A method and system for determining correlation of wafer test parameters

Abstract

The present invention provides a method for determining the correlation of wafer test parameters, including: data acquisition to obtain N test parameter groups; data preprocessing of the N test parameter groups to obtain N first parameter groups; dimension reduction of the N first parameter groups to obtain N second parameter groups; determining the number k of N second parameter groups to be grouped to obtain k starting centroids; automatic grouping and correlation determination. The method can automatically identify the correlation of wafer test parameters under different test methods, quickly find wafer test parameter groups with high correlation, and quickly perform data analysis, saving time and cost; and is conducive to further improving the accuracy of yield analysis. The present invention also provides a system for determining the correlation of wafer test parameters, which has corresponding advantages due to the use of a method for determining the correlation of wafer testing of the present invention.

Description

Technical Field

[0001] The present invention relates to the field of semiconductor design and production, and in particular to a method and system for determining the correlation of wafer test parameters measured under different test methods. Background Art

[0002] As the design scale of integrated circuits continues to expand, the density of electronic devices on a single chip is increasing, while the feature size of electronic devices is decreasing. At the same time, the integrated circuit process flow contains many complex process steps, each of which has specific process manufacturing deviations, resulting in a reduction in the yield of integrated circuit chips. In the context of manufacturability design, in order to improve the yield of integrated circuit products and shorten the yield maturity cycle, wafer qualification testing (WAT) is usually used to perform electrical testing on wafers to obtain the data necessary for manufacturing process and design yield improvement.

[0003] WAT generates many electrical parameters and values, through which users can evaluate the yield of the tested wafers and find problems that may occur in the semiconductor manufacturing process. However, the types of WAT parameters are very complicated. Through different test methods, different types of test parameters can be obtained, which may reach more than 300 types. It is not easy to find problems in WAT parameters manually. On the other hand, different WAT parameters may be correlated with each other; when a parameter exceeds the preset range, other parameters related to this parameter may also exceed the preset range, but this correlation is not easy to confirm manually.

[0004] Therefore, it is currently very necessary to study a method for determining the correlation of WAT parameters measured under different test methods, so as to save the manpower cost of yield analysis on WAT parameters and improve the accuracy of yield analysis. Summary of the invention

[0005] The present invention is to solve all or part of the problems of the above-mentioned prior art. On one hand, the present invention provides a method for determining the correlation of wafer test parameters. Another aspect of the present invention provides a system for determining the correlation of wafer test parameters, which adopts the method for determining the correlation of wafer test parameters of the present invention.

[0006] According to one aspect of the present invention, a method for determining the correlation of wafer test parameters is provided, and the specific steps include: step S1. using N test methods to perform wafer electrical tests to obtain test results, that is, obtaining N test parameter groups; wherein N is a positive integer not less than 2; step S2. performing data preprocessing on each of the test parameter groups to obtain N first parameter groups, so that the parameter distribution of each of the first parameter groups conforms to the normal distribution or the log-normal distribution; step S3. presetting the feature dimension g, g is a positive integer; performing feature extraction and dimensionality reduction on the N first parameter groups to obtain N second parameter groups, wherein the second parameter groups include g-dimensional feature data; step S4. determining the number of the N second parameter groups to be grouped, denoted as k; and obtaining k starting centroids; step S5. automatic grouping and performing correlation judgment, including: calculating k reasonable centroids based on the result of step S4; dividing the N second parameter groups into k groups based on the reasonable centroids; then determining that the second parameter groups in the same group are correlated, that is, the test parameter groups in the same group are correlated.

[0007] In general, the test parameter group refers to a wafer electrical parameter group, and each electrical parameter in the wafer test parameter group corresponds to a test result obtained by performing an electrical test on a test unit at a position coordinate in the wafer.

