Nanoscale high precision bonding mark metrology system

CN122602913APending Publication Date: 2026-08-18NORTHWEST INST OF ELECTRONIC EQUIP TECH (SECOND RES INST OF CHINA ELECTRONICS TECH GRP CORP)
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Patent Information

Application Number
CN202611046919.3
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-07-15
Publication Date
2026-08-18

AI Technical Summary

Technical Problem

[0005]为克服现有纳米级高精度键合标记量测系统存在的干涉鬼影干扰、系统复杂性高且对承物台参数敏感的技术缺陷,本发明提出一种纳米级高精度键合标记量测系统

Benefits of technology

[0038] The nanoscale high-precision bonding mark measurement system provided by this invention is equipped with a collimated light source and an anti-reflection film on the optical window of the transparent stage. The collimated light source reduces stray light, and the anti-reflection film reduces the intensity of light reflected from the upper and lower surfaces of the transparent stage. The two work together to effectively suppress the generation of interference ghosting and ensure the accuracy of mark measurement. At the same time, compared with traditional Köhler illumination, the collimated light source simplifies the optical system structure, reduces equipment cost and assembly difficulty while ensuring illumination uniformity. Moreover, the collimated light source is not sensitive to parameters such as the thickness of the transparent stage, provides stable illumination conditions, and does not require frequent calibration, thereby improving production efficiency and stability.

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Abstract

The present application relates to the technical field of semiconductor manufacturing, in particular to a nanometer high-precision bonding mark measurement system, which mainly solves the technical problems of interference ghost interference, high system complexity and sensitivity to object table parameters in the existing nanometer high-precision bonding mark measurement system. The system comprises a transparent object table, a collimating light source, an imaging module and a processing module; the upper and lower surfaces of the optical window of the transparent object table are provided with an antireflection film; the collimating light source is arranged below the transparent object table to provide collimated light penetrating the optical window and the wafer pair; the imaging module collects the superimposed image of the alignment marks of the upper and lower wafers; and the processing module is used for determining the center positions of the upper and lower wafer marks and calculating the alignment deviation. The system suppresses the interference ghost caused by the multiple reflections of the transparent object table through the collimating light source, and the antireflection film suppresses the reflection loss, thereby improving the image contrast and positioning accuracy; at the same time, the optical path structure is simplified, and the system is not sensitive to the thickness of the transparent object table, thereby improving the system stability and production efficiency.
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Description

Technical Field

[0001] This invention relates to the field of semiconductor manufacturing technology, and in particular to a nanoscale high-precision bonding mark measurement system. Background Technology

[0002] With the continuous shrinking of semiconductor device feature sizes and the development of 3D integration technology, wafer-level bonding has become a key process for achieving high-density interconnects. Nanoscale high-precision bonding, in particular, places extremely high demands on alignment accuracy, as alignment deviations directly affect the electrical performance of the interconnects and the overall device yield. Taking hybrid bonding as an example, it achieves extremely high interconnect density by simultaneously performing metal bonding and dielectric bonding, requiring alignment accuracy at the nanometer scale. In the bonding process, after pre-bonding of the upper and lower wafers, the alignment marks fabricated on the two wafer layers need to be measured to calculate positional deviations and guide subsequent bonding alignment compensation. Therefore, high-precision and high-reliability measurement of alignment marks is an indispensable core component of nanoscale high-precision bonding processes.

