Evaluation, training methods, and structural parameter measurement methods for spectral computation models.

Abstract

This specification provides a method for evaluating and training a spectral computation model, as well as a method for measuring structural parameters. The method includes: acquiring a training dataset, wherein each training sample in the training dataset includes a set of structural parameters describing a grating structure and a first theoretical spectrum of a first spectral dimension; inputting the structural parameters into a spectral computation model to output a predicted spectrum of a target spectral dimension; calculating a loss value between the predicted spectrum and a second theoretical spectrum of the target spectral dimension, wherein the second theoretical spectrum is obtained by dimensionality reduction of the first theoretical spectrum, and the loss value is used to train the spectral computation model; and multiplying the loss value by a correction factor to obtain a correction evaluation index, which is used to evaluate the performance of the spectral computation model, wherein the correction factor is the ratio of the target spectral dimension to the first spectral dimension.

Description

Technical Field

[0001] This specification relates to the field of semiconductor manufacturing process technology, and in particular to the evaluation and training methods of spectral calculation models and the measurement methods of structural parameters. Background Technology

[0002] With the development of the semiconductor integrated circuit manufacturing industry, the critical dimensions in the process are getting smaller and smaller, and the number of device structural parameters that need to be controlled is increasing. Traditional optical imaging analysis methods cannot meet the measurement of critical dimensions in the process.

[0003] Traditional OCD (Optical Critical Dimension) technology is a non-contact measurement technique used to measure the size and morphology of semiconductor microstructures. The basic measurement process involves using an OCD measuring device (such as an ellipsometer or reflectometer) to actually illuminate the sample, thereby collecting the diffracted light signal from the sample to obtain the measurement spectrum. The measured spectrum is then matched with a theoretical spectral database that stores a vast amount of mapping relationships between structural parameters and theoretical spectral values. The structural parameter corresponding to the theoretical spectrum that best matches the measured spectrum is selected as the measured value of the actual structural parameter of the sample.

[0004] As semiconductor geometries become increasingly complex and structural parameters multiply, the amount of data in theoretical spectral databases grows exponentially. Therefore, theoretical spectral databases typically require very large storage spaces.

[0005] To address the aforementioned technical issues, patent (CN119377682A) proposes a spectral calculation model. Based on structural parameters and theoretical spectra from a theoretical spectral database as training samples, the spectral calculation model is trained to predict the corresponding spectral values ​​for input structural parameters. In applications measuring the structural parameters of a sample, a large number of structural parameters can be temporarily sampled, and the corresponding predicted spectral values ​​can be calculated instantly based on the spectral calculation model. Then, the measured spectrum of the sample to be tested is matched with each predicted spectrum to filter out target predicted spectra that meet the matching conditions. The target structural parameter corresponding to the target predicted spectrum is then used as the measured value of the actual structural parameter of the sample to be tested. This patent "replaces" the theoretical spectral database with a spectral calculation model, saving storage space and improving the flexibility of matching.

[0006] However, the spectral calculation model in this patent outputs the dimensionality-reduced predicted spectral values. During the training process, in order to accurately evaluate the training effect of the spectral calculation model, it is necessary to restore the dimension of the dimensionality-reduced predicted spectral values ​​to the same dimension as the theoretical spectrum through restoration calculation before evaluating the error between the two.

[0007] Therefore, before each evaluation of the training effect, it is necessary to perform restoration calculations on the predicted spectral values, resulting in huge computational overhead and high performance requirements for computer hardware. Summary of the Invention

[0008] To overcome the problems existing in related technologies, this specification provides methods for evaluating and training spectral calculation models, as well as methods for measuring structural parameters.

[0009] According to a first aspect of the embodiments of this specification, a model evaluation method is provided, the method comprising:

[0010] Obtain a training dataset, wherein each training sample in the training dataset includes a set of structural parameters describing the grating structure and a first theoretical spectrum of the first spectral dimension.

[0011] The structural parameters are input into the spectral calculation model to output a predicted spectrum of the target spectral dimension; wherein the first spectral dimension is greater than the target spectral dimension.

[0012] Calculate the loss value between the predicted spectrum and the second theoretical spectrum of the target spectral dimension; wherein the second theoretical spectrum is obtained by dimensionality reduction of the first theoretical spectrum, and the loss value is used to train the spectral calculation model.

[0013] The loss value is multiplied by the correction factor to obtain the correction evaluation index, which is used to evaluate the performance of the spectral calculation model; wherein the correction factor is the ratio of the target spectral dimension to the first spectral dimension.

[0014] According to a second aspect of the embodiments of this specification, a method for training a spectral calculation model is provided, the method comprising:

[0015] Obtain a training dataset, wherein each training sample in the training dataset includes a set of structural parameters describing the grating structure and a first theoretical spectrum of the first spectral dimension.

[0016] The structural parameters are input into the spectral calculation model to output a predicted spectrum of the target spectral dimension; wherein the first spectral dimension is greater than the target spectral dimension.

[0017] Calculate the loss value between the predicted spectrum and the second theoretical spectrum of the target spectral dimension; wherein the second theoretical spectrum is obtained by dimensionality reduction of the first theoretical spectrum.

[0018] The loss value is multiplied by the correction factor to obtain the correction evaluation index; wherein the correction factor is the ratio of the target spectral dimension to the first spectral dimension.

[0019] If the correction evaluation index does not meet the preset performance conditions, then the spectral calculation model is trained based on the loss value; if it does meet the conditions, then the training of the spectral calculation model is stopped.

[0020] According to a third aspect of the embodiments of this specification, a method for measuring structural parameters is provided, the method comprising:

[0021] Obtain all structural parameters generated from the structural model of the sample to be tested.

[0022] The structural parameters are respectively input into the spectral calculation model trained as in the second aspect to output the predicted spectrum corresponding to each structural parameter.

[0023] Obtain the measurement spectrum obtained by measuring the sample to be tested.

[0024] The measured spectra are matched with each predicted spectrum to select target predicted spectra that meet the matching conditions, and the target structural parameters corresponding to the target predicted spectra are used as the measured values ​​of the actual structural parameters of the sample to be tested.

[0025] According to a fourth aspect of the embodiments of this specification, a model evaluation apparatus is provided, the apparatus comprising:

[0026] The first training dataset acquisition module is used to acquire the training dataset, wherein each training sample in the training dataset includes a set of structural parameters for describing the grating structure and a first theoretical spectrum of the first spectral dimension.

[0027] The first predicted spectrum output module is used to input the structural parameters into the spectral calculation model to output a predicted spectrum of the target spectral dimension; wherein the first spectral dimension is greater than the target spectral dimension.

[0028] The first loss value calculation module is used to calculate the loss value between the predicted spectrum and the second theoretical spectrum of the target spectral dimension; wherein the second theoretical spectrum is obtained by dimensionality reduction of the first theoretical spectrum, and the loss value is used to train the spectral calculation model.

[0029] The first correction evaluation index calculation module is used to multiply the loss value by the correction factor to obtain the correction evaluation index, which is used to evaluate the performance of the spectral calculation model; wherein the correction factor is the ratio of the target spectral dimension to the first spectral dimension.

[0030] According to a fifth aspect of the embodiments of this specification, a training apparatus for a spectral calculation model is provided, the apparatus comprising:

[0031] The second training dataset acquisition module is used to acquire the training dataset, wherein each training sample in the training dataset includes a set of structural parameters for describing the grating structure and a first theoretical spectrum of the first spectral dimension.

[0032] The second predicted spectrum output module is used to input the structural parameters into the spectral calculation model to output a predicted spectrum of the target spectral dimension; wherein the first spectral dimension is greater than the target spectral dimension.

[0033] The second loss value calculation module is used to calculate the loss value between the predicted spectrum and the second theoretical spectrum of the target spectral dimension; wherein the second theoretical spectrum is obtained by dimensionality reduction of the first theoretical spectrum.

[0034] The second correction evaluation index calculation module is used to multiply the loss value by the correction factor to obtain the correction evaluation index; wherein the correction factor is the ratio of the target spectral dimension to the first spectral dimension.

[0035] The model parameter training module is used to train the spectral calculation model based on the loss value if the correction evaluation index does not meet the preset performance conditions; otherwise, the training of the spectral calculation model is stopped.

[0036] According to a sixth aspect of the embodiments of this specification, a device for measuring structural parameters is provided, the device comprising:

[0037] The structural parameter acquisition module is used to acquire all structural parameters generated from the structural model of the sample to be tested.

[0038] The predictive spectrum module is used to input the structural parameters into the spectral calculation model trained as in the second aspect to output the predicted spectrum corresponding to each structural parameter.

[0039] The measurement spectrum acquisition module is used to acquire the measurement spectrum obtained by measuring the sample to be tested.

[0040] The sample structure measurement module is used to match the measured spectrum with each predicted spectrum to filter out the target predicted spectrum that meets the matching conditions, and use the target structural parameters corresponding to the target predicted spectrum as the measured values ​​of the actual structural parameters of the sample to be tested.

[0041] According to a seventh aspect of the embodiments of this specification, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method as described in any one of the first to third aspects.

[0042] According to an eighth aspect of the embodiments of this specification, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the method as described in any one of the first to third aspects.

