Wafer arc defect detection method based on statistical test and multi-feature fusion

Abstract

The invention discloses a wafer arc defect detection method based on statistical test and multi-feature fusion, and belongs to the technical field of wafer defect detection. The method comprises the following steps: constructing a four-layer framework of defect classification, multi-dimensional inspection, interference elimination and mode output, selecting a curvature value, a defect length, defect continuity and a direction angle change rate as features, realizing preliminary classification of defects through a hierarchical clustering algorithm, executing differentiated multi-dimensional special inspection on various pre-classified arc-shaped defects, and carrying out multi-dimensional special inspection on the arc-shaped defects; interference is eliminated in combination with a double-threshold screening and spatial separation mechanism, and a complete defect mode report is output after algorithm optimization and adaptation. Specific inspection schemes are designed for different types of defects such as arc-shaped scratches and particle clusters, the detection accuracy is improved through dynamic threshold and algorithm optimization, noise interference is effectively eliminated, an output report comprises classified statistics, key parameters and process suggestions, reliable support is provided for wafer production process optimization, and the production efficiency is improved. And the pertinence and effectiveness of complex arc defect detection are improved.

Description

Technical Field

[0001] This invention relates to the field of semiconductor manufacturing and wafer defect detection technology, and in particular to a method for detecting arc-shaped defects in wafers based on statistical testing and multi-feature fusion. Background Technology

[0002] In the semiconductor manufacturing industry, wafers are a core component, and their surface defects directly determine chip yield and product reliability. Arc-shaped defects are a typical and complex type of defect in wafer manufacturing, encompassing various forms such as arc-shaped scratches, particle clusters, annular bands, and segmented arcs. These defects exhibit significant differences in parameters such as curvature, length, and orientation angle, and often display irregular distribution characteristics across grids, posing a significant challenge to single-wafer defect detection. Accurate identification of these diverse and complex arc-shaped defects is a crucial step in ensuring wafer production quality and optimizing process parameters, and has significant practical implications for improving semiconductor manufacturing efficiency.

[0003] While existing wafer defect detection solutions have made some progress, there are still significant shortcomings in specialized detection of diverse and complex arc-shaped defects. For example, patent CN119540198A discloses a wafer defect detection method and apparatus. This method generates a comprehensive defect distribution map by superimposing defect data from multiple wafers, identifies COP defect distribution patterns using spatial clustering algorithms, and calculates risk scores based on a defect identification model to determine COP defects. However, its core focus is on batch-level COP defect detection, failing to design specialized detection logic for complex arc-shaped defects with multiple types and parameters on a single wafer. It lacks targeted extraction and differentiated inspection strategies for the core features of arc-shaped defects, and cannot solve the problems of confusion in arc-shaped defect classification and poor adaptability.

[0004] Another patent, CN113095438A, discloses a wafer defect classification method. This method identifies defect types through secondary classification based on feature parameters such as defect size and signal strength values, along with sample images. However, the selected defect feature parameters do not cover the key attributes of arc-shaped defects (such as curvature value, rate of change of orientation angle, and defect continuity), and the classification model is not optimized for the morphological characteristics of arc-shaped defects, making it difficult to distinguish between different types of arc-shaped defects. Furthermore, it lacks an effective mechanism to eliminate noise interference, making it prone to false detections.

[0005] Another patent, CN118096767B, discloses a method for detecting wafer dicing defects. This method combines a multi-classification model with machine vision technology, using contour extraction and rectangular distance calculation to determine the level of dicing defects. However, it only targets the specific defect type of dicing defects and does not cover the specialized detection of various arc-shaped defects such as arc-shaped scratches, particle clusters, and annular bands. Furthermore, it does not construct a multi-dimensional inspection system and algorithm optimization mechanism adapted to different arc-shaped defects, thus failing to meet the detection needs of diverse arc-shaped defects.

