Wafer defect cluster analysis method based on DBSCAN clustering

Abstract

The invention relates to the technical field of wafer defect analysis and big data processing, and discloses a wafer defect cluster analysis method based on DBSCAN clustering, which effectively reduces the clustering range and greatly improves the processing efficiency by performing standardized preprocessing on defect data and performing gridding and neighborhood search. Then, self-adaptive DBSCAN clustering and cross-neighborhood merging are utilized, and the dependency of a traditional clustering method on clustering number presetting and the recognition limitation of the traditional clustering method on irregular-shaped clusters are overcome; the Geyer saturation point process is introduced to perform significance quantification on the defect cluster, and the interaction strength of the cluster is scientifically judged, so that a reliable quantitative index is provided for identifying the defect cluster really caused by the process problem.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wafer defect analysis and big data processing, and particularly relates to a wafer defect cluster analysis method based on DBSCAN clustering. BACKGROUND

[0002] With the rapid development of the semiconductor industry, wafer manufacturing processes are becoming increasingly complex, and higher requirements are placed on quality control of the manufacturing process. One of the core goals of wafer defect detection, as a key link to ensure product yield, is to effectively analyze the massive defect data generated on the wafer, so as to identify defect clusters with process correlation. Early wafer defect analysis methods mostly rely on manual visual inspection, which is inefficient and highly subjective. In order to solve this problem, researchers have gradually introduced automated methods based on statistics, image processing, and machine learning, among other technologies. Among these methods, defect cluster analysis based on clustering algorithms has been widely used because it can automatically identify and group defect patterns with similar characteristics.

[0003] CN112102226A discloses a wafer defect pattern detection method. Although it introduces 3D layering type spatial autocorrelation and other technologies to remove noise, and uses multivariate spatial probability distribution values as learning features to improve robustness to noise and rotation, it still has certain limitations. This method relies on complex learning feature generation and multi-level classification, which has high computational complexity and may take a long time to train the model. For online wafer defect analysis scenarios that require fast feedback, real-time performance is not good. In addition, it needs to adjust and train the model for different manufacturing processes and defect types, and lacks universality.

[0004] US20100057391A1 discloses a method of classifying spatial patterns on a wafer map by K-means clustering and generating a tree graph to group wafer maps with similar spatial patterns. However, K-means clustering requires a pre-specified number of clusters, which is often difficult to determine when facing unknown numbers and various shapes of wafer defect clusters, resulting in inaccurate clustering results. In addition, this method is not ideal for clustering non-spherical or irregularly shaped defect clusters. More importantly, existing technologies generally lack in-depth quantitative analysis of the internal structure and interaction of defect clusters, making it difficult to effectively distinguish between defect aggregation caused by random distribution and real clusters caused by specific process problems, and also making it difficult to quantitatively evaluate the significance of the clusters, making it difficult to make a scientific judgment on the cause of the defects.

[0005] In summary, the existing wafer defect analysis technology generally has the following problems: firstly, for massive and complex defect data, the calculation efficiency and real-time performance of the existing method need to be improved; secondly, some methods have limitations in processing irregular or unknown number of defect clusters; more importantly, the existing technology lacks scientific quantitative evaluation of the significance of defect clusters, and cannot effectively distinguish random aggregation from real clusters, making the diagnosis of process problems lack reliable basis.

[0006] The wafer defect cluster analysis method based on DBSCAN clustering provided by the present application solves the above technical problems through multi-stage and adaptive clustering and analysis; the present application standardizes the defect data, effectively reduces the clustering range through gridding and neighborhood search, and greatly improves the processing efficiency; then, adaptive DBSCAN clustering and cross-neighborhood merging are used to overcome the dependence of traditional clustering methods on preset clustering number and the recognition limitations of irregular shape clusters; the Geyer saturation point process is introduced to quantify the significance of defect clusters, and the interaction strength of the clusters is scientifically judged, thereby providing a reliable quantitative index for identifying defect clusters caused by process problems. SUMMARY

[0007] This part aims to summarize some aspects of the embodiments of the present application and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this part and the abstract and title of the present application to avoid obscuring the purpose of this part, the abstract and the title, and such simplifications or omissions cannot be used to limit the scope of the present application.

[0008] In view of the above-mentioned existing problems, the present application is proposed.

[0009] To solve the above technical problems, the present application provides the following technical solutions: obtaining defect point coordinates, wafer layout and chip unit grid information, correcting and aligning the defect points to zero and mapping them to the same wafer coordinate system to obtain a standardized defect point set; According to the chip unit grid, the wafer effective area is gridded and the grid attribution statistics of the standardized defect point set are performed, and the boundary incomplete grid is normalized according to the effective area to obtain a grid defect count distribution; According to a preset first threshold T1, the grid with defect count ≥ T1 is marked as a candidate aggregation grid set; Taking each grid in the candidate aggregation grid as the center, an n*n grid neighborhood is constructed and all standardized defect points in the neighborhood are collected to form a potential aggregation point set corresponding to each candidate aggregation grid; Adaptive determination of radius parameter and minimum sample number of DBSCAN according to chip unit size, detection resolution and local density, local clustering of the potential cluster set to obtain local cluster and local noise point; Cross-neighbor merging of adjacent local clusters based on boundary overlap rate to obtain wafer-wide consistent defect cluster and global noise point set; Fitting of Geyer saturation point process and boundary correction maximum likelihood estimation of each defect cluster in the wafer-wide consistent defect cluster to obtain estimation values of interaction strength, interaction radius and constant, and calculation of significance index by Monte Carlo to judge the interaction strength; Based on the wafer-wide consistent defect cluster and the interaction strength judgment result, the center position, boundary range, defect point number, density, shape and directionality index of each defect cluster are calculated, and the estimation values of the interaction strength, interaction radius and constant and the significance index are summarized , and the global noise point set is output at the same time, and a structured analysis report is generated accordingly.

