Patent Publication Number: US-6912304-B1

Title: Two-dimensional scatter plot technique for defect inspection

Description:
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   A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever. 37 CFR 1.71(e). 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   This invention generally relates to digital image processing and, more particularly, to systems and methods for detecting defects in a semiconductor device using image comparison techniques. 
   2. Description of the Related Art 
   Image comparison techniques are used to detect defects in a semiconductor wafer. Typically, a test image is acquired and then compared to a reference image. A defect-detection algorithm is then used to detect variations between the images and to determine whether such variations are real defects. In the so-called random-logic inspection mode, an image of a first die is acquired and then compared to the image of a second die in the same wafer. Array-inspection mode is similarly performed except that a section of a die is compared to another section in the same die having an identical structure. Array-inspection mode is used, for example, in testing devices with repeating structures such as memory cells. In lieu of comparing images from a wafer being tested, defects may also be detected by comparing an acquired test image with a known good image from a database. 
     FIG. 1  illustrates a defect-detection method in the prior art. A test image and a reference image of the wafer feature being analyzed are acquired from different sections of the wafer using, for example, conventional electron-beam imaging techniques (step  110 ). Each image comprises a plurality of pixels, with each pixel being defined by its location within the image and its intensity or gray level. The use of gray levels in image processing is known in the art and is described in R. C. Gonzales and R. E. Woods, “Digital Image Processing,” Addison-Wesley (1992), e.g. pages 6-7, which is incorporated herein by reference in its entirety. The two images are then aligned pixel-by-pixel such that each feature in the test image matches up with the corresponding feature in the reference image (step  120 ). A difference image is then generated by subtracting the gray levels of the two images (step  130 ). Because matching pixels with identical gray levels will be subtracted out, the difference image represents pixel gray level variations between the reference image and the test image. The gray level of each pixel in the difference image is scaled, normalized, and then plotted in a one dimensional histogram such as histogram  200  shown in  FIG. 2  (step  140 ). Histogram  200  plots the number of pixels in the difference image having a specific gray level. For instance, histogram  200  indicates that there are 20,000 pixels in the difference image having a gray level of 50. 
   A pixel from the test image can be different from a corresponding pixel in the reference image even if there are no defects in the two images. Intensity variations can be caused by, for example, differences in the physical layer structures, noise in the image acquisition electronics and signal paths, and varying noise modulation level within a single image across different gray levels. Thus, pixels in the difference image do not necessarily indicate that a defect exists. To differentiate real defects from false or “nuisance” defects, each pixel in the difference image is compared to a threshold window ( FIG. 1 , step  150 ). Pixels with a gray level outside the threshold window are declared defects. For example, if the threshold window is ±50 and a pixel in the difference image has a gray level of 60 (i.e. the gray levels of the test and reference images differ by 60 units), a defect event is declared ( FIG. 1 , step  160 ). The defect event is then verified by an operator to ensure that the die is indeed defective before the die is discarded in subsequent processing. 
   Finding the optimum threshold value for a given test image is an important but imprecise task. The threshold value must be chosen such that real defects are detected while differentiating nuisance defects. The narrower the threshold value, the more nuisance defects will be declared. Nuisance defects adversely affect production throughput because each defect event must be checked and verified. On the other hand, widening the threshold window will reduce nuisance defect events at the expense of letting real defects go undetected. Thus, a method for evaluating the effectiveness of a threshold or thresholding scheme is highly desirable. 
   SUMMARY 
   The invention provides for a method and associated apparatus for relating a test image with a reference image. In an embodiment of the invention, the test and reference images are aligned. A two-dimensional scatter plot is then created by plotting the gray level of a test image pixel against the gray level of a corresponding reference image pixel for each aligned pixel location. The invention is applicable to electron-beam, bright-field, dark-field, laser, and atomic-force microscopy (“AFM”) inspection systems. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  shows a defect detection method in the prior art. 
       FIG. 2  shows a one-dimensional histogram plot of gray levels. 
       FIG. 3  shows the steps of an embodiment of the present invention. 
       FIGS. 4A-4   c  show an alignment step in accordance with the present invention. 
       FIGS. 5A-5B  show a two-dimensional scatter plot in accordance with the present invention. 
       FIGS. 6-7  show a test image and a reference image, respectively, taken from a device wafer. 
       FIGS. 8-9  show a two-dimensional scatter plot in accordance with the present invention. 
   