[0008] In step S2, the data preprocessing includes removing outliers, adding missing data and testing normal distribution; the outlier removal includes: presetting a data range, judging the parameters in the test parameter group that exceed the data range as outliers and deleting them; the adding missing data includes: adding missing parameters by interpolation; the normal distribution testing includes: presetting a judgment threshold M, performing a KS test on the test parameter group and calculating a p-value; comparing the p-value and M: if p>M, then it is judged that the parameter distribution in the test parameter group conforms to the normal distribution; if p≤M, then it is judged that the parameter distribution in the test parameter group does not conform to the normal distribution, and taking the logarithm of the parameters in the test parameter group so that the parameter distribution in the test parameter group conforms to the log-normal distribution.

[0009] In other cases, in step S2, the data preprocessing also includes standardization processing; the standardization processing includes: scaling the parameters in the test parameter group proportionally so that the scaled parameters meet preset conditions; the preset conditions include parameter value range, parameter mean or variance.

[0010] In step S3, the feature dimension g is preset based on: for the wafer test parameter group, the ratio of the data feature characterization capability after dimension reduction to g dimensions to the data feature characterization capability before dimension reduction is not less than a preset ratio.

[0011] Preferably, in step S3, the dimension reduction method includes a principal component analysis method.

[0012] Preferably, in step S4, the method for determining the number k of N second parameter groups to be grouped includes using a K-means algorithm or a Mini batch k-means algorithm to perform grouping, and the number of groups obtained is k.

[0013] In step S4, the method for obtaining k starting centroids includes factor analysis, and the process includes: selecting k common factors, characterizing each of the second parameter groups, and determining k eigenvalues ​​corresponding to the k common factors in each of the second parameter groups; each of the common factors corresponds to N eigenvalues ​​in N of the second parameter groups, and taking the common factor corresponding to the largest eigenvalue among the N eigenvalues ​​as a starting centroid; and obtaining k starting centroids from the k common factors.

[0014] In general, after step S5, the following is further performed: calculating a correlation coefficient X between any two test parameter groups in each group, wherein the correlation coefficient X is used to characterize the correlation between different test parameter groups; Wherein, if the first parameter groups of the two test parameter groups both conform to the normal distribution, the correlation coefficient X=β1×Pearson correlation coefficient+β2×Spearman correlation coefficient; if one of the first parameter groups of the two test parameter groups conforms to the normal distribution and the other conforms to the lognormal distribution, the correlation coefficient X=β3×Spearman correlation coefficient+β4×Pearson correlation coefficient; if the first parameter groups of the two test parameter groups both conform to the lognormal distribution, the correlation coefficient X=β5×Spearman correlation coefficient+β6×Pearson correlation coefficient; wherein, the Pearson correlation coefficient and the Spearman correlation coefficient are indicators for measuring the correlation between two variables in statistics, and are obtained by calculating the parameters of the first parameter group; the β1, β2, β3, β4, β5, and β6 are respectively the preset weights of the Pearson correlation coefficient or the Spearman correlation coefficient; wherein, 1>β1>β3>0.5>β4>β2>0, 1>β5>β3>0.5>β4>β6>0.

[0015] Another aspect of the present invention provides a wafer test parameter correlation judgment system, including a storage device, wherein the storage device stores a plurality of instructions, the instructions are loaded by a processor and executed according to the wafer test parameter correlation judgment method.

[0016] Compared with the prior art, the main beneficial effects of the present invention are:

[0017] The present invention can quickly and automatically identify the correlation of wafer test parameters under different test methods by executing limited steps, thereby facilitating wafer test parameter analysis; utilizing the correlation results of the present invention is conducive to improving the accuracy of yield analysis through wafer test parameters.

[0018] The present invention provides a wafer test parameter correlation judgment system, which adopts the above-mentioned wafer test parameter correlation judgment method, and can quickly find a wafer test parameter group with high correlation, quickly perform data analysis, and save time and cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 The present invention is a flowchart of a method for determining the correlation of wafer test parameters according to the first embodiment of the present invention.

[0020] Figure 2 This is a schematic diagram of the grouping effect of a wafer test parameter group according to the fifth embodiment of the present invention. DETAILED DESCRIPTION

[0021] The technical solutions in the specific embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0022] Embodiment 1

[0023] This embodiment provides a method for determining the correlation of wafer test parameters, and determines the correlation of wafer test parameter groups under different test methods. Figure 1 As shown, specifically including:

[0024] Step S1. Use N test methods to perform wafer electrical test to obtain test results, that is, obtain N test parameter groups.