[0003] Currently, widely used bonding mark measurement systems are based on the imaging principle of optical microscopy and employ Köhler illumination. Köhler illumination uses a combination of optical elements such as a condenser lens, field lens, and aperture stop to image the light source onto the back focal plane of the objective lens, thus providing uniform illumination on the sample plane. Under this illumination method, pre-bonded upper and lower wafers are stacked on a transparent stage (Chuck). Light passes sequentially through the stage, the lower wafer, and the upper wafer, and the marks on both wafers are simultaneously imaged on the same image sensor. Since the two marking patterns are superimposed in the same image, a mask is needed to shield one layer of marking area, and a template is used to perform normalized cross-correlation (NCC) matching on the other layer of markings to extract the center positions of the upper and lower markings and calculate the deviation. However, the above-mentioned scheme has the following inherent defects in the measurement of nanoscale high-precision bonding marks: First, interference ghosting is severe. The light passing through the stage will be reflected multiple times between its upper and lower surfaces, forming interference fringes and ghosting. In the scenario of superimposed imaging of upper and lower marks after pre-bonding, the ghosting and the two layers of mark patterns are further intertwined, resulting in a sharp drop in contrast and severe edge blurring. This greatly reduces the accuracy of mask shielding and template matching, seriously affecting the accuracy and repeatability of mark center position extraction. Second, the system is complex and sensitive to stage parameters. Köhler illumination relies on the precise coordination of a series of precision optical components such as condenser lenses, field lenses, and aperture stops. The structure is complex, difficult to assemble and adjust, and expensive. Moreover, its illumination uniformity is very sensitive to the thickness and position changes of the components in the optical path. Stages with different thicknesses or flatness errors will introduce additional aberrations, requiring frequent recalibration, which reduces production efficiency and stability.

[0004] Therefore, there is an urgent need in this field for a nanoscale high-precision bonding mark measurement system that can effectively suppress interference ghosting, has a simplified structure, and is insensitive to the thickness of the stage. Summary of the Invention

[0005] To overcome the technical shortcomings of existing nanoscale high-precision bonding mark measurement systems, such as interference ghosting, high system complexity, and sensitivity to stage parameters, this invention proposes a nanoscale high-precision bonding mark measurement system.

[0006] The nanoscale high-precision bonding marker measurement system provided by this invention includes:

[0007] A transparent stage is used to support pre-bonded wafer pairs. The transparent stage is provided with an optical window, and both the upper and lower surfaces of the optical window are provided with anti-reflective coatings.

[0008] A collimating light source is disposed below the transparent stage, and the collimating light source is used to provide collimated light that can sequentially penetrate the optical window and the wafer pair;

[0009] An imaging module is located above the transparent stage, and the imaging module is used to acquire superimposed images of alignment marks on the wafer pair;

[0010] The processing module is communicatively connected to the imaging module. The processing module is used to determine the center positions of the upper wafer mark and the lower wafer mark respectively based on the superimposed image, and to calculate the alignment deviation.

[0011] Furthermore, the antireflective membrane is a composite membrane, which is prepared by physical vapor deposition and is composed of alternating layers of MgF2 membrane and SiO2 membrane.

[0012] Furthermore, the collimated light source includes a light source and a collimating lens, wherein the light source is a superluminescent diode or a low-coherence laser.

[0013] Furthermore, the operating wavelength of the antireflection film is matched with the emission wavelength of the collimated light source.

[0014] Furthermore, the imaging module includes an objective lens and an image sensor, wherein the objective lens collects transmitted light signals that penetrate the wafer pair and images them on the image sensor.

[0015] Furthermore, the processing module is configured as follows:

[0016] The image area of ​​the upper wafer mark is shielded by the first mask, and the lower wafer mark is normalized cross-correlation matched by the first template to determine the center position of the lower wafer mark;

[0017] The image area of ​​the lower wafer marker is shielded by the second mask, and the upper wafer marker is normalized cross-correlation matched by the second template to determine the center position of the upper wafer marker.

[0018] Calculate the alignment deviation based on the center positions of the upper and lower wafer marks.

[0019] Furthermore, when the processing module performs normalized cross-correlation matching, it slides the first template or the second template pixel by pixel on the overlay image, at each sliding position... Calculate the normalized cross-correlation score. :

[0020] ;

[0021] in, Represents the local coordinates of the template and , Represents the pixel area of ​​the template. Indicates the template in coordinates Pixel value at that location, This represents the average pixel value of the template. Indicates the pixel coordinates of the overlaid image Pixel value at that location, Indicates the superimposed image with The average pixel value of the corresponding region starting from the specified point;

[0022] Select normalized cross-correlation score The highest sliding position is taken as the peak position. Subpixel interpolation is performed at the peak position and its neighborhood to obtain the marker center position with subpixel accuracy.