[0043] The technical solutions provided in the embodiments of this specification may include the following beneficial effects:

[0044] In the embodiments described in this specification, this scheme utilizes a correction factor derived from theoretical proof. Multiplying this correction factor by the loss value yields a correction evaluation index used to assess the training effect of the spectral calculation model. The correction evaluation index calculated by this scheme is almost equal in value to the correction evaluation index calculated based on the error between the predicted spectrum after restoration calculation and the theoretical spectrum.

[0045] As can be seen, before each evaluation of the training effect, this scheme can obtain the correction evaluation index without performing a reduction calculation on the predicted spectral values. Thus, it saves computational overhead and reduces the performance requirements of computer hardware while accurately evaluating the correction evaluation index between the output dimensionality-reduced predicted spectrum and the theoretical spectrum.

[0046] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this specification. Attached Figure Description

[0047] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this specification and, together with the description, serve to explain the principles of this specification.

[0048] Figure 1 This is a schematic diagram illustrating a conventional method for calculating and correcting evaluation indicators according to an exemplary embodiment of this specification.

[0049] Figure 2 This is a flowchart illustrating a model evaluation method according to an exemplary embodiment of this specification.

[0050] Figure 3 This is a schematic diagram illustrating an improved method for calculating calibration evaluation metrics according to an exemplary embodiment of this specification.

[0051] Figure 4 This is a flowchart illustrating a training method for a spectral calculation model according to an exemplary embodiment of this specification.

[0052] Figure 5 This is a schematic diagram illustrating a conventional method for finding the spectral dimension of a target according to an exemplary embodiment of this specification.

[0053] Figure 6This is a schematic diagram illustrating, according to an exemplary embodiment, a method for calculating the restored spectrum of a P-dimensional restoration.

[0054] Figure 7 This is a schematic diagram illustrating, according to an exemplary embodiment, a method for comparing conventional methods of calculating reconstructed spectra and an improved method.

[0055] Figure 8 This is a flowchart illustrating a method for measuring structural parameters according to an exemplary embodiment of this specification.

[0056] Figure 9 This is a schematic diagram of the structure of an electronic device according to an exemplary embodiment of this specification.

[0057] Figure 10 This is a block diagram illustrating a model evaluation apparatus according to an exemplary embodiment of this specification.

[0058] Figure 11 This is a block diagram of a training apparatus for a spectral calculation model, as illustrated in this specification according to an exemplary embodiment.

[0059] Figure 12 This is a block diagram illustrating a structural parameter measuring device according to an exemplary embodiment of this specification. Detailed Implementation

[0060] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this specification. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this specification as detailed in the appended claims.

[0061] The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to be limiting of this specification. The singular forms “a,” “the,” and “the” as used in this specification and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any and all possible combinations of one or more of the associated listed items.

[0062] It should be understood that although the terms first, second, third, etc., may be used in this specification to describe various information, this information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, without departing from the scope of this specification, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to determination."

[0063] Before constructing a theoretical spectral database, OCD technology requires determining the grating structure based on the design drawings and manufacturing process information of the product under test (DUT). This allows for the identification of a structural model of the DUT, from which key structural parameters to be measured can be selected. For example, for a grating structure under test in an integrated circuit, key structural parameters may include critical dimensions (CD), such as the top and bottom widths of the grating lines; sidewall angles (SWA) relative to the substrate surface; and the total height (HT) of the grating structure. Other structural parameters may also be included, but the specific variables vary depending on the DUT structure and will not be elaborated upon here. A set of all structural parameters of the grating structure under test can be represented by a structural parameter vector x = (CD, SWA, HT, ...) or a subset thereof.

[0064] Engineers can set the value range and variation step size for each structural parameter, and iterate through all possible combinations of these structural parameters. For each set of structural parameters, the corresponding theoretical spectrum can be calculated using the Rigorous Coupled Wave Analysis (RCWA) algorithm.

[0065] Finally, a theoretical spectral database is established that stores these structural parameters and their corresponding theoretical spectra.

[0066] The increasing complexity of semiconductor geometries has led to a surge in the number of structural parameters required to simulate them, resulting in a dramatic increase in the size of theoretical spectral databases. This is primarily due to the fact that each factor—the number of structural parameters, the number of step points for structural parameters, the number of wavelengths, and the spectral dimensions—significantly increases the data volume of the theoretical spectral database. For example, adding a single structural parameter, even with only two step points (upper and lower limits), doubles the data volume. Similarly, a theoretical spectral database with n step points becomes n times larger. Even doubling the step point for a single structural parameter doubles the data volume for n structural parameters, resulting in 2^n times the original size. nIn theoretical spectra, the dimensionality (i.e., the number of wavelength points) of spectral data is extremely high, generally related to the number of pixels in the spectrum image acquired by the spectrometer's camera. For example, it can be 512, 1024, 4096, 2048, or even more dimensions, or other values. Therefore, spectral data constitutes the vast majority of the overall data in a theoretical spectral database, and changes in its dimensionality have a greater impact on the overall data volume than changes in the step size of a single structural parameter. In summary, theoretical spectral databases typically require a very large amount of storage space; some can only be stored in server clusters, resulting in poor portability, inconvenience for users, and significant time consumption for data extraction, with full extraction easily causing memory overflow.

[0067] The relevant patent proposes a spectral calculation model that can "replace" the theoretical spectral database. Based on the input structural parameters, it can quickly obtain the "theoretical spectral value". It has a small memory footprint, shorter calculation time than the traditional RCWA algorithm, and high matching flexibility. It solves the problems of difficult storage and application migration of theoretical spectral databases.

[0068] In addition, other technical solutions propose a structural parameter calculation model, which directly outputs the structural parameters corresponding to the measured spectrum based on the input measured spectrum. This allows engineers to directly predict structural parameters based on the structural parameter calculation model, instead of matching pre-set structural parameters, thus saving the matching step.

[0069] Compared to structural parameter calculation models, spectral calculation models still use the matching approach of "theoretical spectral databases" but add the advantage of reverse verification. That is, the structural parameters of the sample can be accurately measured and input into the spectral calculation model to output the predicted spectrum. Finally, the output predicted spectrum can be compared with the measured spectrum of the actual sample. The smaller the error between the two, the higher the accuracy of the spectral calculation model, thus allowing reverse verification of the model accuracy.

[0070] In practice, the applicant found that in order to meet the increasing accuracy requirements of OCD, the increase in structural parameters leads to an increase in theoretical spectral data. However, due to the high spectral dimension of the original theoretical spectrum, the amount of data that needs to be processed to train the spectral calculation model increases explosively with the increase in spectral data, resulting in longer and longer training times and larger and larger memory resources.

[0071] To address the aforementioned issues, existing approaches involve determining the dimensionality of the target spectrum after dimensionality reduction before model training, and then outputting the predicted spectrum from the spectral computation model. The predicted spectrum consists of spectral values ​​at the target spectral dimension, which is smaller than the original spectral dimension. This dimensionality reduction of the output spectral values ​​compresses the data, thereby optimizing the performance of the spectral computation model.

[0072] When verifying the training effect of the spectral calculation model, in order to accurately evaluate the training effect of the spectral calculation model, it is necessary to restore the dimension of the predicted spectral value after dimensionality reduction to the same dimension as the theoretical spectrum through restoration calculation before evaluating the error between the two, so as to determine the target spectral dimension with appropriate accuracy.

[0073] For example, such as Figure 1 As shown, assume that a set of training samples obtained from a theoretical spectral database includes a set of structural parameters and a corresponding first theoretical spectrum of a first spectral dimension. After inputting the structural parameters into the spectral computation model, the output is a predicted spectrum of a target spectral dimension, which is smaller than the first spectral dimension. To calculate the loss between the predicted spectrum and the first theoretical spectrum, the first theoretical spectrum needs to be dimensionality-reduced to a second theoretical spectrum with the same spectral dimension as the predicted spectrum. Then, the loss between the predicted spectrum and the second theoretical spectrum is calculated, and this loss is used to train the parameters of the spectral computation model. To accurately evaluate the training effect of the spectral computation model, the conventional approach is to restore the current spectral dimension of the predicted spectrum to the first spectral dimension through restoration calculation, and use the error between the first theoretical spectrum and the predicted spectrum of the first spectral dimension as a calibration evaluation metric to measure the training effect of the model.

[0074] Therefore, before each evaluation of training effectiveness, it is necessary to perform a restoration calculation on the predicted spectral values ​​to obtain the restored predicted spectrum, and then calculate the correction evaluation index between the restored predicted spectrum and the first theoretical spectrum. Each of these calculations involves the intensive processing of massive amounts of high-dimensional spectral data. Repeatedly performing such calculations not only consumes a large amount of time, storage, and computing resources, making it difficult to meet the stringent requirements of semiconductor processes and new product development for measurement performance, but also poses an extremely high challenge to the performance of computer hardware.

[0075] To address the aforementioned technical issues, this specification provides a model evaluation method that reduces the performance requirements of computer hardware and improves semiconductor measurement efficiency by saving computer overhead and processing time.

[0076] The embodiments described in this specification will now be described in detail.

