Wafer Map Defect Detection Method Based on Multi-Block Principal Component Analysis Network

Abstract

The present invention relates to a wafer map defect detection method based on multiple principal component analysis networks, and its steps are as follows: First, perform preprocessing of size unification and noise filtering on the wafer map; then, use the K-means clustering technique to divide the high-dimensional wafer map features extracted by the PCANet model into different feature sub-blocks, and then apply the support vector data description method to each feature sub-block to establish a monitoring sub-model; finally, use the Bayesian fusion strategy to fuse the monitoring models of different sub-blocks into an overall monitoring model, and detect the wafer map defects according to the overall monitoring model. The present invention can extract deep features in the wafer map that are helpful for defect detection, and uses a block strategy to reduce the influence of feature differences on wafer map defect detection, and can effectively improve the performance of wafer map defect detection.

Description

Technical Field

[0001] The present invention belongs to the field of wafer map defect detection in industrial processes, and particularly relates to a method for detecting defective wafer maps in industrial processes by using a multi-block principal component analysis network (abbreviation: MBPCANet). Background Art

[0002] In this rapidly developing information age, semiconductor components, as the foundation and core of the modern information technology industry, have been applied in all aspects of social production and life. As a basic raw material for manufacturing semiconductor components, wafers are of great importance. In the process of manufacturing wafers, including process operations such as ion implantation, polishing, and etching, almost any link in these process operations will cause defects in wafers due to inaccurate technology or external environmental pollution. In order to ensure the quality of the manufactured wafers, it is necessary to detect the wafers for defects and perform corresponding processing on the defective wafers.

[0003] In the early days, manual inspection was mainly used for wafer map defects, but manual inspection had problems of low efficiency and poor effect. With the development of artificial intelligence technology and the increasing difficulties encountered in manual inspection, methods based on machine learning and deep learning have been widely used in wafer map defect detection and achieved good results. However, traditional machine learning methods cannot well extract deeper features in wafer maps, and there are problems such as poor computational scalability and dimensionality disaster. Although traditional deep learning methods can extract deep features of wafer maps, there are problems such as the need for a large amount of training data and too long parameter training time.

[0004] The principal component analysis network (abbreviation: PCANet) model is a lightweight deep learning model. It is both a deep learning method and integrates traditional machine learning models. It can well extract deep features in wafer maps, uses fewer parameters, and can effectively shorten the model training time. However, if the wafer map features extracted by PCANet are equally input into the detector for detection, it will cause the features without discrimination to cover the influence of the features with discrimination on detection, thus affecting the detection effect. Therefore, how to reduce the influence of the difference between wafer map features on the detection effect needs further research. Summary of the Invention

[0005] Aiming at the problem that the PCANet wafer map defect detection model ignores the feature difference, the present invention proposes a method for detecting wafer map defects based on a multi-block principal component analysis network. This method can effectively extract important features in wafer map data that are helpful for wafer map defect detection, reduce the influence of feature difference on wafer map defect detection, and improve the accuracy of wafer map defect detection.

[0006] To achieve the above object, the present invention provides a method for detecting wafer map defects based on multiple principal component analysis networks, comprising the following steps:

[0007] (1) Collect normal wafer map samples in the industrial process as training data set I, and preprocess the wafer map samples in training data set I. The preprocessing process includes image size unification and median filtering. The training data set after preprocessing is denoted as I p ;

[0008] (2) Use the preprocessed training data set I p to train the PCANet model and extract the training data feature set F. Standardize the training data feature set F by using the mean mF and variance sF of the training data feature set F. The training data feature set after standardization is denoted as Then use the K-means clustering algorithm to divide the standardized training data feature set into k feature sub-blocks

[0009] (3) Apply the support vector description (abbreviation: SVDD) method to each feature sub-block in the k feature sub-blocks to establish a basic monitoring sub-model, and project the standardized training data feature set onto the corresponding SVDD model to calculate the monitoring variable D b (1 ≤ b ≤ k), and use the kernel density estimation method to determine the confidence limit of each feature sub-block according to the confidence level β Then use the Bayesian fusion strategy to construct the overall statistic BD, and use the kernel density estimation method to calculate the overall detection threshold BD according to the confidence level β lim ;

