RCWA simulation calculation method of target structure and scattering electromagnetic field acceleration calculation equipment

Abstract

The invention provides an RCWA simulation calculation method of a target structure and scattering electromagnetic field acceleration calculation equipment, and belongs to the field of field calculation speed increase application. The RCWA simulation calculation method comprises the steps of calculating an index matrix corresponding to a transmission matrix, calculating the transmission matrix, calculating a scattering matrix corresponding to the transmission matrix by utilizing a layer scattering matrix conversion formula, calculating scattering matrixes of all layers, and obtaining a global scattering matrix by utilizing Redheffer star product operation connection; the scattering electromagnetic field accelerated calculation device comprises an information acquisition module, a GPU calculation cluster module, a simulation calculation module and a simulation application module. The simulation calculation module is used for solving near-field electromagnetic scattering characteristics of the periodic target structure based on an RCWA algorithm, simulating and calculating a far-field imaging process and outputting a simulation optical image; according to the RCWA algorithm based on matrix index calculation, the speed of multilayer structure field calculation is increased, and the RCWA algorithm is convenient to popularize and apply in the fields related to layer structure electromagnetic field calculation, such as wafer detection, photoetching processing, AR / VR display and the like.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of field calculation speed improvement application, and particularly relates to a RCWA simulation calculation method of a target structure and a scattered electromagnetic field acceleration calculation device. BACKGROUND

[0002] The rigorous coupled wave analysis method (RCWA) is mainly used for numerical simulation calculation of periodic medium light scattering, and plays a key role in scenes such as optical defect detection, key size measurement and photolithography process simulation optimization in semiconductor manufacturing. The basic principle of RCWA is to expand the periodic permittivity distribution and electromagnetic field into a spatial Fourier series, to establish a coupled wave equation through Maxwell's equations, to calculate the characteristic state of the electric field and the magnetic field, to calculate the scattering matrix of a single layer, and finally to connect to obtain the global scattering matrix by using the Redheffer star product operation. The most time-consuming part in the traditional RCWA method is to solve a large-scale eigenvalue problem: . Wherein the electromagnetic field transformation matrix is: , ; Wherein, and represent the diagonal matrix composed of the wave vector in the x and y directions, and are the convolution matrix corresponding to the permittivity and permeability, represents the electric field characteristic matrix, represents the diagonal matrix composed of the wave vector eigenvalue in the z direction.

[0003] Suppose and are the unilateral harmonic numbers in the x and y directions, the size of the above eigenvalue problem is , wherein is the total harmonic number. The larger the periodic structure is, the higher the required calculation precision is, the larger the harmonic number is required, and the larger the size of the eigenvalue problem is. The time required for calculating the problem is proportional to .

[0004] In the classical theory of RCWA, the eigenvalue decomposition of the matrix PQ is obtained, and the characteristic state of the electric field is obtained, and then the characteristic state of the magnetic field is calculated, and then the layer scattering matrix is calculated according to the following steps: where d is the thickness of the optical device, is the incident light wavelength, here is the vacuum layer magnetic field eigenstate, which can be expressed as ; where , I is the identity matrix. It can be verified that the relation .

[0005] For a patterned wafer, with the scattering matrix of each layer, the global scattering matrix Figure 1 for the multi-layer structure in can be obtained by connecting the scattering matrices of each layer with Redheffer star product operation. Here the scattering matrices of the input and output layers are expressed as follows.

[0006] , .

[0007] where and are the input and output layer magnetic field eigenstates, respectively, whose specific forms are similar to the vacuum layer magnetic field eigenstate, which will not be described here. The definition of the Redheffer star product operation is as follows: .

[0008] The eigenvalue solving step accounts for more than half of the total RCWA simulation time, becoming the bottleneck of the simulation efficiency and limiting the application of RCWA in optical simulation.

[0009] The parallel computing architecture of modern GPUs provides revolutionary acceleration capabilities for large-scale matrix operations in RCWA, mainly in the following two points: first, the computing cores of GPUs are particularly suitable for processing regular operations such as matrix multiplication and inversion. These operations can be perfectly decomposed into a large number of parallel sub-tasks, achieving almost linear speedup; second, matrix operations have a regular memory access pattern, which can fully utilize the high-bandwidth memory of GPUs. In contrast, the serial architecture of CPUs is often limited by the memory bandwidth bottleneck when dealing with such problems.

