A photolithography mask optimization method and device based on linear convolution, equipment and medium

Abstract

The application discloses a photolithography mask optimization method and device based on linear convolution, equipment and medium, and relates to the technical field of computers, and comprises the following steps: determining a mask matrix and a propagation matrix based on photolithography imaging; performing frequency domain convolution on a convolution kernel block corresponding to a mask sub-region and the propagation matrix corresponding to an image block corresponding to a target imaging pattern; determining a to-be-tested imaging pattern based on an effective region corresponding to a region convolution result obtained; determining a global gradient based on the difference between the target imaging pattern and the to-be-tested imaging pattern, determining a region gradient based on the global gradient and an adjoint kernel corresponding to the convolution kernel block, updating the mask matrix based on the region gradient to obtain a new mask matrix, jumping to the step of extracting a mask sub-region corresponding to an image block, and obtaining a target mask matrix until a target convergence condition is met, and determining a target mask layout based on the target mask matrix. In the photolithography scene, large-scale convolution calculation is performed to realize iterative optimization of high-precision mask parameters.

Description

Technical Field

[0001] This invention relates to the field of computer technology, and in particular to a method, apparatus, device and medium for optimizing photolithography masks based on linear convolution. Background Technology

[0002] In large-scale physical system simulations, enormous convolution calculations and inverse gradient optimizations are required. For example, the inverse optimization of a 20-millimeter lithography mask involves linear convolution calculations on a 100TB matrix and requires inverse gradient derivation.

[0003] Currently, the main technical approaches for large-scale physical simulation and optimization are divided into two categories: traditional high-performance computing (HPC) and large model training and optimization. However, traditional HPC implementations, such as those in geophysics, are based on CPU computation, failing to fully utilize the high parallel scheduling capabilities of GPU clusters, resulting in extremely low computational efficiency for large-scale convolutions. Furthermore, the computation process generally employs approximate pruning strategies, such as truncating the propagation matrix and reducing numerical precision, leading to outputs that are approximate simulation values. This fails to meet the stringent requirements for imaging accuracy in lithography scenarios and easily introduces systematic errors. It only supports forward physical simulations and does not construct backward gradient derivation and optimization processes. In contrast, large model training and optimization techniques employ hierarchical models, with each layer containing only 1-10GB of data. There are no dependencies between layers, allowing for independent parallel processing. However, in high-precision physical convolution scenarios (such as lithography), the propagation matrix is ​​globally coupled, requiring convolution computation and gradient aggregation to be completed as a whole, unlike large models which can be split and parallelized in layers. Moreover, large model training can distribute computational power by calculating in batches based on the target corpus, while physical convolution scenarios only have a single fitting target, making it impossible to reduce the scale of a single computation through parallel processing of multiple batches of data.

[0004] As can be seen from the above, how to perform large-scale convolution calculations in photolithography scenarios to achieve iterative optimization of high-precision mask parameters is a problem that urgently needs to be solved. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a method, apparatus, device, and medium for optimizing photolithography masks based on linear convolution, which can perform large-scale convolution calculations in photolithography scenarios to achieve iterative optimization of high-precision mask parameters. The specific solution is as follows: In a first aspect, this application provides a photolithography mask optimization method based on linear convolution, including: The mask matrix is ​​determined based on the transmittance probability of each physical pixel of the mask in photolithography imaging, and the propagation matrix is ​​determined based on the spherical propagation characteristics of light passing through the mask. The first matrix side length of the propagation matrix is ​​determined based on the propagation angle, the pixel size of the target imaging pattern formed on the photoresist, and the propagation distance from the mask to the photoresist. The second matrix side length of the mask matrix is ​​determined based on the first matrix side length and the side length of the target imaging pattern. The propagation angle is the maximum angle at which the light emitted from the light-transmitting point deviates from the vertical direction. The target imaging pattern is divided into blocks to obtain image blocks, and the propagation matrix is ​​divided into blocks to obtain convolution kernel blocks. The mask sub-regions corresponding to the image blocks are extracted from the mask matrix based on the side length of the second matrix. Frequency domain convolution is performed based on the mask sub-regions and the convolution kernel blocks to obtain region convolution results. The imaging pattern to be tested is determined based on the effective region corresponding to the region convolution results. The global gradient is determined based on the difference between the target imaging pattern and the imaging pattern to be tested. The adjoint kernel corresponding to the convolution kernel block is determined. The region gradient corresponding to the mask sub-region is determined based on the global gradient and the adjoint kernel. The region gradients are accumulated and summed to obtain the mask gradient matrix. The mask matrix is ​​updated using the mask gradient matrix to obtain a new mask matrix. Then, the process jumps to the step of extracting the mask sub-region corresponding to the image block from the mask matrix based on the side length of the second matrix, until the target convergence condition is met to obtain the target mask matrix. The target mask pattern on the mask plate is determined based on the target mask matrix.

