A method for determining a lithography process window based on unsupervised learning

Abstract

The present application relates to a kind of based on the determination method of photolithography process window of unsupervised learning, comprising: training stage: S1: obtain a large number of unlabeled photolithography image matrix for unsupervised learning;S2: by unsupervised contrast learning neural network automatically extract image features and carry out similarity evaluation, to obtain similarity evaluation index.Application stage: S3: input the photolithography image matrix to be analyzed, calculate similarity matrix;S4: according to similarity matrix, construct graph structure, wherein each image is as graph node, similarity is used to construct the edge between graph;S5: photolithography image matrix is classified and determined using graph clustering algorithm, and the cluster group with the highest clustering score is determined as photolithography process window.The present application overcomes the defects of relying on artificial label and subjective evaluation, realizes the automatic judgment of photolithography process window.With the help of large sample unsupervised learning, this method has superior performance in feature extraction, and brings higher accuracy and robustness for photolithography process quality evaluation.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of lithography process in integrated circuit manufacturing and the field of computer image processing, and particularly relates to a method for determining a lithography process window based on unsupervised learning. BACKGROUND

[0002] Lithography is a key process in integrated circuit manufacturing, which is a process of transferring the pattern prepared in advance on a mask to a wafer substrate by using photochemical reaction principle. In the lithography process, the mask, the exposure system and the photoresist and their interactions ultimately determine the quality of lithography, which is crucial to the yield of integrated circuit manufacturing.

[0003] The focus and energy of exposure are two core parameters in the lithography process. Due to the interference of various external environments in the lithography process, the fluctuation range of the preset parameters is also called the lithography process window. Controlling the appropriate and accurate determination of the lithography process window, controlling the lithography process parameters of different regions on the wafer, and monitoring and adjusting in real time during the production process are important steps in the integrated circuit production process; and an inappropriate process window will seriously reduce the yield of products.

[0004] In order to select an appropriate lithography process window, the corresponding lithography image is usually obtained by electron microscope for different exposure parameters to form a focus-energy matrix image (FEM), and then the FEM matrix image is analyzed by experienced engineers to determine the process window. In addition, during the production process, the two important parameters of focus and energy will still have "parameter drift" between the set value and the actual value due to the interference of external conditions such as vibration waves, resulting in a decrease in the yield of products.

[0005] However, the current method of determining the process window by engineers cannot meet the production test requirements, and it is necessary to rely on intelligent analysis of lithography images to effectively control and monitor more lithography process windows determined in the research and development process, control more exposure parameters in actual production, and monitor the "parameter drift" in the production process to ensure a high enough yield.

[0006] At present, the parameter analysis of the process window mainly relies on experienced engineers. However, there are the following problems: a) the subjectivity of people is strong, the quality is very unstable, the precision is low, the yield of product production is affected, and the efficiency is low, the labor cost is relatively high; b) a large number of manpower is invested, the cost is high, the working intensity is large, and it also causes the instability of the engineer team.

[0007] And based on artificial intelligence technology to lithography process window decision and monitoring, not only can improve the production efficiency of chip process, the lithography process window decided by the result compared to artificial screening is more stable, and the chip yield will be improved. SUMMARY

[0008] The purpose of the present application is to provide a lithography process window determination method based on unsupervised learning, aiming to determine the process window of the current lithography image matrix, thereby significantly improving the accuracy and efficiency of lithography technology quality evaluation. By adopting the method of the present application, the deficiencies of artificial labels and subjective evaluation in the prior art are overcome, and automatic judgment of the lithography process window is realized.

