A Feature Selection Method Applicable to Optical Scattering Measurement

Through the hybrid feature selection method, redundant features in optical scattering measurements are eliminated and feature combinations are optimized, which solves the problem of too long establishment time of optical feature library, and achieves faster parameter extraction and higher accuracy.

CN111553064BActive Publication Date: 2025-05-27HUAZHONG UNIV OF SCI & TECH
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Patent Information

Application Number
CN202010319290.1
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2020-04-21
Publication Date
2025-05-27
Estimated Expiration
2040-04-21

AI Technical Summary

Technical Problem

The existing optical scattering measurement technology consumes too much time due to feature redundancy when establishing an optical feature library, and the library matching method is huge in calculation under dense grids, making it difficult to meet the time requirements of online measurement.

Method used

The hybrid feature selection method is adopted, and redundant features are eliminated through the filtered feature selection algorithm, and the feature combination is optimized by the wrapped feature selection algorithm to build a sparse optical feature library to reduce the library construction time and improve the accuracy of parameter extraction.

Benefits of technology

It significantly shortens the time for establishing optical feature library, reduces the time for online parameter extraction, and improves the accuracy of parameter extraction.

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Abstract

The present invention belongs to the technical field related to optical scattering measurement, and discloses a feature selection method applicable to optical scattering measurement. The method includes the following steps: (1) determining the nanostructure morphology, the critical dimension to be measured, and the material optical constants of the structure to be measured according to semiconductor processes; (2) constructing a forward optical property model of the nanostructure of the structure to be measured; (3) dividing a sparse grid X S , and calculating all discrete point-corresponding full optical feature combinations f a in the sparse grid, and then forming a sparse optical feature library Ω S ; (4) obtaining a candidate feature combination f a from the full optical feature combinations f c based on a filter feature selection algorithm; (5) further refining, based on a wrapper feature selection algorithm, the feature combination used in the evaluation function in the library matching method from the candidate feature combination f c to obtain a final optimized feature combination f * . The present invention shortens the time for offline library building in the library matching method and improves the parameter extraction accuracy.
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Description

Technical Field

[0001] The present invention belongs to the technical field related to optical scattering measurement, and more specifically, relates to a feature selection method suitable for optical scattering measurement. Background Art

[0002] In the semiconductor process, the manufacturing process of integrated circuits includes multiple processes such as material preparation, lithography, cleaning, etching, doping, chemical mechanical polishing, etc., among which the lithography process is the most critical. The main indicators of the lithography process are critical dimension, resolution, depth of focus, alignment, and overlay accuracy, etc. In the lithography process, in order to evaluate and control the processing accuracy of the lithography pattern, a special line pattern reflecting the characteristic line width of the integrated circuit is designed, and the characteristic dimension of the line pattern is called the critical dimension (Critical Dimension, CD). Therefore, in the semiconductor manufacturing process, accurately and quickly measuring the critical dimension online is the key to ensuring the yield of integrated circuits.

[0003] Traditional critical dimension measurement techniques include scanning electron microscope (SEM), atomic force microscope (AFM), and scanning tunneling microscope (STM). Although they can achieve high measurement accuracy, they often cause destructive damage to the measurement samples. Compared with the foregoing measurement means, the OCD measurement technology has attracted particular attention due to its advantages such as fast speed, easy integration, low cost, non-contact, and non-destructive measurement, and is widely used in online monitoring and parameter regulation in the process.

[0004] The OCD measurement mainly includes two steps: forward optical property modeling of nanostructures and topography reconstruction based on measured optical features. The forward optical property model modeling techniques include rigorous coupled wave analysis (RCWA), finite element method (FEM), boundary element method (BEM), or finite difference time domain method (FDTD), etc.

