IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 23, NO. 1, FEBRUARY 2010 141

Defect Detection of IC Wafer Based on SpectralSubtraction

Hongxia Liu, Member, IEEE, Wen Zhou, Qianwei Kuang, Lei Cao, and Bo Gao

Abstract—In this paper, spectral subtraction is successfully ap-plied to image processing and to detect defects in the integratedcircuit (IC) image. By utilizing the characteristics of many of thesame chips in a wafer, three images with defects located in the sameposition and different chips are obtained. The defect images con-tain the spectrum of standard image without any defects. Spectralsubtraction presented in the paper can extract the standard imagefrom the three defect images. The algorithm complexity of spectralsubtraction detecting defects is close to that of Fourier transform.After obtaining the standard image, the speed and accuracy of de-fects detection can be greatly enhanced using the detection methodpresented in the paper. Using the image gray-scale matching tech-nology, impact of illumination on IC defect detection is solved. Ex-periments demonstrate that spectral subtraction is fast and accu-rate to defect detection in an IC image, and the method has highrobustness for illumination.

Index Terms—Defects detection, integrated circuit (IC) wafer,spectral subtraction.

NOMENCLATURE

List of Symbols:

Maximal value in .

AVJ Operation of automatic threshold processing.

Result of automatic threshold processing to.

Defect image in .

Result after operating the power transform on.

Each value in divided by .

DEFECT Defects detected in .

Spectrum subtracted from spectrum .

Spectrum subtracted from spectrum .

Manuscript received June 10, 2009; revised September 02, 2009. Currentversion published February 03, 2010. This work was supported in part by theProject of National Natural Science Foundation of China under Grant 60976068,in part by the Key Project of the National Natural Science Foundation of Chinaunder Grant 60936005, in part by the Cultivation Fund of the Key Scientific andTechnical Innovation Project, Ministry of Education of China Program underGrant 708083, and in part by the Specialized Research Fund for the DoctoralProgram of Higher Education under Grant 200807010010.

The authors are with the Key Lab of Ministry of Education for WideBand-Gap Semiconductor Materials and Devices, School of Microelectronics,Xidian University, Xi’an 710071, China, (e-mail: hxliu@mail.xidian.edu.cn;www200503@sohu.com; kqw3606@163.com; dudupi2000@sina.com; bob-bygoff@163.com).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TSM.2009.2039185

Spectrum subtracted from spectrum .

E2200 Intel E2200.

FILTER Morphological filter.

Unit of computer memory.

Standard image.

Power.

IC image with defects.

Image .

Image .

Image .

Gray value of defect in .

Gray value of the same position in .

Multiplication.

Set of defect coordinates in image.

List of Abbreviations:

CPU Central processing unit.

D FFT Dimensional Fourier transform.

FFT Fourier transform.

IC Integrated circuit.

IFFT Anti-Fourier transformed.

Q–Q Quantile-quantile.

I. INTRODUCTION

W ITH the rapid progress of microfabrication technology,multilayers interconnect technology and chemical–me-

chanical polishing technology, development trends of integratedcircuit (IC) manufacturing technology are high density, highspeed, high yield, high reliability, and long life. However,defects in IC manufacturing are inevitable, different processescause different kinds of defects. So, how to detect defectsautomatically and accurately in IC is a very complex andchallenging task. Artificial vision inspection is widely usedto detect defects early. However, artificial vision inspectionis difficult to ensure detection accuracy and efficiency. So, itis difficult to realize automatization of the detection process.However, modern measurement and control technology requiredetection and classification of defects automatically. Manypapers investigate the method of defect detection and classifica-tion [1]–[5], some of them have been applied to detect defects