[0010] (4) Collect the test data set I containing normal wafer map samples and defective wafer map samples t , and preprocess the wafer map samples in the test data set I t . The preprocessing process includes image size unification and median filtering. The test data set after preprocessing is denoted as

[0011] (5) Use the trained PCANet model to extract the wafer map feature set F of the preprocessed test data set t , and standardize the test data feature set F by using the mean mF and variance sF of the training data feature set F t . The test data feature set after standardization is denoted as

[0012] (6) Project the standardized test data features onto the corresponding SVDD model to calculate the monitoring variable and calculate the overall monitoring variable BD of the test sample through the Bayesian fusion strategy t , and compare the overall monitoring variable BD of the test sample t with the detection threshold BD lim . If BD t > BD lim , it means that the test sample is a defective wafer map, otherwise it is a normal wafer map.

[0013] Furthermore, in step (1), the training data set I = [I1, I2,..., I N containing N normal wafer map samples is preprocessed. First, the wafer maps are scaled using the bicubic interpolation algorithm to unify the size of the wafer maps to (28, 28). Then, the preprocessed training data set is median-filtered using a filter kernel of (3, 3). The preprocessed training data set is denoted as

[0014] Furthermore, in step (2), first, the PCANet model is trained using the preprocessed training data set I p and the training data feature set F is extracted. Training the PCANet model and extracting features mainly include four stages: the first-stage principal component analysis, the second-stage principal component analysis, binary hashing coding, and block histogram Figure 3 . The specific steps are as follows:

[0015] (1) The first-stage principal component analysis

[0016] First, the wafer maps in the training data set are block-sampled pixel by pixel with a size of k1×k2, and then cascade learning is performed on all the sampled blocks. The th wafer map is represented as:

[0017]

[0018] where [k1 / 2] represents the integer operation; then the collected blocks are zero-meaned, and the processed wafer map blocks are represented as:

[0019]

[0020] Similarly, similar processing is performed on each wafer map in the training data set. The processed training set matrix is:

[0021]

[0022] Assume that the number of PCA filters in the first layer is L1, then the first-layer PCA filters of the PCANet model are represented as follows:

[0023]

[0024] where, represents mapping X to the matrix W with a matrix size of k1×k2 l 1 , q l (XX T ) represents the l-th principal eigenvector of XX T ;

[0025] (2) Second-stage principal component analysis

[0026] The second-stage PCA is similar to the first-stage PCA. First, calculate the mapping output generated by the first-stage PCA:

[0027]

[0028] I i performs a convolution operation with W l 1 . Before performing the convolution operation, in order to ensure that the mapping result has the same size as the original wafer map, the boundaries of the image are filled with zero values. Similar to the first stage, in the second stage, the input matrix (the output matrix of the first-stage PCA of the PCANet) is also subjected to block sampling, concatenation, and zero-mean processing:

[0029]

[0030]

[0031] Then, similar processing is performed on each matrix to obtain the block-sampled form of the second-layer input matrix:

[0032]

[0033] Similarly, the second-layer PCA filters are also composed of the corresponding principal eigenvectors. Assume that the number of PCA filters in the second layer is L2, then the second-layer PCA filters are represented as:

[0034]

[0035] Finally, through the first two stages of the PCANet model, each wafer map will generate L1×L2 output feature matrices:

[0036]

[0037] (3) Hash coding and block histogram

[0038] First, the output matrix in the second stage is binarized, and the data in the output matrix after processing only contains integers and zeros. Then, these output matrices are subjected to binary hash coding through formula (11):

[0039]

[0040] where H(·) is a unit step function. After the above processing, each pixel value in the data of the output matrix in the second stage is encoded as an integer between For the i-th wafer map, there are L1 output Ts i l (l = 1, 2,..., L1). Each output T i l is divided into B blocks, and then the histogram statistics are performed on each block and cascaded to obtain the output:

