Defect hotspot detection method based on two-dimensional profile extraction

Abstract

The application provides a defect hotspot detection method based on two-dimensional contour extraction, relates to the field of semiconductor processing technology, and combines a dynamic gradient tracking method (DGT) with a probability propagation network (PPN). The former extracts two-dimensional contours in a layout accurately through adaptive step length and turning point identification, and overcomes the limitation of poor adaptability of traditional static edge detection to complex patterns. The latter propagates probability through an adjacency graph, fuses local contour features and global layout information, and breaks through the limitation of traditional isolated analysis methods. The fusion can not only predict potential defect hotspots in the design stage, but also dynamically adapt to different process nodes and layout densities, significantly improves detection accuracy and robustness, provides unprecedented early optimization capability for photolithography research and development, and thus reduces the defect occurrence rate in the manufacturing process and accelerates the product launch time.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of semiconductor processing, in particular to a defect hotspot detection method based on two-dimensional profile extraction. BACKGROUND

[0002] In the field of semiconductor manufacturing, defect hotspot detection is a key link to improve yield and accelerate product launch. Traditional defect detection methods mainly rely on design rule checking, simulation analysis after optical proximity correction, and comparison of scanning electron microscope (SEM) images after manufacturing. These methods usually use static rules or simulation indexes (such as exposure energy) to identify potential problems in the design stage, or locate defect hotspots through actual measurement data after manufacturing is completed. For example, the prior art assesses layout risks through a multi-index scoring system, while other methods detect defects based on profile comparison after manufacturing. However, these methods often show inadequate adaptability, limited detection accuracy, and low efficiency when facing complex layouts and high-density patterns, especially in the design stage, making it difficult to achieve efficient automated prediction, resulting in prolonged research and development iteration cycles and increased reliance on manual work.

[0003] According to the Chinese patent No. "CN106896126A" disclosed a junction profile detection sample and preparation method, and a junction profile detection method, the preparation method of the junction profile detection sample provided by the application comprises the following steps: providing a semiconductor sample, the semiconductor sample is formed with P junction and / or N junction; providing hot phosphoric acid, placing the semiconductor sample in the hot phosphoric acid for a predetermined time; taking out the semiconductor sample for cleaning to obtain a junction profile detection sample. Compared with the prior art, the application has low cost, appropriate sample preparation time, strong controllability, and can obtain better junction profile and good repeatability.

[0004] The above patent document and prior art have the following technical problems when used:

[0005] Problem one, traditional defect detection methods such as DRC or OPC simulation usually rely on static rules or a single simulation parameter, and have poor adaptability to complex layouts and high-density patterns, especially in the design stage, it is difficult to accurately predict defect hotspots. Traditional edge detection is prone to breakage or misjudgment in areas with complex gradient changes, and isolated analysis methods ignore the global context of the layout, resulting in insufficient prediction accuracy and robustness, and a large number of trial and error and adjustments are still needed in the manufacturing process;

[0006] Secondly, traditional defect pattern recognition methods usually use fixed rules or single feature analysis (such as curvature or length), and clustering methods (such as K-means) need to preset the number of clusters, which is difficult to adapt to the diversity and complexity of layout patterns. In addition, these methods often rely on manual labeling or post-validation, and have low automation degree and efficiency, which leads to the extension of the research and development cycle. Traditional methods cannot dynamically adjust the analysis strategy to cope with the different characteristics of high-density or low-density areas, increasing the workload of manual detection. SUMMARY

[0007] TECHNICAL PROBLEMS SOLVED

[0008] In view of the deficiencies of the prior art, the present application provides a defect hot spot detection method based on two-dimensional contour extraction, which solves the following problems:

[0009] 1. The traditional method has poor defect hot spot prediction accuracy and robustness for complex layout in the design stage, which leads to the problem that manufacturing defects are difficult to avoid in advance.

[0010] 2. The traditional defect pattern recognition method lacks flexibility and automation efficiency, and is difficult to adapt to diversified layout and reduce manual intervention.

[0011] TECHNICAL SCHEME

[0012] In order to achieve the above purpose, the present application is realized by the following technical scheme: a defect hot spot detection method based on two-dimensional contour extraction, the defect hot spot detection method comprising the following steps:

[0013] Sp1: inputting a semiconductor layout design file, performing grid division and generating a two-dimensional intensity map;

[0014] Sp2: extracting two-dimensional contours in the layout by dynamic gradient tracking method to obtain a contour set;

[0015] Sp3: extracting contour dynamic feature vectors from the contour set, and generating contour clusters of potential defect patterns by adaptive density clustering;

[0016] Sp4: constructing a probability propagation network based on the contour clusters, calculating the defect probability of each cluster and marking the defect hot spots;

[0017] Sp5: outputting a hot spot distribution map containing the position and probability of the defect hot spots;

[0018] The dynamic gradient tracking method in step Sp2 tracks the contour path along the gradient direction and identifies turning points by adaptive step size. The contour dynamic feature vector in step Sp3 includes static geometric features, dynamic evolution features and context features. The adaptive density clustering in step Sp3 dynamically adjusts the number of clusters according to the layout density. The probability propagation network in step Sp4 propagates probabilities through adjacency graph to fuse local and global information.

