Patent Publication Number: US-10330608-B2

Title: Systems and methods for wafer surface feature detection, classification and quantification with wafer geometry metrology tools

Description:
TECHNICAL FIELD 
     The disclosure generally relates to the field of wafer surface metrology, and particularly to systems and methods for wafer surface feature detection, classification and quantification with wafer geometry metrology tools. 
     BACKGROUND 
     Thin polished plates such as silicon wafers and the like are a very important part of modern technology. A wafer, for instance, may refer to a thin slice of semiconductor material used in the fabrication of integrated circuits and other devices. Other examples of thin polished plates may include magnetic disc substrates, gauge blocks and the like. While the technique described here refers mainly to wafers, it is to be understood that the technique also is applicable to other types of polished plates as well. The term wafer and the term thin polished plate may be used interchangeably in the present disclosure. 
     Generally, certain requirements may be established for the flatness and thickness uniformity of the wafers. There exist a variety of techniques to address the measurement of shape and thickness variation of wafers. However, most existing wafer inspection tools can only inspect the wafer surface and detect the surface defects. Some wafer surface inspection tools may also calculate the defect areas and classify the defect types, but there is no information reported about the defect height or depth, and therefore there is no defect volume information provided by the existing inspection tools. 
     Therein lies a need for systems and methods for wafer surface feature detection, classification and quantification wherein the detected defects are classified and the important defect metrology information of height/depth, area and volume is reported, providing more values for quantifying the negative effect of these defects on the wafer quality. 
     SUMMARY 
     The present disclosure is directed to method for inspecting a wafer. The method may include setting up a data acquisition and a data processing recipe; acquiring a wafer surface image; filtering the wafer surface image to improve signal to background contrast; performing wafer edge treatment to suppress strong filter response; performing defect detection and classification based on the filtered wafer surface image; calculating at least one of: a height, a depth, an area and a volume of the defect utilizing surface fitting; and reporting the at least one of: a height, a depth, an area and a volume of the defect detected and classified. 
     A further embodiment of the present disclosure is directed to a method for inspecting patterned or filmed wafers. The method may include various data processing steps for a patterned wafer surface. Such steps may include correcting wafer XY distortions to obtain uniform patterns; generating a reference wafer and aligning the wafer under operation to the reference wafer; or performing wafer-to-wafer operations to suppress the pattern signal and produce residue wafer surface images. Similarly, the method may include various data processing steps for a filmed wafer surface. Such steps may include performing film response calibration and compensation for the filmed wafer surface to reduce signal variations from different film materials and film structures. Upon completion of such data processing steps, subsequent inspecting steps may include filtering the wafer surface image to improve signal to background contrast; performing defect detection and classification based on the filtered wafer surface image; calculating at least one of: a height, a depth, an area and a volume of the defect utilizing surface fitting; and reporting the at least one of: a height, a depth, an area and a volume of the defect detected and classified. 
