A Measurement Equipment Adjustment Method and System Based on RCWA Algorithm Optimization

Abstract

This invention proposes a measurement equipment adjustment method and system based on the RCWA algorithm optimization. Based on a preset structure to be measured, a reference spectrum and several orders of electric fields are obtained. Based on the electric fields of these orders, an order importance ranking is obtained. Based on the order importance ranking, an approximate spectrum is obtained. Based on the reference spectrum, the order ratio of the approximate spectrum is adjusted to obtain an order selection result. Based on the order selection result and a preset RCWA algorithm, an optimized RCWA algorithm is obtained to adjust the measurement equipment parameters. This invention considers the order importance and flexibly adjusts the Fourier expansion order selection in the RCWA algorithm to adjust the equipment measurement parameters and improve the reliability of the measurement results.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic simulation, and in particular to a measurement equipment adjustment method and system based on RCWA algorithm optimization. Background Technology

[0002] Rigorous Coupled Wave Analysis (RCWA) is a numerical method in computational electromagnetics, suitable for solving light wave scattering problems in periodic dielectric structures. Its main process is to represent the dielectric constant distribution and electromagnetic field as a superposition of spatial harmonics through Fourier expansion. The order of the Fourier expansion is used to capture the characteristics of the dielectric constant distribution. After integrating the RCWA algorithm into the measurement equipment, the measurement equipment can be adjusted.

[0003] Currently, existing technologies typically employ fixed or empirically-based order selection. When dealing with complex periodic media structures, this method offers limited options for order selection and is computationally complex with poor adaptability. Other existing technologies utilize computation in compressed Fourier space, iteratively increasing or decreasing the order. Each iteration requires a complete RCWA calculation. However, when measuring devices encounter complex periodic media structures, the limited order selection leads to unreliable measurement results. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a measurement equipment adjustment method and system based on RCWA algorithm optimization. This method considers the importance of the order and flexibly adjusts the selection of the Fourier expansion order in the RCWA algorithm to adjust the equipment measurement parameters and improve the reliability of the equipment measurement results.

[0005] To achieve the above objectives, embodiments of the present invention provide a measurement device adjustment method based on RCWA algorithm optimization, comprising: obtaining a reference spectrum and several orders of electric fields based on a preset structure to be measured; obtaining an order importance ranking based on the several orders of electric fields; obtaining an approximate spectrum based on the order importance ranking; adjusting the order ratio of the approximate spectrum based on the reference spectrum to obtain an order selection result; and obtaining an optimized RCWA algorithm based on the order selection result and a preset RCWA algorithm to adjust the parameters of the measurement device.

[0006] This invention proposes a measurement equipment adjustment method based on RCWA algorithm optimization. The method analyzes a preset structure to be measured to obtain a reference spectrum and several orders of electric fields. The importance of these orders of electric fields is ranked, and an approximate spectrum of the preset structure is calculated based on this ranking. The order selection result is then obtained by analyzing the reference spectrum and the approximate spectrum, thereby optimizing the RCWA algorithm to adjust the measurement equipment parameters. By considering the order importance of several orders of electric fields on the preset structure to be measured, an approximate spectrum of the preset structure is obtained. Combined with the reference spectrum of the preset structure, the order ratio of the approximate spectrum is adjusted to obtain the order selection result. Based on the order selection result, the order selection of the RCWA algorithm is flexibly adjusted, thereby optimizing the RCWA algorithm to adjust the measurement equipment parameters and improve the reliability of the measurement results.

[0007] Furthermore, the step of obtaining a reference spectrum and several orders of electric fields based on a preset structure to be measured includes: calculating the overall spectrum of the preset structure to be measured until the overall spectrum meets a preset accuracy requirement, based on the preset structure to be measured and a preset order ratio, to obtain a reference spectrum; performing a Fourier expansion on the dielectric constant of each layer of the preset structure to be measured to obtain several orders of electric displacement vectors; and obtaining several orders of electric fields based on the several orders of electric displacement vectors and a preset approximation relationship algorithm.

[0008] The above scheme calculates the overall spectrum of the pre-defined structure to be measured at a pre-defined order ratio, ensuring the overall spectrum meets the pre-defined accuracy requirements and obtaining a reference spectrum. Then, Fourier expansion analysis is performed on the dielectric constant of each layer of the pre-defined structure to be measured. The Fourier expansion matrix can characterize the relationship between several orders of electric displacement vectors and several orders of electric fields. Based on a pre-defined approximation algorithm, approximate relationships between several orders of electric displacement vectors and several orders of electric fields are obtained, yielding several orders of electric fields. Thus, by accurately obtaining the reference spectrum of the measured structure, reliable reference values ​​are provided for subsequent optimization of the RCWA algorithm. Furthermore, obtaining approximate relationships between several orders of electric displacement vectors and several orders of electric fields for the dielectric constant of each layer of the measured structure provides an accurate data foundation for subsequent order importance ranking, thereby improving the reliability of the RCWA algorithm optimization, enhancing the reliability of parameter adjustments for the measurement equipment, and ultimately improving the reliability of the equipment measurement results.

[0009] Furthermore, the step of obtaining the order importance ranking based on the electric fields of several orders includes: obtaining order importance results based on the electric fields of several orders and a preset order electric field; obtaining the order importance ranking of each direction of the incident light based on the order importance results and a preset incident light direction weighting algorithm; obtaining the order importance ranking of each layer structure based on the order importance results and a preset multilayer structure weighting algorithm; obtaining the order importance ranking of each wavelength based on the order importance results and a preset multiwavelength weighting algorithm; and obtaining the order importance ranking based on the order importance ranking of each direction of the incident light, the order importance ranking of each layer structure, and the order importance ranking of each wavelength.

[0010] The above scheme analyzes the importance of electric field orders of several orders to determine the contribution of electric fields of different orders. Then, by considering factors such as incident light direction, multilayer structure, and multiwavelength, the importance of orders is ranked to achieve dynamic evaluation of order importance. This provides a reliable data foundation for flexibly adjusting the Fourier expansion order selection in the RCWA algorithm, improving the reliability of RCWA algorithm optimization, thereby improving the reliability of adjusting measurement equipment parameters, and ultimately improving the reliability of equipment measurement results.

