CN109977808B

CN109977808B - Wafer surface defect mode detection and analysis method

Info

Publication number: CN109977808B
Application number: CN201910181768.6A
Authority: CN
Inventors: 于乃功; 徐乔; 魏雅乾; 王宏陆; 王林
Original assignee: Beijing University of Technology
Current assignee: Beijing University of Technology
Priority date: 2019-03-11
Filing date: 2019-03-11
Publication date: 2020-10-27
Anticipated expiration: 2039-03-11
Also published as: CN109977808A

Abstract

The invention provides a method for detecting and analyzing a wafer surface defect mode, which can detect the surface defect of a crystal grain and judge the distribution mode and the defect mode cause of the defect crystal grain. The method belongs to the field of defect detection in the wafer production and manufacturing process, and aims to solve the problems of high labor intensity, low detection efficiency and the like in the conventional defect detection method. The specific process comprises the following steps: obtaining a crystal grain image, and generating a wafer defect mode diagram by a machine vision method; constructing and training a wafer defect mode detection model and a classification model, wherein the detection model is used for judging whether a wafer has a defect mode, and the classification model is used for judging the specific defect mode category; and finally, searching a marked sample which is most similar to the sample to be detected in the database according to a similarity measurement algorithm, and deducing the defect mode cause of the sample to be detected by analyzing the defect mode cause of the known sample.

Description

Wafer surface defect mode detection and analysis method

The technical field is as follows:

the invention belongs to the field of defect detection in the wafer production and manufacturing process. In particular to a method for detecting the surface defects of a wafer by adopting a machine vision method, judging the type of a defect mode and analyzing the cause of the defect mode.

Background

The integrated circuit is the foundation and the source of the high-speed development of the current information technology industry, has been highly penetrated and fused into each field of national economy and social development, and the technical level and the development scale of the integrated circuit become one of the important marks for measuring the competitiveness and the comprehensive national strength of the national industry. In recent years, industry policies and guidelines are continuously introduced in our country to promote and guide the development of the integrated circuit industry. The production and fabrication of integrated circuits have a very complicated process, in which the wafer is the main material for manufacturing the chip, and the surface defects thereof are the main obstacles affecting the yield of the product. By detecting the surface defects of the wafer, not only can defective crystal grains be found, but also faults existing in the process flow can be judged according to the distribution mode of the defective crystal grains, and an engineer can conveniently improve the process. Currently, wafer defect detection is mainly classified into two types: the electrical performance of the crystal grains is detected through probe test and the defects on the surface of the wafer are detected through manual visual inspection, and after a wafer defect mode diagram is generated, the cause of the defect mode is judged by an experienced engineer. The manual visual inspection has low efficiency, low speed and high labor intensity, and a method capable of automatically detecting the surface defects of the wafer and judging the cause of the defect mode is urgently needed.

For wafer defect pattern detection and analysis, methods based on statistical analysis, such as defect density distribution estimation, defect cluster analysis, and the like, are adopted in the early days. These methods often focus on statistical analysis of defect patterns only, and cannot classify defect patterns specifically. Template matching has also been widely used in wafer defect pattern detection and analysis, the method is a pixel level image comparison algorithm, and by establishing a standard template library of different surface defect patterns, a sample to be detected is matched and compared with a template, so as to judge the defect type. However, this method can only rely on the existing surface defect samples when building the standard library, and the surface defects in the same pattern have large morphological changes, and the surface defect samples cannot reflect all the surface defect patterns. In recent years, machine learning methods have been widely used in the field of wafer surface defect pattern analysis, such as nearest neighbor, support vector machine, BP neural network, and the like. However, these methods have complicated feature engineering, require manual extraction of wafer defect pattern diagram features, and have low classification accuracy. Meanwhile, the above method is limited to wafer defect mode classification, and the root defect causes of the wafer are different in each defect mode, and the above method cannot analyze the defect mode causes.

Disclosure of Invention

The invention mainly aims to provide a method for detecting and analyzing a defect mode of a wafer surface, which can be applied to the wafer production and manufacturing process, replaces the conventional manual visual inspection mode, realizes automatic detection of crystal grains with defects on the wafer surface by a machine, judges the type of the defect mode of the wafer according to the distribution mode of the defect crystal grains and analyzes the cause of the defect mode. The present invention aims to solve the following problems:

1. the wafer surface defect detection mainly generates a wafer defect mode diagram through manual visual inspection, and has low efficiency, low speed and high labor intensity;

2. the current wafer surface defect mode classification algorithm has low accuracy, and the characteristics of a defect mode diagram of a wafer to be detected need to be manually extracted;

3. the existing wafer defect mode detection algorithm is only limited to defect mode classification, the defect causes in each type mode are different, and the existing method cannot analyze the root causes of the wafer defect mode.

