TWI912508B - Method, system, and non-transitory computer readable medium for semiconductor inspection - Google Patents

Abstract

Inspection of a profile image of a semiconductor wafer image can be performed, such as to detect delamination near wafer edges. To estimate a reference image, a defect-free profile edge is determined and the reference image is generated from the defect-free profile edge. A difference image is determined from the reference image and the profile image. After binarizing, inspection is performed on the difference image.

Description

Methods, systems, and non-transitory computer-readable media for semiconductor testing

This invention relates to semiconductor testing.

The evolution of the semiconductor manufacturing industry places higher demands on yield management, especially on metrology and inspection systems. Critical dimensions continue to shrink, but the industry needs to shorten the time required to achieve high-yield, high-value production. Minimizing the total time from detecting a yield problem to resolving it maximizes the return on investment for semiconductor manufacturers.

Fabricating semiconductor devices, such as logic devices and memory devices, typically involves using numerous fabrication processes to work semiconductor wafers to form the various features and multiple layers of the semiconductor device. For example, lithography is a semiconductor fabrication process involving transferring a pattern from a scaled-down mask to a photoresist disposed on a semiconductor wafer. Additional examples of semiconductor fabrication processes include, but are not limited to, chemical mechanical polishing (CMP), etching, deposition, and ion implantation. Multiple semiconductor devices fabricated on a single semiconductor wafer can be configured and separated into individual semiconductor devices.

Bonded (or stacked) wafers are frequently used in the semiconductor industry. One example of a bonded wafer is one where one or more ultrathin wafers are bonded to a carrier wafer, although other semiconductor wafer designs can also be bonded. For example, a bonded wafer may include a top wafer bonded to one of a carrier wafers (e.g., a device wafer). These bonded wafers can be used for both memory and logic applications. Bonded wafers can be used to create three-dimensional integrated circuits (3D ICs).

Bonded wafers can have complex edge profiles. The various layers of a bonded wafer can have different heights and diameters. These dimensions can be affected by the size of the various wafers or the processing steps prior to stacking.

Previously, manual re-inspection was performed on images of the edge contours of the bonded wafers. This was tedious, slow, and prone to user errors. Images used for manual re-inspection also had reduced sensitivity.

An improved technique is needed for detecting edge contours.

In a first embodiment, a method is provided. A contour image of an edge of a semiconductor wafer is received at a processor. A reference image is estimated from the contour image using the processor. The estimation includes: determining a defect-free contour edge and generating the reference image using the defect-free contour edge. A difference image between the reference image and the contour image is determined using the processor. The difference image is binarized using the processor. After binarization, defects are detected in the difference image using the processor.

Determining the defect-free contour edge may include: binarizing the contour image; removing stripes from the contour image; extracting the edges of the contour image after binarization and removal to generate an edge image; and removing defects from the edge image. Removing defects from the edge image may include: receiving the edge image; estimating one edge in the edge image using a piecewise polynomial fitting to generate an estimated edge image; and removing mismatches between the edge image and the estimated edge image to generate the defect-free contour edge. Estimating the edge and removing the mismatches can be repeated.

Generating the reference image may include: receiving the defect-free contour edge; applying a distance transformation to the defect-free contour edge to generate a distance-transformed image; extracting pixels from the contour image that extend beyond an edge of the distance-transformed image by a distance to generate an extracted trajectory; and applying a one-dimensional averaging filter to the extracted trajectory. Extracting the pixels and applying the one-dimensional averaging filter can be repeated until the distance is less than a threshold value.

This estimate can be made immediately.

The method may further include using the processor to preprocess the profile image before estimating the reference image. This preprocessing may include flipping the profile image.

A non-transitory computer-readable medium storing a program can be configured to instruct a processor to execute the method of the first embodiment.