[0041]

[0042] The training data feature set extracted by PCANet is represented as F = [f1, f2,..., f N . Then, the mean mF and variance sF of the training data feature set F are used to perform standardization processing on the training data feature set F through formula (13). The expression of formula (13) is:

[0043]

[0044] The training data feature set after standardization processing is represented as Then, the K-means clustering algorithm is used to divide the standardized training data feature set into k feature sub-blocks

[0045] Furthermore, in step (iii), for each feature sub-block in the training data feature set SVDD is applied to establish a basic monitoring sub-model. The optimization process of SVDD is to find the smallest hypersphere with c as the center and radius R. Using the block feature vectors of each wafer map sample in to establish the smallest hypersphere for each feature sub-block, and its objective function of the smallest hypersphere is:

[0046]

[0047] where ζ i is a slack variable and γ is a penalty coefficient. Then, the Lagrangian function is introduced to optimize the above problem, and the expression of the hypersphere center c is obtained as:

[0048]

[0049] Among them, a i represents the Lagrange coefficient, projects the standardized training data features onto the corresponding SVDD model, and calculates the block feature vector of the wafer map sample according to formula (16). The distance from the hyper-sphere center c is used as the monitoring variable D for each feature sub-block. b :

[0050]

[0051] Among them, represents the Gaussian kernel function, and then uses the kernel density estimation method to determine the confidence limit of each feature sub-block according to the confidence level β. Uses the Bayesian fusion strategy to construct the overall monitoring index BD, and calculates the standardized training data feature set through formula (17). The block feature vector of the wafer map sample in The probability of generating defects in the b-th feature block

[0052]

[0053] Among them, P b (M) and P b (N) respectively represent the block feature vectors of the wafer map sample The prior probabilities of generating defects and normality in the b-th block. If the confidence level of the normal sample is set to β, then P b (M) = 1 - β and P b (N) = β, and respectively represent the block feature vectors of the wafer map sample The posterior probabilities of generating defects and normality in the b-th block, and their solutions are shown in formulas (18) and (19):

[0054]

[0055]

[0056] Then combine the defect probabilities generated in different sub-feature spaces to obtain the overall monitoring index, use the defect probability to weight the equation, and thus the obtained overall monitoring index BD is shown in formula (20):

[0057]

[0058] Among them is the fusion weight, which can be calculated through formula (21):

[0059]

[0060] Finally, the kernel density estimation method is used to calculate the overall detection threshold BD according to the confidence level β lim .

[0061] Further, in step (iv), a test data set I including normal wafer images and defective wafer images is t The size is unified and the median filter is processed. The same as step (a), the bicubic interpolation algorithm is used to unify the wafer image size to (28, 28), and the median filter algorithm with a filter kernel of (3, 3) is used for filtering. The processed test data set is expressed as

[0062] Furthermore, in step (5), the preprocessed test data set is extracted using the PCANet model trained in step (2). The wafer map feature set F t , and use the mean mF and variance sF of the training data feature set F to calculate the test data feature set F through formula (22) t After standardization, the expression of formula (22) is:

[0063]

[0064] The standardized test data feature set is expressed as

[0065] Furthermore, in step (six), the standardized test data features Project it onto the corresponding SVDD model trained in step (3) and calculate the monitoring variables of each feature sub-block Then, the overall monitoring variable BD of the test wafer image sample is calculated according to the Bayesian fusion strategy in step (iii) t , the overall monitoring variable BD of the test wafer image sample t And the detection threshold BD calculated in step (iii) lim For comparison, if BD t >BD lim , it means that the test wafer image sample is a defective wafer image, otherwise it is a normal wafer image.