In order to solve the above problems, the present invention provides a method for detecting and analyzing a defect pattern on a wafer surface, the method firstly detects a die having a defect on the surface, the defective die will aggregate into a certain distribution pattern on the wafer, the type of the defect pattern related to the method includes: center, Donut, Edge-Loc, Edge-Ring, Loc, Random, Scratch, Near-Full. And judging whether a defect mode exists on the wafer or not through the constructed wafer defect mode detection model, if not, judging the wafer to be a normal wafer, and if the defect mode exists, judging the specific defect mode type through the classification model. And finally, searching a marked sample which is most similar to the sample to be detected in the database according to a similarity measurement algorithm, and analyzing the defect mode cause of the known sample so as to deduce the defect mode cause of the sample to be detected.

The specific working process of the invention is as follows:

step 1, scanning crystal grains on a wafer one by using an industrial electron microscope to obtain original images of the crystal grains;

step 2, extracting the color histogram features of the crystal grain images, and carrying out similarity judgment on the color histogram features of the crystal grain images and the features of the standard crystal grain images and the background images in the template library to generate a wafer defect feature matrix;

step 3, after the scanning is finished, converting the wafer defect feature matrix into a wafer defect mode diagram, and carrying out median filtering;

step 4, constructing a wafer defect mode detection model based on the WM811K wafer data set, training, judging whether the wafer map has a known defect mode type by using the model, if the wafer map has no defect mode, judging the wafer map to be a normal wafer, ending the detection process, and if the wafer map has the defect mode, performing step 5;

step 5, constructing a wafer defect mode classification model based on the WM811K wafer data set, training, and judging the specific wafer defect mode type by using the model;

and 6, extracting the characteristics of the wafer defect pattern diagram output by the Fc2 layer based on the defect pattern classification model constructed in the step 5, searching a marked defect sample which is most similar to the sample to be detected in the database by adopting a similarity measurement algorithm, and judging the defect cause of the sample to be detected by analyzing the defect pattern cause of the marked sample.

In the step 4, the wafer defect mode detection model consists of three convolution layers and two full-connection layers, the model is built based on a Tensorflow framework, and the specific model structure is shown in the following table:

the convolution layer uses convolution kernel sizes of 3 × 3, step sizes of 1 × 1, and an activation function of ReLU. Each convolutional layer is then downsampled using a 3 x 3 maximum pooling layer. The full-connection layer Fc1 adopts Sigmoid as an activation function, Dropout is added to prevent overfitting, and the Dropout probability value is 0.5.

Before training, the image processed in step 3 is randomly rotated and cut, and the input image is normalized and normalized, i.e. the image size is limited to 224 × 224, and the normalization limits the pixels of three channels to (0, 1). Based on the WM811K data set, 22038 wafer maps with no defect mode were selected as positive samples, and 15311 wafer maps with defect mode were selected as negative samples. During training, the loss function selects an Adam optimization algorithm, the learning rate η is 0.0001, the sample batch _ size is 64, each iteration comprises 583 batches, and the iteration number is epoch is 10.

In the step 5, the wafer defect mode detection model consists of seven convolutional layers and three full-connection layers, the model is built based on a Tensorflow framework, and the specific model structure is shown in the following table:

the convolution layer uses convolution kernel sizes of 3 × 3, step sizes of 1 × 1, and an activation function of ReLU. The output characteristics of the convolutional layers Conv2, Conv4 and Conv7 were all downsampled with a maximum pooling layer of 3 × 3. And the full connection layers Fc1 and Fc2 adopt Sigmoid as an activation function, Dropout is added to prevent overfitting, and the Dropout probability value is 0.5.

The sample image was randomly rotated and cropped before training, and the image size was limited to 224 x 224, limiting the pixels of the three channels to between (0, 1). 25519 total defect samples marked in the WM811K wafer dataset were selected as a training set, namely Center: 2576, Donut: 333, Edge-Loc: 3113, Edge-Ring: 5808, Loc: 2155, Random: 519, Scratch: 715, Near-Full: 93. the loss function adopts Adam optimization algorithm, learning rate η is 0.0001, sample batch _ size is 128, each iteration includes 199 batches, and iteration number is epoch is 250. Introducing L2 regularization limits the parameters to prevent overfitting, as shown in equation (1).