[0009] In order to achieve the above purpose, the present application adopts the following specific technical solutions:

[0010] A lithography process window determination method based on unsupervised learning, the method comprising:

[0011] S1: Obtain a large number of unlabeled lithography image matrix data sets;

[0012] S2: Train an unsupervised contrast learning neural network to extract image high-dimensional features;

[0013] S3: Input a set of lithography image matrix, and calculate the similarity between different lithography images through the contrast learning neural network;

[0014] S4: Construct a graph structure according to the similarity matrix;

[0015] S5: Use a graph clustering algorithm to classify and determine the lithography image, and obtain the lithography process window;

[0016] Wherein: step S2 specifically includes:

[0017] The training of the unsupervised contrast learning neural network learns the image features by comparing the similarities and differences between different data samples; a SimCLR contrast learning neural network is adopted, which consists of:

[0018] S20: Data enhancement: perform random data enhancement operations on the original image, such as cropping, flipping, color and distortion, to generate a pair of image transformation samples, namely anchor and positive samples;

[0019] S21: Feature extractor: use a deep convolutional neural network as a feature extractor to extract features from the anchor and positive samples, and generate corresponding feature vectors;

[0020] S22: Projection head: map the feature vectors to a low-dimensional space, so that similar images are close in the low-dimensional space, and dissimilar images are far apart;

[0021] S23: contrastive loss function: calculate the similarity of anchor points and positive samples in low-dimensional space, and maximize the similarity between sample pairs from the same image, while minimizing the similarity between sample pairs from different images;

[0022] The step S5 specifically comprises:

[0023] Using the Louvain algorithm based on community discovery, fast hierarchical clustering is performed in the similarity graph structure of lithography images; the Louvain algorithm determines the community structure in the network by optimizing the modularity Q index, and can accurately discover groups of nodes with close connections; in the graph structure, each node represents a lithography image, and the weight of the edge represents the similarity between images; by using the Louvain algorithm, lithography images with high similarity are divided into the same cluster group, thereby revealing the potential relationship between lithography images, and providing a strong basis for determining the lithography process window.

[0024] Modularity is an important indicator for evaluating the quality of community structure, which represents the ratio between the number of edges within the community and the expected number of random edges. When the modularity is high, it means that there is a significant community structure in the network.

[0025] The modularity Q thereof is an index for measuring the community structure of the network, and the calculation formula thereof is:

[0026]

[0027] Wherein, m represents the total number of edges in the network; is the element of the adjacency matrix, when there is an edge between node i and node j,

[0028] = 1, otherwise = 0; and respectively represent the degree of node i and node j, that is, the number of edges connected thereto; is an indicator function, when node i and node j belong to the same community, = 1, otherwise = 0;

[0029] The Louvain algorithm specifically comprises:

[0030] S50: initialization: first, regard each node as an independent community;

[0031] S51: local optimization: for each node, calculate the change in modularity caused by moving it to the adjacent community; then move the node to the community that maximizes the increase in modularity; if the modularity cannot be increased, keep the original community; repeat this process until the community assignment of all nodes is stable and the modularity Q remains unchanged;

[0032] S52: Merge communities: after the local optimization is completed, the nodes in the same community are merged into a new node to obtain a community clustered network; in this process, the edges within the original same community are merged, while the edges between different communities are retained;

[0033] S53: Repeat steps S51 and S52: repeat steps S51 and S52 on the newly generated network until the modularity no longer increases;

[0034] S54: Output results: when the modularity no longer increases, the algorithm ends; the final community division result is the optimal community structure, and the optimal community is the finally determined lithography process window.

[0035] The step 3 specifically comprises:

[0036] S30: input a set of lithography image matrices, and obtain a high-dimensional vector corresponding to each image through a SimCLR contrast learning neural network;

[0037] S31: calculate the similarity between images using cosine similarity; the calculation formula of the cosine similarity is as follows:

[0038]

[0039] Where, · represents the dot product of vectors A and B, and respectively represent the Euclidean norm of vectors A and B, i.e., the length of the vector; and respectively represent each element in vectors and.

[0040] The obtained cosine similarity value effectively reflects the similarity of two lithography images in the feature space; the cosine similarity value ranges from -1 to 1, and the closer the value is to 1, the more similar the two vectors are, the closer the value is to -1, the less similar the two vectors are, and the value of 0 indicates that the two vectors are completely irrelevant.

