A method for wafer defect cluster analysis based on DBSCAN clustering

Abstract

This 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. By standardizing and preprocessing the defect data, and through gridding and neighborhood search, the clustering range is effectively narrowed, greatly improving processing efficiency. Subsequently, adaptive DBSCAN clustering and cross-neighborhood merging are used to overcome the dependence of traditional clustering methods on the preset number of clusters and the limitation in identifying irregularly shaped clusters. The Geyer saturation point process is introduced to quantify the significance of defect clusters, scientifically evaluating the interaction strength of clusters, thus providing a reliable quantitative indicator for identifying defect clusters truly caused by process problems.

Description

Technical Field

[0001] This invention relates to the technical field of wafer defect analysis and big data processing, and in particular to a wafer defect cluster analysis method based on DBSCAN clustering. Background Technology

[0002] With the rapid development of the semiconductor industry, wafer manufacturing processes have become increasingly complex, placing higher demands on quality control. As a key link in ensuring product yield, wafer defect detection has one of its core objectives: to effectively analyze the massive amounts of defect data generated on wafers and identify defect clusters with process-related characteristics. Early wafer defect analysis methods relied heavily on manual visual inspection, which was inefficient and highly subjective. To address this issue, researchers have gradually introduced automated methods based on various technologies such as statistics, image processing, and machine learning. Among these, defect cluster analysis methods based on clustering algorithms have been widely used because they can automatically identify and group defect patterns with similar characteristics.

[0003] CN112102226A discloses a wafer defect pattern detection method. Although it introduces techniques such as 3D layered spatial autocorrelation 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 the model training process may be time-consuming. For online wafer defect analysis scenarios that require fast feedback, its real-time performance is poor. In addition, it requires readjustment and retraining of the model for different manufacturing processes and defect types, lacking versatility.

[0004] US20100057391A1 discloses a method for classifying spatial patterns on wafer maps. This method uses K-means clustering and generating dendrograms to group wafer maps with similar spatial patterns. However, K-means clustering requires pre-specifying the number of clusters, which is often difficult to determine when faced with wafer defect clusters of unknown number and diverse shapes, leading to 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 relationships of defect clusters, making it impossible to effectively distinguish defect clusters caused by random distribution from true clusters caused by specific process problems, and also unable to quantitatively assess the significance of clusters, thus lacking a scientific basis for judging the cause of defects.

[0005] In summary, existing wafer defect analysis techniques generally suffer from the following problems: First, for massive and complex defect data, the computational efficiency and real-time performance of existing methods need improvement; second, some methods have limitations when dealing with irregularly shaped or unknown-quantity defect clusters; more importantly, existing technologies lack a scientific quantitative assessment of the salience of defect clusters, failing to effectively distinguish between random clusters and true clusters, thus lacking a reliable basis for diagnosing process problems. This invention proposes a wafer defect cluster analysis method based on DBSCAN clustering, which solves the above-mentioned technical problems through multi-stage, adaptive clustering and analysis. This invention performs standardized preprocessing of defect data, effectively narrowing the clustering range through gridding and neighborhood search, greatly improving processing efficiency; subsequently, adaptive DBSCAN clustering and cross-neighborhood merging overcome the dependence of traditional clustering methods on the preset number of clusters and the limitation in identifying irregularly shaped clusters; the introduction of the Geyer saturation point process quantifies the salience of defect clusters, scientifically evaluating the interaction strength of clusters, thereby providing a reliable quantitative indicator for identifying defect clusters truly caused by process problems. Summary of the Invention

[0006] The purpose of this section is to outline some aspects of the embodiments of the present invention and to briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section, as well as in the abstract and title of the present application, to avoid obscuring the purpose of this section, the abstract and title of the invention. Such simplifications or omissions shall not be used to limit the scope of the present invention.

[0007] In view of the aforementioned existing problems, the present invention is proposed.

[0008] To solve the above-mentioned technical problems, the present invention provides the following technical solution: obtain the coordinates of defect points, wafer layout and chip cell grid information, perform distortion correction and zero-position alignment on the defect points and uniformly map them to the same wafer coordinate system to obtain a standardized defect point set;

[0009] The effective area of ​​the wafer is gridded according to the chip cell grid, and the grid assignment statistics of the standardized defect point set are performed. The boundary incomplete grids are normalized according to the effective area to obtain the grid defect count distribution.

[0010] Based on a preset first threshold T1, grids with a defect count ≥ T1 are marked as candidate clustered grid sets;

[0011] Centered on each grid in the candidate clustering grid, an n×n grid neighborhood is constructed and all standardized defect points within the neighborhood are collected to form a potential clustering point set corresponding one-to-one with each candidate clustering grid;

[0012] The radius parameter and minimum number of samples of DBSCAN are adaptively determined by combining chip unit size, detection resolution and local density, and the potential aggregation point set is locally clustered to obtain local clusters and local noise points;

[0013] 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.

[0014] For each defect cluster in the whole-wafer consistent defect cluster, a Geyer saturation point process is fitted, and the estimated values ​​of interaction strength, interaction radius, and constant are obtained by maximum likelihood estimation after boundary correction. The significance index is calculated by Monte Carlo. To obtain the results of the interaction strength assessment;

[0015] Based on the whole-wafer consistent defect clusters and their interaction strength evaluation results, the center location, boundary range, number of defect points, density, shape, and orientation indices of each defect cluster are calculated. The estimated values ​​of the interaction strength, interaction radius, and constant are then summarized along with the significance index. It also outputs a global noise point set, based on which a structured analysis report is generated.

[0016] The beneficial effects of this invention are as follows: This invention effectively decomposes and parallelizes the whole wafer clustering problem by going from gridded coarse screening to local clustering and then to global merging, which greatly improves the computational efficiency of processing massive wafer defect data. Secondly, the adaptive DBSCAN parameter determination and cross-neighborhood merging mechanism solve the limitations of traditional clustering methods in dealing with complex and irregular defect clusters, and ensure the accuracy of identification.