[0006] In summary, existing technologies have the following shortcomings: First, there is a lack of a specialized detection framework for the diverse and complex arc-shaped defects on a single wafer. Existing solutions mostly focus on specific defect types or batch-level detection, which is insufficiently adapted to the multi-morphological and multi-parameter characteristics of arc-shaped defects. Second, the selection of defect features is incomplete, failing to cover the core differentiating features of arc-shaped defects, resulting in low classification accuracy. Third, a differentiated multi-dimensional inspection strategy has not been designed, and fixed inspection modes are difficult to match the detection needs of different types of arc-shaped defects. Fourth, the interference elimination mechanism is imperfect, easily affected by noise and non-arc-shaped defects, resulting in a high false detection rate. Fifth, the algorithm's adaptability is insufficient, lacking optimization methods such as feature weight adjustment and multi-model fitting for arc-shaped defects, resulting in limited detection accuracy. Sixth, the output results are mostly simple defect judgments, failing to provide a complete report including process-related suggestions, thus offering weak support for production process optimization. Therefore, there is an urgent need for a specialized detection method for the diverse and complex arc-shaped defects on wafers with strong adaptability and high accuracy to solve the above-mentioned problems of existing technologies. Summary of the Invention

[0007] This invention addresses the shortcomings of existing technologies for detecting diverse and complex arc-shaped defects on single wafers by providing a wafer arc-shaped defect detection method based on statistical testing and multi-feature fusion. This method constructs a four-layer framework, selects four core features, and after hierarchical clustering pre-classification, difference testing, interference elimination, and algorithm optimization, outputs a defect pattern report containing classification statistics, parameters, and process suggestions. It offers multiple advantages, solves a series of problems in arc-shaped defect detection, and can be integrated into existing wafer quality control systems to facilitate process optimization.

[0008] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: A method for detecting arc-shaped defects in wafers based on statistical testing and multi-feature fusion, characterized by comprising the following steps: Step S1: Obtain wafer defect samples containing arc-shaped scratches, arc-shaped particle clusters, annular defect bands, and segmented arcs; construct a four-layer framework for defect classification, multi-dimensional inspection, interference elimination, and mode output; and select curvature value, defect length, defect continuity, and orientation angle change rate as features of wafer arc-shaped defects. Step S2: Perform preliminary classification of wafer defects using a hierarchical clustering algorithm. After hierarchical clustering is completed, calculate the curvature within the cluster, including parameters such as the standard deviation of curvature and the mean curvature, to obtain the pre-classified defect results. Step S3: Perform differentiated multi-dimensional special tests on various types of defects after pre-classification, and at the same time perform optimized distribution verification and statistical tests on various types of defects; Step S4: Combine dual threshold screening and spatial separation mechanism to eliminate interference in the inspected defect data; Step S5: After algorithm optimization and adaptation, output a complete defect mode report.

[0009] Furthermore, the execution process of the hierarchical clustering algorithm described in step S2 is as follows: Step S21: Dynamically classify the wafer historical defect data using the K-means algorithm, select the peak change rate exceeding the threshold based on the peak change rate, and confirm the size of K by combining the original number of patterns. K is the preset number of clusters, that is, the total number of categories into which the target data needs to be divided. Step S22: Subdivide the large class data output by K-means using the Ward method. The Ward method follows the principle of bottom-up merging and minimizing variance increment. It enhances the local features of the large class data output by K-means, supplements local density and sub-region label features, standardizes them, and removes outliers. Step S23: Initialize the defect points within the major category as independent sub-clusters, calculate the variance increment after merging the sub-clusters, and repeatedly merge the sub-clusters with the lowest cost until the sub-cluster number threshold is reached or the merging cost exceeds the limit. Step S24: Perform size screening, spatial continuity verification, and duplicate merging on the merged subclusters, remove invalid small clusters and assign isolated points to obtain subdivided subclusters; at the same time, calculate intra-class feature similarity to verify the classification effectiveness and output the classification results.

[0010] Furthermore, the differential multi-dimensional special test of the arc-shaped scratch in step S3 is a multi-segment fitting and curvature consistency test. The long arc is divided into grids and then fitted using the least squares method. The fitting model includes circular arc, elliptical arc, and parabolic arc. When the deviation of the curvature of each segment from the overall average curvature is less than a preset threshold, it is determined to be a continuous arc with consistent parameters. The dimensional standard for mesh segmentation is as follows: the segmentation is based on the principle of balancing fitting accuracy and computational efficiency, and ensuring that the arc segment within a single mesh is approximately smooth without inflection points. The size is dynamically determined by combining the length L of the long arc and the curvature change. The side length s is from L / 20 to L / 5. The upper limit is taken for gentle curvature and the lower limit is taken for large fluctuations, and 5μm≤s≤20μm. The side length is reduced to 1 / 2 of the original at places where the curvature changes abruptly. If there are fewer than 3 defect points, adjacent meshes are merged. If the local curvature standard deviation exceeds 30% of the overall standard deviation, the mesh is subdivided until the smoothness requirement is met.