     An additional embodiment of the present disclosure is directed to system for inspecting a wafer. The system may include an optical system configured for acquiring a wafer surface image. The system may also include a wafer surface feature detection, classification and quantification module. The wafer surface feature detection, classification and quantification module may be configured for: filtering the wafer surface image to improve signal to background contrast; performing defect detection and classification based on the filtered wafer surface image; calculating at least one of: a height, a depth, an area and a volume of the defect utilizing surface fitting; and reporting the at least one of: a height, a depth, an area and a volume of the defect detected and classified. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not necessarily restrictive of the present disclosure. The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate subject matter of the disclosure. Together, the descriptions and the drawings serve to explain the principles of the disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The numerous advantages of the disclosure may be better understood by those skilled in the art by reference to the accompanying figures in which: 
         FIG. 1  is a flow diagram illustrating a method for detection, classification and quantification of bare wafer surface defects; 
         FIG. 2  is a flow diagram illustrating a method for detection, classification and quantification of patterned wafer surface defects; 
         FIG. 3  illustrates exemplary mapping images for a wafer edge treatment process; 
         FIG. 4  illustrates an exemplary image containing detected EPI crowns; 
         FIG. 5  illustrates two-dimensional radius-size histograms generated based on the radius positions and the sizes in pixels of the detected EPI crowns; 
         FIG. 6  illustrates projections of the angular positions of the defect pixels in the wafer edge region; 
         FIG. 7  is a flow diagram illustrating a method for scratch detection and classification process; 
         FIGS. 8 and 9  illustrate an example of scratch structure enhancement in accordance with the present disclosure; 
         FIG. 10  illustrates partitioning a wafer surface for slipline structure enhancement; 
         FIG. 11  illustrates an example of slipline structure enhancement in accordance with the present disclosure; 
         FIG. 12  illustrates two exemplary non-linear shaped slipline defects; 
         FIG. 13  illustrates two object histogram of oriented gradient plots for two defect objects; 
         FIG. 14  illustrates the detected slipline defects of  FIG. 12 ; 
         FIG. 15  illustrates various types of image areas defined for performing surface fitting; 
         FIG. 16  illustrates a surface fitting testing result performed with the defect pixels included compared against a surface fitting testing result performed without the defect pixels; 
         FIG. 17  illustrates areas in the scanning sequence for an exemplary long scratch; 
         FIG. 18  illustrates utilizing defect height information for eliminating weak defects; and 
         FIG. 19  illustrates the ability of the system and method in accordance with the present disclosure to provide volume information in addition to the defect height and area information. 
     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made in detail to the subject matter disclosed, which is illustrated in the accompanying drawings. 
     Currently, certain wafer geometry metrology tools are capable of measuring the surface height of a wafer and providing nanotopography of the wafer. Nanotopography is defined as the deviation of a surface within a spatial wavelength of around 0.2 to 20 mm. Nanotopography bridges the gap between roughness and flatness in the topology map of wafer surface irregularities in spatial frequency. Since the flatness properties of incoming 200- and 300-mm wafers undergo only minor changes during wafer processing, precise and comprehensive measurement capabilities are necessary to detect minute variations in topography on the final wafer surface. 
     Wafer metrology tools and interferometer systems, such as WaferSight metrology system from KLA-Tencor, may scan both the front and back surfaces of a wafer at the same time. By combining wafer shape, edge roll-off, thickness or flatness, and nanotopography measurements in a single scan, such wafer metrology tools may provide complete data sets that are necessary for nanotopography and wafer geometry monitoring in wafer manufacturing. 
     The present disclosure is directed to systems and methods for providing micro defect inspection capabilities for optical systems such as wafer metrology tools and interferometer systems. The systems and methods in accordance with the present disclosure may detect, classify and quantify wafer surface features, wherein the detected defects are classified and the important defect metrology information of height/depth, area and volume is reported. The systems and methods in accordance with the present disclosure therefore provide more values for quantifying the negative effect of these defects on the wafer quality. 
       FIG. 1  shows a flow diagram illustrating major steps performed by a method  100  for detection, classification and quantification of bare wafer surface defects in accordance to the present disclosure. In step  102 , the data acquisition and the data processing recipe is set up. In step  104 , the wafer surface images (e.g., the front and back surface images) are acquired using an optical system such as WaferSight. In step  106 , the surface images are filtered using specially designed filters according to the features of interest to improve the feature signal to background contrast, and the wafer edge treatment is performed to suppress the strong filter response from the sharp wafer edge roll-off or from the data discontinuity created by the wafer edge exclusion. 
     Various types of filters may be utilized in step  106 . For instance, filters such as a double Gaussian high-pass filter, a Laplace band-pass filter, a Sobel line filter or the like may be applied on the surface image maps acquired in step  104 . These filters may remove the long wavelength shape components in the original wafer surface images and thus boost the defect feature signal to the background contrast of the wafer surface images. However, these filters may have strong response in the wafer edge region due to the sharp wafer edge roll-off or the data discontinuity created by the wafer edge exclusion operation. The strong edge response may affect the detection capability of defect features in the wafer edge region, such as edge EPI crowns and sliplines. 