   DETAILED DESCRIPTION 
   The present invention provides for a method and associated apparatus for relating the pixel of a test image with the corresponding pixel on a reference image. The invention can be used in determining the effectiveness of a threshold or thresholding scheme. The invention is also useful in other image processing applications such as those disclosed by the same inventor in the related co-pending U.S. patent application Ser. No. 09/365,503 filed Aug. 2, 1999, “Adaptive Mask Technique For Defect Inspection,” which is incorporated herein by reference in its entirety. Other uses for the invention are in electron-beam, bright-field, dark-field, laser, and atomic-force microscopy (“AFM”) inspection systems. 
   FIG.  3 . illustrates the steps of an embodiment of the present invention. In step  310 , a test image and a reference image of, for example, semiconductor structures are acquired using conventional image acquisition techniques. The images can also be acquired using the step-and-image acquisition system disclosed in commonly-owned U.S. patent application Ser. No. 09/226,967, “Detection of Defects In Patterned Substrates,” filed Jan. 8, 1999, which is incorporated herein by reference in its entirety. 
   In step  320 , the test and reference images are aligned to match up corresponding pixels between the two images. A variety of alignment techniques can be used with the present invention including the technique disclosed in commonly-owned U.S. patent application Ser. No. 09/227,747, “Feature-Based Defect Detection,” filed Jan. 8, 1999, which is incorporated herein by reference in its entirety. 
   Step  320  is further illustrated in  FIGS. 4A-4C .  FIG. 4A  shows a test image  410  comprising pixels  411 - 416 . Each pixel is defined by its gray level and its location on the image. As an example, pixel  413  is on location i=10 and j=30 (i.e. (10, 30)). The gray level of pixel  413  is 50 for purposes of this illustration. Table 1 provides the coordinate location and gray level for each pixel of test image  410  while Table 2 provides the same information for pixels  421 - 426  of reference image  420  (FIG.  4 B). 
   
     
       
         
             
             
             
           
             
               TABLE 1 
             
             
                 
             
             
               Pixel 
               Location (i, j) 
               Gray Level 
             
             
                 
             
           
          
             
                 
             
          
         
         
             
             
             
          
             
               411 
               (10, 10) 
               100 
             
             
               412 
               (10, 20) 
               150 
             
             
               413 
               (10, 30) 
               50 
             
             
               414 
               (20, 30) 
               180 
             
             
               415 
               (20, 20) 
               200 
             
             
               416 
               (20, 10) 
               250 
             
             
                 
             
          
         
       
     
   
   
     
       
         
             
             
             
           
             
               TABLE 2 
             
             
                 
             
             
               Pixel 
               Location (i, j) 
               Gray Level 
             
             
                 
             
           
          
             
                 
             
          
         
         
             
             
             
          
             
               421 
               (10, 10) 
               100 
             
             
               422 
               (10, 20) 
               150 
             
             
               423 
               (10, 30) 
               50 
             
             
               424 
               (20, 30) 
               150 
             
             
               425 
               (20, 20) 
               100 
             
             
               426 
               (20, 10) 
               0 
             
             
                 
             
          
         
       
     
   
     FIG. 4C  graphically shows the alignment of test image  410  with reference image  420 . Aligned pixel location  431  comprises the pixels  411  and  421 , aligned pixel location  432  comprises the pixels  412  and  422 , and so on. 
   Once the reference and test images are aligned, the pixel-to-pixel correspondence between the test image and the reference image is known. For each aligned pixel location, the gray level of a pixel from the test image is plotted against the gray level of the corresponding pixel in the reference image ( FIG. 3 , step  330 ). Using  FIG. 4C  as an example, the gray level of pixel  411  is plotted against the gray level of pixel  421 , the gray level of pixel  412  is plotted against the gray level of pixel  422 , and so on. Using step  330  for locations  431 - 436  yields the data points shown in Table 3. The resulting two-dimensional scatter plot  500  is shown in FIG.  5 A. 
   
     
       
         
             
             
             
           
             
               TABLE 3 
             
             
                 
             
             
                 
               Test Image 
               Reference Image 
             
             
               Location 
               Gray Level 
               Gray Level 
             
             
                 
             
           
          
             
                 
             
          
         
         
             
             
             
          
             
               431 
               100 
               100 
             
             
               432 
               150 
               150 
             
             
               433 
               50 
               50 
             
             
               434 
               180 
               150 
             
             
               435 
               200 
               100 
             
             
               436 
               250 
               0 
             
             
                 
             
          
         
       
     
   
