RCWA simulation calculation method of target structure and scattered electromagnetic field acceleration calculation device

Abstract

The application provides a RCWA simulation calculation method and a scattered electromagnetic field acceleration calculation device of a target structure, belongs to the field of field calculation speed improvement application, and the RCWA simulation calculation method comprises the following steps: calculating an exponential matrix corresponding to a transfer matrix, calculating the transfer matrix, calculating a scattering matrix corresponding to the transfer matrix by using a layer scattering matrix conversion formula, calculating scattering matrices of all layers, and obtaining a global scattering matrix by using Redheffer star product operation connection; the scattered electromagnetic field acceleration 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 solves the near-field electromagnetic scattering characteristics of a periodic target structure based on the RCWA algorithm and simulates and calculates a far-field imaging process, and outputs a simulation optical image; the RCWA algorithm based on matrix exponential calculation realizes the speed improvement of the field calculation of a multilayer structure, and is convenient for popularization and application in the fields of wafer detection, photolithography processing, AR / VR display and the like which involve electromagnetic field calculation of a layer structure.

Description

Technical Field

[0001] This invention belongs to the field of field computing speed improvement applications, specifically involving an RCWA simulation calculation method for a target structure and a device for accelerating the calculation of scattered electromagnetic fields. Background Technology

[0002] Rigorous Coupled-Wave Analysis (RCWA) is primarily used for numerical simulation of light scattering in periodic media, playing a crucial role in semiconductor manufacturing scenarios such as optical defect detection, critical dimension measurement, and photolithography process simulation optimization. The basic principle of RCWA is to expand the periodic dielectric constant distribution and electromagnetic field into spatial Fourier series, establish the coupled-wave equations using Maxwell's equations, calculate the characteristic states of the electric and magnetic fields, then calculate the scattering matrix of a single layer, and finally use Redheffer star product operations to obtain the global scattering matrix. The most time-consuming part of traditional RCWA methods is solving large-scale eigenvalue problems. The electromagnetic field transformation matrix is: , ; in, and This represents a diagonal matrix formed by the wave vectors in the x and y directions. and These are the convolution matrices corresponding to the permittivity and permeability, respectively. W represents the electric field characteristic matrix, and D represents the diagonal matrix composed of the wave vector eigenvalues ​​in the z-direction.

[0003] Assumption and These are the single-sided harmonic numbers in the x and y directions, respectively. The scale of the aforementioned eigenvalue problem is... ,in This refers to the total harmonic number. The larger the periodic structure, the higher the required computational accuracy, the greater the required harmonic number, and the larger the scale of the eigenvalue problem to solve. The time required to compute this problem and... Proportional.

[0004] In the classical RCWA theory, the eigenvalue decomposition of matrix PQ is calculated. Obtain the characteristic state W of the electric field, and then calculate the characteristic state of the magnetic field. Next, calculate the layer scattering matrix using the following steps: In the formula, d represents the thickness of the optical device. Here, is the wavelength of the incident light. It is the characteristic state of the magnetic field of the vacuum layer, which can be represented as ;in, Let I be the identity matrix. The relation can be verified. .

[0005] For patterned wafers, given the scattering matrix of each layer, for Figure 1 The multi-layered structure allows the scattering matrices of each layer to be concatenated using Redheffer star product operations to obtain the global scattering matrix. The scattering matrices of the input and output layers are represented as follows.

[0006] , .

[0007] In the formula, and These are the magnetic field characteristic states of the input and output layers, respectively. Their specific forms are similar to those of the vacuum layer magnetic field characteristic states, and will not be elaborated upon here. The Redheffer star product operation is defined as follows: .

[0008] The eigenvalue solving step accounts for more than half of the computation time of the entire RCWA simulation, becoming a bottleneck that restricts simulation efficiency and limits the application of RCWA in optical simulation.

[0009] The parallel computing architecture of modern GPUs provides revolutionary acceleration for large-scale matrix operations in RCWA, mainly in two aspects: First, the GPU's computing cores are particularly well-suited for handling regular operations such as matrix multiplication and inversion. These operations can be perfectly decomposed into a large number of parallel subtasks, achieving near-linear speedup. Second, matrix operations have regular memory access patterns, which can fully utilize the high bandwidth of the GPU's video memory. In contrast, the serial architecture of CPUs is often limited by memory bandwidth bottlenecks when handling 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, i is 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] ②12th order expansion A 12th-order Taylor expansion can be achieved with only 4 matrix multiplications.

[0048] For i from 0 to 3, execute ; Execute m times .

[0049] ③ 18th order expansion An 18th-order Taylor expansion can be achieved with only 5 matrix multiplications.

[0050] For i from 0 to 4, execute ; Finally, execute m times. .

[0051] The preceding form 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.

[0052] Assign values ​​to i from 0 to 4.

[0053] Finally, perform the following operation m times.

[0054] S2. Calculate the transfer matrix T after stacking vacuum dielectric layers on adjacent sides.

[0055] .

[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.

[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, ; The 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, The RCWA simulation computation method runs on a GPU computing cluster module. The master node and compute nodes of the GPU computing cluster module are interconnected via IB network interface cards (NICs). The master node coordinates task allocation based on the CPU. Compute nodes transmit data to each GPU within the node via a high-speed PCIe bus. The GPU array achieves multi-GPU collaborative parallel computing based on a high-speed chip interconnect protocol. The computation results are transmitted from the corresponding compute nodes to the master node for aggregation and output. The GPU computation employs matrix block operations. The RCWA simulation computation method includes: S1. Construct a device for accelerating the calculation of scattered electromagnetic fields; S2. Collect the pattern structure, material information of each layer, and thickness information of each layer of the target structure, and determine the simulated optical state information; S3. Calculate the exponential matrix E corresponding to the transfer matrix T using the fast matrix exponential approximation method. This method utilizes a GPU (GPU) for matrix block operations within a scattered electromagnetic field acceleration computing device. The fast matrix exponential approximation method includes approximating the exponential matrix E through the summation of 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. The wavelength of the incident light is represented by P and Q, which are electromagnetic field transformation matrices. S4. Express the transmission matrix T after stacking vacuum dielectric layers on both sides using the exponential matrix E; S5. Using the layer scattering matrix transformation formula, calculate the scattering matrix S corresponding to the transmission matrix T expressed by the exponential matrix E; S6. Traverse all layers of the target structure and calculate the scattering matrix of each layer. j=1,2,…,L; S7. Obtain the global scattering matrix by using Redheffer star product operation. .

2. The RCWA simulation calculation method according to claim 1, characterized in that: Transmission matrix in S4 Expressed using the exponential matrix E: ； 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.

3. 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, based on the RCWA simulation calculation method described in claim 1 or 2, solves the near-field electromagnetic scattering characteristics of the periodic structure and simulates the far-field imaging process, outputting optical simulation information and simulated optical images; The simulation application module is suitable for applications that require optical simulation.

4. The scattered electromagnetic field acceleration computing device according to claim 3, 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.

5. The scattered electromagnetic field acceleration computing device according to claim 3, 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.

6. The scattered electromagnetic field acceleration computing device according to claim 3, 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, .

7. The scattered electromagnetic field acceleration computing device according to claim 6, 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 is used to calculate and simulate imaging: ; in, ; The 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.

8. The scattering electromagnetic field acceleration computing device according to claim 3, 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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