L＝E+λ∑_jω_j ²(1)

Wherein E is an original cost function, and lambda is a regularization coefficient, and the value of lambda in the method is 1 multiplied by 10^-6，ω_jAnd (4) randomly initializing the weight parameters after each iteration of the neural network is updated, and L is a loss function after regularization is introduced.

In step 6, the sample to be detected is input into the classification model in step 5, and the output characteristics of the Fc2 layer are extracted as the original characteristic vector a₀. Extracting the original characteristics of all samples in the database by the same method, setting the number of the samples in the database as N, and forming an original characteristic matrix A with the samples to be detected_(N+1)×1024. Reducing the original characteristic matrix to 254 dimension by PCA algorithm, and obtaining matrix X after dimension reduction_(N+1)×254One sample reduced dimension feature vector per line. Applying equation (2) to map vector elements to the interval [0,1 ]]Forming a sample set D ═ μ₀，μ₁，μ₂，…，μ_N}。

Wherein x is_iIs the i-th row eigenvector, X, of the matrix X_i，minAnd x_i，maxMinimum and maximum values, μ, of the vector, respectively_iIs the normalized ith sample feature vector.

And (3) carrying out interval mapping on the N +1 eigenvectors in the sample set matrix D according to a formula (3). Calculating the characteristic vector mu of the mapped sample to be detected by using the formula (4)₀ ^*And the feature vector mu in the database_k ^*And (k is equal to the Hamming distance of {1, 2, 3.., N }), selecting a sample with the minimum distance as an approximate search result, marking the defect mode cause of the sample in the database, and analyzing the defect mode cause of the sample to infer the root defect cause of the sample to be detected.

Wherein, mu_i，jIs the jth element in the ith feature vector.

Wherein, mu₀ ^*Representing the characteristic vector, mu, of the sample to be measured_k ^*Representing the kth sample feature vector in the database.

The invention has the following advantages:

the method adopts a machine vision method to detect the surface defects of the wafer and generate a wafer defect mode diagram, thereby greatly reducing the labor cost and improving the wafer detection efficiency. A convolutional neural network is adopted to construct a wafer surface defect mode detection and classification model, the defect detection rate of the trained detection model in 5104 defect samples is 99.5%, and the classification model can accurately judge 8 defect modes which are respectively as follows: center, Donut, Edge-Loc, Edge-Ring, Loc, Random, Scratch, Near-Full, the accuracy rate when testing is: 99.8%, 88.5%, 92.1%, 97.1%, 85.4%, 96.2%, 98.9%, 99.9%, the model detection effect is superior to that of the existing algorithm. On the basis of the classification model, the similarity measurement algorithm is provided for analyzing the cause of the defect mode of the sample to be detected, so that the model can judge the defect mode and analyze the root cause of the defect mode. The invention can be applied to the field of defect detection in the wafer manufacturing process, and can replace manual work to detect and analyze the wafer defects.

Drawings

FIG. 1 is a flow chart of a method for detecting and analyzing a defect pattern on a wafer surface;

FIG. 2(a) is a schematic diagram of a manner in which a camera scans a die, and (b) is a schematic diagram of a wafer defect feature matrix;

FIG. 3 is a wafer defect pattern diagram generated from the wafer defect feature matrix, wherein (a) is the generated original defect pattern diagram None, which is a normal wafer, and (b) is the filtered defect pattern diagram;

FIG. 4 WM811K wafer data set wafer defect pattern example;

FIG. 5 is a schematic diagram of a wafer defect mode inspection model;

FIG. 6 is a schematic diagram of a wafer defect model classification model;

fig. 7 is a schematic diagram of similarity ranking results, in which the leftmost sample in the query results is the sample with the highest similarity.

Detailed Description

The method is described in detail below with reference to the accompanying drawings and examples.