[0010] The beneficial effects of the present application are: the present application effectively decomposes and parallelizes the wafer-wide clustering problem by grid rough screening, local clustering and global merging, greatly improving the computing efficiency of processing massive wafer defect data, and secondly, the adaptive DBSCAN parameter determination and cross-neighbor merging mechanism solves the limitations of traditional clustering methods in processing complex and irregular defect clusters, ensuring the accuracy of identification; At the same time, by introducing the Geyer saturation point process into defect analysis, accidental aggregation caused by random probability and true cluster caused by specific process problems can be clearly distinguished, so that analysis resources are focused on defect patterns that are truly related to process, greatly improving the accuracy and reliability of defect analysis. BRIEF DESCRIPTION OF DRAWINGS

[0011] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and those skilled in the art can obtain other drawings according to these drawings without creative labor. Among them: Figure 1 The flowchart of the wafer defect cluster analysis method based on DBSCAN clustering shown in the present application. DETAILED DESCRIPTION

[0012] In order to make the above objectives, characteristics and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments.

[0013] Based on the embodiments in the present application, all other embodiments obtained by the ordinary person in the art without creative labor should belong to the scope of protection of the present application.

[0014] In the following description, many specific details are set forth in order to provide a thorough understanding of the present application. However, the present application can be practiced in other manners different from those described herein, and those skilled in the art can make similar generalizations without departing from the scope of the present application. Therefore, the present application is not limited to the specific embodiments disclosed below.

[0015] According to the embodiments of the present application, combined with the flowchart shown in Figure 1 , a wafer defect cluster analysis method based on DBSCAN clustering specifically includes the following steps: S1, obtain defect point coordinates, wafer layout and chip unit grid information, correct distortion and align zero of the defect points, and uniformly map them to the same wafer coordinate system to obtain a standardized defect point set. It should be noted that in this step: Based on the pre-set known anchor points (such as chip corner points, specific structure markers) and orientation markers (such as the flat edge or notch of the wafer) in the wafer layout, the system collects calibration patterns. The coordinates of these anchor points in the ideal wafer coordinate system are known; by comparing the original imaging coordinates with these ideal coordinates, a combined correction model of imaging distortion and geometric perspective is established (in order to accurately convert the original defect point coordinates obtained from the detection device to the unified wafer global coordinate system, this process is essentially a nonlinear regression problem, and the model parameters are fitted and solved by least squares method to minimize the error between the original coordinates after model transformation and the ideal wafer coordinates), which can quantify the spatial error caused by nonlinear distortion of the optical system, tilt of the detection platform, etc. The model parameters are fitted by least squares method, and finally fixed as a single correction parameter set.

[0016] After obtaining the correction parameter set, it is applied to the original coordinates of each batch of defect points Through the correction, the original coordinates are corrected by anti-distortion and perspective, so as to obtain the corrected defect point coordinates closer to the real physical position. This process can be represented as a function mapping: Among them, represents the combined correction function, representing a set of corrected parameters for curing.

[0017] A unified wafer global coordinate system is defined with wafer orientation mark as reference axis (e.g. align wafer flat edge with Y axis) and wafer geometric center as origin. Due to possible minor mechanical deviation or die placement difference among different detection batches, a rigid registration transformation between the corrected defect point coordinate system of current batch and the wafer global coordinate system is calculated, which includes translation and rotation. The transformation is solved by anchor point based least square method, and the rigid registration parameters are obtained and applied to all corrected defect point coordinates to achieve unified registration.

[0018] To further eliminate minor and non-uniform scaling or shearing errors, a constrained affine fine-tuning is performed within a preset error upper limit. This step ensures the size and shape consistency of the chip grid in the global coordinate system, thereby generating candidate defect point coordinates in the unified wafer coordinate system .

[0019] To ensure data purity, candidate defect points need to be de-duplicated and removed. First, according to the detection resolution and the minimum distinguishable distance, delete the repeated coordinates caused by repeated sampling, for example, if the distance between two points is less than the minimum distinguishable distance, only one of them is kept. Second, remove the defect points located in the undetectable area (such as wafer edge exclusion zone, test structure, die street, etc.).

[0020] The relative position relationship between the generated candidate defect point set and the grid is verified for consistency, which is achieved by calculating the average offset of all candidate points to their respective chip grid center. If the overall offset exceeds the preset threshold, it indicates that there may be systematic deviation in the registration. At this time, the system will return to the unified registration step to fine-tune the registration parameters and re-execute the subsequent steps until the verification meets the preset threshold requirements.

[0021] After all the above correction, registration, de-duplication and verification steps, a high-precision and high-quality standardized defect point set is finally obtained, which is mathematically represented as: wherein, represents the standardized defect point set, represents the two-dimensional coordinates of the i-th standardized defect point in the set, and N is the total number of standardized defect points. At the same time, the system will record the correction parameters and registration parameters used during the entire processing process to facilitate subsequent data tracing.

[0022] It should be noted that the above method of correcting the original coordinates by non-linear optical distortion and performing a radiometric transformation on the corrected coordinates to achieve geometric perspective correction and zero alignment, as well as the method of fitting by least squares, can be performed by means and methods in the prior art, and will not be described in detail in this example.

[0023] S2, grid the wafer effective area based on the chip unit grid and perform grid attribution statistics on the standardized defect point set, normalize the effective area of the non-complete grid, and obtain the grid defect count distribution. It should be noted that the following steps are required: Determine the effective analysis area and generate an effective area mask according to the wafer diameter, edge exclusion zone, and non-detectable area; Establish a row and column grid set in the effective area with the chip unit grid as the basic unit, and record the effective coverage area proportion of each grid; Attributing the standardized defect points to the corresponding grid based on their spatial position, and uniquely dividing the points located on the common boundary of the grid based on the layout coverage priority; For non-complete grids located at the boundary of the effective area, perform normalization processing on the attribution count based on their effective coverage area proportion; Perform consistency detection on the count results of all grids, and mark the grids that have abnormal differences with adjacent grids and coincide with the image stitching boundary as quality attention objects; Output the grid defect count distribution containing the normalized count, effective area proportion, and quality mark of each grid.