[0019] Preferably, the dynamic gradient tracking method in step Sp2 specifically includes the following steps:

[0020] Sp2.1: Base: Two-dimensional intensity map calculates the gradient direction and gradient magnitude of each pixel to generate a gradient field;

[0021] Sp2.2: Starting from the pixel where the gradient magnitude exceeds the adaptive threshold T, trace the contour path along the gradient direction, where the step size S is determined according to the formula... Dynamic adjustment The gradient magnitude is k, and the adjustment coefficient is k.

[0022] Sp2.3: When the gradient direction changes by more than 45°, it is recorded as an inflection point;

[0023] Sp2.4: When the tracing path returns to the starting point or enters a region where the gradient magnitude is less than T / 2, the contour is closed, and a contour set is generated.

[0024] Preferably, the extraction of the contour dynamic feature vector in step Sp3 includes the following steps:

[0025] Sp3.1: Calculate static geometric features, including profile length L, inflection point density TD, and local curvature fluctuation LCF, where inflection point density TD is the number of inflection points divided by profile length, and local curvature fluctuation LCF is the rate of change of curvature near the inflection points.

[0026] Sp3.2: Calculate dynamic evolution characteristics, including gradient rate of change (GCR), where GCR is the mean square error of the gradient magnitude along the contour path;

[0027] Sp3.3: Calculate context features, including neighborhood interaction strength (NIS) and region complexity (RC), where NIS is the reciprocal of the average distance between a contour and its nearest neighbor contour, and RC is the ratio of the number of contours to the area within a grid cell.

[0028] Sp3.4: Integrate the above features to form a contour dynamic feature vector CDFV = [L, TD, LCF, GCR, NIS, RC].

[0029] Preferably, the adaptive density clustering in step Sp3 specifically includes the following steps:

[0030] Sp3.5: Initialize the number of cluster centers k, where k is dynamically determined based on the number of contours N within the grid cell, k≈√N;

[0031] Sp3.6: Uses a weighted Euclidean distance to measure the similarity between dynamic feature vectors of the contour, where the weights are adaptively adjusted during iteration based on the relevance of the features to the defects;

[0032] Sp3.7: Iteratively update the cluster center as the mean of the feature vectors within the cluster, and merge clusters when the cluster spacing is less than the adaptive threshold δ, where δ is calculated from the layout density;

[0033] Sp3.8: Clustering is terminated and contour clusters are generated when the change in cluster center is less than the preset value ε or the maximum number of iterations is reached.

[0034] Preferably, the construction and computation of the probability propagation network in step Sp4 includes:

[0035] Sp4.1: Calculate the cluster risk index CRI for each contour cluster, where CRI = w1 × LCF + w2 × GCR + w3 × NIS, and w1, w2, and w3 are weights obtained through training with historical data;

[0036] Sp4.2: Construct an adjacency graph between grid cells, with edge weights being the cosine similarity of the dynamic feature vectors of the cell contours;

[0037] SP4.3: Initialize the defect probability for each cluster The probability is updated using the iterative formula P(t+1)=α×P(t)+(1-α)×Σadjacent cluster P(t)×edge weight, where α is the propagation factor;

[0038] Sp4.4: Once the probabilities converge, output the final defect probability P for each cluster.

[0039] Preferably, the adaptive threshold T in Sp2.2 is dynamically calculated from the local gradient mean, and the calculation formula is T=β×μ+σ, where μ is the mean gradient magnitude within the grid cell, σ is the standard deviation, and β is an adjustment parameter with a value range of 1.5 to 2.5.

[0040] Preferably, in the calculation of the local curvature fluctuation (LCF) in Sp3.1, the curvature κ is determined by fitting the circular arcs of three adjacent points on the contour path, and the rate of change... The sampling length before and after the inflection point is calculated as 5% of the contour length.

[0041] Preferably, the weight adjustment of the weighted Euclidean distance in Sp3.6 is optimized by gradient descent, with the objective function being the ratio of intra-cluster variance to inter-cluster variance, and the optimal weights minimizing this ratio.

[0042] Preferably, the propagation factor α in Sp4.3 is dynamically adjusted according to the complexity of the layout. When the region complexity RC is greater than a preset threshold, the value of α is in the range of 0.6 to 0.8, otherwise the value is in the range of 0.8 to 0.9.

[0043] Preferably, in step Sp1, the unit size of the grid division is adaptively adjusted according to the density of the layout pattern. When the density is higher than the average value, the unit size is reduced to 5μm×5μm, and when the density is lower than the average value, it is enlarged to 15μm×15μm to optimize computational efficiency and detection accuracy.

[0044] Beneficial effects

[0045] This invention provides a defect hotspot detection method based on two-dimensional contour extraction. It has the following beneficial effects:

[0046] 1. This invention combines Dynamic Gradient Tracking (DGT) with Probabilistic Propagation Network (PPN). The former accurately extracts the two-dimensional contours in the layout through adaptive step size and inflection point identification, overcoming the limitation of traditional static edge detection in adapting to complex patterns. The latter propagates probabilities through adjacency graphs, fusing local contour features with global layout information, breaking through the limitations of traditional isolated analysis methods. It can not only predict potential defect hotspots in the design stage, but also dynamically adapt to different process nodes and layout densities, significantly improving detection accuracy and robustness. This provides unprecedented early optimization capabilities for lithography R&D, thereby reducing the defect rate in the manufacturing process and accelerating product time-to-market.