     To suppress the strong filter response from the wafer edge region or from the data discontinuity created by the edge exclusion, the following edge treatment operations may be performed:
         a) Convert the wafer edge region into an image band in polar space. The band height direction is the radial direction and the size in this direction is determined by the filter kernel size and the wafer roll-off profile sharpness. The band width direction is the tangential direction and the size in this direction is determined by the sampling rate in the angular direction.   b) Perform the one-dimensional median filtering on this band image along the tangential direction row by row. The filter length is selected to be able to follow the trend of the edge profile variations in the angular direction and preserve the interested edge feature in the edge treatment. Currently, the filter length is defaulted to cover a five-degree data span. It can be adjusted according to the feature angular property for the optimal performance.   c) The filtered image is subtracted from the original image to obtain the edge response suppressed image. One segment of the original edge image, the filtered edge image and the edge artifact reduced image are shown in  FIG. 3  for illustrative purposes.   d) Since the edge region usually has more noisy signals than the wafer interior region, to reduce the noise components in the edge region while preserving the feature signal, the following polarity trimmed mean may be performed on the edge-treated image in the very edge region, where invalid pixels will exist due to the measurement capability limit of the metrology system. That is, for the given pixel I(x,y) from the median filter edge treatment in step c), the trimmed output signal O(x,y) will be calculated as defined in:       

     
       
         
           
             
               
                 
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                 Where, A +  and A −  are the positive and negative pixel sets inside the filter window, N +  and N −  are the numbers of the positive and negative pixels, respectively. In other words, if I(x,y)&gt;0, then take the average of the positive pixels in the specified filter window; otherwise, if I(x,y)&lt;0, take the average of the negative pixels in the specified filter window. 
               
             
           
         
       
    
     It is contemplated that this polarity trimmed mean will effectively reduce the edge noise components and preserve the signal contrast of many bipolar defect signals from EPI crowns and sliplines. This helps to obtain the improved performance for defect detection and classification in the wafer edge regions. It is also contemplated, however, that the various types of filters and the filter response suppression techniques described above are exemplary. Other types of filters and noise reduction techniques may also be utilized in step  106  without departing from the spirit and scope of the present disclosure. 
     Subsequently, the defect detection and classification steps in accordance with the present disclosure may be performed to produce defect maps, composed of various defect groups and defect positions. Useful defect properties may be calculated according to these defect types and the defect positions, and may then be used to define the positions, size and shape of the measurement areas on the wafer surfaces. From these measurement areas, the accurate defect height/depth, area and volume may be calculated and reported to provide valuable information for wafer production. 
     For instance, step  108  may perform the feature detection and classification from the filtered image maps using various feature properties to obtain the specified feature groups of interest, such as dimples/pits, wafer edge EPI crowns, scratches, sliplines and the like. The term dimple/pit may refer to a surface depression; edge EPI crowns may refer to the difference between the surface elevation from the edge of the slice (associated with epi layer deposition); scratch may refer to a shallow groove or cut below the established plane of the surface; and slipline may refer to a process of plastic deformation in which one part of a crystal undergoes a shear displacement relative to another in a manner that preserves the crystallinity of each part of the material. Step  110  may measure the feature height, depth, area and volume using the robust surface fitting on the original surface image areas accurately defined by detected feature pixel positions, and the detection, classification and quantification results may be reported in step  112 . 
     It is contemplated that while method  100  may be applied to bare wafer surface defects detection, classification and quantification, patterned wafer surface defects may need to be handled differently.  FIG. 2  shows a flow diagram illustrating major steps performed by a method  200  for detection, classification and quantification of patterned wafer surface defects in accordance to the present disclosure. Similar to steps  102  and  104  described above, steps  202  and  204  may set up the data acquisition and the data processing recipe of the optical system (e.g., WaferSight) and acquire the front and back surface image data of the wafer. After that, however, many steps of the data processing common in the patterned wafer inspection may be performed in step  206 . 