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142 IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 23, NO. 1, FEBRUARY 2010

in IC [6]–[13]. In the following are several typical methodsof defects detection. Based on morphology, [6] presents themethod called Morphological Filtering for defect detection.First, we calculate the difference between the IC image withdefects and the standard image without defects. Then, wedigitize the differential image to two gray levels. The binaryimage is processed by means of mathematical morphology todetect defects. This method requires the standard image to bepresented in advance. Reference [7] proposes the method calleda quantile–quantile plot based on the pattern matching to detectdefects. A pattern-matching image based on the quantile–quan-tile plot (Q–Q plot) is proposed, and the method also needsthe standard image. Reference [8] introduces the directionalmorphological gradient to detect the defects in IC, this methodcan only detect the edge of defects. In order to detect defects,the standard image should be presented. Reference [9] detectsdefects using digital holography, the standard images are alsorequired. References [10]–[12] only can detect the defects ofwell-regulated patterning. The image preprocessing method ofIC wafer inspection is introduced in [13].

From above, it is concluded that traditional methods of de-fect detection need standard image, and defects are detected bycomparing the real image with the standard image. Generallyspeaking, it is very difficult for us to get the standard image.In this paper, the standard image can be extracted quickly fromthe image with defects by the method of defect detection pre-sented. This method can detect the defects accurately, its algo-rithm complexity is close to that of Fourier transform (FFT). De-fects can be detected conveniently after extracting the standardimage. The experiments demonstrate that the method is fast, ac-curate, and practical in detecting IC defects.

II. THEORY OF SPECTRAL SUBTRACTION DETECTING DEFECTS

The spectral subtraction technique is widely used in speechsignal processing and other areas [14]–[19]. Pure speech spec-trum is obtained by noise spectrum subtracted from speechsignal spectrum with noise, which is called spectral subtraction.Based on the same principle, noise spectrum can be obtained bypure speech spectrum subtracted from speech signal spectrumwith noise. Indeed, a lot of methods are introduced to study thenoise removal in image processing [20]–[25]. Unfortunately,nobody has ever used spectral subtraction to investigate thenoise in an image. Similar to the speech detection, an IC imagewith defects is regarded as the speech signal with noise, astandard image is regarded as the pure speech, and defects areregarded as the noise. Defect spectrum is obtained by spectrumof standard image subtracted from spectral of IC image withdefects, and defects are detected by anti-Fourier transform(IFFT) and filtered to the defect spectrum. The spectral subtrac-tion algorithm is close to that of the FFT algorithm. Calculationtime of the defect detection proposed in this paper is alsoclose to that of FFT. Its calculation time is short. It is easy toperform with the hardware. There are one-dimensional Fouriertransforms (1-D FFT) and two-dimensional Fourier transforms(2-D FFT) for image processing. For 1-D FFT and 2-D FFT,it is found that the defect spectrum is almost no difference. In

Fig. 1. Defects in different chips. (a) � . (b) � . (c) � .

order to detect defects more quickly, 1-D FFT is used in thispaper.

Finding the standard image is very important for defect de-tection. In IC manufacturing, there are a lot of the same chips ina wafer. For different chips, the probability of defects existingat the same position is very low. Defects are considered to gen-erate randomly in different chips. As long as a defect in one ofthe three defect images is detected, a standard image can be ob-tained by replacing the pixels located in defects by the pixels lo-cated in the corresponding location of another image. A standardimage can be obtained from three defect images by the methodproposed in the paper. The defects in different chips are shownin Fig. 1. Fig. 1(a)–(c) shows three images with defects , ,and respectively.

White and gray spots represent different defects, which aremarked with circles. These three images contain the spectrumof a standard image. A standard image can be obtained by thefollowing operations:

FFT FFT (1)

FFT FFT (2)

where , , and are three images with defects in IC, FFTis the Fourier transform, represents spectrum subtractedfrom spectrum , represents spectrum subtracted fromspectrum . and can be obtained by (1) and (2), respec-tively. Defects in can be obtained by

IFFT IFFT (3)

where is the defect image in . If is greater than zero,we just keep it. If is less than zero, we make equal tozero. That is the meaning of “ ” in the equation. IFFT repre-sents the anti-Fourier transform. can be obtained by (1)–(3).However, the defects cannot be separated from the image per-fectly because the pixels of defect in are a little greater thanthe pixels of other location in . In order to separate defectsperfectly, we operate the power transform for . The powertransform of is