In a second embodiment, a system is provided. The system includes: a stage configured to support a wafer; an imaging system configured to generate a contour image of a circumferential edge of the wafer; and a processor electronically communicating with the imaging system. The imaging system includes a light source configured to generate collimated light and a detector configured to generate the contour image. The processor is configured to: receive the contour image of an edge of a semiconductor wafer; estimate a reference image from the contour image; determine a difference image between the reference image and the contour image; binarize the difference image; and detect defects in the difference image after binarization. The estimation includes determining a defect-free contour edge and using the defect-free contour edge to generate the reference image.

Determining the defect-free contour edge may include: binarizing the contour image; removing stripes from the contour image; extracting the edges of the contour image after binarization and removal to generate an edge image; and removing defects from the edge image. Removing defects from the edge image may include: receiving the edge image; estimating one edge in the edge image using a piecewise polynomial fitting to generate an estimated edge image; and removing mismatches between the edge image and the estimated edge image to generate the defect-free contour edge. Estimating the edge and removing the mismatches can be repeated.

Generating the reference image may include: receiving the defect-free contour edge; applying a distance transformation to the defect-free contour edge to generate a distance-transformed image; extracting pixels from the contour image that extend beyond an edge of the distance-transformed image by a distance to generate an extracted trajectory; and applying a one-dimensional averaging filter to the extracted trajectory. Extracting the pixels and applying the one-dimensional averaging filter can be repeated until the distance is less than a threshold value.

The processor can be further configured to preprocess the profile image before estimating the reference image. This preprocessing may include flipping the profile image.

Cross-reference to related applications This application claims priority to the Indian patent application filed on April 19, 2021, and to the assigned application No. 202141017914, the disclosure of which is hereby incorporated by reference.

Although the claimed subject matter will be described with reference to certain embodiments, other embodiments, including those that do not provide all the benefits and features set forth herein, are also within the scope of this invention. Various structural, logical, procedural, and electronic changes may be made without departing from the scope of this invention. Therefore, the scope of this invention is defined only with reference to the appended claims.

The embodiments disclosed herein can be used to detect delamination (e.g., peeling) near the wafer edge using a silhouette image of one of the edge profiles. The profile shape of stacked or joined wafers can vary across the wafer. Due to this shape variation, aligning and subtracting two profile images can be cumbersome. Therefore, an image is used to estimate a reference image. This reduces the cumbersome process.

In one example, wafer edge profile images are collected during a job run. For instance, wafer edge profile images are collected for up to 180 bits, though more or fewer images can be collected. The number of images may be based on memory limitations, but increasing the number of images for certain wafers may be helpful. During preprocessing, multiple calibrations can be applied to the images. Edge maps can be extracted from these calibrated images. A defect-free edge map can be estimated from the true edge map. A reference image can be estimated from this defect-free edge map. The difference between the calibrated image and the reference image can be determined and then binarized. Finally, post-processing such as filtering and merging candidate defect pixels in the binary image provides defect information for all bits.

Figure 1 is a flowchart of one method 50. Some or all of the steps of method 50 may use a processor.

At point 51, a contour image of one edge of a semiconductor wafer is received. This may be a raw contour image. An exemplary contour image is shown to the right of step 51. Additional examples of images with delamination defects are shown in Figures 2 and 3. In Figures 2 and 3, the delamination defect is highlighted using a box inside a dashed ellipse.

In one example, at step 52, the profile image is preprocessed before the reference images are estimated sequentially. Preprocessing may include flipping the profile image. The image may have been collected upside down, so flipping it can correct the image. Other preprocessing may include calibrating the original image, such as performing dead pixel correction, distortion analysis, and/or laser beampath correction.

At point 52, a reference image is estimated from the contour image. An example of a reference image is shown to the right of step 52.

At step 52, estimating a reference image may include determining a defect-free contour edge and using the defect-free contour edge to generate the reference image. Estimation can occur instantly. The reference image can compensate for contour variations between wafers or portions of the same wafer.