[0066] Compared with the prior art, the present invention has the following beneficial effects:

[0067] The wafer map defect detection method based on the multi-block principal component analysis network provided by the present invention first preprocesses the wafer map, then uses the K-means clustering algorithm to perform block processing on the features extracted by the PCANet, divides the wafer map features into multiple sub-feature blocks, then trains an SVDD model for each feature sub-block to calculate the monitoring sub-model, and then uses the Bayesian fusion strategy to fuse the monitoring models of different sub-blocks into an overall monitoring model. Finally, the wafer map defects are detected according to the overall monitoring model. The present invention can extract deep features in the wafer map that are helpful for defect detection, and uses the block strategy to reduce the influence of feature differences on wafer map defect detection, and can effectively improve the performance of wafer map defect detection. Description of the Drawings

[0068] Figure 1 It is a flowchart of the wafer map defect detection method based on the multi-block principal component analysis network according to the embodiment of the present invention;

[0069] Figure 2 It is an effect diagram of the wafer map after size normalization processing according to the embodiment of the present invention;

[0070] Figure 3 It is an effect diagram of the wafer map after median filtering processing according to the embodiment of the present invention;

[0071] Figure 4 It is a structural diagram of the PCANet model according to the embodiment of the present invention;

[0072] Figure 5 It is nine types of wafer maps in the WM-811K dataset according to the embodiment of the present invention; Detailed Embodiments

[0073] The present invention will be described in detail below with reference to specific embodiments. However, it should be understood that without further description, the elements, structures, and features in one embodiment can also be beneficially combined into other embodiments.

[0074] Figure 1 It is a flowchart of the wafer map defect detection method based on the multi-block principal component analysis network in the embodiment of the present invention. As shown in Figure 1, the wafer map defect detection method based on the multi-block principal component analysis network provided by the present invention includes the following steps:

[0075] (1) Preprocess the training data set I = [I1, I2,..., I N containing N normal wafer map samples. First, use the bicubic interpolation algorithm to scale the wafer map, and unify the size of the wafer map to (28, 28) (such as Figure 2As shown, then median filtering is performed on the training data set after size unification using a filtering kernel of (3, 3) (as shown in Figure 3). The training data set after preprocessing is denoted as

[0076] (2) First, through the preprocessed training data set I p Train the PCANet model and extract the training data feature set F. Training the PCANet model and extracting features mainly include the first-stage principal component analysis, the second-stage principal component analysis, binary hashing encoding, and block histogram Figure 3 Three stages (the PCANet model structure is as Figure 4 shown), and the specific steps are as follows:

[0077] (1) First-stage principal component analysis

[0078] First, perform block sampling of size k1×k2 on the wafer maps in the training data set pixel by pixel, and then perform cascade learning on all sampled blocks. The representation of the nth wafer map is:

[0079]

[0080] where [k1 / 2] represents the integer part operation; then perform zero-mean processing on the above-acquired blocks. The processed wafer map blocks are represented as:

[0081]

[0082] Similarly, perform similar processing on each wafer map in the training data set. The training set matrix after processing is:

[0083]

[0084] Assume that the number of PCA filters in the first layer is L1. Then the first-layer PCA filters of the PCANet model are represented as follows:

[0085]

[0086] where represents mapping X to a matrix W of size k1×k2 l 1 , q l (XX T ) represents the lth main eigenvector of XX T ;

[0087] (2) Second-stage principal component analysis

[0088] The second - stage PCA is similar to the first - stage PCA. First, the mapping output generated by the first - stage PCA is calculated:

[0089]

[0090] I i is convolved with W l 1 Before the convolution operation, to ensure that the mapping result has the same size as the original wafer map, the boundaries of the image are filled with zeros. Similar to the first stage, in the second stage, the input matrix (the output matrix of the first - stage PCA of PCANet) is also subjected to block sampling, concatenation, and zero - mean normalization:

[0091]

[0092]

[0093] Then, similar processing is performed on each matrix to obtain the block - sampled form of the second - layer input matrix:

[0094]

[0095] Similarly, the second - layer PCA filters are also composed of the corresponding principal eigenvectors. Assuming the number of second - layer PCA filters is L2, the second - layer PCA filters are expressed as:

[0096]

[0097] Finally, through the first two stages of the PCANet model, each wafer map will generate L1×L2 output feature matrices:

[0098]