[0047] 2. This invention integrates Adaptive Density Clustering (ADC) and Contour Dynamic Feature Vector (CDFV) to achieve flexible identification and efficient classification of potential defect patterns. CDFV integrates static geometric features, dynamic evolution features, and contextual features, breaking through the limitations of traditional single feature analysis and providing a multi-dimensional perspective to capture defect characteristics. ADC dynamically adjusts the number of clusters and optimizes weights according to the layout density, surpassing the limitations of fixed-cluster clustering, adapting to the diversity of complex layouts, significantly improving the flexibility and computational efficiency of defect pattern recognition, reducing subjective errors and time costs of manual inspection, introducing a new automated analysis paradigm for semiconductor design verification, and promoting the intelligent and efficient process of lithography R&D iteration. Attached Figure Description

[0048] Figure 1 This is a diagram illustrating the method steps of the present invention;

[0049] Figure 2 This is a two-dimensional intensity diagram of the present invention;

[0050] Figure 3 This is a diagram showing the adaptive density clustering results of the present invention;

[0051] Figure 4 This is a diagram illustrating the iterative process of the probability propagation network in this invention. Detailed Implementation

[0052] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Specific Implementation Example 1:

[0054] like Figures 1 to 4 As shown, a defect hotspot detection method based on two-dimensional contour extraction includes the following steps:

[0055] Sp1: Input semiconductor layout design file, mesh it and generate a 2D intensity map. Adaptive meshing and intensity map generation ensure the structure of input data, providing an efficient foundation for subsequent calculations.

[0056] This step is the starting point of the entire detection method, aiming to transform complex semiconductor layout designs into a processable two-dimensional data form. First, a semiconductor layout design file (such as GDSII format) is input, containing the geometric pattern information of the layout. Next, the layout is divided into multiple grid cells, the size of which is adaptively adjusted according to the layout pattern density. When the density is higher than the average, the cell size is reduced to 5μm × 5μm, and when the density is lower than the average, it is enlarged to 15μm × 15μm to optimize computational efficiency and detection accuracy, providing higher resolution in high-density areas while reducing computational burden in low-density areas. Subsequently, each grid cell is grayscaled to generate a two-dimensional intensity map. The intensity values ​​reflect the density distribution of the pattern, providing basic data for subsequent contour extraction. The entire process, through adaptive grid division and intensity map generation, transforms the raw design data into a structured input suitable for algorithm analysis, ensuring that subsequent steps can operate efficiently in layouts of varying complexity.

[0057] Sp2: Extracts two-dimensional contours from the layout using the dynamic gradient tracing method to obtain a set of contours. The dynamic gradient tracing method accurately extracts contours by adjusting dynamic thresholds and step sizes, adapting to complex layouts.

[0058] This step utilizes an innovative Dynamic Gradient Tracing (DGT) method to extract the 2D contours of the layout from the 2D intensity map, forming a contour set that lays the foundation for subsequent feature analysis. The specific implementation process includes the following sub-steps: First, the gradient direction and magnitude of each pixel are calculated based on the 2D intensity map to generate a gradient field, which reflects the intensity of changes in the pattern boundary. Next, starting from pixels where the gradient magnitude exceeds an adaptive threshold T, the contour path is traced along the gradient direction. T is dynamically calculated from the local gradient mean using the formula T = β × μ + σ, where μ is the mean gradient magnitude within the grid cell, σ is the standard deviation, and β is an adjustment parameter ranging from 1.5 to 2.5. This dynamic threshold can adapt to the gradient characteristics of different regions. During the tracing process, the step size S is determined according to the formula... Let T be the gradient magnitude and k be an adjustment coefficient. Dynamic adjustment makes the step size smaller in regions with large gradient changes to capture details and larger in smooth regions to improve efficiency. When the gradient direction changes by more than 45°, it is recorded as an inflection point, indicating a significant change in the contour shape. When the tracing path returns to the starting point or enters a region with a gradient magnitude lower than T / 2, the contour is closed, generating a complete contour path. Finally, all contours within each grid cell form a contour set. This method, through dynamic step size and inflection point identification, can accurately extract boundary information in complex layouts. Compared with traditional static edge detection, it is more adaptable and accurate, providing high-quality contour data for subsequent defect analysis.

[0059] Sp3: Extracts dynamic feature vectors of contours from the contour set and generates contour clusters of potential defect patterns through adaptive density clustering. Multidimensional feature extraction and adaptive clustering combine geometric, dynamic and contextual information to generate highly discriminative defect patterns.

[0060] This step transforms the contour set into a structured pattern that can be used for defect prediction by extracting multidimensional features and performing cluster analysis. The specific process is divided into two parts: feature extraction and clustering.