[0005] Zhu Jinlong et al. mentioned in the literature "Research on Morphology Reconstruction Method in Optical Scattering Measurement of Nanostructures" that the morphology reconstruction of nanostructures is essentially to solve an inverse problem based on measured optical characteristics. At present, the methods for solving inverse problems in optical scattering measurement mainly include nonlinear regression, machine learning, and library matching. Although the nonlinear fitting method can solve with high precision, it not only highly depends on a suitable initial value, but also cannot meet the time requirements of online measurement because the forward optical model needs to be repeatedly calculated during the solution process. For machine learning methods, because they need to ensure the convergence of the loss function, compared with the library matching method, they generally need to spend more time in the training process. Chen Xiuguo et al. mentioned in the literature "Improved measurement accuracy in optical scatterometry using correction-based library search" and "Improved measurement accuracy in optical scatterometry using fitting error interpolation based library search" that although the library matching method needs to generate a large number of optical signals offline, because it can not only ensure the online measurement accuracy and meet the time requirements, this method is widely used in OCD measurement. In addition, CN102798342A, CN104679774A, US6768967B2, and US7043387B2 all mentioned this method. Generally speaking, the library matching method first needs to determine the range of the critical dimension x to be extracted and discretely divide the grid X within the range of x, and then calculate the full optical feature combination f of all discrete points in X under a certain measurement configuration through the optical forward characteristic model a (spectrum or angular resolved spectrum), which contains several optical characteristics. The set of all optical signals f a constitutes the optical feature library Ω. During the measurement process, it is considered that the critical dimension value corresponding to the optical feature that minimizes the evaluation function is the critical dimension extraction value Specifically, the mean square error χ (RMSE) in Equation (1) is used as the evaluation function to illustrate how to solve through the library matching method

[0006]

[0007] where y a represents the full optical feature combination obtained by measurement, k represents the serial number of the optical feature in f a , K represents the total number of optical features in f a , M represents the number of critical dimensions to be measured, and σ k represents the measurement standard deviation of the k-th optical feature

[0008] It is also mentioned in the literature "Improved measurement accuracy in optical scatterometry using fitting error interpolation based library search" that the extraction accuracy of critical dimension parameters based on the library matching method is closely related to the density of X. It is easy to understand that when the discrete points in the grid X are denser, the error between the estimated value of the critical dimension and the true value is smaller. However, as the density of the grid X increases, the computational amount of the optical feature f a will increase exponentially, and the time consumed to establish the optical feature library will be out of the acceptable range. In addition, the parameter extraction time of the library matching will also become longer. Therefore, when the grid X becomes dense, a method needs to be proposed to reasonably discard the features in f a to reduce the time consumption for establishing the optical feature library.

[0009] It can be seen from Equation (1) that the calculation of the evaluation function in the library matching method is determined by the feature combination f a , and the value of the evaluation function determines the parameter extraction value which directly affects the parameter extraction accuracy of the library matching. It should be noted that in the optical signal f a , because the optical features in f a are highly correlated with each other, many optical features are actually redundant and cannot bring more information to the evaluation function, but instead increase the burden when establishing the optical feature library Ω. Zhengqiong Dong proposed to select optical features based on the eigenvalue decomposition of the Jacobi matrix J T in the literature "Dependence-Analysis-Based Data-Refinement in Optical Scatterometry for Fast Nanostructure Reconstruction" to improve the parameter extraction accuracy of the nonlinear fitting algorithm, but it did not optimize the library matching method. The literature "Scatterometry-based metrology with feature region signatures matching" and CN104807398B both proposed to calculate the evaluation function according to the optically sensitive feature part with higher sensitivity to improve the accuracy of the library matching, but they did not consider the redundancy between the highly sensitive features. SUMMARY OF THE INVENTION

[0010] In view of the above deficiencies or improvement requirements of the prior art, the present invention provides a feature selection method applicable to optical scattering measurement. In order to reduce the time consumed in establishing an optical property library, overcome the problem of feature redundancy, a hybrid feature selection method using a library matching method is adopted to eliminate redundant features, achieving the effect of reducing the library building time and enabling faster parameter extraction, while improving the accuracy of parameter extraction.