[0010] While GPUs excel in general matrix operations, they face significant computational bottlenecks in eigenvalue decomposition. Firstly, at the algorithmic level, eigenvalue algorithms like QR decomposition have strict data computation dependencies, requiring subsequent steps to wait for preceding steps to complete, severely limiting parallelization potential. Secondly, in terms of hardware architecture, eigenvalue computation is extremely sensitive to numerical errors, typically requiring double-precision arithmetic, which doesn't fully utilize the GPU's computing power. Furthermore, conditional branches such as convergence checks can cause GPU thread divergence, significantly reducing execution unit utilization. Finally, in automatic differentiation scenarios, such as backpropagation, eigenvalue decomposition requires constructing complex auxiliary matrices to calculate gradients, with computational complexity far exceeding that of the simple chain rule in conventional matrix operations. Therefore, in practical engineering applications, directly calculating eigenvalues ​​and eigenma matrices using GPUs should be avoided as much as possible. Summary of the Invention

[0011] In order to overcome the shortcomings of the prior art, the purpose of this invention is to provide an RCWA simulation calculation method for a target structure and an accelerated calculation device for scattered electromagnetic fields, which can solve the above-mentioned problems.

[0012] Design Principles: To improve computational efficiency, this invention modifies the computational architecture of RCWA, shifting the computational focus from solving for eigenvalues ​​and eigenmatrices to calculating matrix exponents. Matrix exponents can be calculated using methods such as Taylor expansion, Pad approximation, or Krylov subspace iteration, effectively avoiding the need to solve for eigenvalues ​​and eigenvectors. This allows the algorithm to better adapt to GPU architectures, fully leveraging the advantages of GPU parallel computing and significantly improving the simulation efficiency of the target structure. The overall scheme is as follows: An RCWA simulation method for a target structure is proposed to solve for the electromagnetic scattering matrix of the target to be simulated. The RCWA simulation method includes: S1, calculating the transmission matrix using the fast matrix exponentiation approximation method. The corresponding exponent matrix S2. Calculate the transfer matrix after stacking vacuum dielectric layers on both sides. S3. Using the layer scattering matrix transformation formula, calculate the scattering matrix S corresponding to the transmission matrix T; S4. Traverse all layers of the target structure and calculate the scattering matrix of each layer. S5. Obtain the global scattering matrix by performing Redheffer star product operations. .

[0013] Furthermore, fast matrix exponent approximation methods include: approximating the exponent matrix by summing an infinite series. First, calculate the index of the reduced matrix. The original matrix exponent is then restored by repeating the squaring operation.

[0014] Furthermore, the transfer matrix in S2 for: In the formula, The imaginary unit, This represents the characteristic state of the electric field in the vacuum layer. This indicates the characteristic state of the magnetic field in the vacuum layer.

[0015] Furthermore, for S3, the transfer matrix T and the scattering matrix S are used together. The transfer matrix is ​​responsible for handling single-layer propagation, and the scattering matrix is ​​used for inter-layer coupling, thus balancing computational efficiency and numerical robustness.

[0016] Furthermore, the RCWA simulation calculation method runs on a GPU computing cluster module. The master node and computing nodes of the GPU computing cluster module are interconnected through IB network cards. The master node coordinates task allocation based on the CPU. The computing nodes transmit data with each GPU in the node through the PCIe high-speed bus. The GPU array realizes multi-card collaborative parallel computing based on the high-speed chip interconnect protocol. The calculation results are transmitted from the corresponding computing nodes to the master node for aggregation and output.

[0017] This invention also provides a device for accelerating the calculation of scattered electromagnetic fields, comprising an information acquisition module, a GPU computing cluster module, a simulation computing module, and a simulation application module. The information acquisition module acquires the simulation pattern information and simulation optical state information of the target corresponding to the simulation application module and transmits them to the simulation computing module. The GPU computing cluster module adopts a distributed cluster architecture, with a master control node and multiple computing nodes working collaboratively, relying on a GPU acceleration array to achieve parallel computing. The simulation computing module, based on the aforementioned RCWA simulation computing method, solves the near-field electromagnetic scattering characteristics of periodic structures and simulates the far-field imaging process, outputting optical simulation information and simulated optical images. The simulation application module is suitable for application devices that require optical simulation.