[0017] Meanwhile, by introducing the Geyer saturation point process into defect analysis, it is possible to clearly distinguish between accidental clusters caused by random probability and true clusters caused by specific process problems. This allows analytical resources to be focused on defect patterns that are truly process-related, greatly improving the accuracy and reliability of defect analysis. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a flowchart illustrating the wafer defect cluster analysis method based on DBSCAN clustering as shown in this invention. Detailed Implementation

[0019] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0020] Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without inventive effort should fall within the scope of protection of this invention.

[0021] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0022] According to an embodiment of the present invention, in combination Figure 1 The flowchart shown illustrates a method for analyzing wafer defect clusters based on DBSCAN clustering, which specifically includes the following steps:

[0023] S1. Obtain the defect point coordinates, wafer layout, and chip cell grid information. Perform distortion correction and zero-position alignment on the defect points and map them uniformly to the same wafer coordinate system to obtain a standardized defect point set. Note that the following points should be noted in this step:

[0024] Based on pre-defined known anchor points (such as chip corners, specific structural markers) and orientation markers (such as flat edges or notches on the wafer) in the wafer layout, the system acquires 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 joint correction model for imaging distortion and geometric perspective is established. (In order to accurately transform the original defect point coordinates obtained from the inspection equipment to a unified global wafer coordinate system, this process is essentially a nonlinear regression problem. The model parameters are fitted and solved using the least squares method to minimize the error between the original coordinates after model transformation and the ideal wafer coordinates.) This model can quantify the spatial errors caused by factors such as nonlinear distortion of the optical system and tilt of the inspection platform. The model parameters are fitted using the least squares method and finally solidified into a single set of correction parameters.

[0025] After obtaining the set of correction parameters, it is applied to the original coordinates of the defect points in each batch at once. Through this correction, the original coordinates are reversed and perspective corrected, thus obtaining corrected defect point coordinates that are closer to their actual physical location. This process can be represented as a function mapping:

[0026]

[0027] in, Represents the joint correction function. This represents the set of correction parameters for curing.

[0028] Using the wafer orientation mark as the reference axis (e.g., aligning the wafer flat edge with the Y-axis) and the wafer geometric center as the origin, a unified global wafer coordinate system is defined. Due to the possibility of slight mechanical deviations or differences in wafer mounting positions between different inspection batches, it is necessary to calculate the rigid registration transformation between the current batch's corrected defect point coordinate system and the global wafer coordinate system. This transformation includes translation and rotation, and is solved using the anchor-point-based least squares method. The rigid registration parameters are obtained and applied to all corrected defect point coordinates to achieve unified registration.

[0029] To further eliminate minor, inconsistent scaling or shearing errors, constrained affine fine-tuning is performed within a preset error limit. This step ensures the consistency of chip mesh size and shape in the global coordinate system, thereby generating candidate defect point coordinates in a unified wafer coordinate system. .

[0030] To ensure data purity, candidate defect points need to be deduplicated and removed. First, based on the detection resolution and minimum distinguishable spacing, duplicate coordinate points caused by repeated sampling are deleted. For example, if the distance between two points is less than the minimum distinguishable spacing, only one of them is retained. Second, defect points located in undetectable areas (such as wafer edge exclusion zones, test structures, dicing paths, etc.) are removed.

[0031] Using the chip cell grid as a reference, a consistency check is performed on the relative positional relationship between the generated candidate defect point set and the grid. This is achieved by calculating the average offset of all candidate points from the center of their respective chip grids. If the overall offset exceeds a preset threshold, it indicates that there may be a systematic deviation in the registration. In this case, the system will return to the unified registration step, fine-tune the registration parameters, and re-execute the subsequent steps until the check meets the preset threshold requirements.

[0032] After all the above correction, registration, redundancy removal, and verification steps, a high-precision, high-quality standardized defect point set is finally obtained, which is mathematically represented as:

[0033]

[0034] in, Represents a standardized set of defect points. Let N represent the two-dimensional coordinates of the i-th standardized defect point in the set, and N be the total number of standardized defect points.

[0035] Meanwhile, the system will record the correction and registration parameters used throughout the entire process to facilitate subsequent data traceability.

[0036] It should be noted that the methods described above for nonlinear optical distortion correction of the original coordinates and radial transformation of the corrected coordinates to achieve geometric perspective correction and zero-position alignment, as well as the method of least squares fitting, can be carried out using existing techniques and means, and will not be elaborated in this example.

[0037] S2. The effective area of ​​the wafer is meshed according to the chip cell grid, and the standardized defect point set is statistically assigned to a specific grid. Incomplete boundary grids are normalized according to their effective area to obtain the grid defect count distribution. Note that the following points should be noted in this step:

[0038] Based on the wafer diameter, edge exclusion zone, and undetectable area, the effective area is determined and an effective area mask is generated;

[0039] A set of row and column grids is established within the effective area using chip cell grids as the basic unit, and the effective coverage area ratio of each grid is recorded.

[0040] Standardized defect points are uniquely assigned to the corresponding grid based on their spatial location, and points located on the grid's common boundary are uniquely classified according to the map coverage priority.

[0041] For incomplete grids located at the boundaries of the effective area, the attribution count is normalized according to the proportion of their effective coverage area;

[0042] A consistency check is performed on the counting results of all grids, and grids that differ abnormally from their neighboring grids and coincide with the image stitching boundary are marked as objects of quality concern;

[0043] The output includes the normalized counts of each grid, the effective area ratio, and the quality label of the grid defect count distribution.

[0044] In a preferred embodiment, the effective region and corresponding mask are determined through the following steps: A circular boundary is determined based on the physical diameter of the wafer, and the area outside this boundary is excluded from the analysis range. Based on the edge exclusion zone information preset in the semiconductor manufacturing process, an annular region is delineated within the circular boundary and marked as an unanalyzable region. Combined with wafer layout data, known undetectable regions are identified, such as test chips, optical alignment marks, process monitoring structures, or dicing traces, and these regions are also marked as unanalyzable. All unanalyzable regions are removed from the total wafer area, and the remaining portion is the effective region that can be used for defect analysis. Subsequently, a digitized effective region mask is generated based on this effective region. This mask marks all points within the effective region as "analyzable," while marking all points within the unanalyzable regions as "unanalyzable." This mask serves as the spatial constraint for all subsequent meshing and attribution operations.