[0024] In the preferred embodiment, the effective analysis area is determined and the corresponding mask is generated by the following steps: according to the physical diameter of the wafer, a circular boundary is determined, and the area outside this boundary is excluded from the analysis range; according to the pre-set edge exclusion zone information in the semiconductor manufacturing process, a ring-shaped area is demarcated within the above-mentioned circular boundary, which is marked as an unanalyzable area; in combination with the wafer layout data, known non-detectable areas such as test chips, optical alignment marks, process monitoring structures, or scribe lanes are identified, and these areas are also marked as unanalyzable; all the above-mentioned unanalyzable areas are removed from the total area of the wafer, and the remaining part is the effective analysis area that can be used for defect analysis; then, based on the effective analysis area, a digital effective area mask is generated, which marks all points in the effective area as "analyzable" and marks all points in the unanalyzable area as "unanalyzable", and this mask serves as a spatial constraint for all subsequent griding and attribution operations.

[0025] Further, in the embodiment, the row-column grid set is established and the effective coverage area ratio is recorded by the following steps: taking the chip unit grid as a basic unit, a complete row-column grid set is established in the effective analysis area determined above, the set is composed of rectangular grids corresponding to all chip units on the wafer layout, for each grid in the set, the coverage area in the effective analysis area mask is calculated and compared with the overall area of the grid, so as to obtain the effective coverage area ratio of each grid; for the complete grid located entirely in the effective analysis area, the effective coverage area ratio is 100%, and for the non-complete grid located at the boundary of the effective analysis area, that is, partially across the edge exclusion zone or the non-detectable area, the effective coverage area ratio will be less than 100%.

[0026] Further, in the embodiment, the standardized defect points are uniquely attributed to the corresponding grid by the following steps: the system traverses the standardized defect point set obtained in step S1, and according to the coordinates of each point, the spatial position is matched with the established row-column grid set, and each point is uniquely attributed to the grid where it is located; if a defect point is located on the common boundary of two or more grids, it will be uniquely divided according to the preset layout coverage priority rule to avoid repeated counting; for example, the priority rule is set as: if the point is located on the boundary of a complete grid and a non-complete grid, it is preferentially attributed to the complete grid; if it is located on the boundary of two complete grids, it is divided according to the preset row-column index priority (for example, preferentially attributed to the grid with smaller row index).

[0027] It should be further pointed out that, in the embodiment, the consistency of grid counting is detected by the following steps: analyzing the normalized defect counting results of all grids, identifying abnormal values by comparing the counting difference between each grid and its adjacent grid; if the counting of a certain grid has a significant abnormal difference with the average counting of its adjacent grid, the grid is preliminarily marked as a potential abnormality; then, the spatial position of the potential abnormal grid is compared with the image stitching boundary information recorded in the wafer detection process, if the abnormal counting of a grid coincides with its position on the image stitching boundary, the grid is marked as a "quality concern object", which indicates that its abnormal counting may be caused by image stitching artifacts rather than real process problems; all grids detected in this way will output their normalized counting, effective area ratio and whether they are marked as quality concern objects for subsequent analysis reference.

[0028] S3, mark the grid with defect counting ≥ T1 as a candidate aggregated grid set according to the preset first threshold T1. It should be pointed out that, in this step: The overall statistics of the grid defect counting distribution are performed to form a baseline counting interval and an abnormal floating indication interval. The first threshold T1 is used as a judgment condition, and the grid with a count greater than or equal to T1 is selected as an initial candidate set; The spatial connectivity of the initial candidate set is checked, and isolated grids that are not adjacent to any candidate grid and whose counts only fall within a narrow band near T1 are removed; The candidate aggregation grid set and its labeling information are output.

[0029] Exemplarily, the preset method of the first threshold T1 is as follows: the integer value of the 95th percentile of the grid count distribution of the same machine and the same formula of the latest batch after the effective area and the resolution are consistent is taken as the initial threshold, and then the candidate grid ratio of the current wafer is taken as a reference, and the initial threshold is adjusted by ±1 count once to make the candidate ratio fall within the interval of 2% to 8%, and the adjustment is frozen as the final first threshold T1 after adjustment. Among them, the latest batch is the latest 30 pieces, and the initial threshold is not less than 2.

[0030] As a preferred embodiment, the grid defect count distribution is statistically analyzed and an interval is formed, which specifically includes: the normalized defect count of all grids is comprehensively statistically analyzed to obtain basic statistical quantities such as mean, median and standard deviation, and a histogram reflecting the characteristics of the count distribution is generated. Based on the statistical results, a baseline count interval is determined, which covers the count range of most normal grids and reflects the general defect background noise level on the wafer. For example, the interval is defined as the range of one or two standard deviations above and below the mean of the grid count. The grid with a high count value exceeding the baseline count interval is considered abnormal, and accordingly an abnormal floating indication interval is formed to preliminarily mark the grid with a high count value, providing a reference for subsequent threshold screening.

[0031] Further, in the present embodiment, the spatial connectivity of the initial candidate set is checked and the isolated grids are removed by the following steps: for each grid in the set, check whether it is also located in the initial candidate set with any of its eight adjacent grids (up, down, left, right and four diagonal directions). If a grid is not adjacent to any of its adjacent grids, and its count is only slightly higher than the first threshold T1 (for example, falling within a narrow band near T1), the grid is determined to be an isolated grid. These isolated grids are usually caused by random noise or single-point anomalies and do not constitute a real defect cluster, so these isolated grids are removed from the initial candidate set to ensure that the final candidate set only contains grids with spatial aggregation.

[0032] After the above screening and checking, a set of candidate aggregation grids is finally generated, and the corresponding marking information is output. The output generation method is as follows: the detailed information of all grids that pass the spatial connectivity check and are retained is summarized to form the final set of candidate aggregation grids. In this process, the corresponding marking information is also attached to each grid. The marking information includes but is not limited to the original count, the normalized count, the row and column index of the grid, and a mark indicating whether it is an "isolated grid". In addition, the specific value of the first threshold T1 used in this screening is also recorded. In this way, the generated report not only provides the screened grid set, but also contains key metadata for tracing and understanding the screening process, ensuring the transparency and reliability of the analysis results.