[0018] Furthermore, the simulated pattern information input to the information acquisition module includes pattern structure, material information of each layer, and thickness information of each layer; the simulated optical state information input to the information acquisition module includes light source parameters, polarization characteristics, and Zernike coefficient.

[0019] Furthermore, the simulation calculation module includes an RCWA module for solving the near-field electromagnetic scattering characteristics of periodic structures, a far-field calculation module for calculating the far-field imaging process of the optical system, and a simulation result output module for outputting the calculated simulated optical images and intermediate process simulation information.

[0020] Furthermore, the simulation calculation module uses a global scattering matrix. Fourier transform of the frequency domain transfer function of the target structure in the simulation: input is a unit vector For transmission systems, For a reflective system, .

[0021] Furthermore, for the target structure of the incoherent system, the Abbe method is used to calculate and simulate the far-field imaging process: For partially coherent systems and target structures within coherent systems, the Hopkins method can be used to calculate and simulate imaging. In the formula, ; Fourier transform of the cross-correlation function of the light source The frequency of the light source's pupil. The Fourier transform of the transfer function of the imaging system For the imaging pupil frequency, for Conjugate, for Conjugate The Fourier transform of the transfer function in the frequency domain of the target structure.

[0022] Furthermore, the corresponding application devices for the simulation application module are wafer / mask inspection devices, optical critical dimension measurement devices, mask design devices, photolithography processing auxiliary devices, lighting optimization design devices, or near-eye AR / VR display devices.

[0023] Compared with the prior art, the beneficial effects of the present invention are as follows: The improved RCWA algorithm based on matrix exponent calculation in this application realizes the speed improvement of multilayer structure field calculation, which is convenient for promotion and application in fields involving layer structure electromagnetic field calculation such as wafer inspection, photolithography, and near-eye AR / VR display. Attached Figure Description

[0024] Figure 1 A schematic diagram of a multilayer structure on a patterned wafer surface; Figure 2 This is a schematic diagram of the electromagnetic field accelerator computing device of the present invention; Figure 3 This is a schematic diagram of a GPU computing cluster module; Figure 4 A schematic diagram of the interface between the scattering matrix and the transmission matrix of a single-layer structure; Figure 5 This is a schematic diagram of the multi-layer structure connection; Figure 6 This is a flowchart illustrating the RCWA simulation calculation method. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.

[0026] A device for accelerating the computation of scattered electromagnetic fields based on an improved RCWA algorithm, see [link / reference]. Figure 2 The electromagnetic field accelerator includes an information acquisition module, a GPU computing cluster module, a simulation computing module, and a simulation application module. The module structure, connections, and functions are described below: The information acquisition module is used to acquire the simulation pattern information and simulation optical state information of the target corresponding to the simulation application module, and transmit them to the simulation computing module; the GPU computing cluster module adopts a distributed cluster architecture, with the master control node and multiple computing nodes working together, relying on the GPU acceleration array to achieve parallel computing; the simulation computing module calculates the received information based on the improved RCWA algorithm of matrix exponential calculation, solves the near-field electromagnetic scattering characteristics of the periodic structure and simulates the far-field imaging process, and outputs the simulation optical image; the simulation application module is suitable for application devices with single-layer or multi-layer structure computing.

[0027] The information acquisition module collects and inputs two types of basic information into the GPU computing cluster module (high-performance computing cluster).

[0028] Simulation pattern information: covering pattern structure, material information of each layer (such as refractive index and dielectric constant), and thickness information of each layer.

[0029] Simulated optical state information includes light source parameters (wavelength, numerical aperture, and intensity distribution, etc.), polarization characteristics (linear polarization, circular polarization, polarization direction, etc.), Zernike coefficients, etc.

[0030] In this GPU computing cluster module, the master node and computing nodes are interconnected through IB network cards. The master node coordinates task allocation based on the CPU. The computing nodes transmit data with each GPU in the node through the PCIe high-speed bus. The GPU array realizes multi-card collaborative computing based on the high-speed chip interconnect protocol. The computing results are finally transmitted from the corresponding computing nodes to the master node for aggregation and output.

[0031] For a specific example, see Figure 3 The GPU computing cluster module consists of a host node and multiple computing nodes working together, and relies on a GPU acceleration array to achieve efficient parallel computing, thus forming a high-performance computing system with a distributed cluster architecture.