[0011] The fitting model selection rule is as follows: adopt a simple-to-complex approach, minimizing residuals and matching curvature features. For single-grid defect points, first fit circular arcs, calculating the fitting residual R1 and constant curvature k1; if R1 exceeds the threshold or the curvature fluctuation exceeds k1±10%, switch to elliptical arcs and calculate R2 and k2; if R2 exceeds the threshold or the curvature deviation exceeds 15%, fit parabolic arcs and calculate R3 and k3. Select the model with the smallest residual, prioritizing models with residuals that closely match the overall arc shape; if none meet the criteria, determine it as a non-parametric arc, and then combine the fitting results of adjacent grids.

[0012] Furthermore, the differential multidimensional special test of the arc-shaped particle cluster in step S3 is a particle density and curvature correlation test. When the particle distribution density is greater than the preset density threshold and the curvature variation coefficient after fitting the particle coordinates is less than the preset variation coefficient threshold, it is determined to be a high-density arc-shaped particle cluster.

[0013] Furthermore, the differentiated multi-dimensional special inspection of the annular defect zone in step S3 is a closure and radius consistency inspection. When the ratio of the distance between the two ends of the arc to the length of the arc reaches the preset closure threshold, and the ratio of the standard deviation of the annular radius to the average radius is less than the preset radius deviation threshold, it is determined to be a complete annular defect zone.

[0014] Furthermore, the segmented arc differential multidimensional special test in step S3 is a segment correlation test. When the cosine similarity of the direction angle of two adjacent arc segments is greater than the preset similarity threshold and the absolute deviation of curvature is less than the preset curvature deviation threshold, they are determined to be segmented arcs from the same source.

[0015] Furthermore, the optimized distribution verification and statistical tests described in step S3 include: adding a direction angle continuity test for arc-shaped scratches, optimizing the arc-shaped global weighted chi-square test for arc-shaped particle clusters, adding a Kruskal-Wallis test for the inner and outer ring defect distributions of the annular defect zone, and adding a segmented arc-shaped path Bezier curve fitting test for the segmented arc.

[0016] Furthermore, the dual-threshold screening and spatial separation mechanism in step S4 is as follows: a dual-dimensional dynamic threshold model is constructed based on the statistical distribution characteristics of historical normal data of wafers. The threshold is adaptively adjusted according to the wafer batch and the process parameters of the inspection area, and the single-segment arc length threshold is... The formula is: In the formula This represents the average length of the arc-shaped structure in historical normal data. The standard deviation of length, These are adaptive coefficients; Arc fit goodness threshold The formula is: In the formula The mean goodness of fit for historical normal arc shapes. The standard deviation of the goodness of fit, This refers to the process adaptability coefficient; When the detected single arc length And goodness of fit Or the total number of arc-shaped defects within the same wafer region When this type of structure is identified as noise, it is directly filtered out. This is the minimum effective quantity threshold based on historical defect density statistics. , To achieve the minimum effective defect density, The area to be detected; The spatial separation mechanism employs an improved Hough transform to extract the defect edge contours and introduces a curvature constraint factor to optimize the accuracy of arc segment recognition. The edge contours are first discretized into a set of pixels. Calculate the curvature of adjacent pixels ,in It is the minimum value. It is the pixel index, representing the position of a single pixel within the defect edge contour, and its value is a positive integer. It is the total number of pixels in the defect edge contour, and is the subscript. The maximum value is a positive integer; a curvature threshold is set. ,in It adaptively adjusts according to the defect size; when the average curvature of consecutive pixels... When it is determined to be an arc segment, It is determined to be a straight line segment; finally, the straight line segment and the arc segment are separated, and only the arc segment is subjected to subsequent testing.