[0011] To achieve the above object, the present invention provides a feature selection method applicable to optical scattering measurement, and the method includes the following steps:

[0012] (1) Determine the nanostructure morphology, the key dimensions to be measured, and the material optical constants of the structure to be measured according to semiconductor processes;

[0013] (2) Construct a forward optical property model of the nanostructure of the structure to be measured through analysis or numerical modeling;

[0014] (3) Divide a sparse grid X S in the floating range of the key dimension parameters of the nanostructure to be measured, and calculate the full optical feature combinations f a corresponding to all discrete points in the sparse grid, and then form a sparse optical feature library Ω S ;

[0015] (4) Based on a filter-based feature selection algorithm, obtain candidate feature combinations f a from the full optical feature combinations f c with a certain feature combination evaluation index;

[0016] (5) Based on a wrapper-based feature selection algorithm, with the accuracy of library matching parameter extraction for random examples as the evaluation index, further refine the feature combinations used in the evaluation function in the library matching method from the candidate feature combinations f c to obtain the final optimized feature combination f*.

[0017] Further, the layer-by-layer topological morphology of the nanostructure is a grating, a thin film, or a periodic array.

[0018] Further, the analysis or numerical modeling methods include methods such as RCWA, FEM, BEM, or FDTD.

[0019] Further, the optical features are the reflectivity measured by a reflectometer, the ellipsometry parameters measured by an ellipsometer, the Stokes vector, or the Mueller matrix measured by a Mueller matrix ellipsometer.

[0020] Further, the divided sparse grid is a grid on a Cartesian coordinate system, a polar coordinate system, a cylindrical coordinate system, or a spherical coordinate system.

[0021] Further, the filtering feature selection algorithm is sequential forward selection, sequential backward selection, or plus-L minus-R selection.

[0022] Further, the feature combination evaluation index is an evaluation index related to correlation, a distance-based evaluation index, or a mutual information-based evaluation index.

[0023] Further, when there are multiple critical dimension parameters to be measured, the candidate feature combination f c is the union of candidate feature combinations obtained by performing filtering feature selection on different critical dimensions.

[0024] Further, the wrapper feature selection algorithm is a genetic algorithm, a particle swarm algorithm, or an ant colony algorithm.

[0025] Further, the extraction accuracy of the library matching parameters for random examples is calculated by the 1-norm, 2-norm, or infinity norm of the vector formed by subtracting the parameter extraction value from the actual value.

[0026] Further, the random examples are selected with equal probability within the range of the sparse grid X S or selected according to a certain probability distribution.

[0027] Generally speaking, compared with the prior art through the above technical solutions conceived by the present invention, the feature selection method applicable to optical scattering measurement provided by the present invention mainly has the following beneficial effects:

[0028] 1. The hybrid feature selection method proposed by the present invention first takes into account the redundancy of features through the filtering algorithm, and secondly, specifically optimizes the feature combination for the widely used library matching algorithm in the wrapper algorithm. It can not only greatly shorten the time for offline library construction in the library matching method, but also reduce the online parameter extraction time, while improving the parameter extraction accuracy.

[0029] 2. In the method proposed by the present invention, all evaluation indexes of the feature selection process only need to be calculated through the sparse grid X S , the sparse optical feature library Ω S , and a small number of random examples, which is easy to implement.