[0041] The graph structure is constructed according to the similarity matrix, specifically comprising:

[0042] The graph structure is constructed according to the similarity matrix; the image similarity between different lithography images is obtained through the SimCLR contrast learning neural network, and the similarity matrix is obtained accordingly: if there are D lithography images, the similarity matrix will be a DxD square matrix, and the value range is between -1 and 1; taking each lithography image as a node, the similarity of each pair of images is taken as the weight of the edge, and a graph structure is constructed to represent the similarity relationship of the lithography images; this representation method facilitates the use of graph theory concepts and algorithms to further mine the potential structure between images.

[0043] The present application can achieve the following technical effects:

[0044] 1.The contrast learning method based on unsupervised learning of the present application can overcome the defects of relying on artificial labels and subjective evaluation in the prior art, thus saving a lot of human labeling cost. Compared with supervised learning, unsupervised learning has better performance in feature extraction, anomaly processing and the like, thereby being able to provide better accuracy and robustness.

[0045] 2.The present application uses a contrast learning neural network to calculate the similarity, which can automatically mine the image similarity features and avoid the complexity of manually defining the features. In addition, the method has better generalization ability and can adapt to different lithography machines and different shapes of lithography images.

[0046] 3.The present application innovatively combines image similarity and graph theory to construct a graph structure to represent the similarity relationship between the lithography images. The images are regarded as nodes, and the similarity is regarded as the weight of the edge, which facilitates the use of graph theory concepts and algorithms to further mine the potential structure between the images. This method can also cluster the images into different clusters, thereby improving the production efficiency and production quality.

[0047] 4.The present application uses the Louvain algorithm for clustering analysis of lithography images, which can better mine the potential relationship between images and provide a strong basis for determining the lithography process window. The high efficiency and local optimization characteristics of the Louvain algorithm make it highly efficient in processing a large number of lithography images, which is of great significance to actual production. In addition, the algorithm also has the advantages of adaptability, robustness and interpretability, thereby further improving the reliability and practicality of the algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0048] Figure 1 is a flowchart of the present application;

[0049] Figure 2 is a process diagram of the present application for analyzing the MSR file;

[0050] Figure 3 is a training schematic diagram of the unsupervised contrast learning neural network of the present application;

[0051] Figure 4 is an application schematic diagram of the unsupervised contrast learning neural network of the present application;

[0052] Figure 5 is a schematic diagram of constructing a similarity matrix of the present application;

[0053] Figure 6 is a schematic diagram of the similarity values of each lithography image and the center image of the present application;

[0054] Figure 7 is a schematic diagram of constructing a complete graph from a similarity matrix of the present application;

[0055] Figure 8 is a schematic diagram of a 10-node complete graph of the present application;

[0056] Figure 9 is a schematic diagram of the Louvain algorithm for implementing graph clustering of the present application;

[0057] Figure 10 is a result graph of the lithography process window after clustering of the present application. DETAILED DESCRIPTION

[0058] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the embodiments of the present application and the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. The detailed description of the embodiments of the present application provided in the following accompanying drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of the present application.

[0059] The present application is based on a method for determining a lithography process window based on unsupervised learning, which specifically comprises:

[0060] S1 step: After the lithography process is completed, the lithography machine can export image files and msr files. By analyzing the msr files, the lithography image matrix is restored, which represents the images produced in the lithography process under different energy and focus conditions. Through this process, a large number of unlabeled lithography image matrices are obtained, and data sets are established accordingly. These data sets provide rich samples for unsupervised learning algorithms, which helps to better analyze the relationship between lithography images and further improve the accuracy and efficiency of lithography process quality evaluation.

[0061] S2 step: training process: first, a SimCLR-based unsupervised contrast learning neural network model is adopted, which uses a large number of unlabeled lithography image matrices for unsupervised learning to capture the similarity between lithography images. The SimCLR unsupervised contrast learning neural network model learns image features by analyzing the similarity and difference between different data samples, showing superior feature extraction capability.