[0011] Furthermore, based on the order importance results and the preset incident light direction weighting algorithm, the order importance ranking of each direction of the incident light is obtained, including: decomposing the order importance results into each direction of the incident light to obtain the order importance results of each direction; weighting the order importance results of each direction based on the preset incident light direction weighting algorithm to obtain the order weighted importance results of each direction; and obtaining the order importance ranking of each direction of the incident light based on the order weighted importance results of each direction.

[0012] Based on the order importance results described above, an incident light weighting mechanism is introduced to consider and rank the order importance of the incident light in each direction, optimize the order selection in different directions, and achieve dynamic evaluation of order importance. This provides a reliable data foundation for flexibly adjusting the Fourier expansion order selection in the RCWA algorithm, improves the reliability of RCWA algorithm optimization, enhances the reliability of adjusting measurement equipment parameters, and ultimately improves the reliability of equipment measurement results.

[0013] Furthermore, based on the order importance results and the preset multi-layer structure weighting algorithm, the order importance ranking of each layer structure is obtained, including: obtaining the order importance results of each layer structure based on the order importance results; weighting the order importance results of each layer structure based on the preset multi-layer structure weighting algorithm to obtain the weighted order importance results of each layer structure; and obtaining the order importance ranking of each layer structure based on the weighted order importance results of each layer structure.

[0014] Based on the order importance results described above, a multi-layer structure weighting mechanism is introduced to consider and rank the order importance of each layer in the multi-layer structure. This optimizes the order selection of different layers, enabling dynamic evaluation of order importance. This provides a reliable data foundation for flexibly adjusting the Fourier expansion order selection in the RCWA algorithm, improving the reliability of RCWA algorithm optimization, thereby enhancing the reliability of adjusting measurement equipment parameters and ultimately improving the reliability of equipment measurement results.

[0015] Furthermore, based on the order importance results and the preset multi-wavelength weighting algorithm, the importance ranking of each wavelength order is obtained, including: obtaining the importance results of each wavelength order based on the order importance results; weighting the importance results of each wavelength order based on the preset multi-wavelength weighting algorithm to obtain the weighted importance results of each wavelength order; and obtaining the importance ranking of each wavelength order based on the weighted importance results of each wavelength order.

[0016] Based on the above scheme, a multi-wavelength weighting mechanism is introduced to consider and rank the importance of each wavelength order, optimize the order selection under different wavelengths, realize dynamic evaluation of order importance, provide a reliable data foundation for flexibly adjusting the Fourier expansion order selection in the RCWA algorithm, improve the reliability of RCWA algorithm optimization, improve the reliability of adjusting measurement equipment parameters, and ultimately improve the reliability of equipment measurement results.

[0017] Furthermore, the step of obtaining an approximate spectrum based on the order importance ranking includes: based on the order importance ranking, removing order importance results that do not meet the preset contribution requirements by a preset proportion to obtain the remaining order importance results; and based on the remaining order importance results, calculating the spectral data of the remaining orders to obtain the approximate spectrum.

[0018] The above scheme sorts the orders by importance, retains only the order importance results that meet the preset contribution requirements, and calculates the spectral data of the remaining orders to obtain approximate spectra. Only the orders with high contribution are retained, so that the approximate spectra represent the set of orders with high contribution. Orders that do not meet the contribution requirements are eliminated, which can reduce unnecessary calculations and provide a reliable data foundation for flexibly adjusting the Fourier expansion order selection in the RCWA algorithm. This improves the reliability of RCWA algorithm optimization, thereby improving the reliability of adjusting the parameters of the measurement equipment, and ultimately improving the reliability of the equipment measurement results.

[0019] Furthermore, based on the reference spectrum, the approximate spectral order ratio is adjusted to obtain the order selection result, including: calculating the root mean square error of the spectrum based on the reference spectrum and the approximate spectrum; if the root mean square error of the spectrum does not meet the preset error tolerance threshold, the approximate spectral order ratio is adjusted until the preset error tolerance threshold is met to obtain the order selection result.

[0020] The above scheme calculates the root mean square error of the spectrum to analyze the error tolerance between the approximate spectrum and the reference spectrum, and judges the reliability of the order selection of the approximate spectrum. After meeting the preset error tolerance threshold, the order selection of the approximate spectrum provides a reliable data basis for the subsequent flexible adjustment of the Fourier expansion order selection in the RCWA algorithm, thereby improving the reliability of RCWA algorithm optimization, improving the reliability of the adjustment of measurement equipment parameters, and ultimately improving the reliability of equipment measurement results.

[0021] Furthermore, based on the order selection result and the preset RCWA algorithm, an optimized RCWA algorithm is obtained to adjust the measurement equipment parameters, including: adjusting the Fourier expansion order selection parameter of the preset RCWA algorithm based on the order selection result to obtain the optimized RCWA algorithm; and adjusting the measurement equipment parameters based on the optimized RCWA algorithm.

[0022] The above scheme adjusts the Fourier expansion order selection parameter of the RCWA algorithm by obtaining reliable order selection results, optimizes the data processing process of the RCWA algorithm, and can flexibly adjust the Fourier expansion order selection in the RCWA algorithm under different structures and working conditions, so as to improve the reliability of the adjustment of measurement equipment parameters and ultimately improve the reliability of equipment measurement results.

[0023] This invention also provides a measurement equipment adjustment system based on the RCWA algorithm optimization, comprising: a target structure analysis module, an order importance ranking module, an approximate spectrum acquisition module, an order selection result acquisition module, and a measurement equipment adjustment module; the target structure analysis module is used to obtain a reference spectrum and several orders of electric fields based on a preset target structure; the order importance ranking module is used to obtain an order importance ranking based on the several orders of the electric fields; the approximate spectrum acquisition module is used to obtain an approximate spectrum based on the order importance ranking; the order selection result acquisition module is used to adjust the order ratio of the approximate spectrum based on the reference spectrum to obtain an order selection result; and the measurement equipment adjustment module is used to obtain an optimized RCWA algorithm based on the order selection result to adjust the parameters of the measurement equipment.