In one example, determining a defect-free profile edge in step 52 includes: binarizing the profile image; removing streaks from the profile image; extracting the edges of the profile image to generate an edge image; and removing defects from the edge image. Streaks may appear at the edges of the wafer due to diffraction. These streaks can interfere with detection or measurement, so they can be removed before continuing detection. Edge extraction identifies the wafer boundaries. Figure 4A shows an example of an calibrated profile image. Figure 4B shows the image of Figure 4A after binarization and streak removal. Binarization converts the image from grayscale to black and white. A binary image can be created by replacing all values higher than a globally determined threshold with 1 and replacing other values with 0. Figure 4C shows the image of Figure 4B after the edge is extracted. Figure 4D, as an edge image, shows the image of Figure 4C after defect removal. Defects on the outer edge of the wafer in the lower left of Figure 4C are removed to form one of the smooth contours in Figure 4D.

Removing defects from an edge image may involve: receiving an edge image; estimating one edge in the edge image using a piecewise polynomial fitting to generate an estimated edge image; and removing mismatches between the edge image and the estimated edge image to generate a defect-free contour edge. A real edge image may have defects. Estimating a defect-free edge image from the real edge image can be used in this method. By comparing the two images, defective areas can be identified. Figure 5A shows the real edge image, and Figure 6A shows the estimated edge image. Comparing these two images allows for the localization of defects.

The algorithm iteratively estimates edges and removes mismatches until matching points are removed. Figure 5A shows a real edge image that matches the image in Figure 4C. Figure 5B shows the image of Figure 5A after piecewise polynomial fitting. Figure 5C shows the image of Figure 5B after identifying and removing mismatches. The image in Figure 5C is similar to the image in Figure 4D. Discontinuities in Figure 5C indicate that those pixels do not follow the piecewise polynomial fitting in the real edge image. The algorithm highlights a difference in those pixel regions, removes those pixels, estimates those pixels, and fills in the gaps.

In one example, mismatches between the ground truth edge image (Fig. 5A) and the estimated edge image (Fig. 5B) can be identified and removed. For each estimated edge point, the system attempts to find the nearest edge point in the ground truth image. If no such edge point is found, it is identified as a mismatch. This process can be repeated until no mismatches remain or until a maximum iteration is completed. The estimated edge image can then be output.

In step 52, generating the reference image may include: receiving a defect-free contour edge; applying a distance transform to the defect-free contour edge to generate a distance-transformed image; extracting pixels from the contour image that extend a distance beyond an edge of the distance-transformed image to generate an extracted trajectory; and applying a one-dimensional averaging filter to the extracted trajectory. Pixel extraction and the application of the one-dimensional averaging filter may be repeated until the distance is less than a threshold. The threshold indicates how far the system needs to move away from the contour edge. In one example, this threshold may be within a first fringe, and therefore may be a fixed number.

Given a binary image, a distance transformation outputs another image, where the intensity of a given pixel will be the nearest non-zero pixel in the binary image. The nearest non-zero pixel in the binary image can be found by performing a distance transformation on each pixel. Then, pixels far from the contour edge are extracted at a distance *d*. The distance *d* can range from zero to one. A one-dimensional averaging filter provides an intensity estimate for a particular pixel. In one example, the average intensity of the pixels surrounding that particular pixel is taken.

Figure 6A is an example of a defect-free contour edge; Figure 6A corresponds to Figure 4D. Figure 6B is an example of a distance-transformed image after applying a distance transform to the image in Figure 6B. This provides the nearest edge point for each pixel. Using the distance-transformed image, all pixels beyond a certain distance (track) from the edge can be extracted. For example, Figure 6C shows pixels 5 pixels from the edge. A one-dimensional averaging filter can be applied to the extracted track. This procedure can be repeated until the distance (track) is less than a maximum distance. Figure 6D shows an estimated reference image after filtering a single track. Due to the averaging, black points may not be considered. Figure 6D shows a side region.