[0030] 3. The flow of the feature extraction method is simple, easy to implement, and has strong applicability, which is conducive to popularization and application. Brief Description of the Drawings

[0031] Figure 1 is a schematic flow chart of the feature selection method applicable to optical scattering measurement provided by the present invention;

[0032] Figure 2 is the nanostructure morphology, materials, and the incident angle, azimuth angle, and incident wavelength in the measurement configuration in the embodiment of the present invention;

[0033] Figure 3 It is a schematic diagram of the processing flow of a typical filtering selection algorithm;

[0034] Figure 4 It is during the filtering feature selection process in the embodiments of the present invention, where the evaluation index changes with the number of loops. Among them, 401, 402, and 403 respectively show that during the selection of f c,1 , f c,2 , f c,3 , the change of MRMR with the number of loops;

[0035] Figure 5 It is a schematic diagram of the processing flow of a typical wrapper selection algorithm;

[0036] Figure 6 Among 601 and 600 in [], they are the full-optical feature combination f a and the final feature combination f* obtained through the present invention in the embodiments of the present invention, and in the embodiments, the parameter extraction performance index ε value of the feature combination;

[0037] Figure 7 Among 701 and 702 in [], they are respectively the time consumption when the full-optical feature combination f a and the final feature combination f* extract critical dimension parameters in the embodiments, and the ratio of the time consumption; Detailed implementation manners

[0038] In order to make the purpose, technical solutions and advantages of the present invention clearer, the following further elaborates on the present invention in combination with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0039] Please refer to Figure 1 , Figure 2 , Figure 3 and Figure 5 , where 100 represents the feature selection method applicable to optical scattering measurement provided by the present invention, 200 represents the schematic diagram of the nanostructure, and the feature selection method applicable to optical scattering measurement provided by the present invention mainly includes the following steps:

[0040] Step 101, determine the nanostructure morphology, the key dimension to be measured, and the material optical constants of the structure to be measured according to the semiconductor process.

[0041] Specifically, the layer-by-layer topological morphology of the nanostructure can be a grating, a thin film, or a periodic array, etc. In this embodiment, from top to bottom, the top layer of the nanostructure is a photoresist grating layer, the middle layer is an antireflection thin film layer, and the substrate is Si, where x 1 and x 3 respectively represent the upper and lower line widths of the photoresist grating, x 2 and x 4 represent the grating wall height and period, and x 5 represents the thickness of the antireflection thin film layer. In this embodiment, it is assumed that x 1 , x 2 , x 3 are the key dimension parameters x to be measured in the photoresist grating.

[0042] In Figure 2 , θ, λ respectively represent the incident angle, azimuth angle, and incident wavelength in the measurement configuration. The optical constants include the refractive index n and the extinction coefficient k, which can be obtained from data or measured by means of instruments such as an ellipsometer.

[0043] Step 102, construct a forward optical property model of the nanostructure of the structure to be measured through analysis or numerical modeling.

[0044] Specifically, for the structure to be measured, use analysis or numerical modeling techniques to solve the Maxwell equations to calculate the optical characteristics corresponding to the key dimension x to be measured. The modeling techniques that can be used for optical characteristic calculation include rigorous coupled wave analysis (RCWA), finite element method (FEM), boundary element method (BEM), or finite difference time domain method (FDTD), etc. Among them, the optical characteristics can be the reflectivity measured by a reflectometer, the ellipsometry parameters measured by an ellipsometer, the Stokes vector, or the Mueller matrix measured by a Mueller matrix ellipsometer, etc.

[0045] In this embodiment, the forward optical property model is RCWA.

[0046] Step 103, divide a sparse grid X S in the floating range of the key dimension parameters of the nanostructure to be measured, and calculate the full optical characteristic combinations f a corresponding to all discrete points in the sparse grid, and then form a sparse optical characteristic library Ω S .

[0047] Specifically, the divided sparse grid can be a grid in a Cartesian coordinate system, a polar coordinate system, a cylindrical coordinate system, or a spherical coordinate system. In this embodiment, the coordinate system used is the Cartesian coordinate system, and the full optical characteristic combination f a is the Stokes vector spectrum. Let x 4 , x 5Fixed at 400 nm and 115 nm, measure the incident angle θ and azimuth angle The incident angles are set to 65° and 0° respectively, the incident wavelength λ ranges from 300 nm to 750 nm, and the interval is 2 nm. Since the Stokes vector contains three components N, C, and S, so f a contains 678 optical features.