[0024] This invention proposes a measurement equipment adjustment system based on the RCWA algorithm optimization. A measured structure analysis module analyzes the preset measured structure to obtain a reference spectrum and several orders of electric fields. An order importance ranking module ranks the importance of these electric fields. An approximate spectrum acquisition module calculates the approximate spectrum of the preset measured structure based on the order importance ranking. An order selection result acquisition module and a measurement equipment adjustment module then analyze the reference spectrum and approximate spectrum to obtain the order selection result, thereby optimizing the RCWA algorithm to adjust the measurement equipment parameters. By considering the order importance of several orders of electric fields of the preset measured structure, an approximate spectrum of the preset measured structure is obtained. Combined with the reference spectrum of the preset measured structure, the order ratio of the approximate spectrum is adjusted to obtain the order selection result. Based on the order selection result, the order selection of the RCWA algorithm is flexibly adjusted, thereby optimizing the RCWA algorithm to adjust the measurement equipment parameters and improve the reliability of the equipment measurement results. Attached Figure Description

[0025] Figure 1 A flowchart illustrating the steps of a measurement equipment adjustment method based on the RCWA algorithm optimization provided in a certain embodiment of the present invention;

[0026] Figure 2 A schematic diagram of a classic checkerboard dual-cycle grating for a measurement device adjustment method based on the RCWA algorithm optimization provided in a certain embodiment of the present invention;

[0027] Figure 3 A schematic diagram of NCS spectra at different order ratios for a measurement device adjustment method based on the RCWA algorithm optimized according to a certain embodiment of the present invention. Figure 1 ;

[0028] Figure 4 A schematic diagram of NCS spectra at different order ratios for a measurement device adjustment method based on the RCWA algorithm optimized according to a certain embodiment of the present invention. Figure 2 ;

[0029] Figure 5 A schematic diagram of NCS spectra at different order ratios for a measurement device adjustment method based on the RCWA algorithm optimized according to a certain embodiment of the present invention. Figure 3 ;

[0030] Figure 6 A schematic diagram illustrating the retention of different proportions of residual order in a measurement device adjustment method based on the RCWA algorithm optimization provided in a certain embodiment of the present invention. Figure 1 ;

[0031] Figure 7 A schematic diagram illustrating the retention of different proportions of residual order in a measurement device adjustment method based on the RCWA algorithm optimization provided in a certain embodiment of the present invention. Figure 2 ;

[0032] Figure 8 A schematic diagram illustrating the retention of different proportions of residual order in a measurement device adjustment method based on the RCWA algorithm optimization provided in a certain embodiment of the present invention. Figure 3 ;

[0033] Figure 9 A schematic diagram illustrating the retention of different proportions of residual order in a measurement device adjustment method based on the RCWA algorithm optimization provided in a certain embodiment of the present invention. Figure 4 ;

[0034] Figure 10 A schematic diagram comparing the computation time before and after RCWA algorithm optimization in a measurement equipment adjustment method based on RCWA algorithm optimization according to a certain embodiment of the present invention;

[0035] Figure 11 This is a schematic diagram of the module structure of a measurement equipment adjustment system based on the RCWA algorithm optimization, provided in a certain embodiment of the present invention. Detailed Implementation

[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] Example 1

[0038] See Figure 1 , Figure 1 This is a flowchart illustrating the steps of a measurement device adjustment method optimized based on the RCWA algorithm, provided in one embodiment of the present invention. Figure 1 As shown, an embodiment of the present invention proposes a method including steps 101 to 105, the specific steps of which are as follows:

[0039] Step 101: Based on the preset structure to be measured, obtain the reference spectrum and several orders of electric fields;

[0040] Step 102: Based on the electric fields of several orders, obtain the order importance ranking;

[0041] Step 103: Based on the importance of the order, an approximate spectrum is obtained;

[0042] Step 104: Based on the reference spectrum, adjust the approximate spectral order ratio to obtain the order selection result;

[0043] Step 105: Based on the order selection result and the preset RCWA algorithm, an optimized RCWA algorithm is obtained to adjust the parameters of the measurement equipment.

[0044] One possible implementation method is described in [link to implementation details]. Figure 2 , Figure 2 A schematic diagram of a classic checkerboard dual-period grating for a measurement device adjustment method optimized based on the RCWA algorithm, provided in a certain embodiment of the present invention; as shown. Figure 2 As shown, for the preset structure to be measured, the following method is used: Figure 2 Using the classic checkerboard dual-period grating as an example, a sufficiently large order is selected, such as -10 to 10 in the x-direction and -10 to 10 in the y-direction. The spectrum of the preset measurement structure is calculated, and the dielectric constant of each layer of the preset measurement structure is analyzed to obtain several orders of electric fields. By confirming the importance of each order of electric field, they are sorted according to their importance to obtain the order importance ranking. Based on the order importance ranking, the truncated approximate spectrum can be calculated. By comparing the spectral values ​​of the reference spectrum and the spectral values ​​of the approximate spectrum, the order ratio of the approximate spectrum is dynamically adjusted to obtain the order selection result. Finally, the order selection result is recorded in the preset RCWA algorithm, and the preset RCWA algorithm is optimized and integrated into the measurement equipment to adjust the parameters of the measurement equipment.

[0045] This invention proposes a measurement equipment adjustment method based on RCWA algorithm optimization. The method analyzes a preset structure to be measured to obtain a reference spectrum and several orders of electric fields. The importance of these orders of electric fields is ranked, and an approximate spectrum of the preset structure is calculated based on this ranking. The order selection result is then obtained by analyzing the reference spectrum and the approximate spectrum, thereby optimizing the RCWA algorithm to adjust the measurement equipment parameters. By considering the order importance of several orders of electric fields on the preset structure to be measured, an approximate spectrum of the preset structure is obtained. Combined with the reference spectrum of the preset structure, the order ratio of the approximate spectrum is adjusted to obtain the order selection result. Based on the order selection result, the order selection of the RCWA algorithm is flexibly adjusted, thereby optimizing the RCWA algorithm to adjust the measurement equipment parameters and improve the reliability of the measurement results.

[0046] As an example of this embodiment, step 101 includes: calculating the overall spectrum of the preset structure to be measured based on a preset structure to be measured and a preset order ratio until the overall spectrum meets a preset accuracy requirement, thereby obtaining a reference spectrum; performing a Fourier expansion on the dielectric constant of each layer of the preset structure to be measured to obtain several orders of electric displacement vectors; and obtaining several orders of electric fields based on the several orders of electric displacement vectors and a preset approximation relationship algorithm.