FIG. 1 is a flow chart of a wafer surface defect mode detection and analysis method, which includes firstly scanning crystal grains on a wafer to generate a wafer defect mode diagram, inputting the wafer defect mode diagram into a trained wafer defect mode detection model after image preprocessing, and if no defect mode exists, determining that the wafer is a normal wafer and exiting the detection process; if the defect mode exists, the defect mode is input into the classification model, and the specific type of the defect mode is judged. And finally, finding out a sample which is most similar to the sample to be detected in the database according to the proposed similarity measurement algorithm, and deducing the root cause of the defect of the sample to be detected by analyzing the defect mode cause of the similar sample. The method comprises the following specific steps:

1. collecting wafer images

The image acquisition equipment adopts an industrial electron microscope, the pixels are 2400 ten thousand, and the acquired images can be transmitted to a computer for processing in real time. Fig. 2 is a schematic diagram of a manner in which a camera scans a die and a generated wafer defect feature matrix, as shown in fig. 2(a), the camera scans a wafer along an arrow direction to obtain a die image and a current camera position.

2. Generating a wafer defect feature matrix

Because the grain image is simple, the gray level distribution of the image can reflect the difference between the normal grain and the defect grain, so the color histogram feature of the grain image is extracted, and the similarity calculation is carried out with the normal grain image and the background image feature. And (3) calculating the similarity by adopting a Bhattacharyya Distance method, as shown in formula (5), respectively calculating the similarity of the actual crystal grain with the standard crystal grain image and the background image, setting a threshold value to be 0.9, and judging the crystal grain as a defect crystal grain when the similarity is lower than the threshold value. A wafer defect feature matrix is generated corresponding to the die position, and as shown in fig. 2(b), the background map is saved as 0, the normal die is saved as 1, and the defective die is saved as 2.

H₁，H₂Histogram features for the actual grain image and the standard image respectively,

the values are the average values of histogram feature data, and N is the number of bins in the histogram.

3. Generating a wafer defect pattern map

The wafer defect feature matrix is generated into a wafer defect pattern diagram according to the conditions that 0 is white, 1 is blue and 2 is purple, as shown in fig. 3(a), at this time, a lot of noise is contained in the wafer diagram, which affects the subsequent determination and analysis. Part of the noise is filtered out by median filtering, and the result after filtering is shown in fig. 3 (b).

4. Wafer defect mode detection

The detection model is used for judging whether the defect grains are gathered into a certain defect mode on the wafer or not. If the defect mode does not exist, the wafer is a normal wafer, and the detection process is finished; if the defect mode exists, subsequent processing is carried out.

(1) Sample preparation

The samples used for training the method were WM811K wafer data set with a total number of samples 811457, of which only 172950 samples were labeled, and fig. 4 shows an example of wafer defect modes in the data set, including 8 wafers with defective modes and one wafer without defective modes (None). 22038 normal wafer maps (None) are selected as positive samples, 15311 wafer maps with defect modes are selected as negative samples, and the defect types are as follows: center, Donut, Edge-Loc, Edge-Ring, Loc, Random, Scratch, Near-Full, the ratio of the number of the samples to the total number of the negative samples is: 16.82%, 2.17%, 20.33%, 37.94%, 14.07%, 3.39%, 4.67%, 0.61%.

(2) Model construction and training

The model is built based on a Tensorflow framework, FIG. 5 is a structural schematic diagram of a wafer defect mode detection model, Conv 1-Conv 3 layers are convolution layers, the sizes of convolution kernels are all 3 x 3, and the convolution step size is 1 x 1. The activation function adopts ReLU, and as shown in formula (6), the activation function accelerates the network fitting speed, enhances the parameter sparsity and prevents the model from being over-fitted. Each convolution layer is then downsampled using a 3 x 3 maximum pooling layer. To prevent overfitting, the model introduced a Dropout method at Fc4 level during training, randomly inactivating a portion of neurons, and set the Dropout probability value to 0.5. Unlike convolutional layers, the activation function of the full link layer Fc4 uses Sigmoid, and the output layer outputs classification probability by the Softmax algorithm as shown in equation (7).

Wherein x is the value of the convolutional layer neuron node in the convolutional neural network.

Wherein z is the value of the fully-connected layer neuron node in the convolutional neural network.

Before training, the image processed in step 3 is randomly rotated and cut, and the input image is normalized and normalized, i.e. the image size is limited to 224 × 224, and the normalization uses formula (8) to limit the pixels of three channels (x, y, z) between (0, 1). The cross entropy loss shown in formula (9) is used as the loss function during training. Optimization is performed by using Adam algorithm packaged in Tensorflow, the learning rate η is 0.0001, the sample batch _ size of each batch is 64, each iteration comprises 583 batches, and the iteration number is epoch is 10.

Where I (x, y, z) represents the input color image three-channel pixel values.

Wherein, y⁽ⁱ⁾In order to be the true value of the value,

for prediction, n is the number of samples per batch.