[0045] Furthermore, in this embodiment, a set of row and column grids is established and its effective coverage area ratio is recorded through the following steps: taking the chip cell grid as the basic unit, a complete set of row and column grids is established within the aforementioned determined effective area. This set consists of rectangular grids that correspond one-to-one with all chip cells on the wafer layout. For each grid in the set, its coverage area within the effective area mask is calculated and compared with the overall area of ​​the grid to obtain the effective coverage area ratio of each grid. For complete grids that are completely located within the effective area, their effective coverage area ratio is 100%. For incomplete grids located at the boundary of the effective area, i.e., partially crossing the edge exclusion zone or undetectable area, their effective coverage area ratio will be less than 100%.

[0046] Furthermore, this embodiment uniquely assigns standardized defect points to corresponding grids through the following steps: The system traverses the set of standardized defect points obtained in step S1, and matches the spatial position of each point with the established row and column grid set according to the coordinates of each point, uniquely assigning each point to its own grid; If a defect point happens to be 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 duplicate counting; for example, the priority rule is set as follows: if the point is located on the boundary between a complete grid and a non-complete grid, it will be preferentially assigned to the complete grid; if it is located on the boundary between two complete grids, it will be divided according to the preset row and column index priority (for example, preferentially assigned to the grid with the smaller row index).

[0047] It should also be noted that the following steps are used to perform consistency detection on the grid count in this embodiment: the normalized defect count results of all grids are analyzed, and outliers are identified by comparing the count differences between each grid and its neighboring grids; if the count of a certain grid has a significant abnormal difference from the average count of its neighboring grids, the grid is initially marked as a potential anomaly; subsequently, the spatial location of these potential anomaly grids is compared with the image stitching boundary information recorded during wafer inspection. If the abnormal count of a grid coincides with its location on the image stitching boundary, the grid is marked as a "quality concern object", indicating that its abnormal count may be caused by image stitching artifacts rather than actual process problems; all grids that have undergone this detection will output their normalized count, effective area ratio, and whether they have been marked as quality concern objects for subsequent analysis reference.

[0048] S3. Mark the meshes with defect counts ≥ T1 as candidate clustered mesh sets according to the preset first threshold T1. Note that the following should be noted in this step:

[0049] Perform overall statistics on the distribution of grid defect counts to form a baseline count interval and an abnormal upward indication interval;

[0050] Using the first threshold T1 as the criterion, select grids with a count ≥ T1 as the initial candidate set;

[0051] Perform a spatial connectivity check on the initial candidate set and remove isolated grids that are not adjacent to any candidate grids and whose counts fall only in a narrow band near T1;

[0052] Output the candidate clustered grid set and its labeling information.

[0053] For example, the method for setting the first threshold T1 is as follows: take the 95th percentile integer value of the grid count distribution of the most recent batch of the same machine and the same formula after the effective area and resolution are consistent as the initial threshold, and then take the candidate grid ratio of the current wafer as a reference, make a one-time ±1 count fine adjustment around the initial threshold so that the candidate ratio falls into the range of 2% to 8%, and freeze it as the final first threshold T1 after fine adjustment.

[0054] Among them, the most recent batch is the most recent 30 pieces, and the initial threshold is not less than 2.

[0055] As a preferred implementation, the distribution of grid defect counts is statistically analyzed to form corresponding intervals. Specifically, this includes: performing a comprehensive statistical analysis on the normalized defect counts of all grids to obtain basic statistics such as mean, median, and standard deviation; simultaneously, generating a histogram reflecting the characteristics of the count distribution; and based on this statistical result, determining a baseline count interval that covers the count range of most normal grids and reflects the general defect background noise level on the wafer. For example, this interval is defined as the range within which the mean of the grid count fluctuates by one or two standard deviations. Grids exceeding this baseline count interval are considered abnormal due to their high count values, thus forming an abnormal upward floating indication interval to initially mark grids with high count values ​​and provide a reference for subsequent threshold screening.

[0056] Furthermore, in this embodiment, spatial connectivity checks and isolated grids are performed on the initial candidate set through the following steps: For each grid in the set, it is checked whether it is also located in the initial candidate set along with any of its eight neighboring grids (up, down, left, right, and four diagonal directions). If a grid is not adjacent to any of its neighboring grids and its count is only slightly higher than the first threshold T1 (e.g., falling within a narrow band near T1), then 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 true defect cluster. Therefore, these isolated grids are removed from the initial candidate set to ensure that the final candidate set only contains grids with spatial clustering.

[0057] After the above screening and checks, a candidate clustered grid set is finally generated, and its corresponding labeling information is output. The output generation method is as follows: the detailed information of all grids that have passed the spatial connectivity check and been retained is summarized to form the final candidate clustered grid set. In this process, corresponding labeling information is also attached to each grid. The labeling information includes, but is not limited to: the original count, normalized count, row and column index of the grid, and a label 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.

[0058] S4. Using each grid cell in the candidate clustering grid as the center, construct an n×n grid neighborhood and collect all standardized defect points within this neighborhood to form a set of potential clustering points corresponding one-to-one with each candidate clustering grid. Note that the following should be noted in this step:

[0059] With each candidate cluster grid as the center, an n×n rectangular neighborhood is constructed by symmetrically expanding along rows and columns, where the selection of n is determined based on the chip cell size and the known process influence radius;

[0060] When a neighboring area extends beyond the effective area, the neighboring area is truncated according to the boundary of the effective area, and the effective coverage ratio of the neighboring area is recorded.

[0061] Collect all standardized defect points in the neighborhood to form an original neighborhood point set that corresponds one-to-one with the central candidate grid;

[0062] For overlapping areas in the neighborhood of adjacent candidate grids, a non-repeated reference strategy is used to assign points to avoid duplicate counting.

[0063] When the effective coverage ratio of the neighborhood is lower than the second threshold T2, a boundary risk marker is added to the original neighborhood point set.