[0047] One possible implementation method is described in [link to implementation details]. Figure 2 , Figure 2 A schematic diagram of a classic checkerboard dual-period grating for a measurement device adjustment method optimized based on the RCWA algorithm, provided in a certain embodiment of the present invention; as shown. Figure 2 As shown, for the preset structure to be measured, the following method is used: Figure 2 Using the classic checkerboard dual-period grating shown as an example, a sufficiently large order is selected, such as -10 to 10 in the x-direction and -10 to 10 in the y-direction. The overall spectrum of the preset structure to be measured is calculated until the overall spectrum converges. At this point, the overall spectrum can characterize the spectrum that meets the accuracy requirements, i.e., the reference spectrum. See [link to documentation] for details. Figure 3 , Figure 4 and Figure 5 , Figure 3 A schematic diagram of NCS spectra at different order ratios for a measurement device adjustment method based on the RCWA algorithm optimized according to a certain embodiment of the present invention. Figure 1 ; Figure 4 A schematic diagram of NCS spectra at different order ratios for a measurement device adjustment method based on the RCWA algorithm optimized according to a certain embodiment of the present invention. Figure 2 ; Figure 5 A schematic diagram of NCS spectra at different order ratios for a measurement device adjustment method based on the RCWA algorithm optimized according to a certain embodiment of the present invention. Figure 3 ;like Figure 3 , Figure 4 and Figure 5 As shown, the NCS spectra with 100% order retention in different dimensions (NSpectrum, CSpectrum, and SSpectrum) are used as the reference spectra; the calculated reference spectral data are stored as follows:

[0048] R exact ={R exact (λ1), R exact (λ2), …, R exact (λ P )};

[0049] In the formula, λ P These are different incident light wavelengths, and P is the total number of wavelength sampling points;

[0050] Then, a Fourier expansion is performed on the dielectric constant of each layer of the structure to be measured to obtain several orders of electric displacement vectors. A pre-defined approximation algorithm is then used to obtain several orders of electric fields. Specifically, in the RCWA algorithm, the Fourier expansion matrix of the dielectric constant of each layer can be used to describe the relationship between the electric displacement vector and the electric field. The specific formula is as follows:

[0051]

[0052] Here, we assume that the expansion orders in the x and y directions are from -M to M and from -N to N, respectively, D(m,n) represents the electric displacement vector of order (m,n), E(j,k) represents the electric field of order (j,k), and ε m-j,n-k These are elements in the dielectric constant matrix;

[0053] To simplify the relationship between the electric displacement vector and the electric field, a next-level approximation can be used, as follows:

[0054]

[0055] Alternatively, a second-order approximation relationship can be established, as follows:

[0056]

[0057] Here, f and g are functions with elements in the dielectric constant matrix as independent variables; by approximating the electric displacement vector and the Fourier coefficients of the electric field of each layer, several orders of electric fields are obtained, denoted as E(m,n).

[0058] The above scheme calculates the overall spectrum of the pre-defined structure to be measured at a pre-defined order ratio, ensuring the overall spectrum meets the pre-defined accuracy requirements and obtaining a reference spectrum. Then, Fourier expansion analysis is performed on the dielectric constant of each layer of the pre-defined structure to be measured. The Fourier expansion matrix can characterize the relationship between several orders of electric displacement vectors and several orders of electric fields. Based on a pre-defined approximation algorithm, approximate relationships between several orders of electric displacement vectors and several orders of electric fields are obtained, yielding several orders of electric fields. Thus, by accurately obtaining the reference spectrum of the measured structure, reliable reference values ​​are provided for subsequent optimization of the RCWA algorithm. Furthermore, obtaining approximate relationships between several orders of electric displacement vectors and several orders of electric fields for the dielectric constant of each layer of the measured structure provides an accurate data foundation for subsequent order importance ranking, thereby improving the reliability of the RCWA algorithm optimization, enhancing the reliability of parameter adjustments for the measurement equipment, and ultimately improving the reliability of the equipment measurement results.

[0059] As an example of an embodiment of the present invention, step 102 includes: obtaining order importance results based on the electric field of several orders and a preset order electric field; obtaining the order importance ranking of each direction of the incident light based on the order importance results and a preset incident light direction weighting algorithm; obtaining the order importance ranking of each layer structure based on the order importance results and a preset multilayer structure weighting algorithm; obtaining the order importance ranking of each wavelength based on the order importance results and a preset multiwavelength weighting algorithm; and obtaining the order importance ranking based on the order importance ranking of each direction of the incident light, the order importance ranking of each layer structure, and the order importance ranking of each wavelength.

[0060] In one specific implementation method, in this embodiment, to evaluate the importance of the order, the relative magnitudes of each order and the (0,0) order electric field (equivalent to a preset order electric field) can be calculated by analyzing their relationship, and the order importance result can be obtained. The specific formula is as follows:

[0061]

[0062] In the formula, E(m,n) is the electric field of order (m,n); E(0,0) is the electric field of order (0,0); and Importance(m,n) reflects the importance of this order to the calculation result.

[0063] Since the structures under test are usually relatively complex, simply calculating the importance of the order is insufficient to accurately analyze the true importance of the order. Therefore, this invention proposes a weighted approach considering the incident light direction, multilayer structure, and multiple wavelengths to analyze the importance of the order under different conditions. Specifically, for the incident light direction (represented by angles θ and φ), the direction of the incident light also affects the choice of order. After decomposing the electric field into three directions (Ex, Ey, Ez), the distribution of the electric field in each direction is combined with the incident light angle decomposition to weight the importance of the order in each direction, resulting in a ranking of the importance of the order in each direction of the incident light. For multilayer structures, the changes in the dielectric constant and geometric parameters of each layer affect the electric field contribution of different orders. The overall importance of the order is calculated by assigning different weights to different layers. Two modes are used for weight allocation for each layer: the first is the default mode, where the weight of each layer is set to... The first method is proportional to the thickness of the layer. The second method is a custom mode, where the weight of each layer can be defined by the importance of the structural parameters of that layer. A suitable weight allocation mode is selected based on the actual application to obtain the order importance ranking of each layer's structure. For multi-wavelength applications, since shorter wavelengths correspond to higher orders, the order importance of the short-wavelength calculation results is prioritized, giving higher weights to the short-wavelength calculations, while longer wavelengths are given lower weights. Weights are set according to wavelength to simulate the order importance within the simulated wavelength range, resulting in the order importance ranking of each wavelength. Finally, by integrating the order importance rankings of the incident light in each direction, the order importance rankings of each layer's structure, and the order importance rankings of each wavelength, all orders are sorted in descending order of Importance(m,n) to obtain the order importance list {(m1,n1),(m2,n2),...}, which represents the overall preset order importance ranking of the structure under test.