[0032] During system operation, the master control node first receives the pattern and process recipe parameters configured by the user (such as the simulation pattern information and simulation optical state information of the target corresponding to the simulation application module transmitted by the information acquisition module). Then, it distributes the computing tasks to each computing node through a dynamic task scheduling algorithm. The computing nodes transmit data to the corresponding GPU devices through the PCIe high-speed bus. The GPU array realizes multi-card collaborative computing based on high-speed chip interconnect protocols such as NVLink, xGMI, UALink or XeLink. Finally, the master control node summarizes the results of each node and outputs them.

[0033] In multi-GPU interconnect schemes, the system prioritizes high-speed chip interconnect protocol technology for data exchange between GPUs, or achieves bidirectional data transmission between GPUs through PCIe interface. The heterogeneous computing architecture supports two modes: (1) master-slave architecture, in which the CPU acts as the master node to coordinate task allocation, and the GPU is responsible for parallel computing; (2) peer-to-peer architecture, in which direct memory access between devices is achieved through GPU Direct RDMA technology, reducing CPU intervention overhead.

[0034] The system's parallel computing strategy includes three optimization modes: (1) data parallel mode, which is suitable for parameter scanning scenarios, assigning tasks of different wavelengths or incident angles to independent GPUs to achieve linear acceleration; (2) model parallel mode, including vertical layering (allocating hierarchical computation according to physical dimensions) and horizontal partitioning (dividing subdomains based on the region decomposition method); (3) hybrid parallel mode, which combines the advantages of data and model parallelism to build a multi-layered computing architecture. In addition, the system optimizes communication efficiency and maximizes hardware resource utilization through asynchronous computation flow, computation-communication overlap, and pipelined data transmission technology.

[0035] The simulation computing module runs on the GPU computing cluster module and includes an RCWA module for solving the near-field electromagnetic scattering characteristics of periodic structures, a far-field computing module for calculating the far-field imaging process of an optical system, and a simulation result output module for outputting the calculated simulated optical images and intermediate process simulation information.

[0036] The simulation computing module is mainly an optical simulation software system, which consists of three modules.

[0037] RCWA module: Based on the input pattern, material, and thickness information, solves the near-field electromagnetic scattering characteristics of periodic structures.

[0038] Far-field calculation module: Propagates the near-field electromagnetic field to the far field and simulates the far-field imaging process of the optical system.

[0039] Simulation Result Output Module: Outputs the simulated optical image of the input pattern under simulated optical conditions and important simulation information of the intermediate process.

[0040] The RCWA module uses an improved RCWA algorithm based on matrix exponentiation to solve for the near-field electromagnetic scattering matrix of single-layer or multi-layer structures. See also Figure 6 The improved RCWA algorithm, also known as the RCWA simulation calculation method, includes the following steps.

[0041] S1. Calculate the matrix exponent E of the transfer matrix T using the fast matrix exponent approximation method. In the formula, d represents the layer thickness of the target structure to be simulated. Indicates the wavelength of the incident light.

[0042] The fast matrix exponent approximation method is introduced below. Taylor expansion and Pad approximation are two common methods for approximating matrix exponents. Taking Taylor expansion as an example, the matrix exponent can be approximated by the following infinite series summation.

[0043] For matrix exponents, they can be approximated by summing an infinite series: The definition of matrix R is... d represents the layer thickness of the target structure to be simulated, while λ represents the wavelength of the incident light; first, the reduced matrix exponent is calculated. The original matrix exponent is then recovered by repeated squaring operations, i.e. Where the integer m takes the following values: That is, the choice of integer m is based on the 1-norm of matrices P and Q.

[0044] By using a fast matrix exponent approximation method, computational accuracy can be maintained while minimizing computational overhead. This strategy avoids the numerical instability that can arise from directly calculating large matrix exponents, while ensuring the accuracy of the final result. To further conserve computational resources, a Taylor expansion similar to the Paterson-Stockmeye process can be used.

[0045] ①8th order expansion An 8th-order Taylor expansion can be achieved with only 3 matrix multiplications.

[0046] Execute m times .

[0047] Where the coefficient For the values ​​of , please refer to the literature Philipp Bader et al. Computing the Matrix Exponential with an Optimized Taylor Polynomial Approximation Mathematics 2019, 7(12), 1174; https: / / doi.org / 10.3390 / math7121174. The coefficients in ② and ③ below can also be found in the literature here.