[0017] Furthermore, the algorithm optimization and adaptation in step S5 includes: using weighted Euclidean distance to measure the feature similarity between defects, and dynamically adjusting the weights of each feature according to the defect type; optimizing the weighted chi-square test for discrete arc-shaped particle clusters, introducing particle size weights; and selecting the optimal fitting model by calculating the normalized goodness of fit of different fitting models; the normalized goodness of fit formula is: In the formula The normalized goodness of fit ranges from [0,1]. The closer it is to 1, the higher the degree of matching between the fitted model and the actual defect data. This represents the total number of wafer defect data points involved in the fitting process, i.e., the number of valid defect points within a single grid. For the first The actual observed values ​​of each defect point, including the defect's coordinates, density characteristics, and other fitted target variables; For the first The model prediction value of each defect point is calculated from a circular arc, elliptical arc, or parabolic arc model. The mean of the actual observed values ​​of all defect points, i.e. ; The sum of squared residuals reflects the degree of deviation between the model's predicted values ​​and the actual data. The total sum of squares reflects the degree of dispersion of the actual data.

[0018] Furthermore, the defect pattern report in step S5 includes defect classification statistics, a list of key parameters, and process correlation suggestions. The classification statistics clearly define the number, proportion, and distribution area of ​​each type of defect. The list of key parameters marks the curvature range, length range, and optimal fitting model of each type of defect. The process correlation suggestions output targeted process troubleshooting directions.

[0019] Compared with the prior art, the present invention, employing the above technical solution, has the following beneficial effects: (1) The present invention proposes a wafer arc defect detection method based on statistical testing and multi-feature fusion, which combines a four-layer framework, four core features and hierarchical clustering pre-classification: first, the K-means algorithm is used to dynamically classify the categories based on the historical defect data of the wafer, and then the Ward method is used to further subdivide the categories. The intra-class feature similarity is calculated simultaneously to verify the classification effectiveness. It can accurately distinguish multiple arc defects, solve the classification confusion problem caused by incomplete feature selection in the existing technology, and greatly improve the classification accuracy.

[0020] (2) This invention designs differentiated multi-dimensional special inspections for different arc-shaped defects, combined with optimized distribution verification and statistical inspections. It supports multi-model fitting and selection of the optimal model by using exclusive logic such as multi-segment fitting, density, curvature correlation and weighted chi-square test methods, adapting to the differences in arc-shaped defect parameters and distribution characteristics. Compared with the traditional fixed inspection mode, it significantly improves the detection accuracy and reduces false detections.

[0021] (3) The present invention adopts a dual interference elimination mechanism of dual threshold screening and spatial separation: a dynamic feature threshold is set based on the normal data of the wafer history to screen noise. If the length of a single arc segment, the goodness of fit is not up to standard, or the total number of defects is insufficient, it is judged as noise; Hough transform separates straight lines and arc segments, and only arc segments are tested, which solves the problem of insufficient interference elimination in the existing technology, focuses on real arc defects, and improves the reliability of the results.

[0022] (4) The present invention optimizes the adaptation through core algorithms: the similarity of defect features is measured by weighted Euclidean distance, and the feature weights are dynamically adjusted according to the defect type; the weighted chi-square test of discrete arc-shaped particle clusters is optimized and particle size weights are introduced; the normalized goodness of fit of different fitting models is calculated and the optimal model is selected, which enhances the adaptability to arc-shaped defects of different shapes and discreteness, solves the pain point of poor adaptation of traditional fixed models, can flexibly cope with large differences in parameters, and adapts to the diverse arc-shaped defect detection needs of semiconductor manufacturing. Attached Figure Description

[0023] Figure 1 This is a flowchart of the wafer arc defect detection method designed by the present invention based on statistical testing and multi-feature fusion; Figure 2 This is a schematic diagram of the hierarchical clustering defect classification process. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] A method for detecting arc-shaped defects in wafers based on statistical testing and multi-feature fusion, the process of which is as follows: Figure 1 As shown, it includes the following steps: Step S1: Obtain wafer defect samples containing arc-shaped scratches, arc-shaped particle clusters, annular defect bands, and segmented arcs; construct a four-layer framework for defect classification, multi-dimensional inspection, interference elimination, and mode output; and select curvature value, defect length, defect continuity, and orientation angle change rate as features of wafer arc-shaped defects. Step S2: Perform preliminary classification of wafer defects using a hierarchical clustering algorithm. After hierarchical clustering is completed, calculate the curvature within the cluster, including parameters such as the standard deviation of curvature and the mean curvature, to obtain the pre-classified defect results. Step S3: Perform differentiated multi-dimensional special tests on various types of defects after pre-classification, and at the same time perform optimized distribution verification and statistical tests on various types of defects; Step S4: Combine dual threshold screening and spatial separation mechanism to eliminate interference in the inspected defect data; Step S5: After algorithm optimization and adaptation, output a complete defect mode report.