   Table 3 shows that locations  434 ,  435 , and  436  have varying gray levels and, thus, indicate the presence of possible defects. Locations  431 ,  432 , and  433  are free of defects because the test image and the reference image have the same gray levels in said location. Scatter plot  500  ( FIG. 5A ) provides information as to the presence of possible defects. All aligned pixel locations with the same gray levels can be represented in scatter plot  500  by an imaginary line  501  (FIG.  5 A). The slope of imaginary line  501  is +1 because it represents the aligned pixel locations wherein the gray level of the test image pixel is the same as the gray level of the corresponding pixel in the reference image. All aligned pixel locations with varying gray level values will lie away from imaginary line  501 . The further a location is plotted away from line  501 , the greater the deviation in gray levels, and the higher the chance that a defect exists in that location. In scatter plot  500 , locations  434 ,  435 , and  436  are not on imaginary line  501  and indicate the presence of possible defects. 
   Scatter plot  500  may be used to evaluate the effectiveness of a threshold or thresholding scheme. For example, a threshold window of ±40 gray level units may be plotted and superimposed on scatter plot  500  as shown by lines  502  and  503  in FIG.  5 B. Line  502  represents all aligned pixel locations wherein the gray level of the test image is greater than the gray level of the reference image by 40 units. Similarly, line  503  represents aligned pixel locations wherein the gray level of the reference image is greater than that of the test image by 40 units. Aligned pixel locations outside lines  502  and  503 , such as locations  435  and  436 , will be declared as defect events. In  FIG. 5B , locations  431 ,  432 ,  433 , and  434  will not trigger a defect event because said locations are within the threshold window. Different threshold windows can be plotted and superimposed on scatter plot  500  to determine which aligned pixel locations will be “captured” and declared as a defect event. Threshold windows may be generated using equations for shapes other than parallel lines. This capability to visualize the extent of a threshold window is particularly useful to the skilled artisan in determining an appropriate threshold during test development. 
   A pseudo code for implementing an embodiment of the invention in computer software is shown below. In the pseudo code, the gray level values are plotted in a memory array variable (“Scatter”). Appendix A lists the source code of a function written in the C programming language. On page 2 of Appendix A, “hist2D8” creates a two-dimensional scatter plot in accordance with the present invention. The code would be executed by a computer or processor which is conventionally coupled to or a part of a defect inspection system. Of course, such a system would typically store this source code and the resulting plots in a computer-readable medium (memory). 
   
     
       
         
             
             
           
             
                 
                 
             
           
          
             
                 
               /* PSEUDO CODE FOR CREATING A 2D SCATTER PLOT */ 
             
             
                 
               Acquire Reference Image; 
             
             
                 
               Acquire Test Image; 
             
             
                 
               Align Test Image to Reference Image; 
             
             
                 
               Create a 256 × 256 Image named Scatter; 
             
             
                 
               Initialize Scatter to 0; 
             
             
                 
               Do for i = 1 to NumRows 
             
             
                 
               { 
             
          
         
         
             
             
          
             
                 
               Do for j = 1 to NumCols 
             
             
                 
               { 
             
          
         
         
             
             
          
             
                 
               p1 = Reference(i,j); 
             
             
                 
               p2 = Test(i,j); 
             
             
                 
               Scatter(p2,p1) = 1; 
             
          
         
         
             
             
          
             
                 
               } 
             
          
         
         
             
             
          
             
                 
               } 
             
             
                 
               Plot Scatter as an Image; 
             
             
                 
               /* END OF PSEUDO CODE */ 
             
             
                 
                 
             
          
         
       
     
   
     FIGS. 6-9  pictorially summarize an embodiment of the present invention.  FIG. 6  shows a test image  600  acquired conventionally from a wafer having a defect  601 . A reference image  700  ( FIG. 7 ) is similarly acquired and then aligned (not shown) with test image  600 . Two-dimensional scatter plot  800  is generated by plotting the gray level of the test image pixel against the gray level of the corresponding reference image pixel for each aligned location (FIG.  8 ). The scatter plot may be generated manually or by using a programmed computer. Aligned pixel locations are plotted as white dots in a dark background. In  FIG. 8 , line  801  defines the aligned pixel locations wherein the gray level of the test and reference image pixels are identical. For example, if test image  600  was identical to reference image  700 , all points in scatter plot  800  would lie on line  801 . To determine the extent of a threshold, the equation or parameters defining the threshold are plotted and shown in  FIG. 9  as lines  901  and  902 . Points outside lines  901  and  902  will be declared as defect events. 
   It is to be understood that the description given above is for purposes of illustration and is not intended to be limiting. Numerous variations are possible without deviating from the scope and spirit of the invention. The invention is set forth in the following claims.