[0077] like Figure 2 As shown, Figure 2This is a flowchart illustrating a model evaluation method according to an exemplary embodiment, including steps 201-204:

[0078] Step 201: Obtain the training dataset, wherein each training sample in the training dataset includes a set of structural parameters for describing the grating structure and a first theoretical spectrum for the first spectral dimension.

[0079] Step 202: Input the structural parameters into the spectral calculation model to output the predicted spectrum of the target spectral dimension; wherein, the first spectral dimension is greater than the target spectral dimension.

[0080] Step 203: Calculate the loss value between the predicted spectrum and the second theoretical spectrum of the target spectral dimension; wherein the second theoretical spectrum is obtained by dimensionality reduction of the first theoretical spectrum, and the loss value is used to train the spectral calculation model.

[0081] Step 204: Multiply the loss value by the correction factor to obtain a correction evaluation index, which is used to evaluate the performance of the spectral calculation model; wherein, the correction factor is the ratio of the target spectral dimension to the first spectral dimension.

[0082] As mentioned earlier, the theoretical spectral database stores a large number of pairs of structural parameters and their corresponding first theoretical spectral data. The training dataset can be taken from the theoretical spectral database.

[0083] The first spectral dimension can be the actual spectral dimension of the first theoretical spectrum stored in a theoretical spectral database. Different theoretical spectral databases store different spectral dimensions of the first theoretical spectrum, and this specification does not limit the size of the first spectral dimension.

[0084] The target spectral dimension is the spectral dimension after dimensionality reduction from the first theoretical spectrum. Before training the spectral calculation model, it is necessary to find a target spectral dimension of appropriate size. The spectral calculation model will output the predicted spectrum based on the selected target spectral dimension. An appropriate target spectral dimension can balance the model training complexity and the information retention of the spectrum. The specific methods for selecting the target spectral dimension will not be elaborated upon here.

[0085] It is understandable that the target spectral dimension is the spectral dimension after dimensionality reduction from the first spectral dimension, and it must satisfy the condition that the first spectral dimension is greater than the target spectral dimension. If the first spectral dimension is equal to the target spectral dimension, then there will be no step of needing to recalculate the predicted output spectrum.

[0086] To obtain the second theoretical spectrum, the first theoretical spectrum in the first spectral dimension can be reduced in dimensionality to obtain the second theoretical spectrum in the target spectral dimension.

[0087] For example, the first theoretical spectrum and structural parameters can be input into the spectral calculation model, the first theoretical spectrum can be reduced to a second theoretical spectrum by the spectral calculation model, and the second theoretical spectrum and the predicted spectrum can be output together.

[0088] By combining the dimensionality reduction of the first theoretical spectrum, which serves as the label of the real spectrum, and the prediction of the spectrum in the same spectral calculation model, the reconstruction error of the dimensionality reduction of the first theoretical spectrum can be avoided. In the spectral calculation model, the predicted spectrum can be made to continuously approach the parameter space of the first theoretical spectrum.

[0089] For example, the first theoretical spectrum can be dimensionality reduced based on the Principal Component Analysis (PCA) algorithm to obtain the second theoretical spectrum.

[0090] The loss between the predicted spectrum and the second theoretical spectrum of the target spectral dimension can be measured by mean squared error (MSE).

[0091] The applicant discovered through mathematical derivation that, for example Figure 3 As shown, Figure 1 There is a certain numerical relationship between the correction evaluation index and the loss value. That is, the correction evaluation index can be obtained by multiplying the loss value by the correction factor, which is the ratio of the target spectral dimension to the first spectral dimension.

[0092] This scheme utilizes a correction factor derived from mathematical theory. Multiplying this correction factor by the loss value yields a correction evaluation index used to assess the training effectiveness of the spectral calculation model. The value of this correction evaluation index is equivalent to the value of the correction evaluation index calculated based on the error between the predicted spectrum after restoration and the theoretical spectrum.

[0093] As can be seen, before each evaluation of the training effect, this scheme can obtain the correction evaluation index without performing restoration calculations on the predicted spectral values. Thus, while accurately evaluating the training effect, it saves computational overhead and significantly improves computational speed, thereby reducing the response time of semiconductor measurement technology to semiconductor new product processes.

[0094] Next, we will introduce the mathematical derivation process:

[0095] Let the data matrix of the predicted spectrum in the first spectral dimension be . The data matrix of the first theoretical spectrum is ,in, For sample size, This is the first spectral dimension.

[0096] Let the data matrix of the predicted spectrum of the target spectral dimension be denoted as . The data matrix of the second theoretical spectrum is ,in, The target spectral dimension.

[0097] The loss value calculated based on MSE between the predicted spectrum of the target spectral dimension and the second theoretical spectrum is:

[0098]

[0099] The correction evaluation index based on MSE calculation between the predicted spectrum and the first theoretical spectrum in the first spectral dimension is:

[0100]

[0101] Comparing the two calculation formulas, the difference lies in calculating the ratio of the squared distance to the respective dimension. Without loss of generality, for a centered random vector... and ,have:

[0102]

[0103] It represents the statistical expectation of a random vector.

[0104] Assuming a centered random vector covariance matrix Has characteristic roots ,consider Linear combinations:

[0105]

[0106]

[0107]

[0108]

[0109] These are called principal components.

[0110] because If it is centralized, then Expectations Similarly,

[0111]

[0112] in .

[0113] By the principal component analysis theorem,

[0114]

[0115]

[0116] and

[0117]

[0118]

[0119] so

[0120]

[0121] Take the front that meets the restoration accuracy requirements One principal component, then

[0122]

[0123] Therefore, the loss value and the correction evaluation index have the following relationship:

[0124]

[0125] To verify the correctness of the above theoretical derivation, the applicant used multiple data sources, respectively... Figure 1 conventional methods and Figure 3 The improved method was used to calculate the correction evaluation index, and the final results are shown in Table 1:

[0126] Table 1

[0127]

[0128] As shown in Table 1, "Dataset" is the name of the training dataset, "num" is the number of spectra, "dim" is the first spectral dimension, "after" is the target spectral dimension, "paranum" is the number of structural parameters, "eva time" is the time spent processing the predicted spectrum of the target spectral dimension into the predicted spectrum of the first spectral dimension through restoration calculation, "epoch time" is the time spent in one training epoch, "Time Ratio" is the proportion of time spent on restoration calculation in that training epoch, and "real mse" indicates the time spent on restoration calculation. Figure 1 The value of the correction evaluation index calculated by the method, "eva mse" indicates that by Figure 3 The value of the corrected evaluation index is calculated using the method described above.

[0129] It is evident that this scheme saves the time spent on restoration calculations, and the accuracy of the calculated correction evaluation index is almost the same as that of the results calculated by conventional methods, proving the feasibility of the derivation results of this scheme.

[0130] Next, this manual will continue to describe the application of the above model evaluation methods in the training process of the spectral calculation model.

[0131] like Figure 4 As shown, Figure 4 This is a flowchart illustrating a training method for a spectral calculation model according to an exemplary embodiment, including steps 401-405:

[0132] Step 401: Obtain the training dataset, wherein each training sample in the training dataset includes a set of structural parameters for describing the grating structure and a first theoretical spectrum for the first spectral dimension.

[0133] Step 402: Input the structural parameters into the spectral calculation model to output the predicted spectrum of the target spectral dimension; wherein, the first spectral dimension is greater than the target spectral dimension.

[0134] Step 403: Calculate the loss value between the predicted spectrum and the second theoretical spectrum of the target spectral dimension; wherein the second theoretical spectrum is obtained by dimensionality reduction of the first theoretical spectrum.

[0135] Step 404: Multiply the loss value by the correction factor to obtain the correction evaluation index; wherein the correction factor is the ratio of the target spectral dimension to the first spectral dimension.

[0136] Step 405: If the correction evaluation index does not meet the preset performance conditions, then train the spectral calculation model based on the loss value; if it does meet the conditions, then stop training the spectral calculation model.

[0137] The calibration evaluation metric is used to assess the error between the predicted spectrum restored to the first spectral dimension and the original theoretical spectrum. This error, compared to the loss value, provides a more accurate measure of the model's training performance, and the loss value is specifically used to train the model's parameters.

[0138] Therefore, the timing for terminating model training can be accurately determined based on the calibration evaluation metric. When the calibration evaluation metric meets the preset performance condition, it indicates that the model's training effect has met the performance requirements, and training can be terminated. The preset performance condition can be a preset error threshold. If the calibration evaluation metric is less than the preset error threshold, it means that the calibration evaluation metric meets the preset performance condition; otherwise, it does not.

[0139] For related embodiments of the calibration evaluation index in this example, please refer to the foregoing description, which will not be repeated here.

[0140] In this embodiment, the solution optimizes the calculation method of the correction evaluation index, thereby saving the time spent on restoration calculation during model training, improving training efficiency, saving the computational overhead of restoration calculation, and reducing the performance requirements of computer hardware for model training.

[0141] Before training the model, it is necessary to determine the target spectral dimension after dimensionality reduction of the first theoretical spectrum. However, a smaller spectral dimension is not always better. Excessive dimensionality reduction will lead to severe loss of spectral information, while an excessively high spectral dimension will increase model complexity and computational cost. Therefore, it is necessary to find a suitable target spectral dimension to balance model complexity and the preservation of spectral information.