5. Wafer defect mode classification

The classification model is used for judging the specific defect mode of the wafer map, and the method can judge 8 defect modes: center, Donut, Edge-Loc, Edge-Ring, Loc, Random, Scratch, Near-Full.

(1) Sample preparation

25519 total defect samples marked in the WM811K wafer data set were selected as a training set, 15% as a verification set and 25% as a test set. In the training set, the number of samples of each defect mode is:

Center：2576；Donut：333；Edge-Loc：3113；Edge-Ring：5808；Loc：2155；Random：519；Scratch：715；Near-Full：93。

(2) model construction and training

The classification model structure is constructed based on a tenserflow framework as shown in fig. 6. The first seven layers are convolutional layers, 3 × 3 convolutional kernels are adopted, the step length is 1 × 1, the activation function is ReLU, and a maximum pooling layer is connected behind Conv2, Conv4 and Conv7 layers respectively for downsampling, so that the characteristic dimension is reduced. And the last three layers are all connection layers, and the sigmoid is selected as the activation function.

Before training, the sample image to be tested is randomly rotated and cut, the image size is limited to 224 × 224, and the pixels of the three channels are limited to (0, 1). During training, Dropout method is introduced at the Fc8 and Fc9 layers to prevent overfitting, and meanwhile, the L2 regularization method is adopted to limit the training parameters, and the principle is shown in formula (10). And selecting cross entropy loss as a loss function, and optimizing by adopting an Adam algorithm packaged by Tensorflow. The learning rate η is 0.0001, the sample batch _ size is set to 128, each iteration contains 199 batches, and the number of iterations epoch is 250.

L＝E+λ∑_jω_j ²(10)

6. Analysis of wafer defect cause

And (4) inputting the samples in the database into the model based on the classification model in the step 5, extracting the features output by the Fc2 layer, storing the features as an HDF5 file, and extracting original feature data from the Fc2 layer to be 1024 dimensions. Extracting the characteristic data of the sample to be detected in the same way to form an original characteristic vector a₀Setting the number of samples in the database as N, and forming an original characteristic matrix A by the to-be-detected samples and the characteristic vectors of the samples in the database_(N+1)×1024＝(a₀，a₁，a₂，...，a_N)^T. And (3) reducing the dimension of the feature matrix by adopting a PCA algorithm, wherein the dimension reduction process is as follows:

(1) centering the matrix A and setting a vector

For the mean vector of each dimension of the matrix, the original characteristic matrix is subtracted by the mean to obtain a matrix A^*As shown in formula (11).

Wherein A is_ijFor the j-th dimension of the ith sample in matrix a,

is the mean of the j-th dimension features of the matrix A, A_ij ^*Is a matrix A^*The j-th dimension of the ith sample.

(2) Computing the matrix A^*Covariance measure the degree of linear correlation, covariance, of two variablesThe variance matrix calculation is shown in equation (12).

Wherein N is the number of samples in the database.

(3) Calculating the eigenvectors and eigenvalues of the covariance matrix, sorting the eigenvalues from large to small, and obtaining an updated eigenvector matrix v through verification and keeping the first 254 principal components with the best effect_1024×254Each column in the matrix is a feature vector.

(4) The original feature data matrix A is obtained according to the formula (13)_(N+1)×1024And the eigenvector matrix v_1024×254Multiplying and converting into matrix X after dimension reduction_(N+1)×254＝(x₀，x₁，x₂，…，x_N+1)^TAt this time, the dimension of the feature vector of each sample after dimension reduction of each row in X is 254 dimensions.

X＝A×v (13)

Wherein, A is an original characteristic matrix, and v is a characteristic vector matrix.

Applying equation (14) to map vector elements to the interval [0,1]Forming a sample set D ═ μ₀，μ₁，μ₂，…，μ_N}。

Wherein x is_iIs the ith row vector of the matrix X, i.e. the ith sample feature, X_i，minAnd x_i，maxMinimum and maximum values, μ, of the vector, respectively_iIs the normalized ith sample feature vector.

And (3) carrying out interval mapping on the N +1 eigenvectors in the sample set matrix D according to a formula (15). Calculating the characteristic vector mu of the sample to be measured by using the formula (16)₀ ^*And the feature vector mu in the database_k ^*(k ∈ {1, 2, 3.., N }), and the sample with the smallest distance is selected as the approximate search result. FIG. 7 is a graph based on the similarityAnd after the similarity is calculated by the similarity measurement algorithm, the result graph is sorted according to the similarity, and the leftmost sample in the sorting result is the sample with the highest similarity and is also used as a reference sample. And (3) marking the sample defect mode cause in the database, and analyzing the defect mode cause of the reference sample to further infer the root defect cause of the sample to be detected.