[0061] First, a contour dynamic feature vector (CDFV) is extracted for each contour in the contour set. CDFV includes three types of features: static geometric features, dynamic evolution features, and contextual features. Static geometric features include contour length L (calculated by path integral), inflection point density TD (number of inflection points divided by contour length), and local curvature fluctuation LCF (rate of curvature change near inflection points Δκ / Δs, where curvature κ is determined by fitting circular arcs between three adjacent points, with a sampling length of 5% of the contour length). These features describe the shape and complexity of the contour. Dynamic evolution features include gradient rate of change GCR (gradient along the contour path). The mean squared error of the amplitude reflects the dynamic characteristics of the contour boundary as it changes with the path; contextual features include neighborhood interaction strength (NIS, the reciprocal of the average distance between the contour and its nearest neighbor contour) and region complexity (RC, the ratio of the number of contours to the area within a grid cell), capturing the interaction between contours and local environmental information; the above features are fused to form CDFV = [L, TD, LCF, GCR, NIS, RC], providing a multidimensional description for each contour; then, contour clusters of potential defect patterns are generated through adaptive density clustering (ADC);

[0062] The clustering process first initializes the number of cluster centers k, k≈√N, where N is the number of contours within a grid cell. Then, a weighted Euclidean distance is used to measure the similarity between CDFVs. The weights are optimized using gradient descent based on the correlation between features and defects (the objective function is the ratio of intra-cluster variance to inter-cluster variance, and the optimal weights minimize this ratio). The cluster centers are iteratively updated to the mean of the intra-cluster feature vectors. When the inter-cluster spacing is less than the adaptive threshold δ (δ is calculated from the layout density), clusters are merged. Clustering terminates when the change in cluster centers is less than a preset value ε or when the maximum number of iterations is reached, generating contour clusters. Each cluster represents a potential defect pattern. The adaptability of the clustering ensures that the algorithm can dynamically adjust according to layout characteristics, improving the ability to identify different defect types.

[0063] Sp4: A probability propagation network is constructed based on contour clusters to calculate the defect probability of each cluster and mark defect hotspots. The probability propagation network propagates through risk index and adjacency graph to achieve probability optimization from local to global.

[0064] This step involves constructing a Probability Propagation Network (PPN) to predict the defect probability of contour clusters and marking defect hotspots. The specific process is as follows: First, calculate the cluster risk index (CRI) for each contour cluster: CRI = w1 × LCF + w2 × GCR + w3 × NIS, where w1, w2, and w3 are weights trained using historical data, comprehensively evaluating the cluster's defect tendency. Next, construct an adjacency graph between grid cells, with edge weights equal to the cosine similarity of the CDFV between cells, representing the spatial and feature correlation between clusters. Then, initialize the defect probability of each cluster P0 = CRI / max(CRI). The risk index is normalized to an initial probability. Based on the adjacency graph, the probability is updated using the iterative formula P(t+1)=α×P(t)+(1-α)×Σadjacency clusters P(t)×edge weights, where the propagation factor α is dynamically adjusted according to the layout complexity (α is 0.6 to 0.8 when RC is greater than a preset threshold, otherwise it is 0.8 to 0.9). This propagation mechanism integrates local and global information, improving the robustness of the prediction. After the probability converges, the final defect probability P of each cluster is output. If P exceeds a preset threshold (e.g., 0.8), the area corresponding to the cluster is marked as a defect hotspot. This step extends the isolated cluster analysis into a global optimization process through the probability propagation network, which can effectively identify high-risk areas in the layout.

[0065] Sp5: Outputs a hotspot distribution map containing the location and probability of defect hotspots. The hotspot distribution map output transforms the analysis results into a practical tool to support design iteration.

[0066] This step integrates the aforementioned analysis results into an intuitive output format for subsequent design optimization or manufacturing verification. Specifically, based on the defect probability P from step (d), a two-dimensional hotspot distribution map is generated, marking the location (grid cell coordinates) and corresponding probability value of each defect hotspot. The output format can be a visual image or a data list for use by designers or EDA tools. By clearly presenting the hotspot locations and probabilities, this step achieves the transformation from data analysis to practical application, supporting iterative optimization in lithography R&D, reducing manual inspection errors, and accelerating product time-to-market. The entire workflow, from inputting layout files to outputting hotspot distribution maps, forms a closed-loop automated inspection solution.

[0067] Among them, the dynamic gradient tracking method in step Sp2 tracks the contour path along the gradient direction and identifies the turning point by adaptive step size; the contour dynamic feature vector in step Sp3 includes static geometric features, dynamic evolution features and context features; the adaptive density clustering in step Sp3 dynamically adjusts the number of clusters according to the layout density; and the probability propagation network in step Sp4 propagates the probability through the adjacency graph to fuse local and global information.

[0068] The entire method is a fully automated process from input to output, designed to detect defect hotspots in semiconductor layout through 2D contour extraction and multi-level analysis. The process begins with inputting a semiconductor layout design file, transforming the complex design into a computable form through adaptive mesh generation and intensity map generation. Next, a dynamic gradient tracing method extracts a set of contours, utilizing adaptive step size and inflection point identification to ensure the accuracy and adaptability of contour extraction. Subsequently, by extracting dynamic feature vectors from the contours and performing adaptive density clustering, the contours are transformed into clusters of potential defect patterns. The multidimensionality of the feature vectors and the dynamic adjustment of clustering improve the ability to capture defect features. Then, a probability propagation network calculates the defect probability based on cluster features and adjacency relationships, fusing global information through iterative propagation to ultimately mark defect hotspots. Finally, the output hotspot distribution map provides an intuitive basis for design optimization. The entire workflow reduces manual intervention through automated analysis and improves efficiency and accuracy through innovative algorithms, making it suitable for lithography R&D and semiconductor manufacturing verification. Specific Implementation Example 2:

[0070] like Figures 1 to 4 As shown, based on the content of the above specific embodiments, the following content is further disclosed:

[0071] The algorithm formulas and execution logic for the entire process further include the following:

[0072] Step Sp1: Input the semiconductor layout design file, mesh it, and generate a 2D intensity map:

[0073] Operation steps and logic: Input semiconductor layout design file (such as GDSII format), calculate the average pattern density D of the entire layout. avg (Number of patterns per unit area), divide the layout into a grid:

[0074] If the local density D>D avg The grid size is set to 5μm×5μm;

[0075] If D≤D avg The grid size is set to 15μm×15μm;

[0076] Each grid cell is grayscaled to generate a two-dimensional intensity map I(x,y) with an intensity value range of [0,255], reflecting the pattern density. Adaptive grid division adjusts the resolution according to the density, high-density areas are refined for analysis, and low-density areas reduce computational load, thus optimizing efficiency and accuracy. The intensity map provides basic data for subsequent contour extraction.

[0077] Step Sp2: Extract the 2D contours from the layout using the dynamic gradient tracing method to obtain the core formula for the contour set:

[0078] Adaptive threshold: T = β × μ + σ

[0079] Where: T is used to determine the starting point of the contour; β is an adjustment parameter, ranging from 1.5 to 2.5, which controls the threshold sensitivity; μ is the mean of the gradient amplitude within the grid cell; and σ is the standard deviation of the gradient amplitude within the grid cell.

[0080] Dynamic step size:

[0081] Where: S is the dynamic step size, which controls the step distance for contour tracking; k is the adjustment coefficient, which adjusts the ratio of step size to gradient; This represents the gradient magnitude of the current pixel.

[0082] Operation steps: Calculate the gradient field: Calculate the gradient direction θ(x,y) and magnitude for each pixel in the intensity map I(x,y). For each grid cell, calculate the mean gradient magnitude μ and standard deviation σ, and substitute them into the formula T = β × μ + σ. The starting point is selected from... The pixel begins tracking; the step size is calculated. Move a distance S along the θ(x,y) direction and record the new position; if the direction change Δθ > 45°, mark it as a turning point; close the contour: if the path returns to the starting point or End tracking to form a contour, repeat the above steps to generate a contour set, start from high gradient points, dynamically adjust the step size to track the contour path, record shape changes at turning points, terminate tracking in low gradient regions to ensure contour integrity, the dynamic step size adapts to gradient changes to improve contour extraction accuracy; adaptive threshold enhances adaptability to different layouts and reduces missed detections and false detections.

[0083] Step Sp3: Extract dynamic feature vectors from the contour set, and generate contour clusters of potential defect patterns through adaptive density clustering, as shown in the following formula:

[0084] Inflection point density:

[0085]

[0086] Where: TD is the inflection point density; N t L represents the number of inflection points on the contour; L is the contour length.

[0087] Local curvature fluctuations:

[0088]

[0089] Where: LCF is the local curvature fluctuation; Δκ is the curvature change near the inflection point; Δs is the sampling arc length (5% of the profile length);

[0090] Gradient rate of change:

[0091]

[0092] Where: GCR is the gradient rate of change; L is the normalization factor, and L is the contour length. Integrating along the contour path; The gradient magnitude at path s; ds is the average gradient magnitude along the contour path; ds is the differential arc length.

[0093] Neighborhood interaction strength:

[0094]

[0095] Where: NIS represents the neighborhood interaction strength; d min The average distance from the contour to its nearest neighbor contour;

[0096] Region complexity:

[0097]

[0098] Where: RC represents the domain complexity; N c A represents the number of contours within a grid cell; A represents the area of ​​a grid cell.

[0099] Weighted Euclidean distance:

[0100]

[0101] Where: D is the weighted Euclidean distance; and represents the square root operation; To sum over 6 features; w i x is the weight of the i-th feature; i y i Let i be the i-th eigenvalue of the two CDFVs;

[0102] Operation steps: Feature extraction: Calculate L: Integral along the contour path; Calculate Count the number of inflection points; calculate LCF, fit the curvature using three points, and sample at 5% of L; calculate GCR, integrate the gradient variance along the path; calculate NIS, measure the nearest neighbor distance, calculate RC, and count the number and area of ​​contours; form CDFV = [L, TD, LCF, GCR, NIS, RC], and perform adaptive density clustering: initialization. Calculate D: Initial weights Subsequent optimization uses gradient descent to assign CDFV to the nearest cluster center and update the center to the mean. If the cluster spacing is less than δ (calculated by density), the clusters are merged. The iteration continues until the change is less than ε or the maximum number of iterations is reached. Feature extraction describes the contour characteristics from multiple dimensions. Clustering identifies defect patterns through weighted distance and dynamic cluster number. Multidimensional features improve discriminability. Adaptive clustering adapts to different layouts and optimizes defect pattern recognition.

[0103] Step Sp4 constructs a probability propagation network based on the contour clusters, calculates the defect probability of each cluster, and marks defect hotspots:

[0104] Cluster Risk Index:

[0105] CRI = w1 × LCF + w2 × GCR + w3 × NIS

[0106] Initial probability:

[0107]

[0108] Probability update:

[0109] P(t+1)=α×P(t)+(1-α)×∑neighbor clusters P(t)×W

[0110] CRI is the cluster risk index; w1, w2, w3 are weights trained from historical data; LCF, GCR, and NIS are cluster feature values.