[0026] Furthermore, the execution process of the hierarchical clustering algorithm described in step S2 is as follows: Figure 2 As shown, specifically: Step S21: Dynamically classify the wafer historical defect data using the K-means algorithm, select the peak change rate exceeding the threshold based on the peak change rate, and confirm the size of K by combining it with the original pattern. K is the preset number of clusters, that is, the total number of categories into which the target data needs to be divided. Step S22: Subdivide the large class data output by K-means using the Ward method. The Ward method adopts a bottom-up merging and minimizing variance increment approach to enhance the local features of the large class data output by K-means, supplement local density and sub-region label features and standardize them, and remove outliers. Step S23: Initialize the defect points within the major category as independent sub-clusters, calculate the variance increment after merging the sub-clusters, and repeatedly merge the sub-clusters with the lowest cost; Step S24: Perform size screening, spatial continuity verification, and duplicate merging on the merged subclusters, remove invalid small clusters and assign isolated points to obtain subdivided subclusters; at the same time, calculate intra-class feature similarity to verify the classification effectiveness and output the classification results.

[0027] Furthermore, the differential multi-dimensional special test of the arc-shaped scratch in step S3 is a multi-segment fitting and curvature consistency test. The long arc is divided into grids and then fitted using the least squares method. The fitting model includes circular arcs, elliptical arcs, and parabolic arcs. When the deviation of the curvature of each segment from the overall average curvature is less than a preset threshold, it is determined to be a continuous arc with consistent parameters.

[0028] The mesh segmentation is based on the core principle of "balancing fitting accuracy and computational efficiency, and ensuring that the arc-shaped segments within a single mesh are approximately smooth segments without inflection points." Specific size standards need to be dynamically determined by combining the overall length L of the long arc-shaped defect (calculated based on wafer defect coordinates, in μm) and the curvature variation amplitude: the single-mesh side length s ranges from L / (10~20) to L / (5~10), with the upper limit used when curvature changes are gradual and the lower limit used when there are large fluctuations. Simultaneously, to adapt to the μm-level detection accuracy of the wafer, the minimum side length is set to be no less than 5μm (to avoid...). The maximum value is 20μm (affected by the coordinate error of a single defect point) to ensure the consistency of curvature of the arc segment. If there is an obvious curvature change in the long arc, the grid side length needs to be reduced to 1 / 2 of the original size at the change point to improve the recognition accuracy. If the number of defect points in a certain grid is less than 3 after segmentation (which cannot meet the least squares fitting sample size requirement), it is merged into the adjacent grid. If the local curvature standard deviation exceeds 30% of the overall average curvature, the grid is further split until the curvature fluctuation of the segment in the grid meets the "approximately smooth" requirement.

[0029] The selection of the fitting model follows a priority logic of "simple first, complex later, based on residual minimization and curvature feature matching." For a defect point within a single grid, the least squares method is first used to fit a circular arc model with the fewest parameters and highest computational efficiency to solve for the center coordinates and radius, and to calculate the fitting residual R1 and constant curvature k1. If R1 exceeds a preset residual threshold, or the actual curvature fluctuation of the defect point exceeds ±10% of k1, the model is switched to an elliptical arc model to solve for the major semi-axis, minor semi-axis, center coordinates, and rotation angle, and to calculate the residual R2 and variable curvature k2. If the elliptical arc fitting still fails to meet the requirements (R2 exceeds the threshold or the local curvature deviates from the theoretical curvature by more than 15%), a parabolic arc model is fitted (y=ax is selected according to the arc direction). 2 +bx+c or x=ay 2(in the form of +by+c), calculate the residual R3 and curvature k3; finally, compare the residuals of the three models and select the model with the smallest residual. If the residuals of multiple models are close (the difference is less than 10% of the residual threshold), then the model whose curvature characteristics match the overall arc shape is selected first (e.g., elliptical arc for slow curvature changes, parabolic arc for linear changes). If the residuals of all models do not meet the standard, then the segment is determined to be a "non-parametric arc". Subsequently, the fitting results of adjacent grids are combined and spliced ​​to ensure that the fitting results of each grid segment meet the parameter consistency requirements of the long arc.