[0006] Optionally, determining the mask matrix based on the transmittance probability of each physical pixel in the photolithography image, and determining the propagation matrix based on the spherical propagation characteristics of light passing through the mask, includes: The light transmittance probability corresponding to each physical pixel of the photomask in photolithography imaging is stored as a two-dimensional matrix using the logit function to obtain the mask matrix; the elements in the mask matrix have a one-to-one correspondence with the physical pixels of the photomask. The propagation matrix is ​​generated based on the spherical propagation characteristics of light passing through the mask and using the point spread function.

[0007] Optionally, determining the first matrix side length of the propagation matrix based on the propagation angle, the pixel size of the target imaging pattern formed on the photoresist, and the propagation distance from the mask to the photoresist, and determining the second matrix side length of the mask matrix based on the first matrix side length and the side length of the target imaging pattern, includes: The propagation length is determined based on the propagation angle and the propagation distance from the mask to the photoresist, and the number of pixels is determined based on the propagation length and the pixel size of the target imaging pattern formed on the photoresist. The first matrix side length of the propagation matrix is ​​obtained by rounding up the number of pixels based on the block length of the target imaging pattern. The second matrix side length of the mask matrix is ​​determined based on the side length of the first matrix and the side length of the target imaging pattern, using the valid rule in linear convolution.

[0008] Optionally, the step of dividing the target imaging pattern into blocks to obtain image blocks, dividing the propagation matrix into blocks to obtain convolution kernel blocks, extracting mask sub-regions corresponding to the image blocks from the mask matrix based on the side length of the second matrix, performing frequency domain convolution based on the mask sub-regions and the convolution kernel blocks to obtain region convolution results, and determining the imaging pattern to be tested based on the effective region corresponding to the region convolution results includes: The target imaging pattern is divided into blocks using the overlap-preserving method of linear convolution to obtain image blocks, and the propagation matrix is ​​split into convolution kernel blocks of a preset side length. Using the side length of the second matrix as a constraint, extract the mask sub-regions corresponding to each image block from the mask matrix; The mask sub-region and the convolution kernel block are subjected to Fast Fourier Transform to obtain the transformed sub-region and the transformed convolution kernel block respectively; The transformed sub-region and the transformed convolution kernel block are multiplied in the frequency domain, and the resulting multiplication is subjected to inverse fast Fourier transform to obtain the region convolution result. The effective regions are extracted from the region convolution results, and the effective regions are accumulated and fused using all-reduce communication to obtain the imaging pattern to be tested.

[0009] Optionally, the step of determining the global gradient based on the difference between the target imaging pattern and the imaging pattern to be measured, determining the accompanying kernel corresponding to the convolutional kernel block, and determining the region gradient corresponding to the mask sub-region based on the global gradient and the accompanying kernel includes: The pixel difference between the target imaging pattern and the imaging pattern to be tested is determined, and the imaging error is determined based on the pixel difference; The global gradient is determined based on the gradient of the imaging pattern to be measured according to the imaging error; Each of the convolutional kernel blocks is flipped and reconjugated to obtain a corresponding adjoint kernel. The gradient and the adjoint kernel are convolved to obtain the region gradient corresponding to the mask sub-region.

