraction is quite simple and fast, this method requires some assumptions such as noise free, non-uniformity and precise alignment. The method based on NCC and eigen value are also require noise free and perfect matching between an referential die and a inspected die. In this paper, we have proposed the method for wafer defect detection using non-parametric subtraction which is less sensitive to alignment. Generating scattergram is the main concept of the proposed method. When the scattergram is constructed, the image is partition into two regions, and the mean of gray level is used. By using region partition and averaging, the sensitivity of 468
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[8] Du-Ming Tasi, Ron-Hwa Yang, “An eigenvalue-based similarity measure and its application in defect detection”, Image and Vision Computing, 2005 [9] K. C. Macukow, “Performance of the pure phase-only correlation method for pattern recognition”, SPIE Optical Information-Processing Systems and Architectures, 1990 – phase only method