[0064] The above scheme analyzes the importance of electric field orders of several orders to determine the contribution of electric fields of different orders. Then, by considering factors such as incident light direction, multilayer structure, and multiwavelength, the importance of orders is ranked to achieve dynamic evaluation of order importance. This provides a reliable data foundation for flexibly adjusting the Fourier expansion order selection in the RCWA algorithm, improving the reliability of RCWA algorithm optimization, thereby improving the reliability of adjusting measurement equipment parameters, and ultimately improving the reliability of equipment measurement results.

[0065] As an example of an embodiment of the present invention, the order importance ranking of the incident light in each direction is obtained based on the order importance result and a preset incident light direction weighting algorithm, including: decomposing the order importance result into each direction of the incident light to obtain the order importance result of each direction; weighting the order importance result of each direction based on the preset incident light direction weighting algorithm to obtain the order weighted importance result of each direction; and obtaining the order importance ranking of the incident light in each direction based on the order weighted importance result of each direction.

[0066] One possible implementation involves considering the direction of the incident light. The direction of the incident light (represented by angles θ and φ) also affects the choice of order. After decomposing the electric field into three directions (Ex, Ey, Ez), the distribution of the electric field in each direction is weighted based on the incident light angle. The specific calculation formula is as follows:

[0067] Ex = E0sinθcosφ;

[0068] Ey = E0sinθsinφ;

[0069] Ez = E0cosθ;

[0070] Where E0 is the total electric field amplitude of the incident light, the preset incident light direction weighting algorithm sinθcosφ is the weighting mechanism for the x direction, sinθsinφ is the weighting mechanism for the y direction, and cosθ is the weighting mechanism for the z direction, and finally, the importance of the order of the incident light in each direction is obtained by comprehensively considering the weighting importance results of each direction.

[0071] Based on the order importance results described above, an incident light weighting mechanism is introduced to consider and rank the order importance of the incident light in each direction, optimize the order selection in different directions, and achieve dynamic evaluation of order importance. This provides a reliable data foundation for flexibly adjusting the Fourier expansion order selection in the RCWA algorithm, improves the reliability of RCWA algorithm optimization, enhances the reliability of adjusting measurement equipment parameters, and ultimately improves the reliability of equipment measurement results.

[0072] As an example of an embodiment of the present invention, the order importance ranking of each layer structure is obtained based on the order importance results and a preset multi-layer structure weighting algorithm, including: obtaining the order importance results of each layer structure based on the order importance results; weighting the order importance results of each layer structure based on the preset multi-layer structure weighting algorithm to obtain the weighted order importance results of each layer structure; and obtaining the order importance ranking of each layer structure based on the weighted order importance results of each layer structure.

[0073] One possible implementation involves a multilayer structure where variations in the dielectric constant and geometric parameters of each layer affect the electric field contribution of different orders. The overall order importance is calculated by assigning different weights to different layers. Two weighting rules are used for each layer: a default mode where the weight is proportional to the layer's thickness, and a custom mode where the weight is defined by the importance of the layer's structural parameters. The appropriate weighting mode is selected based on the specific application to obtain the order importance ranking of each layer. For example, in a given scenario, the structure under test is pre-defined as having K layers. The order importance of each layer is calculated in step 101, and the order importance of the k-th layer is denoted as Importance. k (m,n)(k=1,2,3,…,K), the weight allocation rules for the default mode are as follows:

[0074]

[0075] In the formula, the molecule d k It is the physical thickness of the k-th layer, and the denominator is the total thickness of all layers, which is used to normalize the weights (to ensure that the sum of the weights of all layers is 1);

[0076] In custom mode, the weights of each layer can be defined by the importance of the structural parameters of that layer. For example, in one scenario, the structure to be predicted is a 3-layer structure, where two parameters, CD1 and CD2, are two important parameters that need to be accurately simulated in the actual simulation process. They are located in the first and second layers, respectively. Therefore, the weights of these two layers should be relatively increased, so w1 = 0.4, w2 = 0.4, and w3 = 0.2 can be defined. After the weights of each layer are defined, the overall order importance of the structure (equivalent to the weighted importance of the order of each layer) can be determined by the following formula:

[0077]

[0078] In the formula, Importance total (m,n) represents the order importance of the entire structure; finally, the order importance of each layer is sorted according to the weighted importance of the order of each layer.

[0079] Based on the order importance results described above, a multi-layer structure weighting mechanism is introduced to consider and rank the order importance of each layer in the multi-layer structure. This optimizes the order selection of different layers, enabling dynamic evaluation of order importance. This provides a reliable data foundation for flexibly adjusting the Fourier expansion order selection in the RCWA algorithm, improving the reliability of RCWA algorithm optimization, thereby enhancing the reliability of adjusting measurement equipment parameters and ultimately improving the reliability of equipment measurement results.

[0080] As an example of an embodiment of the present invention, the importance ranking of each wavelength order is obtained based on the order importance results and a preset multi-wavelength weighting algorithm, including: obtaining the importance results of each wavelength order based on the order importance results; weighting the importance results of each wavelength order based on the preset multi-wavelength weighting algorithm to obtain the weighted importance results of each wavelength order; and obtaining the importance ranking of each wavelength order based on the weighted importance results of each wavelength order.