[0048] ②12th order expansion A 12th-order Taylor expansion can be achieved with only 4 matrix multiplications.

[0049] For i from 0 to 3, execute ; Execute m times .

[0050] ③ 18th order expansion An 18th-order Taylor expansion can be achieved with only 5 matrix multiplications.

[0051] For i from 0 to 4, execute ; Finally, execute m times. .

[0052] The preceding format needs to be processed. The matrix is ​​large, which can be a significant burden on GPU memory. To address this, GPU computation uses block operations on the matrix to calculate twice the total harmonics of the base version (the version before partitioning), improving memory utilization. For example, with an 18th-order expansion, this only requires 22 operations. The specific steps for matrix multiplication are as follows.

[0053] Assign values ​​to i from 0 to 4.

[0054] Finally, perform the following operation m times.

[0055] S2. Calculate the transfer matrix T after stacking vacuum dielectric layers on adjacent sides. .

[0056] S3. Using the layer scattering matrix transformation formula, calculate the scattering matrix S corresponding to the transmission matrix T.

[0057] In RCWA simulations of multilayer structures, directly using the transfer matrix for interlayer coupling leads to numerical instability and condition number deterioration. Conversely, the interlayer coupling process using the scattering matrix is ​​numerically stable. This invention proposes a hybrid approach that combines the transfer matrix and scattering matrix methods: the transfer matrix handles single-layer propagation, while the scattering matrix is ​​used for interlayer coupling, thus balancing computational efficiency and numerical robustness.

[0058] For the layer scattering conversion formula, firstly, the transfer matrix directly relates the electromagnetic field components on both sides of the structure through matrix multiplication, which is particularly suitable for recursive calculations of layered media.

[0059] for Figure 4 The layered structure includes: .

[0060] The scattering matrix describes the relationship between the input and output fields when an electromagnetic wave passes through an optical structure (i.e., the target structure to be simulated), and can be expressed as: This is typically used to analyze reflection and transmission characteristics.

[0061] The transfer matrix and the scattering matrix are two equivalent descriptive forms, which can be converted using the following formula: .

[0062] S4. Traverse all layers of the multilayer structure and calculate the scattering matrix of each layer. , j=1,2,3…,L.

[0063] S5. Obtain the global scattering matrix by using Redheffer star product operation. .

[0064] Theoretically, it can be proven that the layer scattering matrix is ​​symmetric, that is... Therefore, S2 and S3 in the above implementation steps can be combined into the following steps: .

[0065] It uses facts .

[0066] for Figure 5 A schematic diagram of the multi-layered structure is obtained by calculation using the above formula. Figure 5 The scattering matrix in the image.

[0067] The simulation calculation module uses the global scattering matrix Fourier transform of the frequency domain transfer function O of the simulated pattern structure: input is a unit vector For transmission systems, For a reflective system, .

[0068] For far-field simulation calculations, either the classic Abbe model or the Hopkins model can be used in the calculation process.

[0069] Specifically, for the target structure of an incoherent system, the Abbe method is used to simulate the far-field imaging process: .

[0070] For partially coherent systems and target structures within coherent systems, the Hopkins method can be used to calculate and simulate imaging: .

[0071] In the formula, ; Fourier transform of the cross-correlation function of the light source The frequency of the light source's pupil. The Fourier transform of the transfer function of the imaging system For the imaging pupil frequency, for Conjugate, for Conjugate The Fourier transform of the transfer function in the frequency domain of the target structure.

[0072] Finally, for simulation application modules, these are suitable for electromagnetic field calculation applications with single-layer or multi-layer structures, including wafer / mask inspection devices, optical critical dimension measurement devices, mask design devices, optical device design, lithography optical auxiliary devices, illumination optimization design, and near-eye AR / VR display devices. The solution presented in this application has already been applied to semiconductor metrology devices and critical dimension measurement devices.

[0073] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An RCWA simulation calculation method for a target structure, used to solve the electromagnetic scattering matrix of the target to be simulated, characterized in that, RCWA simulation calculation methods include: S1. Calculate the transmission matrix using the fast matrix exponent approximation method. The corresponding exponent matrix ; S2. Calculate the transmission matrix after stacking vacuum dielectric layers on both sides. ; S3. Using the layer scattering matrix transformation formula, calculate the scattering matrix S corresponding to the transmission matrix T; S4. Traverse all layers of the target structure and calculate the scattering matrix of each layer. j=1,2,…,L; S5. Obtain the global scattering matrix by using Redheffer star product operation. .