[0062] Unsupervised learning is a method of machine learning that does not rely on labeled data samples during the training process. Unlike supervised learning, unsupervised learning does not have a pre-defined target output during training, but instead automatically mines valuable information by analyzing the internal structure and patterns of the data. The advantage of unsupervised learning is that it can be directly applied to unlabeled data, avoiding the time and cost consumption of labeling data. In addition, unsupervised learning can discover unknown or potential structures and relationships in data, providing useful insights for further data analysis and supervised learning tasks.

[0063] Contrastive learning is an unsupervised learning method that aims to learn useful representations by comparing the similarities and differences between data samples. During training, contrastive learning tries to make different transformations from the same data sample (positive examples) close in the feature space, while making transformations from different data samples (negative examples) far apart in the feature space. Contrastive learning can automatically mine deep information in the process of calculating similarity, avoiding the definition of similarity features by hand.

[0064] SimCLR is an unsupervised contrastive learning neural network that mainly includes data augmentation, feature extractor and projection head. This method generates a pair of image transformation samples using data augmentation, extracts feature vectors through the feature extractor, and maps the feature vectors to a low-dimensional space through the projection head. Finally, the similarity between samples is calculated through the contrastive loss function. Through this structure, SimCLR can effectively extract features from unlabeled lithography image matrices, revealing the internal relationship between different lithography images. In the subsequent clustering and lithography process window determination process, this feature extraction capability will help improve the accuracy and efficiency of lithography technology quality evaluation.

[0065] S3 step: A set of lithography image matrices using the same template but with different processing parameters is input into the previously constructed SimCLR contrastive learning neural network model. Through this model, the deep features of each image can be effectively extracted, and the similarity between each image can be accurately evaluated. This process helps to reveal the internal relationship of lithography images under different processing parameters, thereby providing strong support for subsequent clustering algorithms and lithography process window determination, further improving the accuracy and efficiency of lithography technology quality evaluation.

[0066] Cosine Similarity is a measure commonly used to evaluate the similarity between vectors. It calculates the cosine of the angle between two vectors in high-dimensional space, reflecting their degree of similarity. The cosine similarity ranges from -1 to 1, where 1 represents complete similarity, -1 represents complete dissimilarity, and 0 represents orthogonality.

[0067] To calculate the similarity between lithography images, the SimCLR network first extracts features from each image through a series of convolutional layers, activation functions, and pooling layers, obtaining a high-dimensional feature vector. Then, by calculating the cosine similarity between these feature vectors, a similarity matrix between lithography images is obtained. This matrix will serve as input for subsequent clustering algorithms, helping to automatically determine the lithography process window. By constructing a SimCLR-based contrastive learning neural network model, the similarity between lithography images can be effectively calculated in an unsupervised learning context. This method provides a reliable foundation for subsequent clustering algorithms, helping to improve the accuracy and efficiency of lithography technology quality evaluation. At the same time, the SimCLR network has strong generalization ability, making it perform well in unsupervised learning tasks in different fields.

[0068] S4 step: By using the above algorithm, the image similarity between different lithography images can be calculated, obtaining a similarity matrix. This method helps to better understand and express the relationship between images. Specifically, images are taken as nodes, and similarity is taken as the weight of edges, constructing a graph structure to represent the similarity relationship between these lithography images. This representation facilitates the use of graph theory concepts and algorithms to further explore the potential structure between images.

[0069] By constructing a graph structure, the relationship between different lithography images can be more intuitively analyzed, and graph theory algorithms can be applied to reveal potential structural information. In addition, constructing a graph structure helps to identify abnormal lithography images. For example, when the similarity value of a certain node in the graph is significantly different from other nodes, it may indicate that the image is abnormal. In this case, further analysis of the abnormal image can be performed to determine potential problems and make corresponding adjustments and optimizations to the lithography process. Using the similarity matrix and graph structure to represent the relationship between lithography images can more intuitively analyze the relationship between different lithography images and provide strong support for subsequent clustering and analysis. This will help improve the accuracy and efficiency of the lithography process window determination method, thereby improving the level of lithography technology quality evaluation.