[0081] One possible implementation is as follows: For multiple wavelengths, since shorter wavelengths correspond to higher orders, the order importance of the calculation results for shorter wavelengths is prioritized, and higher weights are given to the orders calculated for shorter wavelengths. Longer wavelengths are given lower weights. The weights are set according to the wavelength to simulate the order importance within the wavelength range, thus obtaining a ranking of the order importance for each wavelength. Assuming that in a certain embodiment, the wavelength range used by the structure under test is preset to be λ... min ~λ max It contains λ1, λ2, ..., λ P There are a total of P discrete wavelengths. Assume that a certain wavelength λ P The importance of the order calculated in step 101 is: p Given (m,n) (p=1,2,3,……,P), the weight of this wavelength is calculated using the following formula:

[0082]

[0083] After the weights for each wavelength are defined, the specific formula for calculating the order importance of the k-th layer within the simulated band range (equivalent to the weighted importance of each wavelength order) is as follows:

[0084]

[0085] Finally, the wavelength order is ranked according to its weighted importance.

[0086] Based on the above scheme, a multi-wavelength weighting mechanism is introduced to consider and rank the importance of each wavelength order, optimize the order selection under different wavelengths, realize dynamic evaluation of order importance, provide a reliable data foundation for flexibly adjusting the Fourier expansion order selection in the RCWA algorithm, improve the reliability of RCWA algorithm optimization, improve the reliability of adjusting measurement equipment parameters, and ultimately improve the reliability of equipment measurement results.

[0087] As an example of an embodiment of the present invention, step 103 includes: based on the order importance ranking, removing order importance results that do not meet the preset contribution requirements by a preset proportion, and obtaining the remaining order importance results; based on the remaining order importance results, calculating the spectral data of the remaining orders to obtain an approximate spectrum.

[0088] One possible implementation involves processing in step 102 to obtain a ranking of order importance, progressively reducing the order, and calculating an approximate spectrum. See, for example, [link to relevant documentation]. Figure 6 , Figure 7 , Figure 8 and Figure 9 ,like Figure 6 Figure 7 , Figure 8 and Figure 9 As shown in the figure, the comparison between the calculated spectra and the reference spectrum after retaining different proportions is illustrated. Hollow dots represent the order of the reference spectrum, and solid dots represent the order of the approximate spectrum. The electric fields are sorted according to their order importance, and orders with higher contributions (such as 5%, 10%, and 30%) are retained at preset proportions. Orders with lower contributions are gradually removed, for example, removing 10% of the lower-ranked orders each time. The truncated approximate spectrum is then calculated based on the importance of the remaining orders, using the following formula:

[0089]

[0090] In the formula, j represents the current truncation level; thus, based on the order of retaining different proportions, an approximate spectrum can be calculated to provide a data basis for subsequent order selection results.

[0091] The above scheme sorts the orders by importance, retains only the order importance results that meet the preset contribution requirements, and calculates the spectral data of the remaining orders to obtain approximate spectra. Only the orders with high contribution are retained, so that the approximate spectra represent the set of orders with high contribution. Orders that do not meet the contribution requirements are eliminated, which can reduce unnecessary calculations and provide a reliable data foundation for flexibly adjusting the Fourier expansion order selection in the RCWA algorithm. This improves the reliability of RCWA algorithm optimization, thereby improving the reliability of adjusting the parameters of the measurement equipment, and ultimately improving the reliability of the equipment measurement results.

[0092] As an example of an embodiment of the present invention, step 104 includes: calculating the root mean square error of the spectrum based on the reference spectrum and the approximate spectrum; if the root mean square error of the spectrum does not meet the preset error tolerance threshold, adjusting the order ratio of the approximate spectrum until it meets the preset error tolerance threshold, and obtaining the order selection result.

[0093] In one specific implementation method, the spectral data of the reference spectrum calculated in step 101 is denoted as R. exact ={R exact (λ1), R exact (λ2), …, R exact (λ P The approximate spectrum calculated in step 103 is denoted as )}. The root mean square error of the spectrum is calculated using the following formula:

[0094]

[0095] In the formula, It is the spectral value calculated after truncation (equivalent to an approximate spectrum); R exact (λ p ) is the spectral value calculated for the complete order (equivalent to the reference spectrum); P is the total number of wavelength sampling points;

[0096] See Figure 3 , Figure 4 and Figure 5 , Figure 3 A schematic diagram of NCS spectra at different order ratios for a measurement device adjustment method based on the RCWA algorithm optimized according to a certain embodiment of the present invention. Figure 1 ; Figure 4 A schematic diagram of NCS spectra at different order ratios for a measurement device adjustment method based on the RCWA algorithm optimized according to a certain embodiment of the present invention. Figure 2 ; Figure 5 A schematic diagram of NCS spectra at different order ratios for a measurement device adjustment method based on the RCWA algorithm optimized according to a certain embodiment of the present invention. Figure 3 ;like Figure 3 , Figure 4 and Figure 5As shown, the electric fields are sorted according to their importance. Unimportant orders of the approximate spectrum are deleted. By setting an error tolerance (equivalent to a preset error tolerance threshold, such as residual = 0.005), the order is gradually reduced or increased until the root mean square error between the approximate spectrum and the reference spectrum is less than the set error tolerance. The proportion of batch deletion or addition is dynamically adjusted according to the magnitude of the error. When the root mean square error is greater than the error tolerance, a certain order is added; when the root mean square error is less than the error tolerance, a certain order is deleted. Specifically, the initial deletion ratio is set to 10. % (e.g., deleting 10% of low-contribution orders at once). If the root mean square error exceeds the threshold (residual(j)>0.005), then back off some of the deleted orders and reduce the deletion ratio (e.g., adjust to 5%). If the root mean square error is small (residual(j)<<0.005), then increase the deletion ratio (e.g., adjust to 20%). This continues until the optimal deletion ratio is found, making residual(j)≈0.005. The final order selection result is then calculated. For example, after multiple rounds of adjustment, the optimal set of truncated orders O is determined. optimal The final calculated spectrum R final satisfy: Explain the optimal order set O optimal The final order selection aims to ensure computational accuracy while minimizing computational complexity. In one example, the initial Fourier expansion order range is assumed to be -20 to 20 in the x and y directions, totaling 41 × 41 = 1681 orders. After prioritizing the order, orders are gradually removed in increments of 10%, 20%, and 30%. When calculating the approximate spectrum, after removing 50% of the orders, residual = 0.012, indicating an error exceeding the limit. The order is then adjusted back to 40%, and after removing 40% of the orders, residual = 0.0048, satisfying the error tolerance (residual(j) << 0.005). Optimization is then stopped, and finally, 60% of the important orders are retained, achieving computational acceleration while ensuring that the error meets the requirements.