[0030] Furthermore, the differential multidimensional special test of the arc-shaped particle cluster in step S3 is a particle density and curvature correlation test. When the particle distribution density is greater than the preset density threshold and the curvature variation coefficient after fitting the particle coordinates is less than the preset variation coefficient threshold, it is determined to be a high-density arc-shaped particle cluster.

[0031] Furthermore, the differentiated multi-dimensional special inspection of the annular defect zone in step S3 is a closure and radius consistency inspection. When the ratio of the distance between the two ends of the arc to the length of the arc reaches the preset closure threshold, and the ratio of the standard deviation of the annular radius to the average radius is less than the preset radius deviation threshold, it is determined to be a complete annular defect zone.

[0032] Furthermore, the segmented arc differential multidimensional special test in step S3 is a segment correlation test. When the cosine similarity of the direction angle of two adjacent arc segments is greater than the preset similarity threshold and the absolute deviation of curvature is less than the preset curvature deviation threshold, they are determined to be segmented arcs from the same source.

[0033] Furthermore, the optimized distribution verification and statistical tests described in step S3 include: adding a direction angle continuity test for arc-shaped scratches, optimizing the arc-shaped global weighted chi-square test for arc-shaped particle clusters, adding a Kruskal-Wallis test for the inner and outer ring defect distributions of the annular defect zone, and adding a segmented arc-shaped path Bezier curve fitting test for the segmented arc.

[0034] Furthermore, the dual-threshold screening and spatial separation mechanism described in step S4 is as follows: A two-dimensional dynamic threshold model is constructed based on the statistical distribution characteristics of historical normal data of wafers. The threshold is adaptively adjusted according to the wafer batch and the process parameters of the inspection area, with a single arc length threshold. The formula is: In the formula This represents the average length of the arc-shaped structure in historical normal data. The standard deviation of length, These are adaptive coefficients; Arc fit goodness threshold The formula is: In the formula The mean goodness of fit for historical normal arc shapes. The standard deviation of the goodness of fit, This is the process adaptability coefficient.

[0035] When the detected single arc length And goodness of fit Or the total number of arc-shaped defects within the same wafer region When this type of structure is identified as noise, it is directly filtered out. This is the minimum effective quantity threshold based on historical defect density statistics. , To achieve the minimum effective defect density, The area to be detected; The spatial separation mechanism employs an improved Hough transform to extract the defect edge contours and introduces a curvature constraint factor to optimize the accuracy of arc segment recognition. The edge contours are first discretized into a set of pixels. Calculate the curvature of adjacent pixels ,in It is the minimum value. It is the pixel index, representing the position of a single pixel within the defect edge contour, and its value is a positive integer. It is the total number of pixels in the defect edge contour, and is the subscript. The maximum value is a positive integer; a curvature threshold is set. ,in It adaptively adjusts according to the defect size; when the average curvature of consecutive pixels... When it is determined to be an arc segment, It is determined to be a straight line segment; finally, the straight line segment and the arc segment are separated, and only the arc segment is subjected to subsequent testing.

[0036] Furthermore, the algorithm optimization and adaptation in step S5 includes: using weighted Euclidean distance to measure the feature similarity between defects, and dynamically adjusting the weights of each feature according to the defect type; optimizing the weighted chi-square test for discrete arc-shaped particle clusters, introducing particle size weights; and selecting the optimal fitting model by calculating the normalized goodness of fit of different fitting models; the normalized goodness of fit formula is: In the formula The normalized goodness of fit ranges from [0,1]. The closer it is to 1, the higher the degree of matching between the fitted model and the actual defect data. This represents the total number of wafer defect data points involved in the fitting process, i.e., the number of valid defect points within a single grid. For the first The actual observed values ​​of each defect point, including the defect's coordinates, density characteristics, and other fitted target variables; For the first The model prediction value of each defect point is calculated from a circular arc, elliptical arc, or parabolic arc model. The mean of the actual observed values ​​of all defect points, i.e. ; The sum of squared residuals reflects the degree of deviation between the model's predicted values ​​and the actual data. The total sum of squares reflects the degree of dispersion of the actual data.