2. The RCWA simulation calculation method according to claim 1, characterized in that: Fast matrix exponent approximation methods include: approximating the exponent matrix by summing an infinite series. , The definition of matrix R is... First, calculate the index of the reduced matrix. The original matrix exponent is then recovered by repeated squaring operations, i.e. In the formula, the integer m takes the value of That is, the choice of integer m is based on the 1-norm of matrices P and Q. This represents the layer thickness of the target structure to be simulated. Let P represent the wavelength of the incident light, and let Q be the electromagnetic field transformation matrix.

3. The RCWA simulation calculation method according to claim 1, characterized in that: Transmission Matrix in S2 for: ； In the formula, The imaginary unit, This represents the characteristic state of the electric field in the vacuum layer. This indicates the characteristic state of the magnetic field in the vacuum layer.

4. The RCWA simulation calculation method according to claim 1, characterized in that: For S3, the transfer matrix T and the scattering matrix S are used together. The transfer matrix is ​​responsible for handling single-layer propagation, and the scattering matrix is ​​used for inter-layer coupling, thus balancing computational efficiency and numerical robustness.

5. The RCWA simulation calculation method according to claim 1, characterized in that: The RCWA simulation calculation method runs on a GPU computing cluster module. The master node and computing nodes of the GPU computing cluster module are interconnected through IB network cards. The master node coordinates task allocation based on the CPU. The computing nodes transmit data with each GPU in the node through the PCIe high-speed bus. The GPU array realizes multi-card collaborative parallel computing based on the high-speed chip interconnect protocol. The calculation results are transmitted from the corresponding computing nodes to the master node for aggregation and output.

6. A device for accelerating computation using scattered electromagnetic fields, characterized in that: The scattered electromagnetic field acceleration computing device includes an information acquisition module, a GPU computing cluster module, a simulation computing module, and a simulation application module; The information acquisition module is used to acquire the simulation pattern information and simulation optical state information of the target corresponding to the simulation application module, and transmit them to the simulation calculation module; The GPU computing cluster module adopts a distributed cluster architecture, with a master node and multiple computing nodes working together to achieve parallel computing by relying on the GPU acceleration array. The simulation calculation module is based on the RCWA simulation calculation method described in any one of claims 1-5, solves the near-field electromagnetic scattering characteristics of the periodic structure and simulates the far-field imaging process, and outputs optical simulation information and simulated optical images; The simulation application module is suitable for applications that require optical simulation.

7. The scattered electromagnetic field acceleration computing device according to claim 6, characterized in that: The simulated pattern information input to the information acquisition module includes the pattern structure, material information of each layer, and thickness information of each layer; the simulated optical state information input to the information acquisition module includes light source parameters, polarization characteristics, and Zernike coefficient.

8. The scattered electromagnetic field acceleration computing device according to claim 6, characterized in that: The simulation calculation module includes an RCWA module for solving the near-field electromagnetic scattering characteristics of periodic structures, a far-field calculation module for calculating the far-field imaging process of an optical system, and a simulation result output module for outputting the calculated simulated optical images and intermediate process simulation information.

9. The scattered electromagnetic field acceleration computing device according to claim 6, characterized in that: The simulation calculation module uses the global scattering matrix Fourier transform of the frequency domain transfer function of the target structure in the simulation: input is a unit vector For transmission systems, For a reflective system, .

10. The scattering electromagnetic field acceleration computing device according to claim 9, characterized in that: For target structures in incoherent systems, the Abbe method is used to simulate the far-field imaging process: ; For partially coherent systems and target structures within coherent systems, the Hopkins method can be used to calculate and simulate imaging: ； in, ; Fourier transform of the cross-correlation function of the light source The frequency of the light source's pupil. The Fourier transform of the transfer function of the imaging system For the imaging pupil frequency, for Conjugate, for Conjugate The Fourier transform of the transfer function in the frequency domain of the target structure.

11. The scattered electromagnetic field acceleration computing device according to claim 6, characterized in that: The application devices corresponding to the simulation application module are wafer / mask inspection devices, optical critical dimension measurement devices, mask design devices, photolithography processing auxiliary devices, lighting optimization design devices, or near-eye AR / VR display devices.

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