     Some operations performed in step  206  for the patterned wafer applications may include, for example: correcting the wafer XY distortions according to the calibrated system XY pattern so that the wafer surface image will have uniform patterns; generating the reference die and/or reference wafers from the neighboring dies or previously acquired wafer image data; aligning the die under operation to the reference die or align the wafer under operation to the reference wafer; and/or performing the die-to-die or wafer-to-wafer operations to suppress the pattern signal and produce the residue wafer surface images. It is contemplated that such operations specially required for the patterned wafer may be carried out only on the front wafer surface where the films and chip patterns are manufactured on. For the back wafer surface, most of the method steps for the bare wafer may be utilized directly or with some small modifications to cover the special properties introduced by the patterning on the front wafer surface. 
     After the residue wafer surface images are generated, the similar data processing procedures described in the system and methods for bare wafer inspection may be utilized. That is, step  208  may filter the residue surface images using specially designed filters according to the features of interest to improve the feature signal to background contrast. Step  210  may perform the feature detection and classification from the filtered image maps using various feature properties to obtain the specified feature groups of interest, such as dimple/pit, wafer edge EPI crowns, scratch, slipline and the like. Step  212  may measure the feature height, depth, area and volume using the robust surface fitting on the original surface image areas accurately defined by detected feature pixel positions, and the detection, classification and quantification results may be reported in step  214 . 
     Steps  108  and  110  (and steps  210  and  212 ) may be jointly referred to as the detection, classification and quantification steps. They will now be described in detail for various features of interest, such as detection and classification of wafer edge EPI crowns, detection and classification of scratches, detection and classification of slipline, as well as defect quantification by adaptive robust surface fitting. 
     In one embodiment, step  108  (and step  210 ) may be configured for detection and classification of wafer edge EPI crowns. Wafer edge EPI crowns are defined as periodic bumps or dimples that occur in a circular pattern with a specific spatial frequency. These EPI crowns are typically located at a fixed distance from the wafer edge. A surface image of the wafer obtained using a metrology tool may be processed (e.g., as described in step  106  for a bare wafer or steps  206  and  208  for a patterned wafer) to detect such wafer edge EPI crowns and the statistics of their metric values.  FIG. 4  depicts an exemplary image containing the detected EPI crowns. 
     The locations and the metric values of the detected EPI crowns may be utilized for reliable detection and classification of defects. For instance, the detection and classification process may first form a two-dimensional radius-size histogram (shown in  FIG. 5 ) based on the radius positions and the sizes in pixels of the detected EPI crowns. The detection and classification process may then smooth the histogram utilizing any histogram smoothing technique, and the peak position of the smoothed histogram may indicate the estimated EPI crown radius position and their most plausible size. For the exemplary image of  FIG. 4 , the estimated radius of these EPI crowns is 147.9 mm and the estimated defect size is 45 pixels for one particular image resolution setting. 
     The detection and classification process may then estimate the angular separation of the EPI crowns. In one embodiment, as shown in  FIG. 6 , the angular positions of the defect pixels in the wafer edge region are projected onto the angular axis and the histogram of the angular separations between the neighboring defects is calculated. As shown in  FIG. 6 , although there are missing data segments from three wafer gripper regions and the wafer notch region in the signal projection (such regions are indicated in  FIG. 4  as well), this process can still produce a very good estimate for the angular separation of these EPI crown defects. In this particular example, the estimated angular separation between the EPI crowns is 1.6 degree. 
     Subsequently, the detection and classification process may utilize the estimated defect radius R, defect size S and defect separation T in the classification to sift the candidate defects. For instance, if the radius, size and separation values of the defects have bigger distances from these estimated reference values than three specified thresholds for them, they will not be considered as EPI crowns. Since the estimated angular separation provides the period information about the EPI crown signal, it can also be used to enhance the EPI crown signal in the frequency domain for improved performance. 