[0111] P0 is the initial defect probability; CRI is the risk index of the current cluster; CRI max The highest CRI among all clusters;

[0112] P(t+1) is the probability of the next round; α is the propagation factor (0.6-0.9); P(t) is the current probability; 1-α is the adjacency influence weight; W is the edge weight (cosine similarity);

[0113] The operation steps are as follows: CRI is calculated by weighted summation of LCF, GCR, and NIS of the cluster; P0 is initialized as normalized CRI; adjacency graph is constructed by calculating CDFV cosine similarity as edge weight; P(t+1) is iteratively updated by propagating probability according to α (adjusted by RC); if the probability converges (change < 0.01), P is output; if P > 0.8, it is marked as a defect hotspot; CRI assesses cluster risk; probability propagation integrates global information; dynamic α optimizes propagation effect; global probability optimization improves prediction accuracy; and dynamic adjustment adapts to complex layouts. Specific Implementation Example 3:

[0115] like Figures 1 to 4 As shown, based on the content of the above specific embodiments, the following content is further disclosed:

[0116] To further verify that the accuracy, efficiency, and adaptability of this technical solution (CDFCPA) are superior to existing methods in defect hotspot detection, and to highlight the distinguishing features of dynamic contour extraction, multidimensional feature analysis, adaptive clustering, and global probability prediction, the following experiments are designed:

[0117] The experimental method is as follows:

[0118] Dataset: Prepare three sets of semiconductor layout design files (GDSII format):

[0119] Dataset A: Low-density simple layout (1000 patterns, density < 0.1);

[0120] Dataset B: Medium-density complex layout (5000 patterns, density 0.3-0.5);

[0121] Dataset C: High-density complex layout (10,000 patterns, density > 0.7);

[0122] Each set of data is labeled with known defect hotspots (confirmed through simulation or historical manufacturing data);

[0123] Comparison methods: This scheme (CDFCPA): Performed according to steps (a)-(e); Method 1 (publication number US7685558B2): Multi-index scoring system, using exposure energy and contrast scoring; Method 2 (publication number US10395362B2): Post-manufacturing contour comparison, simulating SEM images and extracting contours using Canny.

[0124] Experimental steps:

[0125] Step 1: Apply CDFCPA, Method 1, and Method 2 to the three datasets respectively;

[0126] Step 2: Record the running time (efficiency metric) for each method;

[0127] Step 3: Calculate the matching rate between the detection results of each method and known defect hotspots (accuracy indicators: true positive rate (TPR) and false positive rate (FPR);

[0128] Step 4: Evaluate the adaptability of the method to different density layouts (by assessing the stability of TPR across three sets of data);

[0129] Experimental conditions:

[0130] Hardware: Intel i9 processor, 32GB RAM, NVIDIA RTX 3080 GPU;

[0131] Software: Python implementation of CDFCPA, MATLAB simulation of method 1 and method 2;

[0132] Parameters: In CDFCPA, β = 2.0, k = 0.5, α = 0.7 (dynamically adjusted), ε = 0.01;

[0133] Expected outcome metrics: Accuracy: True Positive Rate (TPR, percentage of detected real hotspots), False Positive Rate (FPR, false positive rate); Efficiency: Runtime (seconds); Adaptability: Standard deviation of TPR on different density datasets (the smaller the deviation, the more stable the performance).

[0134] The experimental results are shown in Table 1 below:

[0135]

[0136] Table 1

[0137] Analysis of experimental results:

[0138] Accuracy verification: CDFCPA's TPR (93.8%-95.2%) was significantly higher than Method 1 (78.9%-85.6%) and Method 2 (82.1%-88.3%), while its FPR (2.1%-2.8%) was lower than Method 1 (5.3%-8.2%) and Method 2 (4.5%-6.9%). DGT accurately extracted the contour, and CDFV multidimensional features and PPN global optimization improved the detection accuracy, verifying the breakthrough advantages of dynamic contour extraction and global prediction.

[0139] Efficiency verification: The running time of CDFCPA (12.5s-25.3s) is much lower than that of Method 1 (20.1s-50.8s) and Method 2 (30.2s-62.3s). Adaptive mesh generation and ADC optimization of computational complexity verify the improvement in automation efficiency.

[0140] Adaptability validation: The TPR standard deviation of CDFCPA (2.3) is much lower than that of Method 1 (6.8) and Method 2 (5.1), indicating that it is more stable in different density layouts. The dynamic adjustment of the number of clusters by ADC and the adaptive propagation factor of PPN enhance the flexibility and validate the creativity of adaptive clustering.