[0025] Step S2: perform data preprocessing on each test parameter group to obtain N first parameter groups, so that the parameter distribution of each first parameter group conforms to the normal distribution or the log-normal distribution.

[0026] Step S3. Preset the feature dimension g, where g is a positive integer; perform feature extraction and dimensionality reduction on the N first parameter groups respectively to obtain N second parameter groups, where the second parameter groups include g-dimensional feature data.

[0027] Step S4: Determine the number of groups of the N second parameter groups to be grouped, denoted as k; and obtain k starting centroids.

[0028] Step S5. Automatically group and perform correlation judgment, including: based on the result of step S4, calculate k reasonable centroids; divide N second parameter groups into k groups based on the reasonable centroids; then determine that the second parameter groups in the same group are correlated, that is, the test parameter groups in the same group are correlated.

[0029] A method for determining the correlation of wafer test parameters in this embodiment can quickly complete correlation determination for a wide variety of wafer test parameters by executing limited steps, thereby assisting in wafer test parameter analysis, and can complete automatic grouping and quickly perform data analysis, saving time and cost.

[0030] Embodiment 2

[0031] In this embodiment, the data acquisition method is specifically as follows: obtain N test parameter groups, each test parameter group is an electrical parameter measured under a test method, and different test parameter groups are measured under different test methods; each electrical parameter in the test parameter group corresponds to a test result obtained by performing an electrical test on a test unit at a position coordinate in the wafer.

[0032] In this embodiment, each test parameter group includes several electrical parameters, i.e., several measured parameter values; each electrical parameter corresponds to a die coordinate (x, y) to cover all the dies to be tested in the entire wafer; a die is a single unit die on a wafer. A test parameter group is a set of parameter values ​​measured for all dies in a wafer under a test method; in other embodiments, it can also be test data after taking the median of test data of multiple wafers.

[0033] In this embodiment, the test unit is a die. In other embodiments, the test unit may also be a device, and each device corresponds to an electrical parameter.

[0034] Embodiment 3

[0035] In this embodiment, the data preprocessing method specifically includes:

[0036] Each test parameter group was processed in turn: removing outliers, adding missing data, testing normal distribution and standardization.

[0037] Removing outliers means judging the parameters in the test parameter group that exceed the preset data range as outliers and deleting them. In this embodiment, points other than (Q1-1.5IQR, Q3+1.5IQR) are defined as outliers, and IQR=Q3-Q1.

[0038] Adding missing data means that each set of test parameters includes a preset number of parameter values, which correspond to the position coordinates in the wafer one by one, find the position coordinates of the missing electrical parameters, and add the missing data using interpolation. In this embodiment, contour lines are constructed by discrete points to grid the existing grain coordinate range (x1, y1) to (x n ,y n ), use resampling geometry to correct the parameter values, here linear correction is used.

[0039] In chip testing, some of the data in the test parameter group obey normal distribution, while others obey log-normal distribution.

[0040] In this embodiment, testing the normal distribution refers to performing a KS test (Kolmogorov-Smirnov test), which is based on the cumulative distribution function and is used to test whether a distribution conforms to a certain theoretical distribution or to compare whether two empirical distributions are significantly different; the p value of each test parameter group is calculated: if p>M, the parameters in the test parameter group are judged to conform to the normal distribution; if p≤M, the parameters in the test parameter group are judged to be inconsistent with the normal distribution, and the parameters in the test parameter group are logarithmized (log processing) to make the parameters in the test parameter group conform to the logarithmic normal distribution. Wherein, M is a preset judgment threshold, and in this embodiment, M is 0.05.

[0041] The standardization process in this embodiment example refers to the standardization of the electrical parameters in each test parameter group. In this embodiment, the electrical parameter values ​​after scaling are made to fall within the range of (0, 1). When the k-means distance is calculated later, the pull of the variables by different unit values ​​can be reduced, the calculated distance offset can be reduced, and the calculation speed can be accelerated. In other embodiments, the parameters in each test parameter group are standardized so that they meet the average value of 0 and the variance of 1 after scaling. In other embodiments, data preprocessing may not be standardized.