     In addition to detection and classification of wafer edge EPI crowns, step  108  (and step  210 ) may also be configured for detection and classification of scratches. As illustrated in the flow diagram in  FIG. 7 , the major processing steps of the scratch detection and classification process are shown. In one embodiment, upon receiving the acquired wafer surface images, step  702  may perform Laplace filtering on the wafer surface images to remove the low frequency surface shape components. Subsequently, a simple intensity threshold or a background adaptive threshold map is used to obtain the initial defect map represented in binary format. For many faint surface scratches with depth less than 2 nm, the scratch signal from the metrology tool may often appear as broken points along the scratch and cannot be reliably separated from other surface features with small extents, making the accurate detection and classification of scratch very difficult. Utilizing this line enhancement technique in accordance with the present disclosure, these broken scratch data points can be effectively connected and other small feature structures can be removed. 
     In one embodiment, step  704  may process the input defect map using the filter bank in parallel. First, the input defect map is rotated about the wafer center with different angles which equally span the 180 degrees. Then the one dimensional median filtering is performed on the rotated image in the image row direction and the data processing is carried for each image out row by row. In this manner, the neighboring data required in the filtering will be in the cache and the fast processing speed can be achieved. Subsequently, the outputs of these oriented filters will be selected using the maximum rule for each pixel position in step  706 . All these operations may be implemented using the Intel Integrated Performance Primitive (IPP) library and the data processing may be performed on the binary image, not on the integer or float type images of the original surface images or the filtered surface images. As a result, the scratch signal enhancement process in accordance with the present disclosure can achieve good scratch enhancement and throughput performance. 
     Coming out from this scratch enhancement process, all gaps shorter than the half of median filter length along the scratch will be bridged and all other features shorter than half of median filter length will be removed. One example of the scratch structure enhancement is shown in  FIG. 8 , where  FIG. 8A  is the initial defect map obtained and there are many broken segments from the scratch and other isolated defects.  FIG. 8B  shows the enhanced defect map. The zoomed-in scratch part is shown in  FIG. 9 . It is clear that the broken scratch segments are well connected and the isolated defect points are effectively removed. Therefore, the scratch enhancement process effectively improves the reliability and accuracy for detection, classification and quantification of scratches. 
     Furthermore, step  108  (and step  210 ) may also be configured for detection and classification of sliplines. Sliplines are structural flaws that occur along the crystallographic planes of the silicon lattice. Such features may be common in two distinct regions: near the edge of the wafer and in the location where process chamber pins support the wafer. The techniques for effective slipline detection and classification in accordance with the present disclosure are designed to improve the feature definition and minimize the damage to the slipline signal by enhancing the line structures differently in the different wafer regions to cover two slipline use cases. 
     It has been observed that the slipline orientation depends on the wafer crystal orientation and the edge slipline orientation strongly depends on the sectors where the crystal structure strength is weaker. Wafer manufactures use the wafer notch and flat to indicate the wafer crystal structure orientation, and the method for detection and classification of sliplines may utilize such wafer properties to define the different line enhancement regions. 
     For instance, the slipline detection and classification process may partition the wafer surface to different regions for the slipline structure enhancement, as shown in  FIG. 10 . More specifically,  FIG. 10  depicts an exemplary 300 mm wafer and the wafer surface crystal orientation is indicated in a pattern described by the Burgers vector. The slipline detection and classification process may perform the line enhancement techniques described above in  FIG. 7  for each region. For instance, in the V regions, the line enhancement using the one-dimensional median filter may be carried out only in vertical direction, and in the H regions, the line enhancement using the one-dimensional median filter may be carried out only in horizontal direction. In the H&amp;V region, both vertical and horizontal enhancement filtering may be performed, which is a special case of the line enhancement described above in  FIG. 7 . With this data processing plan, the edge sliplines are smoothed and connected without introducing the crossing between them, which will damage the resolution of these short edge sliplines. 
     One example of the slipline enhancement by the process described above is shown in  FIG. 11 . The differences between the original slipline defect map (left) and the processed slipline defect map (right) demonstrate the effectiveness of line enhancement and noise removal. 
     It is contemplated that, in addition to the enhancement process described above, more complex partition and weighting transition schemes may be used for improved performance at the cost of more required computation. For the wafers with other crystal orientations, the same principles may be utilized to partition the wafer surface into different regions and apply the line filters in different orientation in these regions for the most effective slipline enhancement. 