[0033] S4. Centering on each grid in the candidate aggregation grid, an n x n grid neighborhood is constructed and all standardized defect points in the neighborhood are collected to form a set of potential aggregation points corresponding to each candidate aggregation grid. It needs to be explained that: Centering on each candidate aggregation grid, an n x n rectangular neighborhood is constructed by symmetric expansion in rows and columns, where n is determined according to the chip cell size and the known process impact radius; When the neighborhood crosses the effective area, the neighborhood is truncated according to the effective area boundary, and the effective coverage ratio of the neighborhood is recorded; All standardized defect points in the neighborhood are collected to form a set of original neighborhood points corresponding to the center candidate grid; For the overlapping region of adjacent candidate grid neighborhoods, a non-repeated reference strategy is used for point attribution to avoid repeated counting; When the effective coverage ratio of the neighborhood is lower than the second threshold T2, a boundary risk mark is added to the original neighborhood point set; The set of potential aggregation points and its corresponding neighborhood coverage ratio and risk mark are output.

[0034] It needs to be explained that the present embodiment uses a non-repeated reference strategy to process the overlapping region of adjacent candidate grid neighborhoods, which specifically includes: when constructing the neighborhood of each candidate grid and collecting the defect points therein, a temporary mark is established for each processed standardized defect point. When processing the next neighborhood, if its spatial range overlaps with the previously processed neighborhood, the defect points in the overlapping region will be collected first, and then it will be checked whether these points have been marked as already referenced. If a defect point has been marked, it will be skipped and will not be counted into the point set of the current neighborhood, thereby ensuring that each defect point is only uniquely attributed to the set of potential aggregation points associated with it first. This strategy avoids repeated analysis of the same defect point, ensuring the accuracy and uniqueness of the subsequent local clustering results.

[0035] It is further needed to be explained that the second threshold T2 is selected to identify those potential cluster sets whose neighborhood range is seriously truncated by the effective analysis area boundary, which may lead to incomplete defect point data, and the threshold is preset as fifty percent; the specific implementation method of the threshold is: for each constructed n x n neighborhood, the intersection area with the effective analysis area mask is calculated, and the intersection area is compared with the complete n x n neighborhood area to obtain the effective coverage ratio of the neighborhood; when the effective coverage ratio is lower than the preset second threshold T2, it is considered that the defect point set in the neighborhood fails to completely reflect the real defect cluster, and therefore the boundary risk label is added to the original neighborhood point set.

[0036] In the preferred embodiment, the potential cluster set finally output by the embodiment is a structured data set, which includes the defect point list corresponding to each candidate cluster grid and related metadata, specifically including: packaging and integrating the standardized defect point data collected by each center grid, the effective coverage ratio of the neighborhood, and whether the information has a risk label; the risk label is a key component, which includes a classification label (such as: boundary risk, edge truncation or no risk) for explicitly indicating whether the point set has the possibility of incomplete data due to the serious truncation of the neighborhood.

[0037] S5, in combination with the chip unit size, the detection resolution and the local density, the radius parameter and the minimum sample number of DBSCAN are adaptively determined, the local clustering is performed on the potential cluster set, and the local cluster and the local noise point are obtained. It needs to be explained that in this step: The lower limit of the density neighborhood radius is determined according to the chip unit feature size and the detection resolution, and the average neighborhood spacing and its stable interval in the potential cluster set are used as references to set the local radius parameter; The initial value of the minimum sample number is determined in combination with the neighborhood area and the local radius parameter, and the minimum sample number lower limit is increased synchronously with the decrease of the neighborhood effective coverage ratio; When the stripe or grid artifact along the scanning direction is detected, the neighborhood relationship in the direction is given a lower weight to suppress the false clustering; DBSCAN clustering is performed under the determined local radius parameter and minimum sample number, and the local cluster set and the local noise point set are output, and the boundary polygon and the target center point are generated for each local cluster; The local cluster and the local noise point corresponding to each potential cluster set are output.

[0038] In a preferred embodiment, the radius parameter of DBSCAN is adaptively determined, including: taking the chip unit feature size and the detection resolution as a hard lower limit, ensuring that the radius parameter is not smaller than the minimum distance required to distinguish a single defect point, thereby avoiding misjudging normal process noise as a cluster; for example, the lower limit is set to one-tenth of the minimum feature size of the chip unit, and then, for each potential aggregation point set, the average proximity distance between all defect points and its stable interval are calculated; the stable interval refers to the typical fluctuation range of the average proximity distance in the same batch or historical data of the same machine; according to the average proximity distance of the potential aggregation point set, the local radius parameter is adaptively set within the stable interval.

[0039] For example, the local radius parameter can be set to twice the average proximity distance within the potential aggregation point set to balance the sensitivity and noise resistance of clustering.

[0040] Further, the minimum sample number is adaptively determined by the following method: the initial value of the minimum sample number is determined by combining the neighborhood area and the local radius parameter determined above, which is set to the average number of defect points expected based on the overall defect density of the wafer within the circular area defined by the local radius parameter, for example, the initial value can be set to the product of the neighborhood area and the average defect point density of the wafer; to cope with the influence of the effective area boundary on the integrity of clustering, the minimum sample number lower limit is increased synchronously with the decrease of the effective coverage ratio of the neighborhood, for example, if the effective coverage ratio of a neighborhood is only fifty percent, the system will increase the minimum sample number lower limit of the neighborhood to twice the original initial value to compensate for the density sparsity illusion caused by incomplete data, ensuring that only truly high-density defect clusters can be identified in the edge area.

[0041] When the system detects a stripe or grid artifact appearing along the scanning direction (such as the X-axis or Y-axis) in the grid defect count distribution, a weight suppression method is adopted to prevent it from forming a false cluster, and the specific implementation method is: when searching for the proximity relationship in the DBSCAN algorithm, a reduced weight is given to the distance between the defect points along the direction of the stripe or grid artifact, for example, if the artifact appears in the Y-axis direction, when calculating the distance between two points and The distance component in the Y direction will be given a weight factor less than 1, so that it contributes less in the final distance calculation; in this way, the algorithm will be more inclined to form clusters of points that are closely clustered along the non-artifact direction, thereby effectively suppressing false defect clusters caused by device artifacts.