[0141] Experimental results show that CDFCPA outperforms existing methods in terms of accuracy, efficiency, and adaptability, fully verifying the distinguishing features and technical advantages of dynamic contour extraction, multidimensional feature analysis, adaptive clustering, and global probability prediction, and providing an innovative solution for defect hotspot detection in the semiconductor design stage. Specific Implementation Example 4:

[0143] like Figures 1 to 4 As shown, based on the content of the above specific embodiments, the following content is further disclosed:

[0144] To further verify the feasibility of this application, case examples are provided, including the following:

[0145] Application Case 1: 28nm Process Node Memory Chip Design Optimization:

[0146] Application Background: A semiconductor company is developing a 28nm process node memory chip (SRAM) with a design including a high-density cell array and complex peripheral circuitry. Due to the high repeatability and density of the memory cells, traditional defect detection methods in the design phase (such as DRC-based rule checking and OPC simulation) are unable to accurately predict defect hotspots during the photolithography process, leading to underexposure or bridging defects discovered after manufacturing, resulting in a yield of only 85% and extending the R&D iteration cycle to 6 months. This case aims to verify the predictive capability and optimization effect of CDFCPA in high-density complex layouts.

[0147] Implementation process:

[0148] Data input: Input the SRAM GDSII design file, which contains approximately 5 million patterns with a density range of 0.4-0.8; perform adaptive meshing according to step Sp1, with a mesh size of 5μm×5μm for high-density regions (cell array) and 15μm×15μm for low-density regions (peripheral circuits), and generate a two-dimensional intensity map;

[0149] Contour extraction: Contours are extracted using DGT with β=2.0 and k=0.5. The adaptive threshold T is dynamically calculated, tracking approximately 100,000 contours and identifying approximately 500,000 turning points.

[0150] Feature extraction and clustering: Calculate CDFV, including features such as contour length L, inflection point density TD, and local curvature fluctuation LCF. Through ADC clustering, initialize the number of clusters k≈√N to generate about 2000 contour clusters, reflecting potential defect patterns.

[0151] Defect prediction: A PPN is constructed, with weights w1, w2, and w3 trained using historical data. α = 0.7. After 10 iterations, the defect probability is output. Regions with a probability P > 0.8 are marked as defect hotspots. A total of 150 hotspots are identified, mainly concentrated at the boundaries of the cell array and the corners of the peripheral circuits.

[0152] Output: Generates a heatspot distribution map, which is provided to the design team to adjust the layout (such as increasing spacing or optimizing pattern shapes).

[0153] Application Results: Compared with post-manufacturing SEM verification, CDFCPA predicts a true positive rate (TPR) of 94% and a false positive rate (FPR) of only 2.5%, which is better than the traditional method's 85% TPR and 6% FPR. The detection process takes 25 minutes, which is nearly 5 times shorter than the traditional OPC simulation of 2 hours. The adjusted design was verified through manufacturing, and the yield rate increased to 92%, and the R&D cycle was shortened to 4 months. DGT accurately extracts the contours of high-density areas, CDFV and ADC identify complex patterns, and PPN integrates global information, proving the feasibility and superiority of the core technology in high-density layout.

[0154] Application Case 2: Lithography Verification of 7nm Process Node Logic Chips

[0155] Application Background: A chip design company faced new challenges brought by extreme ultraviolet lithography (EUV) technology when developing logic chips at the 7nm process node. The design contained approximately 20 million patterns with large density variations (0.1-0.9). Traditional post-manufacturing contour comparison methods (such as US10395362B2) required the production of prototypes, which was time-consuming and costly, and could not effectively predict defect hotspots during the design phase, leading to multiple tape-out failures. This case study verifies the adaptability and predictive capabilities of CDFCPA in ultra-high density and diverse layouts.

[0156] Implementation process:

[0157] Data input: Input the 7nm logic chip GDSII file, adaptive mesh generation, low density region (power area) 15μm×15μm, high density region (core logic) 5μm×5μm, generate intensity map;

[0158] Contour extraction: Using DGT, β=1.8, k=0.6, approximately 500,000 contours and approximately 2 million inflection points were extracted, adapting to gradient changes in different density regions;

[0159] Feature extraction and clustering: Calculate CDFV, including dynamic feature GCR and contextual feature NIS, capture minute changes in EUV lithography, perform ADC clustering, dynamically adjust the number of clusters k, generate approximately 5000 contour clusters, and identify high-risk patterns (such as sharp corners and dense lines).

[0160] Defect prediction: Construct PPN, α is dynamically adjusted according to the region complexity RC (0.6-0.9), iterate 15 times, and predict about 300 defect hotspots, mainly located in dense logic regions and transition regions;

[0161] Output results: Output a hotspot distribution map, marking the location and probability of hotspots, for the design team to optimize (such as adjusting line width or adding auxiliary patterns);

[0162] Application results: Compared with the EUV trial production results, CDFCPA achieved a TPR of 93% and an FPR of 2.8%, which is better than the 88% TPR and 5% FPR of the post-manufacturing comparison method. The testing time was 40 minutes, which is significantly more efficient than the 2 weeks required for trial production verification.

[0163] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising a reference structure" does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0164] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A defect hotspot detection method based on two-dimensional contour extraction, characterized in that: The defect hotspot detection method includes the following steps: Step Sp1: Input the semiconductor layout design file, mesh it, and generate a 2D intensity map; Step Sp2: Extract the 2D contours from the layout using the dynamic gradient tracing method to obtain a contour set; Step Sp3: Extract dynamic feature vectors from the contour set and generate contour clusters of potential defect patterns through adaptive density clustering; Step Sp4: Construct a probability propagation network based on the contour clusters, calculate the defect probability of each cluster, and mark defect hotspots; Step Sp5: Output a hotspot distribution map containing the location and probability of defect hotspots; The dynamic gradient tracking method in step Sp2 tracks the contour path along the gradient direction and identifies turning points by adaptive step size. The contour dynamic feature vector in step Sp3 includes static geometric features, dynamic evolution features and context features. The adaptive density clustering in step Sp3 dynamically adjusts the number of clusters according to the layout density. The probability propagation network in step Sp4 propagates probabilities through adjacency graph to fuse local and global information.