     It is also contemplated that in the acquired wafer images, the sliplines may have different shapes from the ideal line shapes as shown in the left side image of  FIG. 12 . In this example, the slipline structures are connected to span a large region. Furthermore, in some other cases, several sliplines are merged together to form one defect object and do not resemble a line shaped object anymore as shown in the right side image of  FIG. 12 . The cases like these make the accurate classification of sliplines very difficult when only using the standard line definitions, such as the length/width ratio of the bounding box. 
     Therefore, to more effectively handle the complicated slipline cases, a new method for identifying slipline features is proposed. This new method extends from the histogram of oriented gradients (HOG) used for image recognition, where the image is partitioned into the areas of a regular rectangular grid and then the histogram of the oriented gradients of each image region is calculated to form a feature vector. 
     When applied to slipline detection and classification, instead of calculating HOG for the regular image areas, the HOG of each binary defect object is calculated. This method may therefore be referred to as OHOG for Object Histogram of Oriented Gradient. Different from the conventional image HOG, where all pixels in the image region make the contribution to the calculated HOG, OHOG gets the contributions only from the boundary pixels of the defect objects, since the interior pixels of the binary defect areas have zero difference. Therefore, the new method has high sensitivity to the shape and orientation of the defect objects and can be used to help identify the slipline defects. 
       FIG. 13  illustrates two OHOG plots for two defect objects. The solid lines are for a vertical slipline and the dashed lines are for a non-slipline defect. In this example, sixteen bins of angles have been used to provide enough feature angular resolution in the OHOG. It can be seen that the vertical slipline has a much stronger histogram peak at 0 degree gradient orientation, while other defect object has very similar peak distributions in different orientations. This information is very important to obtain the correct classification for the cases similar to the slipline defect structures as shown in  FIG. 12 . Utilizing OHOG in accordance with the present disclosure allows the two exemplary slipline defects of  FIG. 12  to be detected and classified correctly, as indicated in  FIG. 14 . 
     In addition to detection and classification of wafer defects, bumps, dimples, EPI crowns, scratches and sliplines as described above, method  100  and  200  in accordance with the present disclosure may also be utilized for the reliable detection and classification of many other types of surface defects, which have the measurement values deviated from the local image surface and have enough defect feature signal to background noise ratio. These defects may have different shapes and polarities, and may be located anywhere on the wafer surface. For patterned wafers, the defect and background signals are defined on the image map after pattern removal by techniques such wafer-to-wafer or die-to-die image subtraction. In such cases, in addition to the defects described above, many pattern defects such as missing or extra pattern structures can also be detected and classified. 
     It is contemplated that the method  100  and  200  in accordance with the present disclosure may also be utilized for detect quantification by adaptive robust surface fitting. That is, in addition to detecting the defect area, accurate information regarding defect height/depth and defect volume can also be calculated in step  110  (and step  212 ) using the adaptive robust surface fitting method. The ability to calculate accurate height/depth and defect volume information utilizing the method in accordance with the present disclosure provides much more useful defect information for the process control in wafer and chip manufacturing compared to conventional detection methods. 
     Since the defects on the wafer surface have been identified in the detection stage (i.e., in step  108  or  210 , respectively), many useful defect geometry properties can be calculated from their positions, such as the mass center O(x 0 ,y 0 ), the maximum distance R d,max  of the defect pixels to its mass center, percentage of the defect area to the minimum bounding box area and the like. Such defect geometry properties may then be used to define the position, shape and size of the image area in the original surface image maps for accurate defect quantification. 