[0042] In this embodiment, after data preprocessing, the electrical parameter distribution in the first parameter group obtained conforms to the normal distribution or the log-normal distribution, and the parameter value is within the range of (0, 1).

[0043] Embodiment 4

[0044] In this embodiment, the method of performing dimensionality reduction processing on each first parameter group specifically includes:

[0045] The feature dimension g is preset; in this embodiment, the principal component analysis (PCA) dimensionality reduction method is used to extract the wafer features of each wafer test parameter group, and the n-dimensional data of each first parameter group is reduced to g dimensions.

[0046] Generally speaking, the value of g needs to ensure that the feature characterization ability after dimensionality reduction is not less than the preset ratio, and the degree of dimensionality reduction is inversely proportional to the characterization ability. In this embodiment, the feature dimension g is 2, and the dimension is reduced to (PC1, PC2). According to actual calculations, PC1 describes 81% of the features and PC2 describes 16% of the features. Therefore, the distribution characteristics of more than 90% of the grains on the wafer can be characterized, which is greater than the preset ratio of 70%; the principal component analysis dimensionality reduction method is very effective for multi-grain data of wafers, and can cover more than 95% of wafer features. In other embodiments, other dimensionality reduction methods can also be used so that the ratio of the feature characterization ability of the second parameter group to the feature characterization ability of the first parameter group is not less than the preset ratio.

[0047] Embodiment 5

[0048] In this embodiment, the method of determining the starting centroid, automatically grouping and performing correlation judgment specifically includes:

[0049] The number k of the obtained N second parameter groups to be grouped is determined. In this embodiment, the number k is obtained by the K-means algorithm: the N second parameter groups after dimensionality reduction are automatically grouped by the K-means algorithm, and a reasonable k is obtained by the XGBoost algorithm. In other embodiments, it can also be directly determined according to specific grouping needs.

[0050] In this embodiment, k common factors f1, f2, ..., f are selected. k-1 、f k , using (α1f1+α2f2+…+α k-1 f k-1 +α k f k ) characterizes each second parameter group, where α1, α2, ..., α k-1 , α k is the eigenvalue corresponding to k common factors one by one; to prevent local optimality, the selection of the centroid is crucial. This embodiment uses the factor analysis method to find the common factor corresponding to the maximum eigenvalue as the starting centroid. As shown in Table 1, find the common factor corresponding to each maximum eigenvalue, and use these k common factors as the starting centroid. In test parameter group 1, the eigenvalue α1 corresponding to f1 is 0.90, the eigenvalue α2 corresponding to f2 is 0.04, ..., f k The corresponding eigenvalue α kis 0.81; the eigenvalues ​​of all test parameter groups are listed in sequence; in N test parameter groups, the common factor f1 corresponds to N eigenvalues ​​α1, which are 0.90, 0.09, ..., 0.78 respectively, and the maximum eigenvalue is 0.90. The common factor f1 corresponding to the maximum eigenvalue is used as a starting centroid; similarly, the common factor f2 corresponding to the maximum eigenvalue 0.98 can be obtained as a starting centroid, and so on, k starting centroids are obtained. In other embodiments, other methods can also be used to determine the starting centroid.

[0051] Table 1 Factor analysis logic table

[0052] <![CDATA[f1]]> <![CDATA[f2]]> … <![CDATA[f k ]]> Test parameter group 1 0.90(max) 0.04 0.81 Test parameter group 2 0.09 0.46 0.96 … Test parameter group N 0.78 0.98 (max) 0.80

[0053] According to the determined k starting centroids, using the K-means algorithm, k reasonable centroids can be found, and then the N test parameter groups can be automatically divided into k groups, that is, the second parameter group in the same group is determined to be relevant, and the correlation judgment of the test parameters under different test methods can be realized. Figure 2 As shown, in this embodiment, the 6 wafer test parameter groups correspond to the 6 wafer data distributions in the figure, and are divided into 2 groups, namely the first group 1 and the second group 2. It can be seen that the data distribution of the second parameter groups of the 3 groups in the first group 1 is concentrated near the center of the circle and is correlated; the data distribution of the second parameter groups of the 3 groups in the second group 2 is concentrated far from the center of the circle and is correlated.