(4)

where is the maximal value in represents the re-sult after operating the power transform on , each value in

divided by is . Power of each value in is

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, is greater than 1, represents multiplication. Be-cause the value at the defect position is close to , which isgreater than other values in after the power transform, thedefects can be separated perfectly by automatic threshold pro-cessing [26]. Automatic threshold processing is defined as

AVJ (5)

where is the result of automatic threshold processing to ,AVJ represents the operation of automatic threshold processing.We compare defect image with real defect image after auto-matic threshold processing, contains some error points exceptdefects defected. The error points are inevitable, and they can beremoved by the morphological filter on . Therefore, the realdefect image can be obtained. A morphological filter is definedas

DEFECT FILTER (6)

where DEFECT represents the defects detected in , FILTERrepresents morphological filter. After obtaining the defects in

, a standard image can be obtained by replacing the pixelsof the defect located in with the pixels of the correspondingposition in , which is as follows:

(7)

where is the set of defect coordinates in , representsthe gray value of defect in , represents the gray valueof the same position in . The meaning of (7) is thatis replaced by .

A standard image is extracted by (1)–(7), defects in an ICimage can be detected quickly using the standard image. De-tailed operations are as follows. Suppose is an IC image in-cluding defects, is the standard image. Defects in can beobtained by

FFT FFT (8)

IFFT (9)

where is the difference of spectrum subtracted from spec-trum , FFT and IFFT represents the Fourier transform and theanti-Fourier transform, respectively. Defect in is extracted by(8) and (9) and (4)–(6). Figs. 2 and 3 show the flowcharts of thestandard image extraction and the defects detection.

The above defect detection process shows that algorithmcomplexity of the defects detection is close to that of FFT. Itis well known that FFT is widely applied to the engineeringpractice because of its fast operation speed. Therefore, themethod presented in the paper can be used to detect defects inan IC image quickly.

III. SPECTRAL SUBTRACTION DETECTING DEFECTS IN IC

Using the novel method presented in this paper, the standardimage is extracted from three images with defects, which is

Fig. 2. Flowchart of standard image extraction.

Fig. 3. Flowchart of defect detection.

shown in Fig. 4. These images are taken at the same position forthree different chips A, B and C, which is shown in Fig. 4(a).Each small grid represents the chips with the same layout. Im-ages with defects in Fig. 4(b)–(d) come from chips A, B, and C,respectively.

The three images with defects come from the same positionof the three different chips. The irregular shapes in the three im-ages are the defects, which are marked with the circles. Defectsare considered to randomly generate in the different chips. Inthe three defect images, defects do not occur at the same posi-tion. So, the standard image can be extracted and defects can bedetected by the method proposed in the paper.

In order to verify the accuracy and practicability of themethod, the standard image is extracted from three imageswith defects shown in Fig. 4. So, we can detect defects in thewafer using the standard image. Experiment results are shownin Fig. 5.

Fig. 5(a) is the standard image extracted from three imagesin Fig. 4. There is no defect appearing in the image. So, theimage can be regarded as the standard image and can be usedto detect defects in an IC wafer. Fig. 5(b)–(d) shows defectsdetected for three images in Fig. 4(b)–(d). So, the method canextract the standard image from the images with defects anddetect defects in wafer accurately. For the computer Intel E2200,with a memory of 1 G and CPU of 2.22 GHz, the total processingtime is 0.611 s. For the image with the size of 640 480 pixels,

144 IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 23, NO. 1, FEBRUARY 2010

Fig. 4. Images with defects come from chips A, B, and C. (a) Chips A, B, andC with the same layout. (b) Image with defects comes from chip A. (c) Imagewith defects comes from chip B. (d) Image with defects comes from chip C.