Returning to Figure 1, at point 53, determine the difference between the reference image and the outline image. An example of a difference image is shown to the right of step 53.

At step 54, the difference image is binarized. An example of a binarized difference image is shown to the right of step 54. The defect is highlighted in a box inside the dashed ellipse.

At point 55, a defect is detected in the difference image after binarization. The defect can be identified. For example, a defect is highlighted in the binarized difference image shown to the right of step 54.

Method 50 can be performed one or more times on a single wafer.

Figures 7A through 7D illustrate examples of delamination detection using the embodiments disclosed herein. Defects are highlighted in boxes within the dashed ellipses. The embodiments disclosed herein eliminate the need for manual re-inspection of all sites and allow semiconductor manufacturers to automatically locate defective sites. A defect-free reference edge profile can be generated from a potentially defective image, providing improved results because the images are correlated. This avoids using a potentially dissimilar reference image, thus preventing errors. Moreover, sensitivity is improved compared to manual re-inspection. Semiconductor manufacturers can receive information about the size and location of defects on the wafer edges.

In one embodiment, a reference can be determined from a local median (of adjacent points) or a global median (of all points), rather than generating a contour-guided reference image for each point. A reference image can be generated by aligning all contour images and extracting a median from them. This method can be used when there are no contour variations across points within the wafer.

In another embodiment, fuzzy k-means clustering is used, followed by dynamic thresholds for the detection of weak defects. Instead of using a fixed threshold on the poor image, a threshold can be dynamically determined by analyzing the statistics of the intensity distribution.

Figures 8 and 9 are a top view of a system 100 and a corresponding cross-sectional side view along line A-A of a block diagram. Figure 10 is a perspective view of a system 100 corresponding to an embodiment of Figures 8 and 9. The system 100 is configured to perform measurement on a bonded wafer by acquiring an image as a shadowgram. The shadowgram applies a shadowing technique and visualizes or images a shadow of the bonded wafer 102 (e.g., a circumferential edge of the bonded wafer 102). A stage 101 can be configured to rotate a bonded wafer 102, although the system 100 can also rotate relative to the bonded wafer 102. This rotation can be step-by-step or continuous. The bonded wafer 102 can remain stationary during imaging, and the components of the system 100 can be fixed.

An exemplary bonded wafer 102 is shown having a carrier wafer 107 and a top wafer 108. The carrier wafer 107 and the top wafer 108 may have different diameters, such as those illustrated in FIG1. For example, the carrier wafer 107 may be a carrier wafer, and the top wafer 108 may be a device wafer. Alternatively, both the carrier wafer 107 and the top wafer 108 may be device wafers, or not only the carrier wafer 107 and the top wafer 108 may form the bonded wafer 102.

A light source 103 is configured to guide collimated light 104 at one edge of a bonded wafer 102. In some embodiments, the collimated light 104 is guided tangentially relative to the bonded wafer 102 to produce a shadow of the edge profile. Thus, the bonded wafer 102 blocks some of the collimated light 104. The collimated light 104 is illustrated as approximately circular, but may be of other shapes. In one exemplary embodiment, the light source 103 utilizes a light-emitting diode (LED). In view of the present invention, other suitable light sources 103 (e.g., lamps that generate collimated light, lasers, supercontinuum lasers, laser-driven phosphors, or laser-driven lamps) will be readily apparent. A combination of light sources 103, such as a laser and an LED, can be used. The light source 103 may include single-band and broadband light sources in a single system or multiple systems. The collimated beam 104 may be parallel to a plane of the bonded wafer 102. For example, the collimated beam 104 may be parallel to the plane of the carrier wafer 107 on which the top wafer 108 is mounted. Diffraction suppression techniques can be used to remove diffraction-related artifacts that may adversely affect measurements. Using the collimated beam 104, the bonded wafer 102, approximately a few millimeters in size, can be seen in an outline, although other sizes are also possible.