[0142] like Figure 5 As shown, assuming the original spectral dimension of the original first theoretical spectrum is n-dimensional, the conventional approach is to traverse between the dimensions d and n. For any traversal dimension, the original first theoretical spectrum is reduced in dimension and restored, and it is determined whether the restored first theoretical spectrum based on the current traversal dimension meets the restoration accuracy.

[0143] For example, in the first round, d dimensions can be initialized as the dimensionality reduction target. The original first theoretical spectrum is first reduced to d dimensions, and then restored to the original spectral dimension through restoration calculation. The restoration accuracy is judged by comparing the error between the restored first theoretical spectrum and the original first theoretical spectrum.

[0144] If the requirements are not met, k dimensions can be added on the basis of the first round. In the second round, (d+k) dimensions can be used as the dimensionality reduction target. First, the original first theoretical spectrum is reduced to (d+k) dimensions. Then, it is restored to the original spectral dimension through restoration calculation. The error between the restored first theoretical spectrum and the original first theoretical spectrum is compared to determine whether the restoration accuracy is met.

[0145] Similarly, if the (i-1)th round still does not satisfy the requirement, k dimensions can be added based on the (i-1)th round. Assuming that in the i-th round, the error between the first theoretical spectrum restored based on (d+ik) dimensions and the original first theoretical spectrum meets the restoration accuracy, the dimension of the target spectrum can be determined as (d+ik) dimensions.

[0146] While related technologies have proposed improvements to the methods for finding the target spectral dimension, their focus is on reducing the number of traversals required. For example, using a binary search method to quickly narrow down the traversal range can reduce the number of traversals required to find the target spectral dimension from 100 to 60.

[0147] However, for each round of dimensionality reduction and restoration calculations, the relevant techniques still perform calculations based on the complete dimensionality to be reduced to in the current round. For example, assuming the goal is to reduce the dimensionality to (d+k) dimensions and then restore it to n dimensions, the relevant techniques still perform dimensionality reduction and restoration calculations based on a (d+k) dimensional data matrix.

[0148] Therefore, the applicant found that there is still room for improvement in the way the dimensionality reduction and restoration calculations are performed in each round, and hopes to reduce the overall computational cost of finding the target spectral dimension by reducing the computational cost of each round of dimensionality reduction and restoration calculations.

[0149] To address the aforementioned technical problems, this specification provides a spectral dimensionality reduction method to solve the issues of high computational overhead and high performance requirements for computer hardware when selecting a suitable target spectral dimension for a spectral calculation model.

[0150] In one embodiment, the first theoretical spectrum of the first spectral dimension n is subjected to dimensionality reduction and restoration processing to obtain a d-dimensional restored reference spectrum;

[0151] If the restoration accuracy of the reference restored spectrum meets the first preset restoration accuracy condition, then the d dimension is taken as the target spectral dimension.

[0152] If not satisfied, the following steps are executed iteratively:

[0153] In each iteration, the iteration step size k is determined, and the k-dimensional restoration matrix of the k-dimensional restoration located at the tail of the candidate restoration dimension is determined for each round.

[0154] For the first iteration, the k-dimensional restoration matrix is ​​determined based on the reference restored spectrum and the k-dimensional restoration matrix. Candidate restored spectra for 3D restoration;

[0155] For iterations other than the first one, the candidate restored spectra for the current round are determined based on the candidate restored spectra determined in the previous round and the k-dimensional restored matrix determined in the current round.

[0156] If the candidate restored spectrum in any round meets the second preset restoration accuracy condition, the iteration stops, and the candidate restoration dimension of the candidate restored spectrum in any round is taken as the target spectral dimension.

[0157] Where n, d, and k are all positive integers, and .

[0158] In applications where a target spectral dimension is selected for a spectral calculation model, this approach, in each iteration, can determine the target dimension based on the candidate restored spectrum obtained from the previous iteration, combined with the k-dimensional restored matrix obtained from the k-dimensional restoration of the iteration step size. Candidate restored spectra for k-dimensional restoration. That is, each round only requires dimensionality reduction and restoration calculations for the k-dimensional data components, without needing to perform dimensionality reduction and restoration calculations on the complete (k-dimensional) data. Dimensionality reduction and restoration calculations are performed on the data components of 3D.

[0159] As can be seen, this solution can reduce the performance requirements of computer hardware by reducing the computational load of dimensionality reduction and restoration calculations.

[0160] Since the higher the number of spectral dimensions of the spectral values, the longer the model computation time, the longer the training time required for the spectral value calculation model to achieve a fit, in order to reduce the training time of the spectral value calculation model, the number of spectral dimensions required by the original database can be reduced to determine the target number of dimensions. However, the smaller the target number of dimensions, the greater the difference between the spectral values ​​output by the spectral value calculation model and the spectral values ​​of the grating under test, which affects the accuracy of OCD.

[0161] like Figure 6 As shown, the meaning of the restored spectrum of P-dimensional reconstruction is that the first theoretical spectrum of the first spectral dimension is processed into a P-dimensional spectrum through dimensionality reduction calculation, and then restored to the spectrum of the first spectral dimension through reconstruction calculation.

[0162] The amount of information retained in the original theoretical spectrum by the P-dimensional restored spectrum depends on the algorithm used for dimensionality reduction and restoration calculations, as well as the size of the spectral dimension. Specifically, the algorithm used for dimensionality reduction and restoration calculations can be based on the principles of Principal Component Analysis (PCA).

[0163] The universality of the above naming convention is not difficult to understand. The baseline restored spectrum for d-dimensional reconstruction is the first theoretical spectrum in the first spectral dimension, which is then processed into a d-dimensional spectrum through dimensionality reduction calculations, and then restored back to the first spectral dimension through reconstruction calculations. Similarly, ( The candidate restored spectrum of the first spectral dimension is the first theoretical spectrum of the first spectral dimension, which is processed by dimensionality reduction calculation to become ( The spectrum of the first spectral dimension is obtained by performing a restoration calculation, and then the spectrum of the first spectral dimension is restored to its original value.

[0164] ( Candidate restoration spectra of 3D restoration Candidate restoration spectra or Candidate restored spectra for dimensionality reduction. The plus and minus signs depend on the traversal direction. If traversing from low to high dimensionality reduction, then add k to the previous d-dimensionality; that is, in the current round, calculate the... Candidate restored spectra for dimensionality reduction; if traversing from high to low dimensionality, then subtract k from the previous round's d-dimensionality, that is, the current round calculates the... Candidate restoration spectra for visceral restoration.

[0165] The applicant proved through theoretical deduction that, There is a certain mathematical relationship between the candidate restored spectrum of d-dimensional reconstruction and the baseline restored spectrum of d-dimensional reconstruction. Based on the known baseline restored spectrum, it is not necessary to perform a complete calculation (…). To obtain the 3D restoration matrix ( To obtain the candidate restored spectrum for k-dimensional restoration, only the k-dimensional restoration matrix needs to be calculated, and combined with the baseline restored spectrum calculated in the previous round, the ( Candidate restoration spectra for 3D restoration.

[0166] Next, let's take an example of traversing the dimensions from smallest to largest. The mathematical relationship described above is derived using the formula, and the derivation process is as follows:

[0167] Let the data matrix of the first theoretical spectrum be . The centered data matrix after centering the first theoretical spectrum is: ,in For sample size, This represents the first spectral dimension. The data matrix after dimensionality reduction and compression by centering the first theoretical spectrum is as follows: ,in The dimension after dimensionality reduction is an uncertain value and needs to be determined based on the accuracy of the restoration. Let's assume the dimension has now been reduced to... Wei, then Specifically .

[0168] The restoration calculation formula is:

[0169]

[0170] This is the data matrix of the d-dimensional restored reference spectrum. It is the mean data matrix of the first theoretical spectrum. Let be the d-dimensional principal component loading matrix of the first theoretical spectrum. for The transpose of .

[0171] Now we need to calculate the increase. Candidate restored spectra of dimensionality, i.e., based on Data matrix of candidate restored spectra obtained by dimensional component restoration The calculation formula is:

[0172]

[0173]

[0174] in, Candidate restoration dimensions based on candidate restored spectra k-dimensional reconstruction of the tail The k-dimensional restoration matrix is ​​used as the k-dimensional restoration matrix. The restoration dimension of the candidate restored spectrum for (d+k)-dimensional restoration. The principal component loading matrix composed of k dimensions at the tail, for The transpose of .

[0175] It is easy to derive the data matrix of the candidate restored spectra for (d+k)-dimensional restoration. Theoretically, this is the data matrix of the baseline restored spectrum in d-dimensional reconstruction. With k-dimensional restoration matrix sum.

[0176] For example, such as Figure 7 As shown, assuming we need to calculate a data matrix of candidate restored spectra in (d+k) dimensions, the conventional approach (represented by dashed lines) is to perform dimensionality reduction on the first theoretical spectrum to obtain a (d+k)-dimensional first theoretical spectrum, and then perform restoration calculations to obtain the (d+k)-dimensional restored spectrum. Therefore, to calculate the data matrix of candidate restored spectra in (d+k) dimensions using the conventional method, we need to calculate... This solution only requires calculation. By combining the data matrix of the baseline restored spectrum in d-dimensional reconstruction calculated in the previous round, we can obtain the data matrix of the candidate restored spectrum in (d+k)-dimensional reconstruction, which reduces the amount of calculation required for the d-dimensional data components.