[0023] Furthermore, the sub-pixel interpolation includes:

[0024] The normalized cross-correlation score of the peak position and its neighboring pixels. Fitting a quadratic surface:

[0025] ;

[0026] in, , , , , and All are fitting coefficients;

[0027] Taking the partial derivative of the quadratic surface and setting it to zero, we can obtain the sub-pixel offset. :

[0028] ;

[0029] Subpixel precision marker center position for:

[0030] ;

[0031] in, Indicates the width of the template. Indicates the height of the template.

[0032] Furthermore, before sliding the first template or the second template pixel by pixel on the overlay image, the processing module further processes the image of the corresponding template as follows to generate an edge mask:

[0033] The images of the corresponding templates are processed in parallel using the Canny operator and the Sobel operator respectively. The initial binary edge map is obtained by the Canny operator, and the edge intensity map is obtained by the Sobel operator.

[0034] A three-level sequential optimization process involving length filtering, strength verification, and connectivity analysis is performed to remove noise and false edges layer by layer, thereby generating the edge mask.

[0035] The edge mask has a value of 1 in the image edge region and a value of 0 in the non-edge region. When calculating the normalized cross-correlation score, the summation is only performed at the pixel positions where the edge mask has a value of 1, and the non-edge region does not participate in the matching calculation.

[0036] Furthermore, the processing module also uses a dilation module to process the image of the corresponding template to obtain a dilated region map, which is used to provide a reference for connectivity analysis.

[0037] The technical solution provided by this invention has the following advantages compared with the prior art.

[0038] The nanoscale high-precision bonding mark measurement system provided by this invention is equipped with a collimated light source and an anti-reflection film on the optical window of the transparent stage. The collimated light source reduces stray light, and the anti-reflection film reduces the intensity of light reflected from the upper and lower surfaces of the transparent stage. The two work together to effectively suppress the generation of interference ghosting and ensure the accuracy of mark measurement. At the same time, compared with traditional Köhler illumination, the collimated light source simplifies the optical system structure, reduces equipment cost and assembly difficulty while ensuring illumination uniformity. Moreover, the collimated light source is not sensitive to parameters such as the thickness of the transparent stage, provides stable illumination conditions, and does not require frequent calibration, thereby improving production efficiency and stability. Attached Figure Description

[0039] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a schematic diagram showing the overall structure of the measurement system in an embodiment of the present invention;

[0042] Figure 2 This image shows a comparison of the labeled images of the system of the present invention and the conventional system; wherein, Figure 2 (a) represents the labeled image of a traditional system. Figure 2 (b) Represents a marker image of the system of the present invention;

[0043] Figure 3 This diagram illustrates the edge mask generation process in an embodiment of the present invention.

[0044] In the picture:

[0045] 1. Transparent stage; 2. Collimated light source; 3. Imaging module; 31. Objective lens; 32. Image sensor. Detailed Implementation

[0046] To better understand the above-mentioned objectives, features, and advantages of the present invention, the solutions of the present invention will be further described below. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other.

[0047] Many specific details are set forth in the following description in order to provide a full understanding of the invention, but the invention may also be practiced in other ways different from those described herein; obviously, the embodiments in the specification are only some embodiments of the invention, and not all embodiments.

[0048] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0049] Reference Figure 1 This embodiment provides a nanoscale high-precision bonding mark measurement system, including a transparent stage 1, a collimating light source 2, an imaging module 3, and a processing module.

[0050] The transparent stage 1 is used to support the pre-bonded wafer pair. The transparent stage 1 is provided with an optical window, and both the upper and lower surfaces of the optical window are provided with anti-reflective coatings.

[0051] It should be noted that the transparent stage 1 is a mature structure in this field, and the wafer pair is fixed by vacuum adsorption.

[0052] Specifically, the antireflective film is a composite film, prepared using physical vapor deposition (PVD) and composed of alternating layers of MgF2 and SiO2 films. The total number of MgF2 and SiO2 layers is not limited; this embodiment has seven layers: four MgF2 layers and three SiO2 layers. This composite film is optimized for the emission wavelength of the collimated light source 2 to reduce reflectivity within that wavelength range and effectively suppress reflected light in that range.