Fig. 5. Standard image and defects detected in Fig. 4. (a) Standard image ex-tracted from Fig. 4. (b) Defects detected in Fig. 4(b). (c) Defects detected inFig. 4(c). (d) Defects detected in Fig. 4(d).

the extraction time of standard image is 1.05 s, detection time ofdefects in one chip is 0.62 s. Therefore, defects can be detectedquickly using the standard image. The algorithm complexity ofthe method is close to that of FFT, it takes very short detectingtime and can be widely used in the project.

For the actual defect detection in IC, image gray scale is dif-ferent because of the impact of brightness. Some images arebright and some images are dark, and it is a challenge for de-tecting defects in IC. In order to extract the standard image fromthe images of different brightness and detect defects in imagesof different brightness, one of the three images with defects isregarded as a reference. We match the histogram of two other

Fig. 6. Three images of different brightness. (a) Image with defects.(b) Brighter image with defects. (c) Brightest image with defects.

Fig. 7. Standard image and the defects detected in Fig. 6. (a) Standard imageextracted from Fig. 6. (b) Defects detected in Fig. 6(a). (c) Defects detected inFig. 6(b). (d) Defects detected in Fig. 6(c).

images with that of the reference, and the brightness of the threeimages with defects is unified. So, the standard image can be ex-tracted from three images by the method. Matching the imagesof different brightness with the standard image, defects in dif-ferent brightness images can be detected. Fig. 6(a)–(c) showsthree images with different brightness, respectively. Fig. 6(a)is the image with defects, Fig. 6(b) is a brighter image with de-fects, and Fig. 6(c) is the image with defects under the conditionof strong brightness.

In order to extract the standard image from the above threeimages, Fig. 6(a) is regarded as the reference image. Matchingthe gray scale histogram of Fig. 6(b) and (c) with that ofFig. 6(a), the standard image can be extracted from threeimages of different brightness in Fig. 6.

Fig. 7 shows the standard image and defects detected inFig. 6. Fig. 7(a) shows the standard image extracted fromFig. 6. Fig. 7(b)–(d) shows the defects detected for differentbrightnesses. Results of the defect detection show that themethod can detect defects in IC for different brightness. It

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Fig. 8. Before and after the power transform. (a) � � �, result of the power transform. (b) Before the power transform. (c) After the power transform of 1-D FFT.(d) After the power transform of 2-D FFT. (e) Defects detected in Fig. 6(a) by 1-D FFT. (f) Defects detected in Fig. 6(a) by 2-D FFT.

can solve the impact of illumination condition on the defectdetection perfectly, and it has good robustness for differentilluminations.

Fig. 8 shows the results of the power transform of 1-D FFTand 2-D FFT, respectively. The power transform is used to ex-tract the standard image and detect defects. The power transformcan enhance the pixels of defects and the defects can be easilyseparated by automatic threshold processing.

Fig. 8(a) shows the curve of the power transform. When thevalue of the curve is close to zero, the slope is very small. Whenthe value of the curve is approaching one, the slope is very big.For the value approaching one, it is enlarged after the powertransform. In Fig. 8(b)–(d), defects correspond to bigger grayvalues. Fig. 8(b) shows the defects detected in Fig. 6(a) beforethe power transform. Fig. 8(c) shows the results after the powertransform of 1-D FFT. Compared with Fig. 8(b), pixel values of

146 IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 23, NO. 1, FEBRUARY 2010

defects in Fig. 8(c) are enhanced by the power transform. So,the power transform contributes a lot to the defect separation byautomatic threshold processing.

In order to detect defects rapidly, a 1-D FFT of the imageis used in this paper. One-D FFT of the image is only a ver-tical or horizontal transform, and 2-D FFT requests both verticaland horizontal transforms. The calculation speed of 1-D FFT isfaster than that of 2-D FFT.