     For example, from the defect mass center O(x 0 ,y 0 ) and the maximum center-to-boundary distance R d,max , a rectangular image area can be defined to center at O(x 0 ,y 0 ) and with the area side length L=K×R d,max , where K(&gt;2) is an area scaling constant so that the defect will be fully contained inside of this rectangular image area and there are enough non-defect image pixels for the estimate of the reference surface.  FIG. 15A  depicts an exemplary rectangular image area  1502  that contains defect  1504 . In addition to rectangular image areas, disk shaped image areas may also be used. In this case, the disk center is aligned with the defect mass center O(x 0 ,y 0 ) and the disk radius is larger than 2×R d,max .  FIGS. 15B and 15C  depict such disk shaped image areas  1506  and  1510  for containing defects  1508  and  1512 , respectively. 
     It is contemplated that the rectangular and disk shaped image areas described above are exemplary. Image areas of various different shapes may also be utilized without departing from the spirit and scope of the present disclosure. Furthermore, if the defect shape is not very solid, whose area is a small percentage of the area defined by the minimum bounding box, then a tighter image area may be used since enough non-defect image pixels can still provide a good estimate for the reference surface. It is also contemplated that for a long extent defect, such as a long scratch  1516  as illustrated in  FIG. 15D , the measurement may be carried out in a scanning mode, with a measurement window  1514  moving along the scratch trace automatically guided by the defect pixel positions. 
     After the image area is defined, the surface fitting with proper polynomial orders, which are determined by the defect type and the area for the surface fitting, is performed on this image area of the original surface image with the pixels in the detected defect positions excluded in the fitting process. Then the estimated defect surface profile D(x,y), i.e., the shape corrected surface image, can be calculated from the original surface image I(x,y) and the fitted surface image F(x,y) according to the equation: D(x,y)=I(x,y)−F(x,y). Subsequently, the defect maximum height value and the maximum depth value can be found from the pixel values of D(x,y) on the detected defect pixel positions. 
     It is contemplated that any surface fitting algorithms may be utilized without departing from the scope and spirit of the present disclosure. However, it is very important to exclude the defect pixels in the surface fitting in order to obtain more accurate defect quantification. When fitting with the defect pixels included, the calculated area surface will be biased by the defects, especially when the defect has high magnitude and large area. This has been observed in various testing samples, including the one demonstrated in  FIG. 16 . In this example, a Gaussian shaped defect with 10 nm height is modeled. When the defect pixels are used in the surface fitting, the estimated defect height is 4.3 nm. When the defect pixels are excluded in the surface fitting, the estimated defect height is 6.3 nm, closer to the accurate defect height value. 
     As previously mentioned, for long extent defects, such as a long scratch  1516  as illustrated in  FIG. 15D , the measurement may be carried out in a scanning mode, with a measurement window  1514  moving along the scratch trace automatically guided by the defect pixel positions. In this scanning mode, a sequence of “focal” image areas covering the long scratch is defined and the surface fittings over these areas are performed. The required defect height and depth values from each area are calculated and then aggregated to form the maximum height and depth values of the complete scratch according to equation: 
               P   complete     =       max   i     ⁢     [       P   1     ,     P   2     ,   …   ⁢           ,       P     i   ,           ⁢     .           .           .     ⁢           ,       ⁢     P   n         ]                     V   complete     =       min   i     ⁢     [       V   1     ,     V   2     ,   …   ⁢           ,       V     i   ,           ⁢     .           .           .     ⁢           ,       ⁢     V   n         ]             
where P i  and V i  are the peak and valley values calculated from i th  window and there are a total n measurement windows in the scanning trace. Other information for the complete scratch can be obtained similarly.
 
     Some areas in the scanning sequence for an exemplary long scratch are shown in  FIG. 17 . When performing the surface fitting for the long scratch, unlike the compact defect such as dimple and EPI crowns where the defect pixel positions will not touch the area boundary, the defect pixel positions will cross the area boundary (as depicted in  FIG. 15D ). However, since the scratch usually only occupies a small part of the image area, there are still enough non-defect pixels for the accurate reference surface estimate, even if all defect pixels are masked off in the surface fitting, providing accurate maximum scratch depth calculation. 
     As previously mentioned, the ability to measure the feature height, depth, area and volume using the robust surface fitting on the original surface image areas in step  110  (and step  212 ) allows method  100  (and method  200 ) to provide valuable information, including defect volume information, for wafer production. 