[0099] (3) Hash Encoding and Block Histogram

[0100] First, the output matrix of the second stage is binarized. After processing, the output matrix data only contains integers and zeros. Then, these output matrices are further subjected to binary hash encoding through formula (11):

[0101]

[0102] where H(·) is a unit - step function. After the above processing, each pixel value in the output matrix data of the second stage is encoded as an integer between For the i - th wafer map, there are L1 output Ts i l (l = 1,2,...,L1). Each output T i lDivided into B blocks, and then the histogram statistics are performed on each block and cascaded, and the output is:

[0103]

[0104] The training data feature set extracted by PCANet is represented as F = [f1, f2,..., f N , and then the training data feature set F is standardized using the mean mF and variance sF of the training data feature set F through formula (13). The expression of formula (13) is:

[0105]

[0106] The training data feature set after standardization is represented as Then the K-means clustering algorithm is used to divide the standardized training data feature set into k feature sub-blocks

[0107] (3) For each feature sub-block in the training data feature set Apply SVDD to establish a basic monitoring sub-model. The optimization process of SVDD is to find the smallest hypersphere with c as the center and radius R. Use the block feature vectors of each wafer map sample in to establish the smallest hypersphere for each feature sub-block. The objective function of its smallest hypersphere is:

[0108]

[0109] where ζ i is the slack variable, γ is the penalty coefficient, and then the Lagrangian function is introduced to optimize the above problem, and the expression of the hypersphere center c is obtained as:

[0110]

[0111] where a i represents the Lagrangian coefficient. Project the standardized training data features onto the corresponding SVDD model, and calculate the distance between the block feature vector of the wafer map sample and the hypersphere center c as the monitoring variable D b :

[0112]

[0113] where represents the Gaussian kernel function, and then the kernel density estimation method is used to determine the confidence limit of each feature sub-block according to the confidence level β Construct the overall monitoring metric BD using the Bayesian fusion strategy, and calculate the standardized training data feature set through formula (17). The block feature vector of the wafer map sample in The probability of a defect occurring in the b-th feature block

[0114]

[0115] where P b (M) and P b (N) respectively represent the block feature vectors of the wafer map sample The prior probabilities of a defect and normal occurring in the b-th block. If the confidence level of the normal sample is set to β, then P b (M) = 1 - β and P b (N) = β. and respectively represent the block feature vectors of the wafer map sample The posterior probabilities of a defect and normal occurring in the b-th block. Their solutions are shown in formulas (18) and (19):

[0116]

[0117]

[0118] Then combine the defect probabilities generated by different sub-feature spaces to obtain the overall monitoring metric. Use the defect probability to weight the equation, and the obtained overall monitoring metric BD is shown in formula (20):

[0119]

[0120] where is the fusion weight, which can be calculated through formula (21):

[0121]

[0122] Finally, use the kernel density estimation method to calculate the overall detection threshold BD according to the confidence level β lim .

[0123] (IV) Perform size unification and median filtering on the test data set I containing normal wafer maps and defective wafer maps t Same as step (I), adopt the bicubic interpolation algorithm to unify the wafer map size to (28, 28), and use the median filtering algorithm with a filtering kernel of (3, 3) for filtering. The processed test data set is denoted as

[0124] (5) Use the PCANet model trained in step (2) to extract the features of the preprocessed test data set of the wafer map to obtain the feature set F t , and use the mean mF and variance sF of the training data feature set F to standardize the test data feature set F t through formula (22). The expression of formula (22) is:

[0125]

[0126] The standardized test data feature set is denoted as

[0127] (6) Project the standardized test data features onto the corresponding SVDD model trained in step (3), and calculate the monitoring variable of each feature sub-block Then calculate the overall monitoring variable BD of the test wafer map sample according to the Bayesian fusion strategy in step (3) t , and compare the overall monitoring variable BD t of the test wafer map sample with the detection threshold BD lim calculated in step (3). If BD t > BD lim , it means that the test wafer map sample is a defective wafer map, otherwise it is a normal wafer map.