[0064] Output the potential cluster set and its corresponding neighborhood coverage ratio and risk label.

[0065] It should be noted that this implementation adopts a non-repeating reference strategy to handle the overlapping areas of adjacent candidate grid neighborhoods. Specifically, when constructing the neighborhood of each candidate grid and collecting defect points therein, a temporary label is established for each processed standardized defect point. When processing the next neighborhood, if its spatial range overlaps with the previously processed neighborhood, when collecting defect points in the overlapping area, it is first checked whether these points have been marked as referenced. If a defect point has been marked, it will be skipped and will not be included in the point set of the current neighborhood, thereby ensuring that each defect point is uniquely assigned to the set of potential cluster points it was first associated with. This strategy avoids repeated analysis of the same defect point and ensures the accuracy and uniqueness of subsequent local clustering results.

[0066] It should be further explained that the selection of the second threshold T2 is intended to identify potential clusters of defect points whose neighborhood range is severely truncated by the effective region boundary, which may lead to incomplete defect point data. The threshold is preset to 50%. The specific implementation method of this threshold is as follows: for each constructed n×n neighborhood, calculate its intersection area with the effective region mask, and compare this intersection area with the area of ​​the complete n×n neighborhood to obtain the effective coverage ratio of the neighborhood. When this effective coverage ratio is lower than the preset second threshold T2, it is considered that the defect point set in the neighborhood fails to fully reflect the real defect cluster, and therefore a boundary risk mark will be added to the original neighborhood point set.

[0067] In a preferred embodiment, the final output of this embodiment is a structured dataset containing a list of defect points corresponding to each candidate cluster grid, as well as related metadata. Specifically, it includes: packaging and integrating standardized defect point data collected from each central grid, the effective coverage ratio of the neighborhood, and information such as whether it has a risk label. The risk label is a key component, which contains a classification label (e.g., boundary risk, edge truncation, or no risk) to clearly indicate whether the point set has the possibility of incomplete data due to severe truncation of the neighborhood.

[0068] S5. Combining chip unit size, detection resolution, and local density, adaptively determine the radius parameter and minimum sample number of DBSCAN, and perform local clustering on the potential aggregation point set to obtain local clusters and local noise points. Note that the following should be noted in this step:

[0069] The lower limit of the density proximity radius is determined based on the chip cell size and detection resolution, and the local radius parameter is set with reference to the average proximity spacing and its stable range within the potential aggregation point set.

[0070] The initial value of the minimum sample number is determined by combining the neighborhood area and local radius parameters, and the lower limit of the minimum sample number is increased synchronously as the effective coverage ratio of the neighborhood decreases.

[0071] When stripes or grid artifacts are detected along the scanning direction, the proximity relationships in that direction are assigned a reduced weight to suppress pseudo-clustering;

[0072] DBSCAN clustering is performed with a defined local radius parameter and a minimum number of samples, outputting a set of local clusters and a set of local noise points, and generating a boundary polygon and a target center point for each local cluster.

[0073] Output the local clusters and local noise points corresponding to each potential aggregation point set.

[0074] In a preferred embodiment, adaptively determining the radius parameter of DBSCAN includes: using the chip cell size and detection resolution as hard lower limits to ensure that the radius parameter is not less than the minimum distance required to distinguish individual defect points, thereby avoiding misjudging normal process noise as clusters; for example, the lower limit is set to one-tenth of the minimum feature size of the chip cell. Subsequently, for each potential cluster set, the average proximity spacing and its stable interval between all defect points are calculated; the stable interval refers to the typical fluctuation range of the average spacing in historical data of the same batch or the same machine. Based on the average proximity spacing of the potential cluster set, the local radius parameter is adaptively set within the stable interval.

[0075] For example, the local radius parameter can be set to twice the average neighbor spacing within the potential cluster set to balance clustering sensitivity and noise resistance.

[0076] Furthermore, this embodiment adaptively determines the minimum sample number using the following method: An initial value for the minimum sample number is determined by combining the neighborhood area and the aforementioned determined local radius parameter. This initial value is set as the expected average number of defect points within the circular area defined by the local radius parameter, based on the overall defect density of the wafer. For example, the initial value can be set as the product of the neighborhood area and the average defect point density of the wafer. To address the impact of the effective region boundary on clustering integrity, the lower limit of the minimum sample number is increased synchronously as the effective coverage ratio of the neighborhood decreases. For example, if the effective coverage ratio of a neighborhood is only 50%, the system will increase the lower limit of the minimum sample number for that neighborhood to twice the original initial value to compensate for the density sparsity artifact caused by incomplete data, ensuring that only truly high-density defect clusters can be identified in the edge region.

[0077] When the system detects stripes or grid artifacts along the scanning direction (such as the X-axis or Y-axis) in the grid defect count distribution, a weight suppression method is used to prevent them from forming false clusters. Specifically, during the proximity search in the DBSCAN algorithm, the distance between defect points along the direction of the stripe or grid artifact is assigned a reduced weight. For example, if the artifact appears in the Y-axis direction, then when calculating the distance between two points... and When calculating the distance between points, the distance component in the Y direction is assigned a weight factor less than 1, reducing its contribution to the final distance calculation. In this way, the algorithm is more inclined to form clusters of points that are closely clustered along non-artifact directions, thereby effectively suppressing false defect clusters caused by device artifacts.

[0078] In this embodiment, after determining the local radius parameter and the minimum number of samples, 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 neighboring points. Points that fail to belong to any cluster are marked as local noise points. After clustering is completed, the set of local clusters and the set of local noise points are output, and their mathematical expressions are as follows:

[0079] Local cluster set:

[0080]

[0081] in, Let J represent the j-th local cluster, which is a subset containing multiple standardized defect points, and M is the total number of local clusters.

[0082] Set of local noise points:

[0083]

[0084] in, Represents the set of local noise points. Represents the original set of potential aggregation points. This represents the k-th local noise point.

[0085] In addition, a boundary polygon and a target center point are generated for each local cluster. The boundary polygon uses a concave hull algorithm (such as Alpha Shapes) to depict the outline of the cluster, thereby providing information on the spatial extent of the cluster. The target center point can be calculated as the geometric center of the boundary polygon to represent the core location of the cluster.