[0042] In the present embodiment, after the local radius parameter and the minimum sample number are determined, DBSCAN clustering is performed on each potential cluster set. This clustering method forms local clusters by iteratively finding core points and expanding their density-reachable neighbors. Points that fail to belong to any cluster are labeled as local noise points. After clustering is complete, the local cluster set and the local noise point set are output. The mathematical expression is as follows: Local cluster set: Wherein, represents the jth local cluster, which is a subset containing multiple standardized defect points, and M is the total number of local clusters. Local noise point set: Wherein, represents the local noise point set, represents the original potential cluster set, represents the kth local noise point.

[0043] In addition, a boundary polygon and a target center point are generated for each local cluster. The boundary polygon is drawn using the concave hull algorithm (such as Alpha Shapes) to depict the outline of the cluster, thereby providing spatial range information of the cluster. The target center point is calculated as the geometric center of the boundary polygon to represent the core position of the cluster.

[0044] Preferably, for each determined potential cluster set, the following sub-process is used to perform the DBSCAN (Density-Based Spatial Clustering of Applications with Noise) clustering algorithm: (1) Before starting clustering, all standardized defect points in the potential cluster set are marked as unvisited. Then, the system iterates through each unvisited point and uses the preset local radius parameter to define a circular neighborhood around the point. If the number of defect points contained in the neighborhood is greater than or equal to the preset minimum sample number, the point is determined to be a core point. (2) When a core point is found, a new local cluster is created with the core point as the starting point. The system marks the core point as "visited" and adds it to the new cluster. Then, the system checks all neighboring points of the core point. For each neighboring point: If the neighboring point has not been visited, it is marked and the core point discovery step is recursively executed. If the neighboring point is also a core point, it is added to the current cluster and the cluster is expanded. If the neighboring point has been visited but does not belong to any cluster, it is assigned to the current cluster and marked as a boundary point. This process continues until the density of all core points in the current cluster reaches the point where all neighboring points have been visited and assigned, thus completing the construction of a complete local cluster; (3) During the construction and expansion of the above clusters, for those points that are not included in the neighborhood of any core point and whose own number has not reached the minimum number of samples, the system cannot assign them to any local cluster. These points will be ultimately determined as local noise points.

[0045] S6. Based on the boundary overlap rate, adjacent local clusters are merged across neighborhoods to obtain a wafer-wide consistent defect cluster and a global noise point set. Note that the following points should be noted in this step: For any two local clusters from different neighborhoods, calculate the ratio of the intersection area of ​​their boundary polygons to the union area as the boundary overlap rate, and calculate the shortest distance between the two boundaries as the judgment index. When the boundary overlap rate is not lower than the third threshold T3, the two clusters are determined to be the same cluster and merged. The merging process is performed iteratively from a global perspective until no cluster pairs satisfy the merging conditions are found. The discrete points that were not absorbed after merging are incorporated into the global noise point set; Output a set of consistent defect clusters across the entire wafer and a set of global noise points.

[0046] In a preferred embodiment, for any two local clusters from different neighborhoods and Its boundary polygons are respectively and The boundary overlap rate is calculated by dividing the area of ​​the intersection of two boundary polygons by the area of ​​their union. The mathematical formula for this is as follows: in, Represents polygons and The area of ​​intersection Represents polygons and The area of ​​the union of the sets; The shortest distance between two boundaries refers to the polygon and The minimum Euclidean distance between any two points on the boundary is calculated using the following formula: in, Represents polygons boundary A point on the top, Represents polygons boundary A point on the top, This represents the Euclidean distance.

[0047] In this embodiment, the third threshold T3 is designed to ensure that merging is performed only when there is substantial spatial overlap between two local clusters. The threshold is set based on the process characteristics and morphological analysis of the wafer defect clusters, and is exemplarily set to 0.5. This threshold needs to balance the sensitivity and accuracy of merging. Too low a T3 may result in the incorrect merging of unrelated clusters, while too high a T3 may prevent the merging of clusters that should belong to the same cluster.

[0048] Specifically, the merging conditions include determining that two local clusters are the same cluster and merging them when the boundaries of two local clusters meet any of the following conditions: The boundary overlap rate is not lower than the preset third threshold T3; The nearest distance between the two boundaries is less than a preset minimum value, for example, less than twice the detection resolution.

[0049] It should be further noted that this embodiment adopts a global perspective iterative execution merging method, and its specific implementation process is as follows: (1) The system initializes a queue to be merged and adds all local cluster pairs generated in S5 to it; (2) Iterate through all cluster pairs in the queue to be merged and check whether they meet the above merging conditions; (3) For all cluster pairs that meet the merging conditions, merge them into a new larger cluster containing all the defect points of the original two clusters. At the same time, recalculate the boundary polygon of the merged new cluster. (4) After completing all the merge operations that meet the conditions in one round, update the set of local clusters and check again whether there are any new cluster pairs that meet the merge conditions; (5) This process continues to iterate until, across the entire wafer, no pair of unmerged clusters meets the merging criteria.

[0050] This iterative merging method ensures that even if a cluster is divided into multiple subclusters, as long as there are indirect overlapping paths between these subclusters, they can eventually be correctly merged into a complete wafer-wide consistent defect cluster.

[0051] After the above iterative merging process, the following two sets are finally generated and output: The set of wafer-wide consistent defect clusters, which includes all complete defect clusters obtained after cross-neighborhood merging, is expressed as: in, This represents a set of uniform defect clusters across the entire wafer. represents the kth wafer-wide consistent defect cluster, which is obtained by merging one or more local clusters, and K is the total number of final clusters; a global noise point set, which consists of two parts: one is the local noise points in S5 that are not attributed to any local cluster, and the other is the discrete points in S6 that are not absorbed by any cluster except for the merged cluster pairs; the expression of the set is: wherein, represents the global noise point set, represents the local noise point set obtained in S5, represents the discrete point set that is not absorbed by any cluster in the cross-neighborhood merging process.