[0128] In the above method, steps (1) to (3) are the offline modeling stage, and steps (4) to (6) are the online testing stage.

[0129] The above wafer map defect detection method based on multiple principal component analysis networks of the present invention first preprocesses the wafer map by size unification and noise filtering; then uses the K-means clustering technique to divide the high-dimensional wafer map features extracted by the PCANet model into different feature sub-blocks, and then applies the support vector data description method to each feature sub-block to establish a monitoring sub-model; finally, uses the Bayesian fusion strategy to fuse the monitoring models of different sub-blocks into an overall monitoring model, and detects the wafer map defects according to the overall monitoring model. The present invention can extract deep features in the wafer map that are helpful for defect detection, and uses the block strategy to reduce the influence of feature differences on wafer map defect detection, and can effectively improve the performance of wafer map defect detection.

[0130] To more clearly illustrate the beneficial effects of the above wafer map detection method of the present invention, the following further illustrates the above wafer map detection method of the present invention in conjunction with specific embodiments.

[0131] Example: The WM-811K wafer map dataset is currently the largest publicly known wafer map dataset. The dataset includes eight types of defective wafer maps (Center, Donut, Edge-local, Edge-ring, Local, Random, Scratch, Near-full) and one type of normal wafer map (Nonpattern). The nine types of wafer maps are as shown in Figure 5 shown.

[0132] In this embodiment, five types of wafer map defects (Center, Donut, Edge-ring, Random, and Scratch) are mainly detected. 1400 wafer maps are randomly selected from the WM-811K dataset. Among them, 150 normal wafer map samples are randomly selected for the training dataset and the validation dataset respectively, and 300 normal wafer map samples and 800 defective wafer map samples are randomly selected for the test dataset. Five simulation experiments are conducted. The principal component analysis network is compared with the wafer map defect detection method based on multiple principal component analysis networks of the present invention, and the accuracy rate, detection rate, and false alarm rate are used to evaluate the performance of the method.

[0133] The accuracy rates of the two methods in five experiments are shown in Table 1:

[0134] Table 1

[0135]

[0136] As can be seen from Table 1 above, the wafer map defect detection method based on multiple principal component analysis networks proposed by the present invention can effectively improve the accuracy rate of wafer map defect detection. However, the accuracy rate only shows the overall situation of correct detection and cannot judge the detection situation of the detection model for defective wafer maps and normal wafer maps. Therefore, in this embodiment, the detection rate and false alarm rate are added to further measure the performance of the detection model. The detection rates of the two methods in five experiments are shown in Table 2, and the false alarm rates are shown in Table 3.

[0137] Table 2

[0138]

[0139] Table 3

[0140]

[0141]

[0142] As can be seen from Table 2 and Table 3 above, the wafer map defect detection method based on multiple principal component analysis networks proposed by the present invention significantly improves the detection rate of defective wafer maps while ensuring that the false alarm rates are basically the same.

[0143] In this embodiment, from the accuracy rate, detection rate, and false alarm rate indicators of five experiments conducted by integrating the above two methods, it can be seen that the wafer map defect detection method based on the multi-block principal component analysis network proposed by the present invention significantly improves the performance of wafer map defect detection.

[0144] The above-described embodiments are only used for conveniently illustrating the present invention by way of example, and are not intended to limit the scope of protection of the present invention. Various simple deformations and modifications made by those skilled in the art within the scope of the technical solution described in the present invention should be included in the scope of the above patent application.