[0037] Furthermore, the defect pattern report in step S5 includes defect classification statistics, a list of key parameters, and process correlation suggestions. The classification statistics clearly define the number, proportion, and distribution area of ​​each type of defect. The list of key parameters marks the curvature range, length range, and optimal fitting model of each type of defect. The process correlation suggestions output targeted process troubleshooting directions.

[0038] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail 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; 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 of the present invention.

Claims

1. A method for detecting arc-shaped defects in wafers based on statistical testing and multi-feature fusion, characterized in that, Includes the following steps: Step S1: Obtain wafer defect samples containing arc-shaped scratches, arc-shaped particle clusters, annular defect bands, and segmented arcs; construct a four-layer framework for defect classification, multi-dimensional inspection, interference elimination, and mode output; and select curvature value, defect length, defect continuity, and orientation angle change rate as features of wafer arc-shaped defects. Step S2: Perform preliminary classification of wafer defects using a hierarchical clustering algorithm. After hierarchical clustering is completed, calculate the curvature within the cluster, including parameters such as the standard deviation of curvature and the mean curvature, to obtain the pre-classified defect results. Step S3: Perform differentiated multi-dimensional special tests on various types of defects after pre-classification, and at the same time perform optimized distribution verification and statistical tests on various types of defects; Step S4: Combine dual threshold screening and spatial separation mechanism to eliminate interference in the inspected defect data; Step S5: After algorithm optimization and adaptation, output a complete defect mode report.

2. The wafer arc defect detection method based on statistical testing and multi-feature fusion according to claim 1, characterized in that, The execution process of the hierarchical clustering algorithm described in step S2 is as follows: Step S21: Dynamically classify the wafer's historical defect data using the K-means algorithm, select the peak change rate exceeding the threshold based on the peak change rate, and confirm the size of K by combining the original defect feature patterns. K is the preset number of clusters, i.e., the total number of categories into which the target data needs to be divided. Step S22: Subdivide the large class data output by K-means using the Ward method. The Ward method adopts a bottom-up merging and minimizing variance increment approach to enhance the local features of the large class data output by K-means, supplement local density and sub-region label features and standardize them, and remove outliers. Step S23: Initialize the defect points within the major category as independent sub-clusters, calculate the variance increment after merging the sub-clusters, and repeatedly merge the sub-clusters with the lowest cost; Step S24: Perform size screening, spatial continuity verification, and duplicate merging on the merged subclusters, remove invalid small clusters and assign isolated points to obtain subdivided subclusters; at the same time, calculate intra-class feature similarity to verify the classification effectiveness and output the classification results.

3. The wafer arc defect detection method based on statistical testing and multi-feature fusion according to claim 1, characterized in that, The differential multidimensional special test of the arc-shaped scratch in step S3 is a multi-segment fitting and curvature consistency test. The long arc is divided into grids and then fitted using the least squares method. The fitting model includes circular arc, elliptical arc and parabolic arc. When the deviation of the curvature of each segment from the overall average curvature is less than a preset threshold, it is determined to be a continuous arc with consistent parameters.

4. The wafer arc defect detection method based on statistical testing and multi-feature fusion according to claim 1, characterized in that, The differential multidimensional special test of the arc-shaped particle cluster in step S3 is the particle density and curvature correlation test. When the particle distribution density is greater than the preset density threshold and the curvature variation coefficient after fitting the particle coordinates is less than the preset variation coefficient threshold, it is determined to be a high-density arc-shaped particle cluster.

5. The wafer arc defect detection method based on statistical testing and multi-feature fusion according to claim 1, characterized in that, The differential multi-dimensional special inspection of the annular defect zone in step S3 is a closure and radius consistency inspection. When the ratio of the distance between the two ends of the arc to the length of the arc reaches the preset closure threshold, and the ratio of the standard deviation of the annular radius to the average radius is less than the preset radius deviation threshold, it is determined to be a complete annular defect zone.