[0048] To generate the sparse optical feature library Ω s , first, uniformly and discretely take the critical dimension x to be measured on the Cartesian coordinate system to form a sparse grid X s , X s The value ranges of x 1 , x 2 , x 3 are 150 - 210 nm, 280 - 340 nm, and 160 - 220 nm respectively. The number of discrete points for all three parameters is 5, and the total number of discrete points in the grid X s is 125. Then, calculate the f s corresponding to all discrete points on X a through RCWA to form the sparse optical feature library Ω s .

[0049] Step 104, based on the filter feature selection algorithm, obtain the candidate feature combination f a from the full optical feature combination f c with a certain feature combination evaluation index.

[0050] Specifically, the filter feature selection algorithm can be sequential forward selection, sequential backward selection, forward selection with removal of the rightmost, etc.; the feature combination evaluation index can be an evaluation index based on correlation, an evaluation index based on distance, an evaluation index based on mutual information, etc.; when there are multiple critical dimension parameters to be measured, the candidate feature combination f c is the union of the candidate feature combinations obtained by performing filter feature selection on different critical dimensions.

[0051] In this embodiment, the filter algorithm is the sequential forward feature selection algorithm, and the evaluation index is the minimal - redundancy - maximal - relevance (MRMR) based on mutual information. As shown in Equation (2), MRMR consists of two parts, Rel and Red, which represent maximal correlation and minimal redundancy respectively. The calculations of Rel and Red are shown in Equations (3) and (4):

[0052] mRMR = Rel - Red (2)

[0053]

[0054]

[0055] where |f| represents the total number of features in the feature combination f, f i and f j represent different features in the feature combination, m represents the serial number of the critical dimension, I Rel represents the mutual information between feature f i and the critical dimension x m , and I Red represents the mutual information between f i and f j , where the calculations of I Rel and I Red are as shown in Equations (5) and (6):

[0056]

[0057]

[0058] In the above formula, F i , F j respectively represent the sets of all values of feature f i , f j in Ω S , X m represents the set of all values of x m in X S , p(f i , x m ) represents the joint probability of feature f i and the critical dimension x m , p(f i , f j ) represents the joint probability of feature f i and f j , p(f i ), p(f j ), p(x m ) respectively represent the probabilities of f i , f j , x m in F i , F j , X m .

[0059] Since the parameters to be measured in this case include three critical dimensions x 1 , x 2 , x 3 , and MRMR has different values for different critical dimension values, in this example, sequential forward feature selection is respectively performed on x 1 , x 2 , x 3 to obtain f c,1 , f c,2 , fc,3 , and take f c = f c,1 ∪ f c,2 ∪ f c,3 as the result of filter-based feature selection. The feature combinations f c,1 , f c,2 , f c,3 all start from the empty set and stop feature selection when MRMR reaches the maximum value. Among them, Figure 4 401, 402, and 403 in respectively show the change of MRMR with the number of cycles during the selection of f c,1 , f c,2 , f c,3 . In this example, f c , 1 , f c , 2 , f c , 3 contain 20, 40, and 20 features respectively, and f c contains 80 features.

[0060] Step 105, based on the wrapper-based feature selection algorithm, with the extraction accuracy of the library matching parameters of random examples as the evaluation index, further refine the feature combination used in the evaluation function in the library matching method from the candidate feature combination f c to obtain the final optimized feature combination f*.

[0061] Specifically, the wrapper-based feature selection algorithm can be a genetic algorithm, a particle swarm algorithm, an ant colony algorithm, etc.; the random examples can be equally probabilistically selected within the range of the sparse grid X S , or can be selected according to a certain probability distribution; the extraction accuracy of the library matching parameters of the random examples can be calculated by the 1-norm, 2-norm, infinity norm or other norms of the vector formed by subtracting the parameter extraction value from the actual value; the evaluation function in the library matching method can be the Root Mean Square Error (RMSE), Mean Square Error (MSE), Cross Entropy Error (CEE), etc.