A detector 105, located away from the light source 103, receives at least some of the collimated light from the collimated light 104. The detector 105 is positioned such that when a bonded wafer 102 is imaged, the detector 105 receives at least a portion of the shadow (i.e., the light that produces the shadow). The detector 105 may be, for example, a charge-coupled device (CCD) or a complementary metal-oxide-semiconductor (CMOS) camera. In this way, an image of the wafer edge silhouette (i.e., a wafer edge contour image) is formed. The detector 105 may be configured to collect hundreds of wafer edge contour images of the bonded wafer 102 for high sampling. For example, between 2 and 500 wafer edge contour images of the bonded wafer 102 may be collected, although more images may be collected. In one example, 16 wafer edge profile images of a bonded wafer were collected. In another example, 36 wafer edge profile images of a bonded wafer were collected. In yet another example, 360 wafer edge profile images of a bonded wafer were collected.

The collimated light 104 may have one or more wavelengths that produce a shadow. For example, visible light such as blue or white light can be used. In view of this invention, other suitable collimated light 104 will be obvious. For example, ultraviolet light can be used. The collimated light 104 may be polarized and may be pulsed or continuous.

Although only a single light source 103 and detector 105 are illustrated in Figures 8 through 10, multiple light sources 103 and detectors 105 can be used. Multiple light sources 103 and detectors 105 can be placed at different locations around the periphery of the bonded wafer 102 to collect images at different locations on the bonded wafer 102. This can increase the detection throughput or the number of images transmitted while minimizing the impact on the detection throughput. If multiple light sources 103 and detectors 105 are placed at different locations around the periphery of the bonded wafer 102, the bonded wafer 102 may not rotate relative to the light sources 103 and detectors 105.

A controller 106 is operatively connected to a detector 105. The controller 106 is configured to analyze an image of one of the edges of the bonded wafer 102 and can use the detector 105 to control the acquisition of the image. For example, the controller 106 can rotate the bonded wafer 102 relative to the light source 103 or the detector 105. The controller 106 can also control the timing or location of image acquisition on the bonded wafer 102. The controller 106 can be configured to use the output of the detector 105 to perform other functions or additional steps. For example, the controller 106 can be programmed to perform some or all of the steps in FIG. 1. The controller 106 may include a processor 109 and a memory 110.

The controller 106, other systems, or other subsystems described herein may take various forms, including a personal computer system, workstation, video computer, mainframe computer system, network appliance, internet appliance, parallel processor, or other device. Generally, the term "controller" may be broadly defined to encompass any device having one or more processors that executes instructions from a memory medium. A subsystem or system may also include any suitable processor known in the art, such as a parallel processor. Additionally, a subsystem or system may include a platform with high-speed processing and software as a standalone tool or a network-connected tool.

If a system comprises more than one subsystem, the different subsystems can be coupled to each other, enabling the transmission of images, data, information, commands, etc., between the subsystems. For example, a subsystem can be coupled to an additional subsystem via any suitable transmission medium, which can include any suitable wired and/or wireless transmission medium known in this art. Two or more of such subsystems can also be effectively coupled via a shared computer-readable storage medium (not shown).

In another embodiment, controller 106 may be communicatively coupled to any of the various components or subsystems of system 100 in any manner known in the art. Furthermore, controller 106 may be configured to receive and/or acquire data or information from other systems via a transmission medium that may include wired and/or wireless components. In this manner, the transmission medium can serve as a data link between controller 106 and other subsystems of system 100 or systems external to system 100.