[0070] S5 step: After constructing the graph structure from the similarity of the lithography images, the Louvain algorithm can be used for graph clustering. The Louvain algorithm is a fast hierarchical clustering algorithm based on community discovery, which can effectively identify groups of nodes with tight connections in large-scale networks. The Louvain algorithm optimizes the modularity Q (Modularity Q) to find the community structure in the network. Modularity Q is an indicator of the quality of network clustering structure, and the larger the value, the more obvious the community structure in the network. Compared with traditional clustering methods, the Louvain algorithm has the advantages of high computational efficiency, adaptability, robustness, and interpretability. In the constructed graph structure, each node represents a lithography image, and the weight of the edge represents the similarity between images. By using the Louvain algorithm, lithography images with high similarity can be divided into the same cluster. This clustering method helps to reveal the potential relationship between lithography images and provides a strong basis for determining the lithography process window. This method not only reveals the potential relationship between lithography images, but also saves a lot of manual labeling costs, bringing significant value to actual production.

[0071] The main advantages of the Louvain algorithm include the following:

[0072] 1) Adaptability: Since the Louvain algorithm is a hierarchical clustering method, it can discover the relationship between images at different scales. This means that the algorithm can adaptively adjust the clustering granularity to better meet the needs of the lithography process window in actual production.

[0073] 2) Robustness: The Louvain algorithm finds community structure through local optimization, which makes the algorithm robust. Even in the presence of noise or abnormal data, the algorithm can accurately discover the potential relationship between lithography images.

[0074] 3) Interpretability: The Louvain algorithm produces a hierarchical structure during clustering, which helps better understand the relationship between lithography images. By analyzing the hierarchical structure, the characteristics of the lithography process window can be further explored to provide a reference for optimization in the production process.

[0075] In summary, combining the concept and characteristics of the Louvain algorithm can effectively determine the lithography process window. This method can reveal the potential relationship between lithography images and bring significant value to actual production. In future research, it can also be tried to combine the Louvain algorithm with other unsupervised learning techniques to further improve the performance of the lithography process window determination method.

[0076] The present application utilizes large-sample unsupervised learning, which has excellent performance in feature extraction. This innovative method not only objectively evaluates the lithography process window, but also brings higher accuracy and robustness to the lithography process quality evaluation. In addition, the present application has strong adaptability and can be flexibly adjusted according to actual production needs, further improving production efficiency.

[0077] The present application provides a lithography process window determination method based on unsupervised learning, which brings significant advantages to lithography technology quality evaluation. By abandoning the artificial label and subjective evaluation limitations in the prior art, the present application realizes automatic judgment of the lithography process window and exhibits superior performance in feature extraction. This method undoubtedly brings higher accuracy and robustness to the field of lithography process quality evaluation, and is expected to play an important role in actual production.

[0078] Embodiments

[0079] Reference Figure 1 The present embodiment provides a lithography process window determination method based on unsupervised learning, comprising the following steps:

[0080] Step S1: As shown in Figure 2 After the lithography process is completed, the lithography machine can export image files and msr files. By parsing the msr file, the lithography image matrix is restored, which represents the images produced in the lithography process under different lithography conditions. The lithography conditions include the lithography energy parameters and the lithography focal length parameters that need to be set in the lithography process flow, which are the most basic control parameters in the lithography process flow. By processing the lithography image to select these parameters, important features such as line width, shape, position and depth can be effectively controlled, thereby obtaining high-quality lithography effect. Through this process, a large number of unlabeled lithography image matrices are obtained, and data sets are established accordingly. These data sets provide rich samples for unsupervised learning algorithms, which help better analyze the relationship between lithography images and improve the accuracy and efficiency of lithography process quality evaluation.

[0081] Step S2: As shown in Figure 3 A SimCLR-based contrast learning neural network model is used, which uses a large number of unlabeled lithography image matrices for unsupervised learning to capture the similarity between lithography images. The SimCLR contrast learning neural network model learns image features by analyzing the similarity and difference between different data samples, showing superior feature extraction capability.