[0086] Preferably, for each identified set of potential clusters, the DBSCAN (density-based noisy spatial clustering) clustering algorithm is executed using the following sub-process:

[0087] (1) Before starting clustering, all standardized defect points in the potential cluster point set are marked as unvisited. Then, the system traverses each unvisited point and uses the point as the center to define a circular neighborhood around it using a preset local radius parameter. The system counts the number of defect points contained in the neighborhood. If the number is greater than or equal to the preset minimum number of samples, the point is determined as the core point.

[0088] (2) When a core point is discovered, a new local cluster is created starting from this 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:

[0089] If the neighboring point has not yet been visited, mark it and recursively perform the core point discovery step;

[0090] If the neighboring point is itself a core point, add it to the current cluster and continue expanding the cluster;

[0091] If the neighboring point has been visited but does not belong to any cluster, it will be assigned to the current cluster and marked as a boundary point;

[0092] 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;

[0093] (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.

[0094] 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:

[0095] 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.

[0096] 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.

[0097] The merging process is performed iteratively from a global perspective until no cluster pairs satisfy the merging conditions are found.

[0098] The discrete points that were not absorbed after merging are incorporated into the global noise point set;

[0099] Output a set of consistent defect clusters across the entire wafer and a set of global noise points.

[0100] 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:

[0101]

[0102] in, Represents polygons and The area of ​​intersection Represents polygons and The area of ​​the union of the sets;

[0103] 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:

[0104]

[0105] in, Represents polygons boundary A point on the top, Represents polygons boundary A point on the top, This represents the Euclidean distance.

[0106] 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.

[0107] 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:

[0108] The boundary overlap rate is not lower than the preset third threshold T3;

[0109] The nearest distance between the two boundaries is less than a preset minimum value, for example, less than twice the detection resolution.

[0110] It should be further noted that this embodiment adopts a global perspective iterative execution merging method, and its specific implementation process is as follows:

[0111] (1) The system initializes a queue to be merged and adds all local cluster pairs generated in S5 to it;

[0112] (2) Iterate through all cluster pairs in the queue to be merged and check whether they meet the above merging conditions;

[0113] (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.

[0114] (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;

[0115] (5) This process continues to iterate until, across the entire wafer, no pair of unmerged clusters meets the merging criteria.

[0116] 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.

[0117] After the above iterative merging process, the following two sets are finally generated and output:

[0118] The set of wafer-wide consistent defect clusters, which includes all complete defect clusters obtained after cross-neighborhood merging, is expressed as:

[0119]

[0120] in, This represents a set of uniform defect clusters across the entire wafer. The kth wafer-wide consistent defect cluster is obtained by merging one or more local clusters, where K is the total number of the final clusters.

[0121] The global noise point set consists of two parts: first, local noise points in S5 that are not assigned to any local cluster; and second, discrete points in S6 that are not absorbed by any cluster, excluding all merged cluster pairs. The expression for this set is:

[0122]

[0123] in, Represents the set of global noise points. This represents the set of local noise points obtained in S5. This represents the set of discrete points that were not absorbed by any cluster during the cross-neighborhood merging process.

[0124] S7. Fit the Geyer saturation point process to each defect cluster in the whole-wafer consistent defect cluster, and obtain the estimated values ​​of interaction strength, interaction radius and constant through boundary-corrected maximum likelihood estimation. Calculate the significance index using Monte Carlo. To obtain the interaction strength assessment results. It should be noted that the following points should be noted in this step:

[0125] For each whole-wafer consistent defect cluster, undetectable areas are removed and boundary correction is performed according to the effective area ratio to obtain the cluster point set and corresponding effective window for fitting.

[0126] The maximum likelihood search is performed within the effective window using the boundary-corrected point set to obtain estimates of the interaction strength, interaction radius, and constant term, and the convergence state is recorded.

[0127] Based on the estimated values, a conditional generation process is constructed, and multiple stochastic simulations are performed to obtain a reference distribution under the weak interaction assumption.

[0128] Calculate significance index and significance threshold Comparison: When When the cluster is statistically significant, it is labeled as a cluster of interactions; when At that time, the cluster is marked as a weakly interacting cluster;

[0129] Output three estimates and significance indexes for each cluster. With judgment labels.

[0130] In an optional implementation, this embodiment performs the following boundary correction procedure on each full-wafer consistent defect cluster to ensure the accuracy of the subsequent Geyer saturation point process fitting:

[0131] For each wafer-wide consistent defect cluster obtained through step S6, all standardized defect points contained therein are first traversed. During this process, based on the pre-established effective area mask, any defect points falling within known undetectable areas (such as wafer dicing lanes, process test units, or optical alignment marks) are identified and removed. The set of points filtered by this step is the cluster point set used for fitting.

[0132] The boundary polygon of the above cluster is geometrically intersected with the effective area of ​​the wafer (i.e., the area of ​​the wafer after deducting edge exclusion strips, scribe lines, etc.). The result of this operation forms an effective window that strictly corresponds to the spatial range of the cluster point set. For clusters located at the edge of the wafer, this effective window will be a geometric shape truncated by the circular boundary or straight edge of the wafer, and its area is smaller than the original area of ​​the cluster boundary polygon.

[0133] 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 of the maximum likelihood function, this effective area ratio is used as a normalization factor. Its role is to correct the data incompleteness caused by the cluster being truncated by the effective region. By multiplying the area term in the likelihood function by this ratio, the influence of missing data due to some defective points possibly falling outside the effective region can be effectively compensated, so that the final parameter estimate more robustly and unbiasedly reflects the true statistical characteristics of the cluster.