6. The wafer arc defect detection method based on statistical testing and multi-feature fusion according to claim 1, characterized in that, The segmented arc differential multidimensional special test mentioned in step S3 is the inter-segment correlation test. When the cosine similarity of the direction angle of two adjacent arc segments is greater than the preset similarity threshold and the absolute deviation of curvature is less than the preset curvature deviation threshold, they are determined to be segmented arcs from the same source.

7. The wafer arc defect detection method based on statistical testing and multi-feature fusion according to claim 1, characterized in that, The optimized distribution verification and statistical tests described in step S3 include: adding a continuity test for the direction angle of the arc-shaped scratch, optimizing the arc-shaped global weighted chi-square test for the arc-shaped particle cluster, adding a Kruskal-Wallis test for the inner and outer ring defect distribution of the ring-shaped defect zone, and adding a Bézier curve fitting test for the segmented arc-shaped path.

8. The wafer arc defect detection method based on statistical testing and multi-feature fusion according to claim 1, characterized in that, The dual-threshold screening and spatial separation mechanism in step S4 is as follows: a two-dimensional dynamic threshold model is constructed based on the statistical distribution characteristics of historical normal data of wafers. The threshold is adaptively adjusted according to the wafer batch and the process parameters of the inspection area, and the single-segment arc length threshold is used. The formula is: In the formula This represents the average length of the arc-shaped structure in historical normal data. The standard deviation of length, These are adaptive coefficients; Arc fit goodness threshold The formula is: In the formula The mean goodness of fit for historical normal arc shapes. The standard deviation of the goodness of fit, This refers to the process adaptability coefficient; When the detected single arc length And goodness of fit Or the total number of arc-shaped defects within the same wafer region When this type of structure is identified as noise, it is directly filtered out. This is the minimum effective quantity threshold based on historical defect density statistics. , To achieve the minimum effective defect density, The area to be detected; The spatial separation mechanism employs an improved Hough transform to extract the defect edge contours and introduces a curvature constraint factor to optimize the accuracy of arc segment recognition. The edge contours are first discretized into a set of pixels. Calculate the curvature of adjacent pixels ,in It is the minimum value. It is the pixel index, representing the position of a single pixel within the defect edge contour, and its value is a positive integer. It is the total number of pixels in the defect edge contour, and is the subscript. The maximum value is a positive integer; a curvature threshold is set. ,in It adapts to the defect size; When the mean curvature of consecutive pixels When it is determined to be an arc segment, It is determined to be a straight line segment; finally, the straight line segment and the arc segment are separated, and only the arc segment is subjected to subsequent testing.

9. The wafer arc defect detection method based on statistical testing and multi-feature fusion according to claim 1, characterized in that, The algorithm optimization and adaptation in step S5 includes: using weighted Euclidean distance to measure the feature similarity between defects, and dynamically adjusting the weights of each feature according to the defect type; optimizing the weighted chi-square test for discrete arc-shaped particle clusters, introducing particle size weights; and selecting the optimal fitting model by calculating the normalized goodness of fit of different fitting models. The normalized goodness of fit formula is as follows: In the formula The normalized goodness of fit ranges from [0,1]. The closer it is to 1, the higher the degree of matching between the fitted model and the actual defect data. This represents the total number of wafer defect data points involved in the fitting process, i.e., the number of valid defect points within a single grid. For the first The actual observed values ​​of each defect point, including the defect's coordinates, density characteristics, and other fitted target variables; For the first The model prediction value of each defect point is calculated from a circular arc, elliptical arc, or parabolic arc model. The mean of the actual observed values ​​of all defect points, i.e. ; The sum of squared residuals reflects the degree of deviation between the model's predicted values ​​and the actual data. The total sum of squares reflects the degree of dispersion of the actual data.

10. The wafer arc defect detection method based on statistical testing and multi-feature fusion according to claim 1, characterized in that, The defect pattern report in step S5 includes defect classification statistics, a list of key parameters, and process correlation suggestions. The classification statistics clearly define the number, proportion, and distribution area of ​​each type of defect. The list of key parameters marks the curvature range, length range, and optimal fitting model of each type of defect. The process correlation suggestions output targeted process troubleshooting directions.

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