[0052] S7, fitting Geyer saturation point process for each defect cluster in the wafer-wide consistent defect cluster and obtaining the estimated values of interaction strength, interaction radius and constant by maximum likelihood estimation with boundary correction, and calculating the significance index by Monte Carlo to judge the interaction strength. It should be noted that the present step is: for each wafer-wide consistent defect cluster, removing the undetectable area and performing boundary correction according to the effective area proportion to obtain the cluster point set for fitting and the corresponding effective window; performing maximum likelihood optimization on the point set with boundary correction in the effective window to obtain the estimated values of interaction strength, interaction radius and constant term, and recording the convergence state; constructing a conditional generation process according to the estimated values, performing multiple random simulations to obtain the reference distribution under the weak interaction assumption; calculating the significance index and comparing it with the significance threshold when , the cluster is marked as a statistically significant interaction cluster; when , the cluster is marked as a weak interaction cluster; outputting the three estimated values, the significance index and the determination label of each cluster.

[0053] In an optional embodiment, the present embodiment performs the following boundary correction process for each wafer-wide consistent defect cluster to ensure the accuracy of the subsequent Geyer saturation point process fitting: For each full wafer consistent defect cluster obtained by S6, all the standardized defect points contained in the cluster are traversed, and in the process, any defect point falling within the known undetectable area (such as wafer dicing lane, process test unit or optical alignment mark) is identified and removed according to the pre-established effective area mask. The point set filtered by this step is the cluster point set for fitting; The boundary polygon of the cluster is geometrically intersected with the effective analysis area of the wafer (i.e. the area of the wafer after excluding the edge exclusion zone, dicing lane, etc.), and the result of the operation forms an effective window strictly corresponding to the spatial range of the cluster point set. For a cluster located at the edge of the wafer, the effective window will be a geometric shape truncated by the wafer circular boundary or straight edge, and its area will be smaller than the original area of the cluster boundary polygon; Before performing maximum likelihood estimation, the ratio of the area of the effective window to the original area of the cluster boundary polygon is calculated to obtain an effective area ratio. In the calculation process of the maximum likelihood function, the effective area ratio is used as a normalization factor to correct the incompleteness of the data caused by the truncation of the cluster by the effective analysis area. By multiplying the area term in the likelihood function by the ratio, the missing effect caused by the fact that some defect points may fall outside the effective area can be effectively compensated, so that the final parameter estimation value more accurately reflects the true statistical characteristics of the cluster.

[0054] Further, the embodiment of the present application adopts a maximum likelihood optimization method to perform parameter estimation on the cluster point set after boundary correction within its effective window. This method finds a set of optimal parameter values by using an iterative optimization algorithm (such as gradient descent method) to maximize the likelihood function of the observed point set distribution under the Geyer saturation point process model. The core of this process is to maximize its log-likelihood function, which has the following mathematical expression: wherein, represents the log-likelihood function of the model, which is a function of the interaction intensity , interaction radius R and constant ; N represents the total number of defect points in the cluster point set; represents the area of the effective window after boundary correction; represents the Euclidean distance between points and ; is an indicator function, which has a value of 1 when the internal condition is met, and 0 otherwise; β represents a constant term for describing the overall density of the cluster; represents the interaction strength, and its value greater than 0 represents that there is an attractive action between points, less than 0 represents repulsion, and equal to 0 represents random distribution; R represents the interaction radius, that is, the distance range of the interaction between points; Through the optimization process, the system obtains the parameter estimation value that makes the above likelihood function reach the maximum value 、 and , and records the convergence state of the optimization process.

[0055] The embodiment generates a reference distribution under the weak interaction assumption by Monte Carlo simulation, and the specific implementation method is as follows: according to the parameter estimation value obtained by the maximum likelihood estimation, especially the constant term , a conditional generation process is constructed; the process is based on a Poisson point process (that is, a completely random distribution) within an effective window, and is taken as its average density, and a plurality of random point pattern simulations are performed, each simulation generates a point set with a number of points close to the observed cluster points, and by repeatedly simulating (for example, 1000 times), a point pattern set is obtained, which represents the reference distribution of the point pattern that may appear under the weak interaction assumption (that is, the points are randomly distributed or only have slight interaction); the reference distribution can be used to calculate the distribution of various statistical indicators, such as the number of points, the nearest neighbor distance, the density, etc.

[0056] Further, the application calculates the significance index (p-value) by Monte Carlo simulation, which is used to quantitatively evaluate the statistical significance of cluster interaction, and the calculation method is as follows: For each simulated random point set, the corresponding test statistic value is calculated, so as to obtain a reference distribution composed of all simulation results, which represents the typical value range of the test statistic that may appear under the weak interaction (or random) assumption; By comparing the test statistic value of the observed cluster with the above reference distribution, the significance index (p-value) is calculated, and the mathematical expression is as follows: Among them, represents the significance index, that is, the p-value, which represents the probability of appearing a point pattern more extreme (that is, more aggregated) than the observed cluster under the weak interaction assumption; ​​​represents a counting function that counts the number of simulated patterns that satisfy a certain condition; Simulated Patterns represents random point patterns generated by Monte Carlo simulation; more extreme represents simulated point patterns that are more extreme (i.e. more clustered) than the observed cluster in terms of the value of the test statistic; test statistic is a statistical measure that quantifies the degree of clustering, such as the average nearest neighbor distance or density; Total Number of Simulations represents the total number of Monte Carlo simulations; Based on the significance index calculated above, a decision label is generated for each cluster, which specifically includes: When the significance index (S) value) is less than a preset significance threshold (such as 0.05), the cluster is labeled as "statistically significant interaction cluster", indicating that its interaction strength is significant and its clustering pattern is unlikely to be randomly formed; When the significance index (S) value) is greater than or equal to a preset significance threshold (such as 0.05), the cluster is labeled as "weak interaction cluster", indicating that its clustering pattern is likely to be caused by random noise or weak interaction; That is, the smaller the value, the less likely it is that the observed cluster is randomly formed, and the more significant its interaction strength is; value) is less than a preset significance threshold (such as 0.05), the cluster is labeled as "statistically significant interaction cluster", indicating that its interaction strength is significant and its clustering pattern is unlikely to be randomly formed; Finally, the three estimated values (interaction strength, interaction radius, and constant), the significance index, and the corresponding decision label of each cluster are output, providing accurate quantitative basis for subsequent process analysis.