[0177] Without loss of generality, traversing the data matrix of candidate restored spectra in (dk)-dimensional dimensions from high to low, Theoretically, this is the data matrix of the baseline restored spectrum in d-dimensional reconstruction. The k-dimensional restoration matrix of the k-dimensional restoration tail of the restored dimension d of the reference restored spectrum. difference.

[0178] Therefore, the dimensionality reduction and restoration calculation formulas in this scheme can be applied to traversal methods with dimensions from high to low and from low to high.

[0179] Next, to verify the correctness of the above theoretical derivation, the applicant used data from multiple theoretical spectral databases as training datasets to verify the application of... Figure 7 The difference in computational speed between the conventional and improved methods is shown in Table 2. The final results are presented in Table 2.

[0180] Table 2

[0181]

[0182] As shown in Table 2, NM7755, NM0316, NM003, and NM931 represent different data sources, such as data from theoretical spectral databases corresponding to different semiconductor structures. 10, 20, 50, and 100 represent the number of iterations. `old` represents the time used for the restoration calculation using the conventional method, and `new` represents the time used for the restoration calculation using this method. `Speed` is (old-new) / old, which indicates the speed improvement compared to the conventional method.

[0183] It is not difficult to conclude, through practice, that this method can reduce the massive amount of computation in existing solutions, improve the speed of restoration calculation, and the time saved becomes more significant as the number of traversals increases. It is especially suitable for scenarios with excessively high spectral dimensions that require multiple traversals to find the target spectral dimension.

[0184] Next, this manual will illustrate the practical application of the above-derived conclusions by traversing from low to high dimension and from high to low dimension respectively:

[0185] (1) Traverse in the direction from low to high dimension.

[0186] In one embodiment, if the restoration accuracy of the reference restored spectrum is not less than a preset restoration accuracy and the restoration accuracy of the restored spectrum of the next lower dimension of the reference restored spectrum is less than the preset restoration accuracy, then the d dimension is taken as the target spectral dimension.

[0187] If the restoration accuracy of the reference restored spectrum is less than the preset restoration accuracy, then the following steps are executed iteratively:

[0188] In each iteration, the iteration step size k is determined, and the k-dimensional restoration matrix of the k-dimensional restoration located at the tail of the candidate restoration dimension is determined for each round.

[0189] For the first iteration, the sum of the baseline restored spectrum and the k-dimensional restored matrix is ​​used as ( Candidate restored spectra for 3D restoration;

[0190] For iterations other than the first round, the sum of the candidate restored spectra determined in the previous round and the k-dimensional restored matrix determined in this round is used as the candidate restored spectra for this round.

[0191] If the restoration accuracy of the candidate restored spectrum in any round is not less than the preset restoration accuracy and the restoration accuracy of the restored spectrum in the next lower dimension of the candidate restored spectrum is less than the preset restoration accuracy, the iteration stops and the candidate restoration dimension of the candidate restored spectrum in any round is taken as the target spectral dimension.

[0192] in, .

[0193] Specifically, when d=1, the first preset restoration accuracy condition is that the restoration accuracy of the reference restored spectrum is not less than the preset restoration accuracy, and the second preset restoration accuracy condition is that the restoration accuracy of any round of candidate restored spectra is not less than the preset restoration accuracy, and the restoration accuracy of the restored spectrum in the next lower dimension of the candidate restored spectrum is less than the preset restoration accuracy. In the case of the first preset restoration accuracy condition and the second preset restoration accuracy condition, the restoration accuracy of the current round's restored spectrum is not less than the preset restoration accuracy, and the restoration accuracy of the lower dimension of the current round's restored spectrum is less than the preset restoration accuracy.

[0194] The accuracy of restoration can be measured by the error between the restored spectrum of the current round and the corresponding first theoretical spectrum. For example, mean squared error (MSE) can be used. Of course, this specification does not limit the method of measuring restoration accuracy; for example, mean absolute error (MAE) and the square of the correlation coefficient can also be used.

[0195] For example, assuming the first spectral dimension of the first theoretical spectrum is n, the initial reference spectral dimension d can be selected from 1 to n. For instance, one can empirically determine which value of d is closer to the target spectral dimension to reduce the number of iterations. Of course, d=1 can also be set, i.e., starting the iteration from the beginning. This specification does not limit the method of determining the value of d.

[0196] After obtaining the d-dimensional restored reference spectrum, if d is greater than 1, it can be determined whether the restoration accuracy of the reference restored spectrum is not less than the preset restoration accuracy, and whether the restoration accuracy of the next lower dimension of the reference restored spectrum is less than the preset restoration accuracy. If d=1, it can be determined whether the restoration accuracy of the reference restored spectrum is not less than the preset restoration accuracy.

[0197] The judgment result falls into three categories:

[0198] ① The restoration accuracy of the reference restored spectrum meets the first preset restoration accuracy condition.

[0199] At this point, we can stop the traversal and use d dimensions as the target spectral dimension after the first theoretical spectrum is reduced to d.

[0200] ② The restoration accuracy of the reference restored spectrum is not less than the preset restoration accuracy, and the restoration accuracy of the restored spectrum in the next lower dimension is not less than the preset restoration accuracy.

[0201] If the restoration accuracy of the reference restored spectrum is not less than the preset restoration accuracy, it means that the restoration accuracy of the reference restored spectrum in the current dimension meets the restoration accuracy requirements. If the restoration accuracy of the restored spectrum in the next lower dimension of the reference restored spectrum is also not less than the preset restoration accuracy, it means that, under the premise of meeting the restoration accuracy requirements, the spectral dimension can be further reduced to find the smallest spectral dimension that just meets the preset restoration accuracy as the target spectral dimension.

[0202] At this point, it can be confirmed that the target spectral dimension must be between 1 and d. We can start from d dimension and traverse in descending order of dimension. Alternatively, we can choose a new, smaller d value and recalculate. If the restoration accuracy of the new d-dimensional restored reference spectrum is less than the preset restoration accuracy, we can start from d dimension and traverse in ascending order of dimension.

[0203] ③ The restoration accuracy of the reference restored spectrum is less than the preset restoration accuracy.

[0204] If the accuracy of the current d-dimensional restored spectrum does not meet the required accuracy, then the restored spectra in dimensions prior to d will also fail to meet the accuracy requirements. In this case, we can continue searching in higher dimensions, traversing from lower to higher dimensions.

[0205] We can first determine the iteration step size k, and then determine the k-dimensional restoration matrix of the candidate restored spectrum located at the tail of the candidate restored dimension (d+k) in this round.

[0206] Therefore, the sum of the baseline restored spectrum and the k-dimensional restored matrix can be determined as the candidate restored spectrum for (d+k)-dimensional restoration.

[0207] If the restoration accuracy of the candidate restored spectrum in (d+k) dimension meets the restoration accuracy requirement, the iteration can be stopped, and (d+k) dimension can be taken as the target spectral dimension.

[0208] If not satisfied, a new iteration step size k can be determined, and then the k-dimensional restoration matrix of the k-dimensional restoration of the candidate restoration spectrum of the (d+2k)-dimensional restoration in the current round can be determined, which is located at the tail of the candidate restoration dimension (d+2k).

[0209] Therefore, the sum of the candidate restored spectrum of the (d+k)-dimensional restoration determined in the previous round and the k-dimensional restoration matrix determined in this round can be used to determine the candidate restored spectrum of the (d+2k)-dimensional restoration.

[0210] If the restoration accuracy of the candidate restored spectrum in the (d+2k) dimension meets the restoration accuracy requirement, the iteration can be stopped, and the (d+2k) dimension can be taken as the target spectral dimension.

[0211] If the condition is not met, the process continues to determine a new iteration step size k and then proceeds with a new calculation. Each round of calculation only requires calculating the k-dimensional restoration matrix, without needing to calculate the restoration matrices for all candidate restoration dimensions of the candidate restoration spectrum in the current round, thereby reducing the computational cost of the restoration matrix.

[0212] It should be noted that the iteration step size k determined in each iteration can be a fixed value, or it can be a variable value; for example, the iteration step size k can be different between different iterations.

[0213] Assuming n=15 and d=3, we can first initialize the reference restoration spectrum for 3D restoration. The restoration accuracy of this reference restoration spectrum is less than the preset restoration accuracy.

[0214] ①k is a fixed value.

[0215] For example, k can take the value 1.

[0216] In each subsequent iteration, candidate restored spectra for 4D and 5D restoration can be calculated sequentially. Since the iteration step size is 1, when determining whether the candidate restored spectra in any round meet the second preset restoration accuracy condition, it is sufficient to determine whether the restoration accuracy of the candidate restored spectra in the current round is not less than the preset restoration accuracy.

[0217] ②k is a variable value, and k is initialized to 4.

[0218] In each subsequent iteration, candidate restored spectra for 7D and 11D can be calculated sequentially. Assuming the restoration accuracy of the candidate restored spectra for 7D is less than the preset restoration accuracy, and the candidate restored spectra for 11D and 10D are not less than the preset restoration accuracy, then the target spectral dimension will be located between 8D and 10D. At this point, the iteration step size can be reduced to k=1, traversing from 8D to 10D in a low-to-high direction, or vice versa.