Claims

1. A wafer map defect detection method based on a multi-block principal component analysis network, comprising the following steps: ( (1) Collect normal wafer map samples in the industrial process as training dataset I, and preprocess the wafer map samples in training dataset I. The preprocessing process includes image size unification and median filtering. The training dataset after preprocessing is denoted as I p ; (2) Using the preprocessed training dataset I p Train the principal component analysis network model and extract the training data feature set F. The principal component analysis network model is abbreviated as PCANet. Standardize the training data feature set F using the mean mF and variance sF of the training data feature set F. The standardized training data feature set is denoted as Then use the K-means clustering algorithm to cluster the standardized training data feature set into k feature sub-blocks (3) For each of the k feature sub - blocks where 1 ≤ b ≤ k, establish a basic monitoring sub - model using the support vector description method, abbreviated as SVDD. Project the standardized training data feature set onto the corresponding SVDD model to calculate the monitoring variable D . Then, where 1 ≤ b ≤ k, use the kernel density estimation method to determine the confidence limit of each feature sub - block according to the confidence level β b . Next, use the Bayesian fusion strategy to construct the overall statistic BD, and use the kernel density estimation method to calculate the overall detection threshold BD according to the confidence level β ; lim ​ (4) Collect test dataset I containing normal wafer map samples and defective wafer map samples t and preprocess the wafer map samples in test dataset I t . The preprocessing process includes image size unification and median filtering. The test dataset after preprocessing is denoted as (5) Use the trained PCANet model to extract the wafer map feature set F of the preprocessed test data set t , and use the mean mF and variance sF of the training data feature set F to normalize the test data feature set F t . The normalized test data feature set is denoted as (6) Project the standardized test data features onto the corresponding SVDD model to calculate the monitoring variable and calculate the overall monitoring variable BD of the test sample through the Bayesian fusion strategy t , and compare the overall monitoring variable BD of the test sample t with the detection threshold BD lim . If BD t > BD lim , it means that the test sample is a defective wafer map, otherwise it is a normal wafer map.