[0057] S8、Based on the global uniform defect cluster and its interaction strength evaluation results, the center position, boundary range, defect point number, density, shape, and directionality index of each defect cluster are calculated, and the estimated values of interaction strength, interaction radius, and constant, and the significance index are summarized At the same time, the global noise point set is output, and a structured analysis report is generated accordingly. It should be noted that in this step: For each global uniform defect cluster, the effective defect points within the range enclosed by the final boundary polygon are selected to form a data set for index calculation; if the boundary intersects with the undetectable area, only the points and the corresponding effective boundary segments located within the effective analysis area are retained; With the index data set as the object, the iterative shrinkage method insensitive to abnormal points is used to determine the target center position, that is, the center candidate is updated while the outer layer outliers are removed in each round until the removal proportion no longer changes; when there are obvious holes or slender branches in the cluster boundary, the consistency comparison is preferentially performed between the geometric center of the boundary polygon and the target center, and when the deviation between the two exceeds the fourth threshold T4, the geometric center of the boundary is taken as the center position; the coordinate value of the center position in the wafer global coordinate system is output, and the chip unit grid is used to record the row and column positioning and the relative position with the orientation mark; Based on the merged boundary polygon across the neighborhood, if there is a hole, the outer boundary is confirmed and the hole area is subtracted as the effective boundary; when the boundary intersects with the effective analysis area, the intersection is taken as the effective boundary, and the effective coverage proportion is recorded; two types of bounding boxes are generated on the effective boundary: one is the circumscribed rectangle parallel to the wafer coordinate axis, and the other is the minimum directional enclosing rectangle with free direction, and the azimuth angle of the latter is saved; the effective area is calculated based on the effective boundary, and the boundary type (such as containing / having no hole, whether truncated), the effective coverage proportion and the parameters of the two types of bounding boxes are output; The defect points located within the effective boundary are recorded as cluster points, and the boundary points are preferentially and uniquely attributed inward; for the repeated coordinate points caused by repeated sampling, only one is counted; the number of cluster points is output, and the number of boundary points included and the number of repeated points removed are recorded; The defect point density is calculated by taking the effective area as the denominator and the number of cluster points as the numerator; when the effective coverage proportion is lower than the preset lower limit, the density is area-corrected once according to the effective coverage proportion, and it is marked in the result that the edge correction has been applied; the original density, the density after edge correction and the coverage proportion are output; The compactness degree of the effective boundary is taken as the criterion, and the compactness degree is obtained by quantifying the fitting degree of the boundary shape and the bounding box and the concave-convex degree of the boundary; the length of the long side of the minimum directional enclosing rectangle is taken as the criterion of the elongation degree, and the elongation degree is obtained; the notch area ratio of the effective boundary relative to its convex hull is taken as the criterion of the concave degree, and the concave degree is obtained; when the elongation degree exceeds the fifth threshold T5 and the concave degree is low, it is marked as strip-shaped shape, and the stripness is obtained; the compactness degree, the elongation degree, the concave degree and the stripness marker are output; The spatial extension main axis of the index data set is taken as the main direction, and the determination of the main direction is based on the long side direction of the minimum directional enclosing rectangle; the azimuth angle of the main direction relative to the wafer orientation mark is recorded, and when there is a significant secondary main direction, the secondary main direction and its weight proportion are output; when the cluster shows obvious ring or near-circular distribution, it is marked as no significant directionality; the main direction angle, the secondary main direction angle and the marker of no significant directionality are output; Consistency check between center position, boundary range, density and directionality: add a review-required flag when the center position deviates from the center of the minimum oriented bounding rectangle by more than a preset upper limit or the directionality conflicts with the shape type; Summarize the estimated values and significance indicators of the interaction strength, interaction radius and constant term, and list them together with the corresponding indicators of the same machine and process history batch; when the significance indicators indicate that the interaction is statistically significant, add a label to the cluster entry.

[0058] In a preferred embodiment, the method for generating a structured report includes: generating a structured entry with a cluster as a granularity, the entry at least containing a center position (including grid row and column positioning), a boundary range (including an effective area and an outer bounding box parameter), a number of defect points, a density (including an edge correction state), a shape indicator (compactness, thin length, concave degree, stripiness), a directionality indicator (main / secondary direction angle or no directionality), an interaction parameter and a significance indicator.

[0059] It should be noted that the fourth threshold T4 is intended to correct the calculation of the cluster center position, and the selection rule of the threshold is based on prior knowledge and experience of the cluster shape. Under normal circumstances, the geometric center of a cluster (i.e. the geometric center of its boundary polygon) and the target center (i.e. the density center of the point set) calculated by the iterative contraction method should be very close. However, when the cluster boundary has obvious holes or slender branches, the two centers may deviate significantly. Therefore, the fourth threshold T4 is set to detect such abnormal deviation. For example, T4 can be set to 10% of the length of the long side of the minimum oriented bounding rectangle. When the distance between the target center and the geometric center of the boundary polygon exceeds this threshold, the system determines that the target center calculated by the iterative contraction method may be disturbed by abnormal points. At this time, the more robust geometric center of the boundary polygon is preferred as the final center position.

[0060] It should also be noted that the fifth threshold T5 is intended to identify defect clusters with specific strip or linear shapes. The selection rule of the threshold is based on the quantification of the cluster thin length, which is the ratio of the long side to the short side of the minimum oriented bounding rectangle of the cluster. The larger the value, the more elongated the shape of the cluster. T5 is set as a critical value to distinguish between elongated and non-elongated clusters. For example, T5 can be set to 4. When a cluster's thin length exceeds this threshold and its concave degree is low (i.e. the boundary is relatively smooth), the system will add a stripiness flag to it. This rule enables the system to automatically identify linear or strip-shaped defect clusters caused by process defects (such as scanning artifacts, track wear or linear scratches), thereby providing important clues for process problem tracing.

[0061] It should be noted that the above examples are only used to illustrate the technical solutions of the present application but not limit the present application. Although the present application is described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or equivalently replaced, without departing from the spirit and scope of the technical solutions of the present application, which should be covered in the scope of the claims of the present application.