[0082] The training process mainly includes the following steps:

[0083] S20: Data augmentation: Perform random data augmentation operations (crop, flip, color distortion, etc.) on the original image to generate a pair of image transformation samples (called anchor and positive samples).

[0084] S21: Feature extractor: Typically use a deep convolutional neural network as the feature extractor to extract features from anchor and positive samples, generating corresponding feature vectors.

[0085] S22: Projection head: Map the feature vectors into a low-dimensional space so that similar images are close in the low-dimensional space and dissimilar images are far apart.

[0086] S23: Contrastive loss function: Use the contrastive loss function to train the model to make the same image under different data augmentation closer in the feature space and different images farther apart in the feature space. For each pair of images, first map them to the feature space through the encoder, then calculate their similarity score. Specifically, the similarity of two feature vectors is calculated by the dot product operation, and then the similarity score is input into the softmax function to get their contribution in the contrastive loss function. The goal of the contrastive loss function is to minimize the feature distance between similar images while maximizing the feature distance between dissimilar images to promote the model to learn better feature representations.

[0087] S24: Use the data in the training set to train the model, optimize the parameters of the model, evaluate the performance of the model through the validation set, and determine whether the model is overfitting or underfitting.

[0088] Through this structure, SimCLR can effectively extract features from the unlabeled photolithography image matrix, revealing the inherent relationship between different photolithography images. In the subsequent clustering and photolithography process window determination process, this feature extraction capability will help improve the accuracy and efficiency of photolithography technology quality evaluation.

[0089] Step S3: As shown in Figure 4 To calculate the similarity between photolithography images, the SimCLR network first extracts features from each image through a series of convolutional layers, activation functions and pooling layers, obtaining a high-dimensional feature vector. Then, by calculating the cosine similarity between these feature vectors, a similarity matrix between photolithography images is obtained. This matrix will be used as input for the subsequent clustering algorithm, which will help to automatically determine the photolithography process window. Details are as follows:

[0090] S30: Input a set of photolithography image matrices, and get the corresponding high-dimensional vectors for each image through the SimCLR network.

[0091] S31: Calculate the similarity between images using cosine similarity. Cosine similarity is a common method for measuring the similarity between vectors. It calculates the cosine of the angle between two vectors in high-dimensional space, reflecting their degree of similarity. Given two vectors A and B, the formula for calculating cosine similarity is as follows:

[0092]

[0093] where • represents the dot product of vectors A and B, and || || and || || represent the Euclidean norm (i.e., the length of the vector) of vectors A and B, respectively.

[0094] By adopting the SimCLR-based contrast learning neural network model, the similarity between lithography images can be effectively calculated in the context of unsupervised learning. This method provides a reliable foundation for subsequent clustering algorithms, helping to improve the accuracy and efficiency of lithography technology quality evaluation. At the same time, the SimCLR network has strong generalization ability, making it perform well in unsupervised learning tasks in different fields.

[0095] Step S4: A method for calculating the similarity of lithography images by constructing a graph structure is proposed. This method takes lithography images as nodes and uses similarity as the weight of edges to construct a graph structure to represent the similarity relationship between lithography images. This method helps to better understand and express the relationship between images, and facilitates the application of graph theory algorithms to reveal potential structural information. The similarity matrix will be able to fully represent the mutual relationship of these images in the feature space.

[0096] As shown in Figure 5 , assuming there are 63 lithography images, the similarity matrix will be a 63x63 square matrix, and each element in the matrix represents the similarity value between two images, usually ranging from -1 to 1. Figure 6 The similarity values of all lithography images and the center image are shown in Figure 7 In the graph structure, each lithography image corresponds to a node, and the edges between nodes represent their distance in the feature space, and the weight of the edge is the similarity value. To more clearly show the internal composition of Figure 7 , a complete graph composed of 10 nodes is shown in Figure 8 This representation makes the relationship between lithography images more intuitive and easy to identify abnormal lithography images. For example, when the similarity value of a certain node is significantly different from other nodes, it may indicate that the image is abnormal. In this case, further analysis of the abnormal image can be performed to determine potential problems and make corresponding adjustments and optimizations to the lithography process.