[0053] The collimating light source 2 is located below the transparent stage 1 and is used to provide collimated light that can pass through the optical window and the wafer pair in sequence.

[0054] Specifically, the collimated light source 2 includes a light source and a collimating lens. The light source is a superluminescent diode or a low-coherence laser. In this embodiment, a superluminescent diode is selected as the light source, with an emission wavelength of 1050 nm and a spectral width of 50 nm. It generates a parallel beam through a collimating lens with a numerical aperture of 0.80.

[0055] Specifically, the operating wavelength of the antireflection film is matched with the emission wavelength of the collimated light source 2. In this embodiment, the emission wavelength of the collimated light source 2 is 1050nm. Therefore, the aforementioned combined film is optimized for the infrared band of 1000nm to 1100nm. The average reflectivity in this band is less than 0.5%, which can effectively suppress reflected light in this band and minimize interference ghosting.

[0056] The imaging module 3 is located above the transparent stage 1 and is used to acquire superimposed images of alignment marks on the wafer pair.

[0057] Specifically, the imaging module 3 includes an objective lens 31 and an image sensor 32. The objective lens 31 collects the transmitted light signal passing through the wafer pair and images it on the image sensor 32. In this embodiment, a 20x objective lens 31 with a numerical aperture of 0.40 is selected, and a CMOS camera is selected as the image sensor 32.

[0058] Reference Figure 2 The left image is a marker image from a traditional system using Köhler illumination without an antireflective coating, while the right image is a marker image from our system. A comparison reveals that the traditional system's marker image exhibits noticeable ghosting and interference fringes, with ghosting at the marker edges; whereas the marker image from our system has a clean and uniform background, sharp marker edges, and significantly improved contrast. Using the local standard deviation of the background region as a quantitative indicator to evaluate the two images, the calculated local standard deviation is 20.79 for the traditional system's marker image, while it is 2.74 for our system's. The quantitative results show that our system significantly improves ripple noise.

[0059] The processing module is communicatively connected to the imaging module 3. The processing module is used to determine the center positions of the upper wafer mark and the lower wafer mark respectively based on the superimposed image, and to calculate the alignment deviation.

[0060] Specifically, the processing module is configured as follows: using a first mask to shield the image area of ​​the upper wafer mark, and using a first template to perform normalized cross-correlation matching on the lower wafer mark to determine the center position of the lower wafer mark; using a second mask to shield the image area of ​​the lower wafer mark, and using a second template to perform normalized cross-correlation matching on the upper wafer mark to determine the center position of the upper wafer mark; and calculating the alignment deviation based on the center positions of the upper and lower wafer marks.

[0061] It is easy to understand that the creation of masks and templates is a mature operation in this field, that is, by manually selecting the region of interest (ROI) and masking irrelevant regions, the effective region is selected.

[0062] More specifically, when the processing module performs normalized cross-correlation matching, it slides the first or second template pixel by pixel on the overlay image, at each sliding position... Calculate the normalized cross-correlation score. :

[0063] ;

[0064] in, Represents the local coordinates of the template and , Represents the pixel area of ​​the template. Indicates the template in coordinates Pixel value at that location, This represents the average pixel value of the template. Indicates the pixel coordinates of the overlaid image Pixel value at that location, Indicates the superimposed image with The average pixel value of the corresponding region starting from the specified point;

[0065] Select normalized cross-correlation score The highest sliding position is taken as the peak position. Subpixel interpolation is performed at the peak position and its neighborhood to obtain the marker center position with subpixel accuracy.

[0066] When the first or second template is slid pixel by pixel on the overlay image, an image pyramid can be constructed for both the template and the overlay image, and coarse matching can be performed from the low-resolution layer to precise matching from the high-resolution layer.

[0067] The range of the neighborhood is not limited; in this embodiment, the neighborhood is set to 3×3.

[0068] More specifically, subpixel interpolation includes:

[0069] The normalized cross-correlation score of the peak position and its neighboring pixels Fitting a quadratic surface:

[0070] ;

[0071] in, , , , , and All are fitting coefficients;

[0072] Taking the partial derivative of the quadratic surface and setting it to zero, we can obtain the sub-pixel offset. :

[0073] ;

[0074] Subpixel precision marker center position for:

[0075] ;

[0076] in, Indicates the width of the template. Indicates the height of the template.