[0219] (2) Traverse in the direction from high to low dimension.

[0220] In one embodiment, when traversing from high to low dimensions, if the restoration accuracy of the reference restored spectrum is not less than a preset restoration accuracy and the restoration accuracy of the restored spectrum of the next lower dimension of the reference restored spectrum is less than the preset restoration accuracy, then the d dimension is taken as the target spectral dimension.

[0221] If not satisfied, iteratively execute the following steps:

[0222] In each iteration, the iteration step size k is determined, and the k-dimensional restoration matrix of the k-dimensional restoration of the candidate restored spectrum in the previous round is determined.

[0223] For the first iteration, the difference between the baseline restored spectrum and the k-dimensional restored matrix is ​​used as the candidate restored spectrum for (dk)-dimensional restoration. At this point, the k-dimensional restored matrix is ​​the k-dimensional restored matrix of the baseline restored spectrum located at the tail of the d-dimensional dimension.

[0224] For iterations other than the first one, the difference between the candidate restored spectrum determined in the previous round and the k-dimensional restored matrix determined in the current round is used as the candidate restored spectrum for the current round. In this case, the k-dimensional restored matrix determined in the current round is the k-dimensional restored matrix of the candidate restored spectrum from the previous round, located at the tail of the candidate restored dimension.

[0225] If the restoration accuracy of the candidate restored spectrum in any round is not less than the preset restoration accuracy and the restoration accuracy of the restored spectrum in the next lower dimension of the candidate restored spectrum is less than the preset restoration accuracy, the iteration stops, and the candidate restoration dimension of the candidate restored spectrum in any round is taken as the target spectral dimension.

[0226] in, .

[0227] When d=n, the iteration direction must be from high to low.

[0228] exist In such cases, the iteration proceeds from high to low. For example, if the restoration accuracy of the baseline restored spectrum is not less than the preset restoration accuracy and the restoration accuracy of the (d-1) dimension restored spectrum is also not less than the preset restoration accuracy, then the iteration process can be carried out from high to low to find the appropriate target spectral dimension.

[0229] There is a special case where the initially chosen d value is too small, causing the target spectral dimension to be missed. This means the restoration accuracy of the baseline restored spectrum in d dimensions is less than the preset restoration accuracy, while the target spectral dimension is larger than d. In this case, a larger d value can be chosen to ensure that the restoration accuracy of the newly selected baseline restored spectrum is not less than the preset restoration accuracy. Then, the traversal continues in descending order of dimension. Alternatively, one can start from the current baseline restored spectrum and traverse in ascending order of dimension within the range of d to n dimensions until the target spectral dimension is found.

[0230] Similar to the aforementioned implementation that traverses from low to high dimensions, k in each iteration can be 1, or it can be greater than 1 in the early stages to quickly traverse to the vicinity of the target spectral dimension, and then reduce the value of k to accurately find the position of the target spectral dimension.

[0231] It should be noted that the aforementioned traversal from high to low dimensions or from low to high dimensions is not mutually exclusive in practical applications and can be used in combination. For example, when traversing from low to high dimensions, if the iteration step size k is too large and the target spectral dimension is missed, it means the target spectral dimension is before the current spectral dimension. In this case, the traversal can proceed in reverse from the currently determined spectral dimension, from high to low. Conversely, when traversing from high to low dimensions, if the value of d is too small, the target spectral dimension will also be missed, indicating that the target spectral dimension is after the current spectral dimension. In this case, the traversal can proceed in reverse from the currently determined spectral dimension, from low to high.

[0232] Furthermore, after missing the target spectral dimension, the dimensional range in which the target spectral dimension is located can be determined. Then, the value of the iteration step size k can be reduced to find the target spectral dimension more accurately within that range.

[0233] Next, this instruction manual will continue to introduce... Figure 4 The application of the spectral calculation model trained by this method in the scenario of measuring the structural parameters of samples.

[0234] like Figure 8 As shown, Figure 8 This is a flowchart illustrating a method for measuring structural parameters according to an exemplary embodiment, including steps 801-804:

[0235] Step 801: Obtain all structural parameters generated from the structural model of the sample to be tested.

[0236] Step 802: Input the structural parameters into the following... Figure 4 The method trains a spectral calculation model to output the predicted spectrum corresponding to each structural parameter.

[0237] Step 803: Obtain the measurement spectrum obtained by measuring the sample to be tested.

[0238] Step 804: Match the measured spectrum with each predicted spectrum to select the target predicted spectrum that meets the matching conditions, and use the target structural parameter corresponding to the target predicted spectrum as the measured value of the actual structural parameter of the sample to be tested.

[0239] As mentioned earlier, different products under test correspond to different structural models. A structural model describes the specific types of structural parameters of the product under test. After determining the value range of all structural parameters in the structural model, structural parameters with different values ​​can be randomly generated.

[0240] Compared to the structural parameters and theoretical spectra stored in theoretical spectral databases, the spectral calculation model in this scheme can predict the measured spectra corresponding to all structural parameters in a very short time. Therefore, in practical applications, it is not necessary to store massive amounts of structural parameters and theoretical spectra locally like a theoretical spectral database. Instead, when there is a measurement requirement, a large number of structural parameters can be temporarily sampled, and the corresponding predicted spectral values ​​can be calculated instantly based on the spectral calculation model.

[0241] In one embodiment, when matching the measured spectrum with each predicted spectrum, the difference k between the dimensions of the measured spectrum and the predicted spectrum can be determined, and a k-dimensional restoration matrix of the k-dimensional restoration of the measured spectrum located at the tail of the dimension can be determined; the dimensions of each predicted spectrum are smaller than the dimensions of the measured spectrum. Based on the k-dimensional restoration matrix, each measured spectrum is upsized to the same dimension as the measured spectrum.

[0242] For example, the dimension of the measured spectrum is n, the dimension of the measured spectrum is m, and the difference between the two is k. In the prior art, to upgrade the dimension of the measured spectrum to the same dimension as the measured spectrum, n-dimensional matrix calculations are required. However, in this embodiment, by utilizing the result of the formula derived above, only a k-dimensional restoration matrix needs to be calculated to upgrade the measured spectrum to the same dimension as the measured spectrum, saving computational overhead and reducing the performance requirements of computer hardware.

[0243] Corresponding to the embodiments of the foregoing methods, this specification also provides embodiments of the apparatus and the terminal to which it is applied.

[0244] Figure 9 This is a schematic diagram illustrating the structure of an electronic device according to an exemplary embodiment. Figure 9 As shown, at the hardware level, the electronic device 900 includes a processor 902, an internal bus 904, a network interface 906, a memory 908, and a non-volatile memory 910. It may also include other hardware required for various services. One or more embodiments of this specification can be implemented in software, for example, the processor 902 can read the corresponding computer program from the non-volatile memory 910 into the memory 908 and then run it. Of course, besides software implementation, one or more embodiments of this specification do not exclude other implementation methods, such as logic devices or a combination of hardware and software. That is to say, the execution entity of the following processing flow is not limited to individual logic modules, but can also be hardware or logic devices.

[0245] Figure 10 This is a block diagram illustrating a model evaluation apparatus according to an exemplary embodiment of this specification. Figure 10 As shown, this device can be applied to, for example Figure 9 The electronic device 900 shown implements the technical solution of this specification. The device includes:

[0246] The first training dataset acquisition module 1002 is used to acquire a training dataset, wherein each training sample in the training dataset includes a set of structural parameters for describing the grating structure and a first theoretical spectrum of the first spectral dimension.

[0247] The first predicted spectrum output module 1004 is used to input the structural parameters into the spectral calculation model to output the predicted spectrum of the target spectral dimension; wherein the first spectral dimension is greater than the target spectral dimension.

[0248] The first loss value calculation module 1006 is used to calculate the loss value between the predicted spectrum and the second theoretical spectrum of the target spectral dimension; wherein the second theoretical spectrum is obtained by dimensionality reduction of the first theoretical spectrum, and the loss value is used to train the spectral calculation model.

[0249] The first correction evaluation index calculation module 1008 is used to multiply the loss value by the correction factor to obtain the correction evaluation index, which is used to evaluate the performance of the spectral calculation model; wherein the correction factor is the ratio of the target spectral dimension to the first spectral dimension.

[0250] Optionally, the device further includes a second theoretical spectrum calculation module, used to reduce the dimensionality of the first theoretical spectrum to the second theoretical spectrum through the spectral calculation model; or, to reduce the dimensionality of the first theoretical spectrum based on the principal component analysis algorithm to obtain the second theoretical spectrum.

[0251] Optionally, the device further includes a target spectral dimension determination module, used to determine the target spectral dimension after the first theoretical spectrum is dimensionality reduced, specifically including: performing dimensionality reduction and restoration processing on the first theoretical spectrum of the first spectral dimension n to obtain a d-dimensional restored reference spectrum; if the restoration accuracy of the reference restored spectrum meets a first preset restoration accuracy condition, then the d dimension is taken as the target spectral dimension; if not, the following steps are iteratively executed: determining the iteration step size k in each iteration, and determining the k-dimensional restoration matrix of the k-dimensional restoration of the candidate restored spectrum located at the tail of the candidate restored dimension in each round; for the first iteration, determining ( The process involves several iterations: n, d, and k are used to determine the candidate restored spectra for the current iteration. For iterations other than the first iteration, the candidate restored spectra for the current iteration are determined based on the candidate restored spectra from the previous iteration and the k-dimensional restoration matrix determined in the current iteration. If the candidate restored spectra from any iteration satisfy the second preset restoration accuracy condition, the iteration stops, and the candidate restored dimension of the candidate restored spectra from that iteration is taken as the target spectral dimension. Here, n, d, and k are all positive integers. .