Wherein, mu_i，jIs a feature vector mu_iThe jth element of (1).

Claims

1. A method for detecting and analyzing a defect pattern on a wafer surface, the method comprising the steps of:

step 6, extracting the wafer defect pattern diagram features output by the Fc2 layer based on the defect pattern classification model constructed in the step 5, calculating the similarity between the sample to be detected and the marked samples in the database by adopting a similarity measurement algorithm, sorting the samples according to the similarity from large to small, reserving the sample with the maximum similarity, and analyzing the defect pattern cause of the sample to further judge the specific defect cause of the sample to be detected;

the step 4 is as follows:

the model is built based on a Tensorflow framework and consists of three convolution layers and two full-connection layers; the convolution kernel size used by the convolution layer is 3 multiplied by 3, the step length is 1 multiplied by 1, and the activation function is ReLU; performing downsampling by adopting a maximum pooling layer of 3 multiplied by 3 after each convolution layer; the full connection layer Fcl adopts Sigmoid as an activation function, Dropout is added to prevent overfitting, and the value of Dropout probability is 0.5;

before training, randomly rotating and randomly cutting the image processed in the step 3, and normalizing the input image, wherein the normalization limits the image size to 224 multiplied by 224, and limits the pixels of three channels between (0, 1); during training, an Adam optimization algorithm is selected as a loss function, and the learning rate eta is 0.0001;

the step 5 is as follows:

the model is built based on a Tensorflow framework and consists of seven convolution layers and three full-connection layers; the size of the convolution layer is 3 multiplied by 3, the step length is 1 multiplied by 1, and the activation function is ReLU; the output characteristics of the convolutional layers Conv2, Conv4 and Conv7 are all sampled with a maximum pooling layer of 3 × 3; the full connection layers Fc1 and Fc2 adopt Sigmoid as an activation function, Dropout is added to prevent overfitting, and the value of Dropout probability is 0.5;

before training, randomly rotating and randomly cutting a sample image to be tested, limiting the size of the image to be 224 multiplied by 224, and limiting the pixels of three channels to be (0, 1); the loss function adopts an Adam optimization algorithm, and the learning rate eta is 0.0001; introducing L2 regularization limits the parameters to prevent overfitting, as shown in equation (1);

L＝E+λ∑_jω_j ²(1)

wherein E is an original cost function, lambda is a regularization coefficient, and lambda is 1 multiplied by 10^-6，ω_jAnd (4) obtaining weight parameters after the random initialization and each iteration update of the neural network, wherein L is a loss function after the regularization is introduced.

2. The method as claimed in claim 1, wherein the step 6 comprises the following steps:

inputting a sample to be detected into the classification model in the step 5, and extracting output characteristics of the Fc2 th layer as an original characteristic vector a₀(ii) a Extracting the original characteristics of all samples in the database by the same method, setting the number of the samples in the database as N, and forming an original characteristic matrix A with the samples to be detected_(N+1)×1024(ii) a Adopting PCA algorithm to reduce the dimension of the characteristic matrix, and reducing the dimension of the matrix X_(N+1)×254Each line is a feature vector of one sample, each sample having 254-dimensional features; applying equation (2) to map vector elements to the interval [0,1 ]]Forming a sample set D ═ μ₀，μ₁，μ₂，…，μ_N}；

Wherein x is_iIs the ith row vector of the matrix X after dimensionality reduction, i.e. the ith sample characteristic, X_i，minAnd x_i，maxMinimum and maximum values, μ, of the vector, respectively_iThe feature vector of the ith sample after normalization;

carrying out interval mapping on N +1 eigenvectors in the sample set matrix D according to a formula (3); calculating the characteristic vector mu of the mapped sample to be detected by using the formula (4)₀ ^*And the feature vector mu in the database_k ^*Where k ∈ {1, 2, 3 …, N }; the defect mode causes of the samples in the database are marked, the distances are sorted from small to large, the sample with the minimum distance is reserved as an approximate search result, and by analyzing the defect mode causes of the sample,further deducing the root defect cause of the sample to be detected;

wherein, mu_i，jIs the jth element in the ith feature vector;