[0062] In this embodiment, after completing the filter-based feature selection algorithm, it is also necessary to further refine the feature combination f c using the wrapper-based algorithm, that is, select the feature combination f* from the subset of the feature combination f c as the final optimization result. To evaluate the extraction accuracy of the parameters corresponding to the feature combination, in this embodiment, within the range of the grid X S , x is randomly selected 30 times to obtain the parameter value x r , forming the set X R; and X is obtained only through RCWA calculation R each key dimension x in r corresponding f c ; The genetic algorithm is used as the wrapper algorithm, the evaluation function in library matching is RMSE, and the feature combination f c '(f c ' ∈ f c ) the parameter extraction accuracy E(f c ) is as shown in Equation (7):

[0063]

[0064] In the formula, ||·|| represents the 2-norm of the vector, r represents the serial number of the random instance, and x r represents the actual value of the key dimension of the rth random instance represents the parameter extraction value obtained for the rth random instance when calculating RMSE through the feature combination f c ', as shown in Equation (8):

[0065]

[0066] where y' c represents the feature combination f of the rth random instance c ', k c represents the serial number of the optical feature in f c ', and K c represents the total number of optical features in f c '; represents the measurement standard deviation of the k c th optical feature. In this example, when the genetic algorithm iterates 100 times, the genetic algorithm converges to the feature combination f*, which only contains 21 optical features, about 1 / 33 of f a . Specifically, the finally selected feature combination f* is shown in Figure 7 .

[0067] Please refer to Figure 6 , to prove the superiority of the feature selection method provided by the present invention, it is necessary to reflect the parameter extraction performance of f* in the dense grid X D through verification examples. For comparison with f*, 100 groups of feature combinations f a (i = 1, 2,..., 100) are randomly selected from f i , and the number of features contained in each combination is the same as that of f*. First, x is uniformly discretized on the Cartesian coordinate system to form the grid X D , where the number of discrete points for all three parameters is 20, and the total number of discrete points in the grid X D is 8000, and X D is calculated through RCWA for each discrete point corresponding fa , forming an optical feature library Ω D . Secondly, for the verification of evaluating the performance of the feature combination, within the grid X D , the parameter value x of the critical dimension x is randomly selected 50 times e , forming a set of verification examples X E , and the f corresponding to each discrete point in X is obtained through RCWA calculation E . a .

[0068] In this embodiment, ε is used to characterize the parameter extraction performance of the feature combination f (f = f*, f i or f a ) in the dense grid X D . The calculation method of ε is as shown in Equation (9):

[0069]

[0070] In the formula, |·| represents the 1-norm of the vector, e represents the serial number of the verification example, and x e represents the actual value of the critical dimension of the e-th verification example represents the parameter extraction value obtained for the e-th verification example when calculating RMSE through the feature combination f, as shown in Equation (10):

[0071]

[0072] Among them, y represents the feature combination f of the e-th verification example, k p represents the serial number of the optical feature in f, and K p represents the total number of optical features in f represents the measurement standard deviation of the kp-th optical feature

[0073] Obviously, compared with the random combination, f* obtained by the present invention has obvious advantages, and even has a certain degree of improvement relative to f a . It is easy to understand that since the number of features in f* has been reduced to 1 / 33 of that in f a , only the f* of all discrete points in X needs to be calculated in the actual measurement process to complete the parameter extraction with high accuracy, which will greatly reduce the time for establishing the optical feature library. In addition, due to the reduction of the number of features, the time for parameter extraction based on library matching will also be reduced. Please refer to D . Generally speaking, on the foregoing 50 verification examples, the feature selection method provided by the present invention not only greatly reduces the time for establishing the optical feature library in OCD measurement, improves the parameter extraction accuracy, but also shortens the time for parameter extraction in library matching Figure 7 .