[0252] Optionally, the target spectral dimension determination module is specifically used to, when traversing from low to high dimensions, if the restoration accuracy of the reference restored spectrum is not less than a preset restoration accuracy and the restoration accuracy of the restored spectrum of the next lower dimension of the reference restored spectrum is less than the preset restoration accuracy, then the d-dimensional dimension is taken as the target spectral dimension; if the restoration accuracy of the reference restored spectrum is less than the preset restoration accuracy, then the following steps are iteratively executed: each iteration determines the iteration step size k, and determines the k-dimensional restoration matrix of the k-dimensional restoration of the candidate restored spectrum located at the tail of the candidate restoration dimension in each round; for the first iteration, the sum of the reference restored spectrum and the k-dimensional restoration matrix is ​​taken as ( The process involves several iterations: 1) reconstructing candidate spectra; 2) for non-first iterations, summing the candidate reconstructed spectra from the previous iteration and the k-dimensional reconstructed matrix determined in the current iteration as the candidate reconstructed spectrum for that iteration; 3) if the reconstructed accuracy of any candidate reconstructed spectrum is not less than the preset reconstructed accuracy and the reconstructed accuracy of the next lower dimension of the candidate reconstructed spectrum is less than the preset reconstructed accuracy, then the iteration stops, and the candidate reconstructed dimension of the candidate reconstructed spectrum from that iteration is taken as the target spectral dimension; where... .

[0253] Optionally, the formula used to determine the reference restored spectrum is:

[0254]

[0255] in, Let m be the data matrix of the reference restored spectrum, where m is the sample size and n is the first spectral dimension. This is the centered data matrix of the first theoretical spectrum; Let be the d-dimensional principal component loading matrix of the first theoretical spectrum. for Transpose of; This is the mean data matrix of the first theoretical spectrum;

[0256] Sure The formula used for the k-dimensional restoration matrix of the candidate restored spectrum is:

[0257]

[0258] in, Candidate restoration dimensions based on candidate restored spectra k-dimensional reconstruction of the tail The k-dimensional restoration matrix is ​​used as the k-dimensional restoration matrix; Candidate restoration dimension of the candidate restored spectrum The principal component loading matrix composed of k dimensions at the tail, for Transpose of;

[0259] The formula used to obtain the candidate restored spectrum based on (d+k)-dimensional component restoration by summing the reference restored spectrum and the k-dimensional restored matrix obtained based on k-dimensional component restoration is as follows:

[0260]

[0261] in, The data matrix of candidate restored spectra obtained by restoring (d+k)-dimensional components.

[0262] Optionally, the target spectral dimension determination module is specifically used to iteratively execute the following steps when traversing in a direction from high to low dimension: determining the iteration step size k in each iteration, and determining the k-dimensional restoration matrix of the k-dimensional restoration of the candidate restored spectrum from the previous round, located at the tail of the candidate restored dimension; for the first iteration, using the difference between the baseline restored spectrum and the k-dimensional restoration matrix as ( The process involves several iterations: 1) reconstructing candidate spectra in k-dimensional space; 2) for non-first iterations, using the difference between the candidate reconstructed spectrum determined in the previous iteration and the k-dimensional reconstructed matrix determined in the current iteration as the candidate reconstructed spectrum for the current iteration; 3) stopping the iteration if the reconstructed accuracy of any candidate reconstructed spectrum is not less than a preset reconstructed accuracy and the reconstructed accuracy of the next lower dimension of the candidate reconstructed spectrum is less than the preset reconstructed accuracy, and using the candidate reconstructed dimension of the candidate reconstructed spectrum in that iteration as the target spectral dimension; where... .

[0263] Figure 11 This is a block diagram illustrating a training apparatus for a spectral calculation model according to an exemplary embodiment of this specification. Figure 11 As shown, this device can be applied to, for example Figure 9 The electronic device 900 shown implements the technical solution of this specification. The device includes:

[0264] The second training dataset acquisition module 1102 is used to acquire a training dataset, wherein each training sample in the training dataset includes a set of structural parameters for describing the grating structure and a first theoretical spectrum of the first spectral dimension.

[0265] The second predicted spectrum output module 1104 is used to input the structural parameters into the spectral calculation model to output the predicted spectrum of the target spectral dimension; wherein the first spectral dimension is greater than the target spectral dimension.

[0266] The second loss value calculation module 1106 is used to calculate the loss value between the predicted spectrum and the second theoretical spectrum of the target spectral dimension; wherein the second theoretical spectrum is obtained by dimensionality reduction of the first theoretical spectrum, and the loss value is used to train the spectral calculation model.

[0267] The second correction evaluation index calculation module 1108 is used to multiply the loss value by the correction factor to obtain the correction evaluation index, which is used to evaluate the performance of the spectral calculation model; wherein the correction factor is the ratio of the target spectral dimension to the first spectral dimension.

[0268] The model parameter training module 1110 is used to train the spectral calculation model based on the loss value if the correction evaluation index does not meet the preset performance conditions; and to stop training the spectral calculation model if the conditions are met.

[0269] Figure 12 This is a block diagram illustrating a structural parameter measuring device according to an exemplary embodiment of this specification. Figure 12 As shown, this device can be applied to, for example Figure 9 The electronic device 900 shown implements the technical solution of this specification. The device includes:

[0270] The structural parameter acquisition module 1202 is used to acquire all structural parameters generated from the structural model of the sample to be tested.

[0271] The predictive spectrum module 1204 is used to input the structural parameters into the spectral calculation model to output the predicted spectrum corresponding to each structural parameter.

[0272] The measurement spectrum acquisition module 1206 is used to acquire the measurement spectrum obtained by measuring the sample to be tested.

[0273] The sample structure measurement module 1208 is used to match the measured spectrum with each predicted spectrum to screen out the target predicted spectrum that meets the matching conditions, and use the target structural parameter corresponding to the target predicted spectrum as the measured value of the actual structural parameter of the sample to be tested.

[0274] The specific implementation process of the functions and roles of each module in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0275] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The modules described as separate components may or may not be physically separate, and the components shown as modules may or may not be physical modules, that is, they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the purpose of the solution in this specification according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0276] This specification also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any of the aforementioned methods provided in this application.

[0277] Specifically, computer-readable media suitable for storing computer program instructions and data include all forms of non-volatile memory, media, and memory devices, such as semiconductor memory devices (e.g., EPROM, EEPROM, and flash memory devices), magnetic disks (e.g., internal hard disks or removable disks), magneto-optical disks, and CD-ROM and DVD-ROM disks.

[0278] This specification also provides a computer program product, including a computer program / instructions that, when executed by a processor, implement the steps of any of the aforementioned methods.

Claims

1. A model evaluation method, characterized in that, The method includes: Obtain a training dataset, wherein each training sample in the training dataset includes a set of structural parameters describing the grating structure and a first theoretical spectrum of the first spectral dimension; The structural parameters are input into the spectral calculation model to output a predicted spectrum of the target spectral dimension; wherein, the first spectral dimension is greater than the target spectral dimension; Calculate the loss value between the predicted spectrum and the second theoretical spectrum of the target spectral dimension; wherein the second theoretical spectrum is obtained by dimensionality reduction of the first theoretical spectrum, and the loss value is used to train the spectral calculation model; The correction evaluation index is obtained by multiplying the loss value by the correction factor. The correction evaluation index is the error between the first theoretical spectrum and the predicted spectrum of the first spectral dimension. The predicted spectrum of the first spectral dimension is obtained by reconstructing the predicted spectrum of the target spectral dimension. The correction evaluation index is used to evaluate the performance of the spectral calculation model. The correction factor is the ratio of the target spectral dimension to the first spectral dimension.

2. The method according to claim 1, characterized in that, The method further includes: The first theoretical spectrum is reduced to the second theoretical spectrum using the aforementioned spectral calculation model; or... The first theoretical spectrum is dimensionality-reduced using principal component analysis to obtain the second theoretical spectrum.

3. The method according to claim 1, characterized in that, The method further includes determining the target spectral dimension after the dimensionality reduction of the first theoretical spectrum, specifically including: The first theoretical spectrum of the first spectral dimension is subjected to dimensionality reduction and restoration processing to obtain the d-dimensional restored reference spectrum; the value of the first spectral dimension is n; If the restoration accuracy of the reference restored spectrum meets the first preset restoration accuracy condition, then the d dimension is taken as the target spectral dimension. If the condition is not met, then iteratively execute the following steps: In each iteration, the iteration step size k is determined, and the k-dimensional restoration matrix of the k-dimensional restoration of the candidate restored spectrum located at the tail of the candidate restored dimension is determined; the k-dimensional dimension and the iteration step size k have the same value and are both k. For the first iteration, the k-dimensional restoration matrix is ​​determined based on the reference restored spectrum and the k-dimensional restoration matrix. Candidate restored spectra for 3D restoration; For iterations other than the first one, the candidate restored spectra for the current round are determined based on the candidate restored spectra determined in the previous round and the k-dimensional restored matrix determined in the current round. If the candidate restored spectrum in any round meets the second preset restoration accuracy condition, the iteration stops, and the candidate restoration dimension of the candidate restored spectrum in any round is taken as the target spectral dimension. Where n, d, and k are all positive integers, and .