[0097] The above scheme calculates the root mean square error of the spectrum to analyze the error tolerance between the approximate spectrum and the reference spectrum, and judges the reliability of the order selection of the approximate spectrum. After meeting the preset error tolerance threshold, the order selection of the approximate spectrum provides a reliable data basis for the subsequent flexible adjustment of the Fourier expansion order selection in the RCWA algorithm, thereby improving the reliability of RCWA algorithm optimization, improving the reliability of the adjustment of measurement equipment parameters, and ultimately improving the reliability of equipment measurement results.

[0098] As an example of an embodiment of the present invention, an optimized RCWA algorithm is obtained based on the order selection result and the preset RCWA algorithm to adjust the parameters of the measurement device, including: adjusting the Fourier expansion order selection parameter of the preset RCWA algorithm based on the order selection result to obtain the optimized RCWA algorithm; and adjusting the parameters of the measurement device based on the optimized RCWA algorithm.

[0099] One possible implementation involves combining all actions performed in steps 101 to 104 to obtain the order selection result, and then optimizing the order selection of the preset RCWA algorithm. (See [link to relevant documentation]). Figure 10 , Figure 10 This diagram illustrates a comparison of the calculation time before and after optimization of the RCWA algorithm in a measurement equipment adjustment method based on the RCWA algorithm, according to a certain embodiment of the present invention. The calculation time of the optimized RCWA algorithm is accelerated from 49.7s (order remain 100%) to 0.005s (order remain 5%). Therefore, the optimized RCWA algorithm is integrated into the measurement equipment to adjust its parameters. After adjusting the measurement equipment parameters through the optimized RCWA algorithm, a large number of simulated spectral databases are generated in a short time during actual measurement analysis. Due to the significant increase in data volume, the measurement results are more accurate and reliable. Furthermore, when it is necessary to use periodic structural standards to calibrate the measurement equipment parameters, the significantly improved calculation speed of the analysis software accelerates the entire calibration process, greatly shortening the daily maintenance time of the measurement equipment.

[0100] The above scheme adjusts the Fourier expansion order selection parameter of the RCWA algorithm by obtaining reliable order selection results, optimizes the data processing process of the RCWA algorithm, and can flexibly adjust the Fourier expansion order selection in the RCWA algorithm under different structures and working conditions, so as to improve the reliability of the adjustment of measurement equipment parameters and ultimately improve the reliability of equipment measurement results.

[0101] Example 2

[0102] See Figure 11 , Figure 11 This is a schematic diagram of the module structure of a measurement device adjustment system optimized based on the RCWA algorithm, provided for one embodiment of the present invention. Figure 11As shown in the figure, this invention proposes a measurement equipment adjustment system based on the RCWA algorithm optimization, including: a structure-to-be-measured analysis module 201, an order importance ranking module 202, an approximate spectrum acquisition module 203, an order selection result acquisition module 204, and a measurement equipment adjustment module 205. The structure-to-be-measured analysis module 201 is used to obtain a reference spectrum and several orders of electric fields based on a preset structure to be measured. The order importance ranking module 202 is used to obtain an order importance ranking based on the several orders of the electric fields. The approximate spectrum acquisition module 203 is used to obtain an approximate spectrum based on the order importance ranking. The order selection result acquisition module 204 is used to adjust the order ratio of the approximate spectrum based on the reference spectrum to obtain an order selection result. The measurement equipment adjustment module 205 is used to obtain an optimized RCWA algorithm based on the order selection result to adjust the parameters of the measurement equipment.

[0103] One possible implementation method is described in [link to implementation details]. Figure 2 , Figure 2 A schematic diagram of a classic checkerboard dual-period grating for a measurement device adjustment method optimized based on the RCWA algorithm, provided in a certain embodiment of the present invention; as shown. Figure 2 As shown, for the preset structure to be measured, the following method is used: Figure 2 Taking the classic checkerboard dual-period grating shown as an example, a sufficiently large order is selected, such as -10 to 10 in the x-direction and -10 to 10 in the y-direction. The spectrum of the preset measured structure is calculated by the measured structure analysis module 201. Then, the dielectric constant of each layer of the preset measured structure is analyzed to obtain several orders of electric fields. The order importance ranking module 202 confirms the importance of each order of electric field and ranks them according to their importance to obtain the order importance ranking. The approximate spectrum acquisition module 203 can calculate the truncated approximate spectrum according to the order importance ranking. The order selection result acquisition module 204 compares the spectral values ​​of the reference spectrum and the spectral values ​​of the approximate spectrum and dynamically adjusts the order ratio of the approximate spectrum to obtain the order selection result. Finally, the measurement equipment adjustment module 205 records the order selection result in the preset RCWA algorithm, optimizes the preset RCWA algorithm, integrates the optimized RCWA algorithm into the measurement equipment, and adjusts the parameters of the measurement equipment.

[0104] This invention proposes a measurement equipment adjustment system based on the RCWA algorithm optimization. A measured structure analysis module analyzes the preset measured structure to obtain a reference spectrum and several orders of electric fields. An order importance ranking module ranks the importance of these electric fields. An approximate spectrum acquisition module calculates the approximate spectrum of the preset measured structure based on the order importance ranking. An order selection result acquisition module and a measurement equipment adjustment module then analyze the reference spectrum and approximate spectrum to obtain the order selection result, thereby optimizing the RCWA algorithm to adjust the measurement equipment parameters. By considering the order importance of several orders of electric fields of the preset measured structure, an approximate spectrum of the preset measured structure is obtained. Combined with the reference spectrum of the preset measured structure, the order ratio of the approximate spectrum is adjusted to obtain the order selection result. Based on the order selection result, the order selection of the RCWA algorithm is flexibly adjusted, thereby optimizing the RCWA algorithm to adjust the measurement equipment parameters and improve the reliability of the equipment measurement results.

[0105] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

[0106] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the described specific features, structures, materials, or characteristics may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0107] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "a plurality of" means two or more, unless otherwise explicitly specified.