[0074] Those skilled in the art can easily understand that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A feature selection method applicable to optical scattering measurement, characterized in that, the method comprises the following steps: (1) Determine the nanostructure morphology, the key dimensions to be measured, and the material optical constants of the structure to be measured according to semiconductor processes; the number of the key dimensions to be measured is 3; (2) Construct a forward optical property model of the nanostructure of the structure to be measured through analysis or numerical modeling; (3) Divide a sparse grid X in the floating range of the key dimension parameters to be measured of the nanostructure S , and calculate the full optical feature combinations f corresponding to all discrete points in the sparse grid a , and then form a sparse optical feature library Ω S ; (4) Obtain a candidate feature combination f from the full optical feature combination f based on a filtering feature selection algorithm with a set feature combination evaluation index a ; c ; (5) Based on the wrapper feature selection algorithm, taking the extraction accuracy of the library matching parameters of random examples as the evaluation index, further refine the feature combination used in the evaluation function in the library matching method from the candidate feature combination f c to obtain the final optimized feature combination f*; The filtering feature selection algorithm is the sequential forward feature selection algorithm, and the evaluation index is the maximum correlation and minimum redundancy based on mutual information. The expression of the evaluation index is: mRMR = Rel - Red; where: mRMR is the evaluation index, Rel is the maximum correlation, and Red is the minimum redundancy; Where: |f| represents the total number of features in the all-optical feature combination f a and f i and f j are different features in the all-optical feature combination f a x m is the critical dimension, I Rel (f i , x m ) is the mutual information between f i and x m , I Red (f i , f j ) is the mutual information between f i and f j ; In step (5), the wrapped feature selection algorithm is a genetic algorithm. In the sparse grid X S range, x is randomly selected 30 times to obtain the parameter value x r , forming the set X R , where x represents the critical dimension to be measured; the corresponding f R for each critical dimension x r in X c is calculated by rigorous coupled-wave analysis (RCWA). The evaluation function in the library matching is RMSE, and for the feature combination f′ c , f′ c ∈f c , the parameter extraction accuracy E(f′ c ) is expressed as: Where: ||·|| represents the 2-norm of a vector, r is the serial number in the random set, and x r is the critical dimension information of the r-th random example, represents the parameter extraction value obtained for x c when calculating RMSE through the feature combination f′ r . k c represents the serial number of the optical feature in f′ c , and K C represents the total number of optical features in f′ c . represents the measurement standard deviation of k c , and y′ c represents the feature combination f′ r of x c .

2. The feature selection method applicable to optical scattering measurement according to claim 1, characterized in that: The layer-by-layer topological morphology of the nanostructure is a grating, a thin film or a periodic array.

3. The feature selection method applicable to optical scattering measurement according to claim 1, characterized in that: The optical features are the reflectivity measured by a reflectometer, the ellipsometry parameters measured by an ellipsometer, the Stokes vector, or the Mueller matrix measured by a Mueller matrix ellipsometer.

4. The feature selection method applicable to optical scattering measurement according to claim 1, characterized in that: The divided sparse grid is a grid on a Cartesian coordinate system, a polar coordinate system, a cylindrical coordinate system or a spherical coordinate system.

5. The feature selection method applicable to optical scattering measurement according to any one of claims 1-4, characterized in that: The feature combination evaluation index is an evaluation index based on correlation, an evaluation index based on distance, or an evaluation index based on mutual information.

6. The feature selection method applicable to optical scattering measurement according to claim 5, characterized in that: When there are multiple key dimension parameters to be measured, the candidate feature combination f c is the union of candidate feature combinations obtained by filtering feature selection for different key dimensions.

7. The feature selection method applicable to optical scattering measurement according to any one of claims 1-4, characterized in that: The random examples are selected with equal probability or according to a certain probability distribution from within the sparse grid X S range.

Citation Information

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