[0077] To achieve human-computer interaction verification, the system can transform abstract coordinate data into intuitive visual coordinates and render a colored crosshair cursor at the actual marked location, thereby completing the closed-loop feedback of "data → vision".

[0078] Furthermore, before sliding the first or second template pixel by pixel on the overlay image, the processing module performs the following processing on the image of the corresponding template to generate an edge mask: the image of the corresponding template is processed in parallel using the Canny operator and the Sobel operator respectively; the initial binary edge map is obtained through the Canny operator, and the edge intensity map is obtained through the Sobel operator; a three-level serial optimization of length filtering, intensity verification, and connectivity analysis is performed sequentially to remove noise and false edges layer by layer to generate an edge mask; the edge mask takes a value of 1 in the image edge region and a value of 0 in the non-edge region; when calculating the normalized cross-correlation score, the summation is only performed at the pixel positions where the edge mask has a value of 1, and the non-edge region does not participate in the matching calculation. The edge mask is generated using a hybrid edge extraction algorithm that combines parallel and serial processing. Compared with traditional single edge extraction algorithms, it has the following advantages: through multi-dimensional feature fusion and verification, it enhances noise resistance and edge structure integrity; through a dynamic filtering mechanism, it improves adaptability to complex lighting and backgrounds, providing a purer and more reliable initial data foundation for subsequent high-precision positioning (such as sub-pixel fitting), which is particularly suitable for high-requirement industrial vision applications such as wafer marking and verification.

[0079] Furthermore, the processing module also employs a dilation module to process the image of the corresponding template to obtain a dilated region map, which is used as a reference for connectivity analysis. The dilation module can increase the coverage of the edge mask and improve robustness.

[0080] Reference Figure 3 The template image is first subjected to parallel feature extraction in three paths: the first path generates an initial binary edge map using the Canny operator, the second path generates an edge intensity map using the Sobel operator, and the third path generates an dilated region map using a dilation module. Then, the initial binary edge map is subjected to three-level serial optimization: the first level is length filtering to remove excessively short edge segments; the second level is intensity verification, which filters weak edges in combination with the edge intensity map; and the third level is connectivity analysis, which extracts isolated noise in combination with the dilated region map. Finally, a high-quality edge mask is obtained.

[0081] It is easy to understand that before parallel feature extraction, the template image needs to undergo multi-level preprocessing, including flat field correction, adaptive median filtering, contrast-limited adaptive histogram equalization (CLAHE), and illumination homogenization, in order to eliminate systematic errors and improve image quality.

[0082] The working principle of the nanoscale high-precision bonding mark measurement system in this embodiment is as follows.

[0083] In use, this system is integrated into a fully automated bonding machine, with all components mounted on a rack. During measurement, system initialization is performed first, including light source preheating and camera focusing. Then, the center positions of the upper and lower wafer markers are determined. Finally, three independent calculation methods—centroid offset, shape parameter comparison, and key point matching—are used, and weighted fusion is performed based on the confidence level of each method to calculate the translational deviations ΔX and ΔY, and the rotational deviation Δθ of the upper and lower wafers. Error analysis and quality control are completed through repeatability measurements and image quality assessment to ensure the accuracy and reliability of the measurement results. In the bonding verification step, the calculated deviations (ΔX, ΔY, Δθ) are sent in real-time to the main controller of the bonding machine via a network protocol. The main controller drives the motion platform for compensation alignment. After bonding is completed under preset bonding pressure and temperature, the system can perform another rapid measurement to confirm that the final alignment error is within the allowable tolerance (±200nm).

[0084] The above are merely specific embodiments of the present invention, enabling those skilled in the art to understand or implement the present invention. Although detailed descriptions have been provided with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments, and they should all be covered within the protection scope of the claims.