2. The defect hotspot detection method based on two-dimensional contour extraction according to claim 1, characterized in that: The dynamic gradient tracking method in step Sp2 specifically includes the following steps: Sp2.1: Base: Two-dimensional intensity map calculates the gradient direction and gradient magnitude of each pixel to generate a gradient field; Sp2.2: Starting from the pixel where the gradient magnitude exceeds the adaptive threshold T, trace the contour path along the gradient direction, where the step size S is determined according to the formula... Dynamic adjustment For gradient magnitude, This is the adjustment coefficient; Sp2.3: When the gradient direction changes by more than 45°, it is recorded as an inflection point; Sp2.4: When the tracing path returns to the starting point or enters a region where the gradient magnitude is less than T / 2, the contour is closed, and a contour set is generated.

3. The defect hotspot detection method based on two-dimensional contour extraction according to claim 1, characterized in that: The extraction of the contour dynamic feature vector in step Sp3 includes the following steps: Sp3.1: Calculate static geometric features, including profile length L, inflection point density TD, and local curvature fluctuation LCF, where inflection point density TD is the number of inflection points divided by profile length, and local curvature fluctuation LCF is the rate of change of curvature near the inflection points. ; Sp3.2: Calculate dynamic evolution characteristics, including gradient rate of change (GCR), where GCR is the mean square error of the gradient magnitude along the contour path; Sp3.3: Calculate context features, including neighborhood interaction strength (NIS) and region complexity (RC), where NIS is the reciprocal of the average distance between a contour and its nearest neighbor contour, and RC is the ratio of the number of contours to the area within a grid cell. Sp3.4: Integrate the above features to form a dynamic feature vector of the contour. .

4. The defect hotspot detection method based on two-dimensional contour extraction according to claim 1, characterized in that: The adaptive density clustering in step Sp3 specifically includes the following steps: Sp3.5: Initialize the number of cluster centers k, where k is dynamically determined based on the number of contours N within the grid cell. ; Sp3.6: Uses a weighted Euclidean distance to measure the similarity between dynamic feature vectors of the contour, where the weights are adaptively adjusted during iteration based on the relevance of the features to the defects; Sp3.7: Iteratively update the cluster center as the mean of the feature vectors within the cluster, and merge clusters when the cluster spacing is less than the adaptive threshold δ, where δ is calculated from the layout density; Sp3.8: Clustering is terminated and contour clusters are generated when the change in cluster center is less than the preset value ε or the maximum number of iterations is reached.

5. The defect hotspot detection method based on two-dimensional contour extraction according to claim 1, characterized in that: The construction and computation of the probability propagation network in step Sp4 includes: Sp4.1: Calculate the Cluster Risk Index (CRI) for each profile cluster, where... , , , The weights are obtained by training with historical data; Sp4.2: Construct an adjacency graph between grid cells, with edge weights being the cosine similarity of the dynamic feature vectors of the cell contours; SP4.3: Initialize the defect probability for each cluster The probability is updated using the iterative formula P(t+1)=α×P(t)+(1-α)×Σadjacent cluster P(t)×edge weight, where α is the propagation factor; Sp4.4: Once the probabilities converge, output the final defect probability P for each cluster.

6. The defect hotspot detection method based on two-dimensional contour extraction according to claim 2, characterized in that: The adaptive threshold T in Sp2.2 is dynamically calculated from the local gradient mean, and the calculation formula is as follows: , where μ is the mean gradient magnitude within the grid cell, σ is the standard deviation, and β is an adjustment parameter with a value ranging from 1.5 to 2.

5.

7. The defect hotspot detection method based on two-dimensional contour extraction according to claim 3, characterized in that: In the calculation of the local curvature fluctuation (LCF) in Sp3.1, the curvature κ is determined by fitting the circular arcs of three adjacent points on the contour path, and the rate of change... The sampling length before and after the inflection point is calculated as 5% of the contour length.

8. The defect hotspot detection method based on two-dimensional contour extraction according to claim 4, characterized in that: The weight adjustment of the weighted Euclidean distance in Sp3.6 is optimized by gradient descent. The objective function is the ratio of intra-cluster variance to inter-cluster variance, and the optimal weight minimizes this ratio.

9. The defect hotspot detection method based on two-dimensional contour extraction according to claim 5, characterized in that: The propagation factor α in Sp4.3 is dynamically adjusted according to the complexity of the layout. When the region complexity RC is greater than the preset threshold, the value of α is between 0.6 and 0.8; otherwise, the value is between 0.8 and 0.

9.

10. The defect hotspot detection method based on two-dimensional contour extraction according to claim 1, characterized in that: In step Sp1, the cell size of the mesh is adaptively adjusted according to the density of the layout pattern. When the density is higher than the average value, the cell size is reduced to 5μm×5μm, and when the density is lower than the average value, it is enlarged to 15μm×15μm to optimize computational efficiency and detection accuracy.

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