An additional embodiment relates to storing program instructions executable on a controller for performing a non-transitory computer-readable medium for a computer implementation method via bonding wafer metrology (such as for performing the techniques disclosed herein). Specifically, as shown in FIG8, controller 106 may include memory 110 or other electronic data storage medium having a non-transitory computer-readable medium containing program instructions executable on controller 106. The computer implementation method may include any step of any method described herein, such as those disclosed in FIG1. Memory 110 or other electronic data storage media may be such as a read-only memory, a random access memory, a magnetic disk or optical disk, a non-volatile memory, a solid-state memory, a magnetic tape, or any other storage medium known in the art suitable for non-transitory computer-readable media.

Program instructions can be implemented in any of the following ways, including process-based techniques, component-based techniques, and/or object-oriented techniques, as well as other techniques. For example, as desired, program instructions can be implemented using ActiveX controls, C++ objects, JavaBeans, Microsoft Foundation Classes (MFC), SSE (Streaming IMD Extension), or other techniques or methods.

In some embodiments, the various steps, functions, and/or operations of the system 100 and methods disclosed herein are implemented by one or more of the following: electronic circuits, logic gates, multiplexers, programmable logic devices, application-specific integrated circuits (ASICs), analog or digital controllers/switches, microcontrollers, or computing systems. The program instructions of the embodiments (such as those described herein) may be transmitted via or stored on a carrier medium. The carrier medium may include an electronic data storage medium such as memory 110 or a transmission medium such as a wire, cable, or wireless transmission link. For example, the various steps described throughout this invention may be performed by a single controller 106 (or computer system), or alternatively, by multiple controllers 106 (or multiple computer systems). Furthermore, different subsystems of system 100 may contain one or more computational or logical systems. Therefore, the above description should not be construed as a limitation of this invention, but is merely an interpretation.

As used herein, the term "wafer" generally refers to a substrate formed of a semiconductor or non-semiconductor material. Examples of such semiconductor or non-semiconductor materials include, but are not limited to, single-crystal silicon, gallium nitride, gallium arsenide, indium phosphide, sapphire, and glass. Such substrates are typically found and/or processed in semiconductor manufacturing facilities.

A wafer may comprise one or more layers formed on a substrate. For example, such layers may include, but are not limited to, a photoresist, a dielectric material, a conductive material, and a semi-conductive material. Many different types of such layers are known in the art, and the term wafer, as used herein, is intended to encompass a wafer comprising all types of such layers.

One or more layers formed on a wafer may be patterned or unpatterned. For example, a wafer may contain a plurality of grains, each having repeatable patterned features or periodic structures. The formation and processing of such material layers ultimately produce a finished device. Many different types of devices can be formed on a wafer, and the term wafer, as used herein, is intended to encompass any type of device known in this art on which such a device is fabricated.

Other types of wafers may also be used. For example, wafers can be used to manufacture LEDs, solar cells, disks, flat panels, or polished sheets. The techniques and systems disclosed herein can also be used to classify defects on other objects.

Each of the steps of the method can be performed as described herein. The method may also include any other steps that can be performed by the controller and/or computer subsystem or system described herein. These steps are performed by one or more computer systems, which can be configured according to any of the embodiments described herein. Alternatively, the method described above can be performed by any of the system embodiments described herein.

Although the invention has been described with respect to one or more specific embodiments, it should be understood that other embodiments of the invention may be made without departing from the scope of the invention. Therefore, the invention is considered to be limited only by the scope of the appended patent application and its reasonable disclosure.

50: Method 51: Step 52: Step 53: Step 54: Step 55: Step 100: System 101: Stage 102: Bonded Wafer / Example Bonded Wafer 103: Light Source 104: Collimated Light 105: Detector 106: Controller 107: Carrier Wafer 108: Top Wafer 109: Processor 110: Memory A-A: Line

For a more comprehensive understanding of the nature and objectives of this invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings, in which: Figure 1 is a flowchart of a method according to this invention; Figures 2 and 3 are exemplary profile images of a wafer with delamination defects; Figures 4A to 4D show exemplary images during the process of determining a defect-free profile edge; Figures 5A to 5C show exemplary images during the process of removing defects; Figures 6A to 6D show exemplary images during the process of generating a reference image; Figures 7A to 7D show examples of delamination detection using the embodiments disclosed herein; Figures 8 and 9 are a top view of a system and a corresponding cross-sectional side view along block diagram A-A; and Figure 10 is a perspective view of one of the systems corresponding to the embodiments in Figures 14 and 15.