Claims

1. A measurement equipment adjustment method based on RCWA algorithm optimization, characterized in that, include: Based on the pre-defined structure to be measured, a reference spectrum and several orders of electric fields are obtained; Based on the electric fields of several orders, the importance of order is ranked, including: obtaining the importance of order results based on the electric fields of several orders and a preset order electric field; obtaining the importance of order in each direction of the incident light based on the importance of order results and a preset incident light direction weighting algorithm; obtaining the importance of order in each layer structure based on the importance of order results and a preset multilayer structure weighting algorithm; obtaining the importance of order in each wavelength based on the importance of order results and a preset multiwavelength weighting algorithm; and obtaining the overall importance of order based on the importance of order in each direction of the incident light, the importance of order in each layer structure, and the importance of order in each wavelength. Based on the order importance ranking, an approximate spectrum is obtained, including: based on the order importance ranking, removing order importance results that do not meet the preset contribution requirements by a preset proportion, and obtaining the remaining order importance results; based on the remaining order importance results, calculating the spectral data of the remaining orders to obtain the approximate spectrum; Based on the reference spectrum, the approximate spectral order ratio is adjusted to obtain the order selection result, including: calculating the root mean square error of the spectrum based on the reference spectrum and the approximate spectrum; if the root mean square error of the spectrum does not meet the preset error tolerance threshold, the approximate spectral order ratio is adjusted until the preset error tolerance threshold is met to obtain the order selection result. Based on the order selection result and the preset RCWA algorithm, an optimized RCWA algorithm is obtained to adjust the parameters of the measurement equipment.

2. The method of claim 1, wherein the RCWA algorithm is based on a Rigorous Coupled Wave Analysis (RCWA) algorithm. The process of obtaining a reference spectrum and several orders of electric fields based on a preset structure to be measured includes: Based on a preset structure to be measured and a preset order ratio, the overall spectrum of the preset structure to be measured is calculated until the overall spectrum meets the preset accuracy requirements, and a reference spectrum is obtained. Fourier expansion of the dielectric constant of each layer of the preset structure to be measured yields several orders of electric displacement vectors; Based on the electric displacement vectors of several orders and a preset approximate relationship algorithm, electric fields of several orders are obtained.

3. The method of claim 1, wherein the RCWA algorithm is based on a Rigorous Coupled Wave Analysis (RCWA) algorithm. Based on the order importance results and the preset incident light direction weighting algorithm, the order importance ranking of each direction of the incident light is obtained, including: The order importance result is decomposed into each direction of the incident light to obtain the order importance result for each direction; Based on a preset incident light direction weighting algorithm, the order importance results of each direction are weighted to obtain the order weighted importance results of each direction; Based on the weighted importance results of the order in each direction, the importance ranking of the incident light in each direction is obtained.

4. The method of claim 1, wherein the RCWA algorithm is based on a Rigorous Coupled Wave Analysis (RCWA) algorithm. Based on the order importance results and the preset multi-layer structure weighting algorithm, the order importance ranking of each layer structure is obtained, including: Based on the order importance results, the order importance results of each layer structure are obtained; Based on a preset multi-layer structure weighting algorithm, the importance results of the order of each layer structure are weighted to obtain the weighted importance results of the order of each layer structure. Based on the weighted importance results of the order of each layer structure, the importance ranking of the order of each layer structure is obtained.

5. The method of claim 1, wherein the RCWA algorithm-based optimization is performed by a computer system. Based on the order importance results and the preset multi-wavelength weighted algorithm, the order importance ranking of each wavelength is obtained, including: Based on the order importance results, the order importance results for each wavelength are obtained; Based on a pre-defined multi-wavelength weighting algorithm, the importance results of each wavelength order are weighted to obtain the weighted importance results of each wavelength order; Based on the weighted importance results of each wavelength order, the importance ranking of each wavelength order is obtained.

6. The measurement equipment adjustment method based on RCWA algorithm optimization as described in claim 1, characterized in that, Based on the order selection result and the preset RCWA algorithm, an optimized RCWA algorithm is obtained to adjust the parameters of the measurement equipment, including: Based on the order selection result, the Fourier expansion order selection parameter of the preset RCWA algorithm is adjusted to obtain the optimized RCWA algorithm. Based on the optimized RCWA algorithm, the parameters of the measurement equipment are adjusted.

7. A measurement equipment adjustment system optimized based on the RCWA algorithm, characterized in that, include: The system includes a module for analyzing the structure to be measured, a module for ranking the importance of order, a module for acquiring approximate spectra, a module for acquiring the results of order selection, and a module for adjusting the measurement equipment. The measured structure analysis module is used to obtain a reference spectrum and several orders of electric fields based on a preset measured structure; The order importance ranking module is used to obtain an order importance ranking based on the electric field of several orders, including: obtaining an order importance result based on the electric field of several orders and a preset order electric field; obtaining an order importance ranking for each direction of the incident light based on the order importance result and a preset incident light direction weighting algorithm; obtaining an order importance ranking for each layer structure based on the order importance result and a preset multilayer structure weighting algorithm; obtaining an order importance ranking for each wavelength based on the order importance result and a preset multiwavelength weighting algorithm; and obtaining an overall order importance ranking based on the order importance ranking for each direction of the incident light, the order importance ranking for each layer structure, and the order importance ranking for each wavelength. The approximate spectrum acquisition module is used to obtain an approximate spectrum based on the order importance ranking, including: based on the order importance ranking, removing order importance results that do not meet the preset contribution requirements by a preset proportion to obtain the remaining order importance results; and based on the remaining order importance results, calculating the spectral data of the remaining orders to obtain the approximate spectrum. The order selection result acquisition module is used to adjust the approximate spectral order ratio based on the reference spectrum to obtain the order selection result, including: calculating the root mean square error of the spectrum based on the reference spectrum and the approximate spectrum; if the root mean square error of the spectrum does not meet the preset error tolerance threshold, adjusting the approximate spectral order ratio until it meets the preset error tolerance threshold to obtain the order selection result. The measurement equipment adjustment module is used to obtain an optimized RCWA algorithm based on the order selection result, so as to adjust the parameters of the measurement equipment.

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