[0134] Furthermore, this embodiment of the invention employs a maximum likelihood optimization method to estimate the parameters of the clustered point set after boundary correction within its effective window. This method uses an iterative optimization algorithm (such as gradient descent) to find a set of optimal parameter values ​​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, the mathematical expression of which is as follows:

[0135]

[0136] in, The log-likelihood function of the model represents the interaction strength. Interaction radius R and constant The function; N represents the total number of defect points in the cluster point set; This represents the area of ​​the effective window after boundary correction; Point and The Euclidean distance between them; It is an indicator function, with a value of 1 when its internal conditions are met, and 0 otherwise; β represents a constant term used to describe the overall density of the cluster; The value represents the interaction strength. A value greater than 0 indicates an attractive force between the points, a value less than 0 indicates a repulsive force, and a value equal to 0 indicates a random distribution. R represents the interaction radius, which is the distance range of the interaction between the points.

[0137] Through this optimization process, the system obtains the parameter estimates that maximize the likelihood function. , and And record the convergence state of the optimization process.

[0138] This implementation method generates a reference distribution under the weak interaction assumption through Monte Carlo simulation. The specific implementation method is as follows: based on the parameter estimates obtained from the maximum likelihood estimation above, especially the constant term... Construct a conditional generation process; this process, within a valid window, is based on a Poisson point process (i.e., a completely random distribution) and uses... As its average density, multiple random point pattern simulations are performed. Each simulation generates a point set with a number of points similar to the observed cluster points. By repeating this simulation multiple times (e.g., 1000 times), a point pattern set is obtained, which represents a reference distribution of point patterns that may occur under the weak interaction assumption (i.e., points are randomly distributed or have only slight interactions). This reference distribution can be used to calculate the distribution of various statistical indicators, such as the number of points, nearest neighbor distance, density, etc.

[0139] It should be further noted that this invention uses Monte Carlo simulation to calculate the significance index ( The value is used to quantify the statistical significance of cluster interactions, and its calculation method is as follows:

[0140] For each random point set generated by the simulation, the corresponding test statistic value is calculated to obtain a reference distribution composed of all simulation results. This distribution represents the typical range of values ​​that the test statistic may have under the assumption of weak interaction (or stochasticity).

[0141] The significance index was calculated by comparing the observed cluster test statistics with the aforementioned reference distribution. The value, its mathematical expression is as follows:

[0142]

[0143] in, Indicates significance index, i.e. The value represents the probability of a point pattern that is more extreme (i.e. more clustered) than the observed clusters, under the weak interaction hypothesis. This represents a counting function that counts the number of simulated patterns that meet specific conditions; Simulated Patterns represents random point patterns generated through Monte Carlo simulation; more extreme represents simulated point patterns that are more extreme (i.e., more clustered) than the observed cluster's test statistic value; test statistic is a statistic used to quantify the degree of cluster clustering, such as average nearest neighbor distance or density; TotalNumber of Simulations represents the total number of Monte Carlo simulations.

[0144] Based on the significance index calculated above, a judgment label is generated for each cluster, specifically including:

[0145] When the significance index ( When the value is less than the preset significance threshold (e.g., 0.05), the cluster is marked as "statistically significant interaction cluster", indicating that its interaction strength is significant and its clustering pattern is unlikely to be randomly formed.

[0146] When the significance index ( When the value is greater than or equal to a preset significance threshold (e.g., 0.05), the cluster is marked as a "weak interaction cluster," indicating that its clustering pattern may be caused by random noise or weak interactions.

[0147] That is, the The smaller the value, the less likely the observed cluster is to be randomly formed, and the more significant its interaction strength;

[0148] Finally, the system outputs three estimated values ​​(interaction strength, interaction radius, and constant), significance index, and corresponding judgment labels for each cluster, providing accurate quantitative basis for subsequent process analysis.

[0149] S8. Based on the evaluation results of the uniform defect clusters across the entire wafer and their interaction strength, calculate the center location, boundary range, number of defect points, density, shape, and orientation indices of each defect cluster, and summarize the estimated values ​​and significance indices of interaction strength, interaction radius, and constant. Simultaneously, it outputs a global noise point set, from which a structured analysis report is generated. It is important to note the following in this step:

[0150] For each whole-wafer consistent defect cluster, select the valid defect points within the range enclosed by its final boundary polygon to form a dataset for index calculation; if the boundary intersects with the undetectable region, only the points located within the valid region and the corresponding valid boundary segments are retained.

[0151] Using the index dataset as the object, an iterative shrinkage method that is insensitive to outliers is adopted to determine the target center position. That is, while removing outliers in each round, the center candidates are updated until the removal ratio no longer changes. When there are obvious holes or thin branches at the cluster boundary, the geometric center of the boundary polygon is compared with the target center first. When the deviation between the two exceeds the fourth threshold T4, the geometric center of the boundary is taken as the center position. The coordinates of the center position in the wafer global coordinate system are output, and its row and column positioning and relative position with the orientation mark are recorded by aligning with the chip cell grid.

[0152] Based on the boundary polygon after merging across neighborhoods, if holes exist, the outer boundary minus the hole area is identified as the effective boundary; when the boundary intersects with the effective area, their intersection is taken as the effective boundary, and the effective coverage ratio is recorded; two types of bounding boxes are generated on the effective boundary: one is the bounding rectangle parallel to the wafer coordinate axis, and the other is the minimum orientation bounding rectangle with free orientation, and the azimuth angle of the latter is saved; the effective area is calculated based on the effective boundary, and the boundary type (e.g., with / without holes, whether truncated), effective coverage ratio, and parameters of the two types of bounding boxes are output;

[0153] Defect points located within the effective boundary are recorded as cluster points, and boundary points are assigned uniquely based on inward priority; duplicate coordinate points caused by repeated sampling are only counted once; the number of cluster points is output, along with records of the number of boundary points included and the number of duplicate points removed.

[0154] The defect point density is calculated using the obtained effective area as the denominator and the number of points in the cluster as the numerator. When the effective coverage ratio is lower than the preset lower limit, the density is corrected for area in one step according to the effective coverage ratio, and the edge correction is marked in the result. The original density, the edge-corrected density and the coverage ratio are output.