50: Methods

51: Steps

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Claims (16)

A method for semiconductor inspection includes: receiving a profile image of an edge of a semiconductor wafer at a processor; estimating a reference image from the profile image using the processor, wherein the estimation includes: determining a defect-free profile edge; generating the reference image using the defect-free profile edge; determining a difference image between the reference image and the profile image using the processor; binarizing the difference image using the processor; and detecting defects in the difference image using the processor after binarization. The method of claim 1, wherein determining the defect-free contour edge comprises: binarizing the contour image; removing stripes from the contour image; extracting the edges of the contour image after binarization and stripe removal to generate an edge image; and removing defects in the edge image. The method of claim 2, wherein removing the defects in the edge image comprises: receiving the edge image; estimating one edge in the edge image using a piecewise polynomial fitting, thereby generating an estimated edge image; and removing mismatches between the edge image and the estimated edge image, thereby generating the defect-free contour edge. The method described in Request 3 involves repeatedly estimating the edge and removing the mismatches. The method of claim 1, wherein generating the reference image comprises: receiving the defect-free contour edge; applying a distance transformation to the defect-free contour edge to generate a distance-transformed image; extracting pixels from the contour image that extend beyond an edge of the distance-transformed image by a distance to generate an extracted trajectory; and applying a one-dimensional averaging filter to the extracted trajectory. The method of claim 5, wherein the pixels are repeatedly extracted and the one-dimensional average filter is applied until the distance is less than a threshold value. The method of Request 1, wherein the estimation occurs in real time. The method of claim 1, wherein the method further includes using the processor to preprocess the profile image before estimating the reference image, and wherein the preprocessing includes flipping the profile image. A non-transitory computer-readable medium storing a program configured to instruct a processor to perform the method as requested in item 1. A system for semiconductor inspection includes: a stage configured to support a wafer; an imaging system configured to generate a contour image of a circumferential edge of the wafer, wherein the imaging system includes a light source configured to generate collimated light and a detector configured to generate the contour image; and a processor electronically communicating with the imaging system, wherein the processor is configured to: receive the contour image of an edge of the semiconductor wafer; estimate a reference image from the contour image, wherein the estimation includes: determining a defect-free contour edge; and using the defect-free contour edge to generate the reference image; determining a difference image between the reference image and the contour image; binarizing the difference image; and detecting defects in the difference image after binarization. The system of claim 10, wherein determining the defect-free contour edge comprises: binarizing the contour image; removing stripes from the contour image; extracting the edges of the contour image after binarization and stripe removal to generate an edge image; and removing defects from the edge image. The system of claim 11, wherein removing the defects in the edge image comprises: receiving the edge image; estimating one edge in the edge image using a piecewise polynomial fitting, thereby generating an estimated edge image; and removing mismatches between the edge image and the estimated edge image, thereby generating the defect-free contour edge. The system, as requested in item 12, repeatedly estimates the edge and removes the mismatches. The system of claim 10, wherein generating the reference image comprises: receiving the defect-free contour edge; applying a distance transformation to the defect-free contour edge to generate a distance-transformed image; extracting pixels from the contour image that extend a distance beyond an edge of the distance-transformed image to generate an extracted trajectory; and applying a one-dimensional averaging filter to the extracted trajectory. The system of claim 14, wherein the pixels are repeatedly extracted and the one-dimensional average filter is applied until the distance is less than a threshold value. The system of claim 10, wherein the processor is further configured to preprocess the profile image before estimating the reference image, and wherein the preprocessing includes flipping the profile image.