[0054] In this embodiment, the K-means algorithm is used for automatic grouping. In other embodiments, especially in application scenarios with large amounts of data, the Mini batch k-means algorithm is a better choice.

[0055] Embodiment 6

[0056] In this embodiment, after completing the grouping and determining whether the test parameter groups are correlated, the correlation coefficient X between any two test parameter groups in each group can be further calculated to characterize the correlation:

[0057] In this embodiment, if the parameter distributions of the two first parameter groups in one group both conform to the normal distribution, the value of the correlation coefficient X between the two test parameter groups is (β1×Pearson correlation coefficient+β2×Spearman correlation coefficient).

[0058] The parameter distributions of the other two first parameter groups in the same group, one conforms to the normal distribution and the other conforms to the lognormal distribution, then the value of the correlation coefficient X between the two test parameter groups is (β3×Spearman correlation coefficient+β4×Pearson correlation coefficient).

[0059] If the parameter distributions of the two first parameter groups in the other group both conform to the log-normal distribution, then the value of the correlation coefficient X between the two test parameter groups is (β5×Spearman correlation coefficient+β6×Pearson correlation coefficient).

[0060] Among them, the Pearson correlation coefficient and the Spearman correlation coefficient are indicators for measuring the correlation between two variables in statistics, and are obtained by calculating the parameters of the first parameter group. Among them, β1, β2, β3, β4, β5, and β6 are preset weights of the Pearson correlation coefficient or the Spearman correlation coefficient, respectively, and satisfy: 1>β1>β3>0.5>β4>β2>0; 1>β5>β3>0.5>β4>β6>0. In this embodiment, β1, β2, β3, β4, β5, and β6 take values ​​of 80%, 20%, 60%, 40%, 80%, and 20%, respectively.

[0061] Embodiment 7

[0062] In this embodiment, a wafer test parameter correlation determination system is provided, including a storage device, wherein a plurality of instructions are stored in the storage device, and the instructions are loaded by a processor and executed according to the above-mentioned wafer test parameter correlation determination method.

[0063] The present embodiment provides a wafer test parameter correlation judgment system, which adopts the above-mentioned wafer test parameter correlation judgment method, and can quickly find a wafer test parameter group with a high correlation, quickly perform data analysis, and save time and cost.

[0064] Some commonly used English nouns or letters used in the present invention for the convenience of clear description are only used for exemplary reference rather than restrictive interpretation or specific usage, and the protection scope of the present invention should not be limited by their possible Chinese translation or specific letters. Specific examples are used herein to illustrate the method and system of the present invention, and the description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. It should be pointed out that for ordinary technicians in this technical field, without departing from the principle of the present invention, the present invention can also be improved and modified, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A method for determining the correlation of wafer test parameters, characterized in that: include: Step S1. Using N test methods to perform wafer electrical test to obtain test results, that is, obtaining N test parameter groups; wherein N is a positive integer not less than 2; Step S2. Perform data preprocessing on each of the test parameter groups to obtain N first parameter groups, so that the parameter distribution of each of the first parameter groups conforms to the normal distribution or the lognormal distribution; Step S3. Preset the feature dimension g; perform feature extraction and dimensionality reduction on the N first parameter groups respectively to obtain N second parameter groups, wherein the second parameter groups include g-dimensional feature data; Step S4. Determine the number of the N second parameter groups to be grouped, denoted as k; and obtain k starting centroids; Step S5. Automatically group and perform correlation judgment, including: Based on the result of step S4, k reasonable centroids are calculated; based on the reasonable centroids, N second parameter groups are divided into k groups; then it is determined that the second parameter groups in the same group are correlated, that is, the test parameter groups in the same group are correlated.