[0097] By constructing graph structures, the relationships between different lithography images can be analyzed more intuitively, providing strong support for subsequent clustering and analysis. The application of similarity matrices and graph structures can improve the accuracy and efficiency of lithography process window determination methods, thereby enhancing the quality assessment level of lithography technology. This method has high practicality and feasibility, bringing new ideas and methods to the development of lithography technology.

[0098] Step S5: As Figure 9 As shown in the figure, Figure a represents the clustering results, and Figure b represents the change in modularity. By employing the Louvain algorithm based on community detection, fast hierarchical clustering can be performed on the similarity graph structure of lithographic images. This algorithm determines the community structure in the network by optimizing the modularity Q-index, thereby accurately identifying groups of tightly connected nodes. Compared with traditional clustering methods, the Louvain algorithm has advantages such as higher computational efficiency, adaptability, robustness, and interpretability. In the constructed graph structure, each node represents a lithographic image, and the edge weights represent the similarity between images. Therefore, by using the Louvain algorithm, lithographic images with high similarity can be grouped into the same cluster, thereby revealing the potential connections between lithographic images and providing a strong basis for determining the lithography process window.

[0099] Modularity is an important indicator for evaluating the quality of community structure. It represents the ratio between the number of internal edges in a community and the expected number of random edges. A high modularity indicates the presence of significant community structure in the network.

[0100] Modularity is a metric for measuring the structure of a network community, and its calculation formula is as follows:

[0101]

[0102] Where m represents the total number of edges in the network; and is an element of the adjacency matrix, representing the number of edges when there is an edge between node i and node j.

[0103] =1 otherwise =0; and represent the degree (number of edges connected to them) of node i and node j, respectively; is an indicator function, which is 1 when node i and node j belong to the same community, and 0 otherwise. This formula calculates the difference between the actual edges in the network and the expected edges under random connection conditions.

[0104] The main steps of the Louvain algorithm are as follows:

[0105] S50: Initialization: First, treat each node as an independent community.

[0106] S51: Local Optimization: For each node, calculate the change in modularity resulting from moving it to a neighboring community. Then move the node to the community that maximizes the increase in modularity. If the increase in modularity is not possible, keep it in its original community. Repeat this process until the community assignments of all nodes stabilize.

[0107] S52: Merging Communities: After local optimization is complete, nodes within the same community are merged into a new node, resulting in a network with community clustering. During this process, edges within the same community are merged, while edges between different communities are retained.

[0108] S53: Repeat steps S51 and S52: Repeat steps S51 and S52 on the newly generated network until the modularity no longer increases.

[0109] S54: Output: The algorithm terminates when the modularity no longer increases. The final community partitioning result is the optimal community structure, and the optimal community is the final determined lithography process window.

[0110] like Figure 10 The image shows the lithography process window after clustering analysis using the Louvain algorithm. In summary, clustering lithography images using the Louvain algorithm can effectively determine the lithography process window. Moreover, this method not only reveals the potential relationships between lithography images but also possesses advantages such as efficiency, robustness, and interpretability, bringing significant value to actual production. Future research could explore combining the Louvain algorithm with other unsupervised learning techniques to further improve the performance of lithography process window determination methods.