Indeed, 2-D FFT does not have more of an advantage than1-D FFT for defect detection. Fig. 8(c) and (d) shows the powertransform of Fig. 6(a) using 1-D FFT and 2-D FFT, respectively.Gray scale of defects is almost the same in Fig. 8(c) and (d).Fig. 8(e) and (f) shows the defects detected in Fig. 6(a) using1-D FFT and 2-D FFT, respectively, and the results of defectdetection are almost the same in Fig. 8(e) and (f). For 1-D FFTand 2-D FFT, results of both the power transform and defectdetection are almost the same. For 1-D FFT, it takes 0.09 s todetect defects using (8) and (9). For 2-D FFT, it takes 0.13 s. So,the speed of defects detection of 1-D FFT is faster than that of2-D FFT. Fig. 8(c)–(f) shows that both 1-D FFT and 2-D FFT fitfor the method presented in the paper, and the defect detectionresults are the same using 1-D FFT and 2-D FFT. In order todetect defects quickly, 1-D FFT is used in this paper.

The filter parameters in Fig. 8(e) and (f) are not the same asthose in Fig. 7(b); the aim of it is to prove different filter pa-rameters can adjust the defects detection sensitivity, requisitedefects are detected, and needless defects are filtered out. Com-paring Fig. 8(e) and (f) with Fig. 7(b), a number of smaller de-fects is detected in Fig. 7(b), a number of big defects is detectedin Fig. 8(e) and (f), and some small defects had been filteredout. These small defects are able to be detected by the methodproposed in the paper. If smaller defects are not required to bedetected, filter parameters can be set to filter out smaller defects.So, the method can detect different sized defects.

In this paper, the defect detection of an IC wafer for in-focusimages is discussed. If the images are out-of-focus images, itwill have an impact on the defect detection in IC. However, ifin-focus images have a little error of one pixel or two pixels,it almost does not impact the accuracy of the defect detectionpresented in the paper.

IV. CONCLUSION

The defect detection of an IC wafer based on spectral subtrac-tion is investigated in the paper, and spectral subtraction is suc-cessfully applied in the image processing. The standard imagecan be extracted from three images with defects, and defectscan be detected quickly by comparing them with the standardimage. The standard image can also be extracted from three im-ages of different illumination conditions. The method fits fordetecting defects of different brightness, and it is robust for illu-mination. The power transform of the defected detection is ana-lyzed. Results of the defect detection for both 1-D FFT and 2-DFFT are compared, and the results are the same for two kinds oftransforms. In order to detect defects quickly, 1-D FFT is used.Different filter parameters can detect defects of different sizes.Theoretical analysis and experimental results demonstrate thatthe method presented in the paper can detect defects of an ICwafer quickly and accurately.

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Hongxia Liu (M’04) was born in December 1968.She received the B.S. degree in physics from North-west University, in 1990, the M.S. degree in electricalengineering from Xi’an Jiaotong University, in 1995,and the Ph.D. degree in microelectronics from XidianUniversity, in 2000.

Her main research interests are the performanceand reliability of nanometer CMOS devices, novelsemiconductor material and devices characterization,and defect detection in IC wafers.

Wen Zhou was born in October 1979. He receivedthe B.S. degree from Xi’an Jiaotong University, in2002, and the M.S. degree from Changchun Univer-sity of Technology, in 2008, both in signal and infor-mation processing. He is pursuing the Ph.D. degreein microelectronics from Xidian University.

His research mainly focuses on the defect detectionand reliability of IC wafers.

Qianwei Kuang was born in August 1983. Hereceived the B.S. degree in electronic engineeringfrom Xi’an University of Technology, in 2004, andthe M.S. degree in microelectronics from XidianUniversity, in 2007. He is pursuing the Ph.D. degreein microelectronics from Xidian University.

His research mainly focuses on growth and char-acterization of high-k gate dielectrics.

Lei Cao was born in January 1983. He received theB.S. and M.S. degrees in microelectronics from Xi-dian University, in 2005 and 2008, respectively. He ispursuing the Ph.D. degree microelectronics from thesame university.

His research area is modeling and optimization ofSOI devices.

Bo Gao was born in July 1984. He received theB.S. and M.S degrees in microelectronics fromXidian University, in 2005 and 2008, respectively.He is pursuing the Ph.D. degree at the School ofMicroelectronics from the same university.

His research concerns the growth of wide band-gapsemiconductor materials.