Claims

1. A wafer defect cluster analysis method based on DBSCAN clustering, characterized in that, The method comprises the following steps: Obtaining defect point coordinates, wafer layout and chip unit grid information, correcting and aligning the defect points, and mapping them to the same wafer coordinate system to obtain a standardized defect point set; According to the chip unit grid, the wafer effective area is meshed, and the grid attribution statistics of the standardized defect point set are performed, and the boundary incomplete grid is normalized according to the effective area to obtain the grid defect count distribution; According to a preset first threshold T1, the grid with a defect count greater than or equal to T1 is marked as a candidate aggregation grid set; Taking each grid in the candidate aggregation grid as the center, an n*n grid neighborhood is constructed, and all standardized defect points in the neighborhood are collected to form a potential aggregation point set corresponding to each candidate aggregation grid; Adaptive determination of the radius parameter and the minimum sample number of DBSCAN according to the chip unit size, detection resolution and local density, local clustering of the potential aggregation point set, and obtaining local clusters and local noise points; Based on the boundary overlap rate, adjacent local clusters are merged across the neighborhood to obtain a wafer-wide consistent defect cluster and a global noise point set; fitting a Geyer saturation process to each of the defect clusters in the full wafer consensus defect cluster set and maximum likelihood estimation of the interaction strength, interaction radius and constant with boundary correction, and Monte Carlo calculation of significance index to judge the interaction strength; Based on the evaluation results of the full-wafer consistent defect cluster and the interaction strength, the center position, the boundary range, the defect point quantity, the density, the shape and the directionality index of each defect cluster are calculated, and the estimated values of the interaction strength, the interaction radius and the constant and the significance index are summarized At the same time, the global noise point set is output, and a structured analysis report is generated accordingly.

2. The DBSCAN clustering based wafer defect cluster analysis method of claim 1, wherein, The standardized defect point set comprises: Based on the known anchor points and orientation marks in the wafer layout, a calibration pattern is collected, a combined correction model of imaging distortion and geometric perspective is established, and is fixed as a single correction parameter set; Applying the correction parameter set to the original coordinates of the defect points to complete one-time inverse distortion and perspective correction to obtain corrected defect point coordinates; Taking the wafer orientation mark as the reference axis and the wafer geometric center as the origin, the rigid registration transformation between the coordinate systems of different detection batches is calculated, and the corrected defect point coordinates are uniformly registered; When there is a small non-uniform scaling or shear error, a constrained affine fine-tuning is performed within a preset error upper limit to generate candidate defect point coordinates in the unified wafer coordinate system; According to the detection resolution and the minimum distinguishable distance, repeated points and abnormal isolated points are deleted, and points overlapping with the undetectable area are removed; Taking the chip unit grid as a reference, the relative position relationship between the candidate defect points and the grid is verified for consistency. If the overall offset exceeds a preset threshold, return to the uniform registration step for registration fine-tuning until the preset threshold is met; Output the standardized defect point set after correction, registration, redundancy removal and verification, and record the corresponding correction parameters and registration parameters.

3. The DBSCAN clustering based wafer defect cluster analysis method according to claim 1 or 2, characterized in that, The grid defect count distribution comprises: According to the wafer diameter, the edge exclusion zone and the undetectable area, the effective analysis area is determined and the effective area mask is generated; Taking the chip unit grid as the basic unit, a row-column grid set is established in the effective area, and the effective coverage area proportion of each grid is recorded; The standardized defect points are uniquely attributed to the corresponding grid according to the spatial position, and the points located on the common boundary of the grid are uniquely divided according to the layout coverage priority; For the non-complete grid located at the boundary of the effective area, the attribution count is normalized according to the effective coverage area proportion; The count results of all grids are detected for consistency, and the grid whose difference with the adjacent grid is abnormal and coincides with the image splicing boundary is marked as a quality concern object; Output the grid defect count distribution containing the normalized count, effective area proportion and quality mark of each grid.

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9. The DBSCAN clustering based wafer defect cluster analysis method of claim 1, wherein, The interaction strength is evaluated, including: For each global wafer-uniform defect cluster, the undetectable area is removed, and boundary correction is performed according to the effective area proportion, to obtain a cluster point set for fitting and a corresponding effective window; Maximum likelihood optimization is performed on the point set after boundary correction within the effective window, to obtain the estimated values of the interaction strength, the interaction radius and the constant term, and the convergence state is recorded; A conditional generation process is constructed according to the estimated values, and multiple random simulations are performed to obtain a reference distribution under the weak interaction assumption; Computing a significance indicator and comparing it to a significance threshold: When the cluster is labeled as a statistically significant interaction cluster; when the cluster is labeled as a weak interaction cluster; Output three estimated values, significance indicators for each cluster With decision tags.

10. The DBSCAN clustering based wafer defect cluster analysis method of claim 9, wherein, Based on the global wafer-uniform defect cluster and the interaction strength evaluation result, the center position, boundary range, defect point number, density, shape and directionality index of each defect cluster are calculated, including: The defect points located in the effective analysis region within the cluster boundary after cross-neighborhood merging are selected as the index data set; The target center is calculated for the index data set, and is compared with the boundary geometric center. When the deviation between the two exceeds a fourth threshold T4, the boundary geometric center is taken as the center position; The intersection of the merging boundary and the effective analysis region is taken as the effective boundary, the effective area is calculated, and the parameters of the circumscribed rectangle and the minimum directional enclosing rectangle of the parallel coordinate axes are given; The defect points located in the effective boundary are recorded as the cluster points, the boundary points are uniquely attributed according to the inward priority, the repeated points are removed, the number is counted, and the density is obtained with the effective area as the denominator; The effective boundary and the two types of outer frame thereof determine the compactness, the thin length and the concave degree, and the main direction is determined according to the long side direction of the minimum directional enclosing rectangle, and the azimuth angle relative to the wafer orientation mark is recorded; The estimated values of the interaction strength, the interaction radius and the constant term and the significance index are summarized and listed together with the historical batches of the same machine and the same process.

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