4. The method according to claim 3, characterized in that, If the restoration accuracy of the reference restored spectrum meets the first preset restoration accuracy condition, then the d-dimensional dimension is taken as the target spectral dimension; if the restoration accuracy of the reference restored spectrum does not meet the first preset restoration accuracy condition, and the traversal is performed in the direction from low to high dimension, then the following steps are executed iteratively: In each iteration, the iteration step size k is determined, and the k-dimensional restoration matrix of the k-dimensional restoration located at the tail of the candidate restoration dimension is determined for each round. For the first iteration, the sum of the baseline restored spectrum and the k-dimensional restored matrix is ​​used as ( Candidate restored spectra for 3D restoration; For iterations other than the first round, the sum of the candidate restored spectra determined in the previous round and the k-dimensional restored matrix determined in this round is used as the candidate restored spectra for this round. If the candidate restored spectrum in any round meets the second preset restoration accuracy condition, the iteration stops, and the candidate restoration dimension of the candidate restored spectrum in any round is taken as the target spectral dimension. in, ; exist In the case of the first preset restoration accuracy condition and the second preset restoration accuracy condition, the restoration accuracy of the current round's restored spectrum is not less than the preset restoration accuracy, and the restoration accuracy of the lower dimension of the current round's restored spectrum is less than the preset restoration accuracy.

5. The method according to claim 4, characterized in that, The formula used to determine the reference restored spectrum is: in, Let m be the data matrix of the reference restored spectrum, where m is the sample size and n is the first spectral dimension. This is the centered data matrix of the first theoretical spectrum; Let be the d-dimensional principal component loading matrix of the first theoretical spectrum. for Transpose of; This is the mean data matrix of the first theoretical spectrum; Sure The formula used for the k-dimensional restoration matrix of the candidate restored spectrum is: in, Candidate restoration dimensions based on candidate restored spectra k-dimensional reconstruction of the tail The k-dimensional restoration matrix is ​​used as the k-dimensional restoration matrix; Candidate restoration dimension of the candidate restored spectrum The principal component loading matrix composed of k dimensions at the tail, for Transpose of; The formula used to obtain the candidate restored spectrum based on (d+k)-dimensional component restoration by summing the reference restored spectrum and the k-dimensional restored matrix obtained based on k-dimensional component restoration is as follows: in, This is the data matrix of candidate restored spectra obtained based on (d+k) dimensional component restoration.

6. The method according to claim 3, characterized in that, When traversing from high to low dimension, the following steps are performed iteratively: In each iteration, the iteration step size k is determined, and the k-dimensional restoration matrix of the k-dimensional restoration of the candidate restoration spectrum in the previous round is determined. For the first iteration, the difference between the baseline restored spectrum and the k-dimensional restored matrix is ​​taken as ( Candidate restored spectra for 3D restoration; For iterations other than the first one, the difference between the candidate restored spectrum determined in the previous round and the k-dimensional restored matrix determined in this round is used as the candidate restored spectrum for this round. If the candidate restored spectrum in any round meets the second preset restoration accuracy condition, the iteration stops, and the candidate restoration dimension of the candidate restored spectrum in any round is taken as the target spectral dimension. The second preset restoration accuracy condition is that the restoration accuracy of the candidate restored spectrum in any round is not less than the preset restoration accuracy and the restoration accuracy of the restored spectrum in the lower dimension of the candidate restored spectrum is less than the preset restoration accuracy. .

7. A training method for a spectral calculation model, characterized in that, The method includes: Obtain a training dataset, wherein each training sample in the training dataset includes a set of structural parameters describing the grating structure and a first theoretical spectrum of the first spectral dimension; The structural parameters are input into the spectral calculation model to output a predicted spectrum of the target spectral dimension; wherein, the first spectral dimension is greater than the target spectral dimension; Calculate the loss value between the predicted spectrum and the second theoretical spectrum of the target spectral dimension; wherein the second theoretical spectrum is obtained by dimensionality reduction of the first theoretical spectrum; The correction evaluation index is obtained by multiplying the loss value by the correction factor; wherein the correction factor is the ratio of the target spectral dimension to the first spectral dimension; the correction evaluation index is the error between the first theoretical spectrum and the predicted spectrum of the first spectral dimension, and the predicted spectrum of the first spectral dimension is obtained by restoring the predicted spectrum of the target spectral dimension. If the correction evaluation index does not meet the preset performance conditions, then the spectral calculation model is trained based on the loss value; if it does meet the conditions, then the training of the spectral calculation model is stopped.

8. A method for measuring structural parameters, characterized in that, The method includes: Obtain all structural parameters generated from the structural model of the sample to be tested; The structural parameters are respectively input into the spectral calculation model trained as described in claim 7 to output the predicted spectrum corresponding to each structural parameter; Obtain the measurement spectrum obtained from the sample to be tested; The measured spectra are matched with each predicted spectrum to select target predicted spectra that meet the matching conditions, and the target structural parameters corresponding to the target predicted spectra are used as the measured values ​​of the actual structural parameters of the sample to be tested.

9. The method according to claim 8, characterized in that, The step of matching the measured spectrum with each predicted spectrum includes: Determine the difference k between the dimension of the measured spectrum and the dimension of the predicted spectrum, and determine the k-dimensional restoration matrix of the measured spectrum located at the tail of the dimension; the dimension of each predicted spectrum is smaller than the dimension of the measured spectrum; k is a positive integer; Based on the k-dimensional restoration matrix, each predicted spectrum is upscaled to the same dimension as the measured spectrum; The measured spectra are matched with the predicted spectra after each dimensionality increase.

10. A model evaluation device, characterized in that, The device includes: The first training dataset acquisition module is used to acquire a training dataset, wherein each training sample in the training dataset includes a set of structural parameters for describing the grating structure and a first theoretical spectrum of the first spectral dimension. The first predicted spectrum output module is used to input the structural parameters into the spectral calculation model to output a predicted spectrum of the target spectral dimension; wherein the first spectral dimension is greater than the target spectral dimension; The first loss value calculation module is used to calculate the loss value between the predicted spectrum and the second theoretical spectrum of the target spectral dimension; wherein the second theoretical spectrum is obtained by dimensionality reduction of the first theoretical spectrum, and the loss value is used to train the spectral calculation model; The first correction evaluation index calculation module is used to multiply the loss value by a correction factor to obtain a correction evaluation index. The correction evaluation index is the error between the first theoretical spectrum and the predicted spectrum of the first spectral dimension. The predicted spectrum of the first spectral dimension is obtained by reconstructing the predicted spectrum of the target spectral dimension. The correction evaluation index is used to evaluate the performance of the spectral calculation model. The correction factor is the ratio of the target spectral dimension to the first spectral dimension.

11. A training device for a spectral calculation model, characterized in that, The device includes: The second training dataset acquisition module is used to acquire a training dataset, wherein each training sample in the training dataset includes a set of structural parameters for describing the grating structure and a first theoretical spectrum of the first spectral dimension. The second predicted spectrum output module is used to input the structural parameters into the spectral calculation model to output a predicted spectrum of the target spectral dimension; wherein, the first spectral dimension is greater than the target spectral dimension; The second loss value calculation module is used to calculate the loss value between the predicted spectrum and the second theoretical spectrum of the target spectral dimension; wherein the second theoretical spectrum is obtained by dimensionality reduction of the first theoretical spectrum; The second correction evaluation index calculation module is used to multiply the loss value by the correction factor to obtain the correction evaluation index; wherein, the correction factor is the ratio of the target spectral dimension to the first spectral dimension, the correction evaluation index is the error between the first theoretical spectrum and the predicted spectrum of the first spectral dimension, and the predicted spectrum of the first spectral dimension is obtained by restoring the predicted spectrum of the target spectral dimension. The model parameter training module is used to train the spectral calculation model based on the loss value if the correction evaluation index does not meet the preset performance conditions; otherwise, the training of the spectral calculation model is stopped.

12. A device for measuring structural parameters, characterized in that, The device includes: The structural parameter acquisition module is used to acquire all structural parameters generated from the structural model of the sample under test. The predictive spectrum module is used to input the structural parameters into the spectral calculation model trained as described in claim 7 to output the predicted spectrum corresponding to each structural parameter. The measurement spectrum acquisition module is used to acquire the measurement spectrum obtained by measuring the sample to be tested; The sample structure measurement module is used to match the measured spectrum with each predicted spectrum to filter out the target predicted spectrum that meets the matching conditions, and use the target structural parameters corresponding to the target predicted spectrum as the measured values ​​of the actual structural parameters of the sample to be tested.

13. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1-9.

14. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by a processor, it implements the steps of the method as described in any one of claims 1-9.

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