2. The wafer map defect detection method based on multiple principal component analysis networks according to claim 1, wherein In step (i), a training data set I = [I1, I2,..., I N containing N normal wafer map samples is preprocessed. First, the wafer maps are scaled using the bicubic interpolation algorithm to uniformly standardize the size of the wafer maps to (28, 28). Then, the training data set after size standardization is median filtered using a filter kernel of (3, 3). The preprocessed training data set is denoted as 3. The method for wafer map defect detection based on multiple principal component analysis networks according to claim 2, wherein In the step (ii), first, through the preprocessed training data set I p Train the PCANet model and extract the training data feature set F. Training the PCANet model and extracting features mainly includes three stages: the first-stage principal component analysis, the second-stage principal component analysis, binary hashing encoding, and block histogram. The specific steps are as follows: (1) First-stage principal component analysis First, for the training data set the wafer maps in are sampled block by block with a size of k1×k2 pixel by pixel, and then cascade learning is performed on all the sampled blocks. The ith wafer map is represented by formula (1), where i = 1, 2, …, N: Among them, [k1 / 2] represents the integer operation; then the above collected blocks are processed to have zero mean, and the processed wafer blocks are represented as: Similarly, similar processing is performed on each wafer map in the training dataset. After processing, the training set matrix is as follows: Assuming that the number of PCA filters in the first layer is L1, the first-layer PCA filters of the PCANet model are represented as follows: Among them, represents mapping X to the matrix W with a matrix size of k1×k2 l 1 , q l (XX T ) represents the l-th principal eigenvector of XX T ; (2) Second-stage principal component analysis The second-stage PCA is similar to the first-stage PCA. First, the mapping output generated by the first-stage PCA is calculated: I i Perform a convolution operation with W l 1 Before performing the convolution operation, in order to ensure that the size of the mapping result is the same as that of the original wafer map, the boundaries of the image are filled with zeros. The output matrix of the first stage of PCANet is the input matrix of the second stage. Block sampling, concatenation, and zero-mean processing are performed on the input matrix blocks of the second stage: Then, similar processing is performed on each matrix to obtain the block sampling form of the second-layer input matrix: Similarly, the second-layer PCA filters are also composed of corresponding principal eigenvectors. Assuming that the number of PCA filters in the second layer is L2, the second-layer PCA filters are represented as: Finally, through the first two stages of the PCANet model, each wafer map will generate L1×L2 output feature matrices: (3) Hash coding and block histogram First, the output matrix of the second stage is binarized. The processed output matrix data only contains integers and zeros. Then, these output matrices are further subjected to binary hash coding through formula (11): where H(·) is a unit step function. After the above processing, each pixel value in the output matrix data of the second stage is encoded as an integer between. There are L1 outputs in the i-th wafer map where l = 1, 2, …, L1. Divide each output T i l into B blocks, then perform histogram statistics on each block and cascade them to obtain the output: The training data feature set extracted by PCANet is represented as F = [f1, f2, …, f N , and then the mean mF and variance sF of the training data feature set F are used to standardize the training data feature set F through formula (13). The expression of formula (13) is: The feature set of the training data after standardization is denoted as Then, the standardized training data feature set is used with the K-means clustering algorithm divided into k feature sub-blocks 4. The wafer map defect detection method based on multiple principal component analysis networks according to claim 3, wherein In the step (iii), for each feature sub-block in the training data feature set where 1 ≤ b ≤ k, an SVDD is applied to establish a basic monitoring sub-model. The optimization process of the SVDD is to find the smallest hypersphere centered at c with a radius of R, and use the block feature vectors of each wafer map sample in to establish the smallest hypersphere for each feature sub-block. The objective function of its smallest hypersphere is as follows: where ζ i is a slack variable, γ is a penalty coefficient, and then the Lagrangian function is introduced to optimize the above problem, and the expression for the hypersphere center c is obtained as follows: Among them, a i represents the Lagrange coefficient. The standardized training data features are projected onto the corresponding SVDD model, and the block feature vectors of the wafer map samples are calculated according to formula (16) The distance from the hypersphere center c is used as the monitoring variable D for each feature sub-block b :[[]]END]] Among them, represents the Gaussian kernel function, and then the kernel density estimation method is used to determine the confidence limit of each feature sub-block according to the confidence level β Use the Bayesian fusion strategy to construct the overall monitoring index BD, and calculate the standardized training data feature set through formula (17) The block feature vector of the wafer map sample in The probability of generating a defect in the b-th feature block Among which P b (M) and P b (N) respectively represent the block feature vectors of the wafer map sample Generate the prior probabilities of defect and normal in the b-th block. If the confidence level of the normal sample is set to β, then P b (M) = 1 - β and P b (N) = β, and respectively represent the block feature vectors of the wafer map sample Generate the posterior probabilities of defect and normal in the b-th block. Their solutions are shown in formulas (18) and (19) as follows: Then, the defect probabilities generated by different sub-feature spaces are combined to obtain an overall monitoring index. The defect probabilities are used to weight the equation, and thus the overall monitoring index BD is as shown in formula (20): Among them is the fusion weight and can be calculated by formula (21): Finally, the overall detection threshold BD is calculated according to the confidence level β using the kernel density estimation method lim .

5. The wafer map defect detection method based on multiple principal component analysis networks according to claim 4, wherein, In the step (iv), for the test data set I including normal wafer maps and defective wafer maps t perform size unification and median filtering processing. Similar to step (i), use the bicubic interpolation algorithm to unify the size of the wafer maps to (28, 28), and use the median filtering algorithm with a filter kernel of (3, 3) for filtering processing. The processed test data set is denoted as 6. The wafer map defect detection method based on multiple principal component analysis networks according to claim 5, wherein In step (v), the preprocessed test data set is extracted using the PCANet model trained in step (ii). of the wafer map feature set F t , and the mean mF and variance sF of the training data feature set F are used to standardize the test data feature set F t through formula (22). The expression of formula (22) is as follows: The feature set of the test data after standardization is represented as 7. The wafer map defect detection method based on multiple principal component analysis networks according to claim 6, wherein, In step (vi), the standardized test data features are projected onto the corresponding SVDD model trained in step (iii), and the monitoring variable of each feature sub-block is calculated Then, the overall monitoring variable BD of the test wafer map sample is calculated according to the Bayesian fusion strategy in step (iii) t , and the overall monitoring variable BD of the test wafer map sample t is compared with the detection threshold BD calculated in step (iii) lim . If BD t > BD lim , it indicates that the test wafer map sample is a defective wafer map; otherwise, it is a normal wafer map.

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