Claims

1. A method for determining a photolithography process window based on unsupervised learning, characterized in that, Includes the following steps: S1: Obtain a large dataset of unlabeled lithographic image matrices; S2: Train an unsupervised contrastive learning neural network to extract high-dimensional features of the image; S3: Input a set of lithographic image matrices, and calculate the similarity between different lithographic images through a contrastive learning neural network; S4: Construct a graph structure based on the similarity matrix; S5: Use graph clustering algorithm to classify and determine the lithography image to obtain the lithography process window; Specifically, step S2 includes: The unsupervised contrastive learning neural network learns image features by comparing the similarities and differences between different data samples; it employs the SimCLR contrastive learning neural network, which comprises: S20: Data Augmentation: Perform random data augmentation operations on the original image, namely cropping, flipping, coloring, and distorting, to generate a pair of image transformation samples, namely anchor points and positive samples; S21: Feature Extractor: A deep convolutional neural network is used as the feature extractor to extract features from anchor points and positive samples, generating corresponding feature vectors; S22: Projection head: Maps feature vectors to a low-dimensional space, so that similar images are close together in the low-dimensional space, while dissimilar images are far apart; S23: Contrast loss function: Calculates the similarity between anchor points and positive samples in low-dimensional space, and maximizes the similarity between sample pairs from the same image while minimizing the similarity between sample pairs from different images; Step S5 specifically includes: The Louvain algorithm, based on community discovery, is used to perform fast hierarchical clustering in the similarity graph structure of lithographic images. The Louvain algorithm determines the community structure in the network by optimizing the modularity Q index, which can accurately discover groups of nodes with close connections. In the graph structure, each node represents a lithographic image, and the edge weights represent the similarity between images. By applying the Louvain algorithm, lithographic images with high similarity are grouped into the same cluster, thereby revealing the connections between lithographic images. The formula for calculating its modularity Q is: Where m represents the total number of edges in the network; A ij A is an element of the adjacency matrix. When there is an edge between node i and node j, A ij =1, otherwise A ij =0;k i and k j Let δ(c) represent the degree of node i and node j, i.e., the number of connected edges, respectively; i c j ) is an indicator function that, when node i and node j belong to the same community, δ(c i c j ) = 1, otherwise δ(c) i c j ) = 0; The Louvain algorithm specifically includes: S50: Initialization: First, treat each node as an independent community; S51: Local optimization: For each node, calculate the change in modularity resulting from moving it to a neighboring community; then move the node to the community that maximizes the increase in modularity; if the modularity cannot be increased, keep the original community; repeat this process until the community assignments of all nodes stabilize and the modularity Q remains unchanged. S52: Merging Communities: After local optimization is completed, nodes in the same community are merged into a new node, resulting in a network after community clustering; during this process, edges within the same community are merged, while edges between different communities are retained; S53: Repeat steps S51 and S52: Repeat steps S51 and S52 on the newly generated network until the modularity no longer increases; S54: Output: The algorithm ends when the modularity no longer increases; the final community partitioning result is the optimal community structure, and the optimal community is the final determined lithography process window.

2. The method for determining the photolithography process window according to claim 1, characterized in that, Step S3 specifically includes: S30: Input a set of lithographic image matrices, and obtain the high-dimensional vector corresponding to each image through the SimCLR contrastive learning neural network; S31: Calculate the similarity between images using cosine similarity; the formula for calculating cosine similarity is as follows: Where A·B represents the dot product of vectors A and B, and ||A|| and ||B|| represent the Euclidean norms of vectors A and B, i.e., the lengths of the vectors, respectively; A i and B i Let A and B represent each element in vectors A and B, respectively. The obtained cosine similarity value effectively reflects the degree of similarity between two lithographic images in the feature space; the range of cosine similarity is [-1, 1]. The closer the value is to 1, the more similar the two vectors are; the closer the value is to -1, the less similar the two vectors are; and a value of 0 indicates that the two vectors are completely unrelated.

3. The method for determining the photolithography process window according to claim 1, characterized in that, The construction of the graph structure based on the similarity matrix specifically includes: The image similarity between different lithography images is obtained by using the SimCLR contrastive learning neural network, and a similarity matrix is ​​obtained accordingly: if there are D lithography images, the similarity matrix will be a DxD square matrix with values ​​ranging from -1 to 1; with each lithography image as a node and the similarity between pairs of images as the weight of the edges, a graph structure is constructed to represent the similarity relationship between the lithography images.

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