2. The method for determining the correlation of wafer test parameters according to claim 1, characterized in that: The test parameter group refers to a wafer electrical parameter group, and each electrical parameter in the wafer test parameter group corresponds to a test result obtained by performing an electrical test on a test unit at a position coordinate in the wafer.

3. The method for determining the correlation of wafer test parameters according to claim 1, characterized in that: In step S2, the data preprocessing includes removing outliers, adding missing data and checking normal distribution; The outlier removal includes: presetting a data range, determining parameters in the test parameter group that exceed the data range as outliers and deleting them; The adding of missing data includes: adding missing parameters by interpolation; The normal distribution test includes: presetting a judgment threshold M, performing a KS test on the test parameter group and calculating a p-value; comparing the p-value with M: If p>M, it is determined that the parameter distribution in the test parameter group conforms to the normal distribution; If p≤M, it is determined that the distribution of the parameters in the test parameter group does not conform to the normal distribution, and the logarithm of the parameters in the test parameter group is taken to make the distribution of the parameters in the test parameter group conform to the log-normal distribution.

4. The method for determining the correlation of wafer test parameters according to claim 3, characterized in that: In step S2, the data preprocessing also includes standardization processing; the standardization processing includes: scaling the parameters in the test parameter group proportionally so that the scaled parameters meet preset conditions; the preset conditions include parameter value range, parameter mean or variance.

5. The method for determining the correlation of wafer test parameters according to claim 1, characterized in that: In the step S3, the feature dimension g is preset based on: for the wafer test parameter group, the ratio of the data feature characterization capability after dimension reduction to g dimensions to the data feature characterization capability before dimension reduction is not less than a preset ratio.

6. The method for determining the correlation of wafer test parameters according to claim 1, characterized in that: In step S3, the dimension reduction method includes a principal component analysis method.

7. The method for determining the correlation of wafer test parameters according to claim 1, characterized in that: In step S4, the method for determining the number k of groups of the N second parameter groups includes using a K-means algorithm or a Mini batch k-means algorithm to perform grouping, and the number of groups obtained is k.

8. The method for determining the correlation of wafer test parameters according to claim 1, characterized in that: In step S4, the method for obtaining k starting centroids includes factor analysis, and the process includes: selecting k common factors, characterizing each of the second parameter groups, and determining k eigenvalues ​​corresponding to the k common factors in each of the second parameter groups; each of the common factors corresponds to N eigenvalues ​​in N of the second parameter groups, and taking the common factor corresponding to the largest eigenvalue among the N eigenvalues ​​as a starting centroid; and obtaining k starting centroids from the k common factors.

9. The method for determining the correlation of wafer test parameters according to claim 1, characterized in that: After step S5, further steps are performed: calculating a correlation coefficient X between any two test parameter groups in each group, wherein the correlation coefficient X is used to characterize the correlation between different test parameter groups; Wherein, if the first parameter groups of the two test parameter groups both conform to the normal distribution, then the correlation coefficient X=β1×Pearson correlation coefficient+β2×Spearman correlation coefficient; If one of the first parameter groups of the two test parameter groups conforms to normal distribution and the other conforms to lognormal distribution, then the correlation coefficient X=β3×Spearman correlation coefficient+β4×Pearson correlation coefficient; If the first parameter groups of the two test parameter groups both conform to the log-normal distribution, then the correlation coefficient X=β5×Spearman correlation coefficient+β6×Pearson correlation coefficient; Among them, the Pearson correlation coefficient and the Spearman correlation coefficient are indicators for measuring the correlation between two variables in statistics, and are obtained by calculating the parameters of the first parameter group; the β1, β2, β3, β4, β5, and β6 are respectively the preset weights of the Pearson correlation coefficient or the Spearman correlation coefficient; among them, 1>β1>β3>0.5>β4>β2>0, 1>β5>β3>0.5>β4>β6>0.

10. A wafer test parameter correlation judgment system, characterized in that: It comprises a storage device, wherein a plurality of instructions are stored in the storage device, and the instructions are loaded by a processor and executed according to a method for determining the correlation of wafer test parameters as described in any one of claims 1 to 9.

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