[0155] The compactness of the effective boundary is quantified based on the degree of fit between the boundary shape and the outer frame, as well as the degree of concavity and convexity of the boundary. The slenderness is quantified by the ratio of the length of the long side to the length of the short side of the minimum oriented bounding rectangle. The indentation is quantified by the ratio of the area of ​​the gap between the effective boundary and its convex hull. When the slenderness exceeds the fifth threshold T5 and the indentation is low, it is marked as a strip shape, resulting in stripness. The compactness, slenderness, indentation, and stripness are output as labels.

[0156] The spatial extension principal axis of the index dataset is used as the principal direction, which is determined by the direction of the long side of the minimum orientation bounding rectangle. The azimuth angle of the principal direction relative to the wafer orientation mark is recorded, and when there is a significant secondary principal direction, the secondary principal direction and its weight ratio are output. When the cluster is obviously ring-shaped or nearly circular, it is marked as having no significant directionality. The principal direction angle, secondary principal direction angle, and the mark of having no significant directionality are output.

[0157] Perform consistency checks on center position, boundary range, density, and orientation: when the center position deviates from the center of the minimum orientation bounding rectangle by more than the preset upper limit or the orientation conflicts with the shape type, add a check mark;

[0158] Summarize the estimated values ​​of interaction strength, interaction radius, and constant term, as well as significance indices, and list them alongside the corresponding indices for historical batches from the same machine and process. When a significance index indicates a statistically significant cluster of interactions, add a label to the cluster entry.

[0159] In a preferred embodiment, the method for generating a structured report includes: generating structured entries at the cluster level, wherein each entry includes at least the center location (including grid row and column positioning), boundary range (including effective area and outer frame parameters), number of defect points, density (including edge correction status), shape indicators (compactness, slenderness, indentation, striping), directionality indicators (primary / secondary direction angles or no directionality), interaction parameters, and saliency indicators.

[0160] It should be noted that the fourth threshold T4 is designed to correct the calculation of the cluster center position. The selection rule of this 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) should be very close to the target center (i.e., the density center of the point set) calculated by the iterative shrinkage method. However, when there are obvious holes or slender branches at the boundary of the cluster, these two centers may deviate significantly. Therefore, the fourth threshold T4 is set to detect such abnormal deviations. For example, T4 can be set to 10% of the length of the long side of the minimum orientation bounding rectangle. When the distance between the target center and the geometric center of the boundary polygon exceeds this threshold, the system will determine that the target center obtained by the iterative shrinkage method may be affected by abnormal points. In this case, the more robust geometric center of the boundary polygon will be preferred as the final center position.

[0161] It should also be noted that the fifth threshold T5 aims to identify defect clusters with specific strip-like or linear shapes. The selection rule for this threshold is based on the quantification of the cluster's thinness length, which is the ratio of the long side to the short side of the smallest oriented bounding rectangle of the cluster. The larger this value, the thinner and longer the cluster shape. T5 is set as the critical value to distinguish between thin and long clusters and non-thin clusters. For example, T5 can be set to 4. When the thinness length of a cluster exceeds this threshold and its concavity is low (i.e., the boundary is relatively smooth), the system will add a strip-like mark to it. This rule enables the system to automatically identify linear or strip-like defect clusters caused by process defects (such as scanning artifacts, track wear, or linear scratches), thereby providing important clues for tracing the source of process problems. It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications and substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A wafer defect cluster analysis method based on DBSCAN clustering, characterized in that, include: Obtain the coordinates of defect points, wafer layout and chip cell grid information, perform distortion correction and zero-position alignment on defect points and uniformly map them to the same wafer coordinate system to obtain a standardized defect point set; The effective area of ​​the wafer is gridded according to the chip cell grid, and the grid assignment statistics of the standardized defect point set are performed. The boundary incomplete grids are normalized according to the effective area to obtain the grid defect count distribution. Based on a preset first threshold T1, grids with a defect count ≥ T1 are marked as candidate clustered grid sets; Centered on each grid in the candidate clustering grid, an n×n grid neighborhood is constructed and all standardized defect points within the neighborhood are collected to form a potential clustering point set corresponding one-to-one with each candidate clustering grid; The radius parameter and minimum number of samples of DBSCAN are adaptively determined by combining chip unit size, detection resolution and local density, and the potential aggregation point set is locally clustered to obtain local clusters and local noise points; 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. For each defect cluster in the whole-wafer consistent defect cluster, a Geyer saturation point process is fitted, and the estimated values ​​of interaction strength, interaction radius, and constant are obtained by maximum likelihood estimation after boundary correction. The significance index is calculated by Monte Carlo. To obtain the interaction evaluation results; Based on the evaluation results of the whole-wafer consistent defect clusters and their interactions, the center location, boundary range, number of defect points, density, shape, and orientation indices of each defect cluster are calculated. The estimated values ​​of the interaction strength, interaction radius, and constant are then summarized along with the significance index. It also outputs a global noise point set, based on which a structured analysis report is generated.

2. The wafer defect cluster analysis method based on DBSCAN clustering according to claim 1, characterized in that, The obtained standardized defect point set includes: Based on the known anchor points and orientation marks in the wafer layout, a calibration pattern is acquired, an imaging distortion and geometric perspective joint correction model is established, and it is solidified into a single set of correction parameters; The original coordinates of the defect point are applied to the correction parameter set to complete a one-time anti-distortion and perspective correction, and the corrected coordinates of the defect point are obtained. Using 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 inspection batches is calculated, and the coordinates of the corrected defect points are uniformly registered. When there are minor non-uniform scaling or shearing errors, constrained affine fine-tuning is performed within the preset error limit to generate candidate defect point coordinates in a unified wafer coordinate system. Duplicate and isolated points are removed according to the detection resolution and minimum distinguishable interval, and points that overlap with undetectable areas are also removed. Using the chip cell grid as a reference, a consistency check is performed on the relative positional relationship between the candidate defect point and the grid. If the overall offset exceeds a preset threshold, the process returns to the unified 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 wafer defect cluster analysis method based on DBSCAN clustering according to claim 1 or 2, characterized in that, The process of obtaining the grid defect count distribution includes: Based on the wafer diameter, edge exclusion zone, and undetectable area, the effective area is determined and an effective area mask is generated; A set of row and column grids is established within the effective area using chip cell grids as the basic unit, and the effective coverage area ratio of each grid is recorded. Standardized defect points are uniquely assigned to the corresponding grid based on their spatial location, and points located on the common boundary of the grid are uniquely classified according to the priority of map coverage. For incomplete grids located at the boundaries of the effective area, the attribution count is normalized according to the proportion of their effective coverage area; A consistency check is performed on the counting results of all grids, and grids that differ abnormally from their neighboring grids and coincide with the image stitching boundary are marked as objects of quality concern; The output includes the normalized counts of each grid, the effective area ratio, and the quality label of the grid defect count distribution.