Claims

1. A nanoscale high-precision bonding mark measurement system, characterized in that, include: A transparent stage (1) is used to support pre-bonded wafer pairs. The transparent stage (1) is provided with an optical window, and the upper and lower surfaces of the optical window are provided with anti-reflective coatings. A collimating light source (2) is disposed below the transparent stage (1). The collimating light source (2) is used to provide collimated light that can pass through the optical window and the wafer pair in sequence. An imaging module (3) is located above the transparent stage (1). The imaging module (3) is used to acquire superimposed images of alignment marks on the wafer pair. The processing module is communicatively connected to the imaging module (3). The processing module is used to determine the center position of the upper wafer mark and the center position of the lower wafer mark according to the superimposed image, and to calculate the alignment deviation.

2. The nanoscale high-precision bonding mark measurement system according to claim 1, characterized in that, The antireflection membrane is a composite membrane, which is prepared by physical vapor deposition and consists of alternating layers of MgF2 and SiO2 membranes.

3. The nanoscale high-precision bonding mark measurement system according to claim 1, characterized in that, The collimated light source (2) includes a light source and a collimating lens, wherein the light source is a superluminescent diode or a low-coherence laser.

4. The nanoscale high-precision bonding mark measurement system according to any one of claims 1 to 3, characterized in that, The operating wavelength of the antireflective coating is matched with the emission wavelength of the collimated light source (2).

5. The nanoscale high-precision bonding mark measurement system according to claim 1, characterized in that, The imaging module (3) includes an objective lens (31) and an image sensor (32), wherein the objective lens (31) collects transmitted light signals that penetrate the wafer pair and images them on the image sensor (32).

6. The nanoscale high-precision bonding mark measurement system according to claim 1, characterized in that, The processing module is configured as follows: The image area of ​​the upper wafer mark is shielded by the first mask, and the lower wafer mark is normalized cross-correlation matched by the first template to determine the center position of the lower wafer mark; The image area of ​​the lower wafer marker is shielded by the second mask, and the upper wafer marker is normalized cross-correlation matched by the second template to determine the center position of the upper wafer marker. Calculate the alignment deviation based on the center positions of the upper and lower wafer marks.

7. The nanoscale high-precision bonding mark measurement system according to claim 6, characterized in that, When the processing module performs normalized cross-correlation matching, it slides the first template or the second template pixel by pixel on the overlay image, at each sliding position... Calculate the normalized cross-correlation score. : ; in, Represents the local coordinates of the template and , Represents the pixel area of ​​the template. Indicates the template in coordinates Pixel value at that location, This represents the average pixel value of the template. Indicates the pixel coordinates of the overlaid image Pixel value at that location, Indicates the superimposed image with The average pixel value of the corresponding region starting from the specified point; Select normalized cross-correlation score The highest sliding position is taken as the peak position. Subpixel interpolation is performed at the peak position and its neighborhood to obtain the marker center position with subpixel accuracy.

8. The nanoscale high-precision bonding mark measurement system according to claim 7, characterized in that, The sub-pixel interpolation includes: The normalized cross-correlation score of the peak position and its neighboring pixels. Fitting a quadratic surface: ; in, , , , , and All are fitting coefficients; Taking the partial derivative of the quadratic surface and setting it to zero, we can obtain the sub-pixel offset. : ; Subpixel precision marker center position for: ; in, Indicates the width of the template. Indicates the height of the template.

9. The nanoscale high-precision bonding mark measurement system according to claim 7, characterized in that, Before sliding the first template or the second template pixel by pixel on the overlay image, the processing module further processes the image of the corresponding template as follows to generate an edge mask: The images of the corresponding templates are processed in parallel using the Canny operator and the Sobel operator respectively. The initial binary edge map is obtained by the Canny operator, and the edge intensity map is obtained by the Sobel operator. A three-level sequential optimization process involving length filtering, strength verification, and connectivity analysis is performed to remove noise and false edges layer by layer, thereby generating the edge mask. The edge mask has a value of 1 in the image edge region and a value of 0 in the non-edge region. When calculating the normalized cross-correlation score, the summation is only performed at the pixel positions where the edge mask has a value of 1, and the non-edge region does not participate in the matching calculation.

10. The nanoscale high-precision bonding mark measurement system according to claim 9, characterized in that, The processing module also employs a dilation module to process the image of the corresponding template to obtain a dilated region map, which is used to provide a reference for connectivity analysis.