     While the examples above illustrate utilizing the system and method in accordance with the present disclosure for surface defect detection, classification and quantification of bare wafers and patterned wafers, it is contemplated that the system and method in accordance with the present disclosure are also applicable for the defect detection in filmed wafer applications. Similar to the handling of patterned wafers, certain additional data processing stages, such as film response calibration and compensation, may be performed to reduce the signal variation from different film materials and film structures so that the processed signals can better represent the wafer surface height information. Subsequently, the detection, classification and quantification steps as described above may be carried out for such filmed wafers. 
     Furthermore, while method  100  (and method  200 ) in accordance with the present disclosure may be utilized with most optical systems (e.g., wafer geometry metrology tools and interferometer systems), it is contemplated that such techniques may provide improved accuracies when utilized with certain interferometer systems that are capable of providing accurate wafer surface height information. For instance, wafer dimensional geometry tools, such as the WaferSight metrology tool, can provide wafer surface height information with accuracy in nanometers and thus can provide very accurate results in inspection and classification. 
     Since the measurements from such wafer dimensional geometry tools provide information about defect polarities, such data can be utilized to identify a defect as protrusion, such as a bump, or intrusion, such as a pit. Combining such data with the defect height profile and area information, the shape of the defects in 3D may be defined and the defect volume information may be calculated. The height, volume and 3D shape information of defects are very helpful in the defect classification and reduction of the irrelevant or false defects in the wafer inspection and classification. It helps defining lower thresholds to achieve more sensitive detection of the defects of interests, without generating unmanageable false or irrelevant defects. 
     For example, since the defect height information is available, it can be utilized to remove irrelevant defects and improve the detection purity level. As shown in  FIG. 18 , using the defect height/depth magnitude information, several weak defects such as  18 E,  18 G,  18 L,  18 M and  18 N may be eliminated from the final reporting. In addition, the defect signal polarity obtained from the quantification can also be helpful to classify the defects. For example, the scratch is a structure into the wafer surface and therefore the negative height value will be reported to improve the scratch defect classification accuracy. 
     Another unique capability provided by the WaferSight (other wafer dimensional geometry tools) based inspection, classification and quantification system is that it can provide valuable defect volume information. From the calculated defect height surface with the adaptive robust surface fitting, the volumes of the detected defects can be calculated by integrating the height values over the defect area defined by the defect positions. The integration can use the absolute defect height values for the volume constructed by the defect surface with the reference surface. Alternatively, the defect volumes can be calculated separately from the positive defect pixels and the negative pixels to get two components. As shown in  FIG. 19 , the defect volume information can describe the defect in one more important dimension, in addition to the defect height and area information. For example, in integrated circuit manufacturing, how much material is missing or extra from the defects may be of a particular concern. The two defects illustrated in  FIG. 19  may have the same heights, the same areas but very different volumes. This volume information may indicate how much material is missing or extra, and is also useful for defect type classification. 
     It is contemplated that while the examples above referred to wafer inspections, the systems and methods in accordance with the present disclosure are applicable to other types of polished plates as well without departing from the spirit and scope of the present disclosure. The term wafer used in the present disclosure may include a thin slice of semiconductor material used in the fabrication of integrated circuits and other devices, as well as other thin polished plates such as magnetic disc substrates, gauge blocks and the like. 
     The methods disclosed may be implemented as sets of instructions, through a single production device, and/or through multiple production devices. Further, it is understood that the specific order or hierarchy of steps in the methods disclosed are examples of exemplary approaches. Based upon design preferences, it is understood that the specific order or hierarchy of steps in the method can be rearranged while remaining within the scope and spirit of the disclosure. The accompanying method claims present elements of the various steps in a sample order, and are not necessarily meant to be limited to the specific order or hierarchy presented. 
     It is believed that the system and method of the present disclosure and many of its attendant advantages will be understood by the foregoing description, and it will be apparent that various changes may be made in the form, construction and arrangement of the components without departing from the disclosed subject matter or without sacrificing all of its material advantages. The form described is merely explanatory.