4. The wafer defect cluster analysis method based on DBSCAN clustering according to claim 3, characterized in that, The step of marking grids with defect counts ≥ T1 as candidate clustered grid sets according to a preset first threshold T1 includes: The overall statistical analysis of the grid defect count distribution is used to form a baseline count interval and an abnormal upward indication interval; Using the first threshold T1 as the judgment condition, select grids with a count ≥ T1 as the initial candidate set; Perform a spatial connectivity check on the initial candidate set and remove isolated grids that are not adjacent to any candidate grid and whose counts fall only in a narrow band near T1; Output the candidate clustered grid set and its labeling information.

5. The wafer defect cluster analysis method based on DBSCAN clustering according to claim 4, characterized in that, The method for setting the first threshold T1 includes: The 95th percentile integer value of the grid count distribution of the most recent batch of the same machine and the same formula after the effective area and resolution are consistent is used as the initial threshold. Then, the candidate grid ratio of the current wafer is used as a reference, and a one-time ±1 count fine adjustment is made around the initial threshold so that the candidate ratio falls into the range of 2% to 8%. After the fine adjustment, it is frozen as the final first threshold T1. The most recent batch refers to the most recent 30 pieces, and the initial threshold is not less than 2.

6. The wafer defect cluster analysis method based on DBSCAN clustering according to claim 4, characterized in that, The formation of a potential cluster point set corresponding one-to-one with each candidate cluster grid includes: With each candidate cluster grid as the center, an n×n rectangular neighborhood is constructed by symmetrically expanding along rows and columns, where the selection of n is determined based on the chip cell size and the known process influence radius; When the neighborhood extends beyond the effective area, the neighborhood is truncated according to the boundary of the effective area, and the effective coverage ratio of the neighborhood is recorded. Collect all standardized defect points in the neighborhood to form an original neighborhood point set that corresponds one-to-one with the central candidate grid. For overlapping areas in the neighborhood of adjacent candidate grids, a non-repeated reference strategy is used to assign points to avoid duplicate counting. When the effective coverage ratio of the neighborhood is lower than the second threshold T2, a boundary risk marker is added to the original neighborhood point set. Output the set of potential cluster points and their corresponding neighborhood coverage ratios and risk markers.

7. The wafer defect cluster analysis method based on DBSCAN clustering according to claim 6, characterized in that, Local clustering is performed on the potential aggregation point set to obtain local clusters and local noise points, including: The lower limit of the density proximity radius is determined based on the chip cell size and detection resolution, and the local radius parameter is set with reference to the average proximity spacing and its stable range within the potential aggregation point set. The initial value of the minimum number of samples is determined by combining the neighborhood area and local radius parameters, and the lower limit of the minimum number of samples is increased synchronously as the effective coverage ratio of the neighborhood decreases. When stripes or grid artifacts are detected along the scanning direction, the proximity relationships in that direction are assigned a reduced weight to suppress pseudo-clustering; DBSCAN clustering is performed with a defined local radius parameter and a minimum number of samples, outputting a set of local clusters and a set of local noise points, and generating a boundary polygon and a target center point for each local cluster. Output the local clusters and local noise points corresponding to each potential aggregation point set.

8. The wafer defect cluster analysis method based on DBSCAN clustering according to claim 7, characterized in that, 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, including: 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 correspond to the same cluster and are 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 the set of uniform defect clusters across the entire wafer and the set of global noise points.

9. The wafer defect cluster analysis method based on DBSCAN clustering according to claim 1, characterized in that, The interaction evaluation results are obtained by: For each whole-wafer consistent defect cluster, undetectable areas are removed and boundary correction is performed according to the effective area ratio to obtain the cluster point set and corresponding effective window for fitting. The maximum likelihood search is performed within the effective window using the boundary-corrected point set to obtain estimates of the interaction strength, interaction radius, and constant term, and the convergence state is recorded. Based on the estimated values, a condition generation process is constructed, and multiple random simulations are performed to obtain a reference distribution under the weak interaction assumption. Calculate significance index and significance threshold Comparison: When When the cluster is statistically significant, it is labeled as a cluster of interactions; when At that time, the cluster is marked as a weakly interacting cluster; Output three estimates and significance indexes for each cluster. The results of the interaction evaluation.

10. The wafer defect cluster analysis method based on DBSCAN clustering according to claim 9, characterized in that, Based on the evaluation results of the whole-wafer consistent defect clusters and their interactions, the center location, boundary range, number of defect points, density, shape, and orientation indices of each defect cluster are calculated, including: Defect points located within the effective area are selected as the indicator dataset, with the cluster boundary after cross-neighborhood merging as the limit. Calculate the target center for the index dataset and compare it with the boundary geometric center. When the deviation between the two exceeds the fourth threshold T4, the boundary geometric center is taken as the center position. The effective area is calculated by taking the intersection of the merged boundary and the effective region as the effective boundary, and the parameters of the circumscribed rectangle and the minimum oriented bounding rectangle parallel to the coordinate axis are given at the same time. Defect points located within the effective boundary are recorded as cluster points. Boundary points are assigned uniquely based on inward priority. Duplicate points are counted after deduplication, and the density is obtained by using the effective area as the denominator. The compactness, fineness, and concavity are determined by the parameters of the effective boundary and the circumscribed rectangle and the minimum orientation bounding rectangle. The main direction is determined according to the long side direction of the minimum orientation bounding rectangle, and the azimuth angle relative to the wafer orientation mark is recorded.

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