[0010] Optionally, the step of summing the gradients of each region to obtain a mask gradient matrix, updating the mask matrix using the mask gradient matrix to obtain a new mask matrix, and then proceeding to the step of extracting the mask sub-regions corresponding to the image blocks from the mask matrix based on the side length of the second matrix, until the target convergence condition is met to obtain the target mask matrix, includes: The gradients of each region are summed to obtain the mask gradient matrix; the mask gradient matrix is ​​used to characterize the optimization direction of each element in the mask matrix; The mask matrix is ​​optimized and updated based on the mask gradient matrix to obtain a new mask matrix, and then the process jumps to the step of extracting the mask sub-regions corresponding to the image blocks from the mask matrix based on the side length of the second matrix, until the imaging error is less than the target error threshold to obtain the target mask matrix.

[0011] Optionally, determining the target mask layout on the mask based on the target mask matrix includes: The target mask matrix is ​​converted into a target binary matrix using a target activation function; the target activation function is a function based on the Sigmoid function and Gumbel noise combined with an annealing mechanism. The target binary matrix is ​​mapped to the physical pixels on the mask to obtain the target mask pattern.

[0012] Secondly, this application provides a photolithography mask optimization device based on linear convolution, comprising: The matrix determination module is used to determine the mask matrix based on the transmittance probability of each physical pixel of the mask in photolithography imaging, and to determine the propagation matrix based on the spherical propagation characteristics of light passing through the mask. The matrix side length determination module is used to determine the first matrix side length of the propagation matrix based on the propagation angle, the pixel size of the target imaging pattern formed on the photoresist, and the propagation distance from the mask to the photoresist; and to determine the second matrix side length of the mask matrix based on the first matrix side length and the side length of the target imaging pattern; the propagation angle is the maximum angle at which the light emitted from the light-transmitting point deviates from the vertical direction. The test pattern determination module is used to divide the target imaging pattern into blocks to obtain image blocks, and divide the propagation matrix into blocks to obtain convolution kernel blocks. Based on the side length of the second matrix, it extracts the mask sub-regions corresponding to the image blocks from the mask matrix, performs frequency domain convolution based on the mask sub-regions and the convolution kernel blocks to obtain region convolution results, and determines the test imaging pattern based on the effective region corresponding to the region convolution results. The mask layout determination module is used to determine the global gradient based on the difference between the target imaging pattern and the imaging pattern to be tested, determine the adjoint kernel corresponding to the convolution kernel block, determine the region gradient corresponding to the mask sub-region based on the global gradient and the adjoint kernel, sum the region gradients to obtain the mask gradient matrix, update the mask matrix using the mask gradient matrix to obtain a new mask matrix, and jump to the step of extracting the mask sub-region corresponding to the image block from the mask matrix based on the side length of the second matrix, until the target convergence condition is met to obtain the target mask matrix, and determine the target mask layout on the mask based on the target mask matrix.

[0013] Thirdly, this application provides an electronic device, comprising: Memory, used to store computer programs; A processor is used to execute the computer program to implement the aforementioned linear convolution-based photolithography mask optimization method.

[0014] Fourthly, this application provides a computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the aforementioned linear convolution-based photolithography mask optimization method.

[0015] This application determines the mask matrix based on the transmittance probability of each physical pixel in a photolithography image, and determines the propagation matrix based on the spherical propagation characteristics of light passing through the mask. A first matrix side length of the propagation matrix is ​​determined based on the propagation angle, the pixel size of the target imaging pattern formed on the photoresist, and the propagation distance from the mask to the photoresist. A second matrix side length of the mask matrix is ​​determined based on the first matrix side length and the side length of the target imaging pattern. The propagation angle is the maximum angle at which the light emitted from the transmitted point deviates from the vertical direction. The target imaging pattern is divided into blocks to obtain image blocks, and the propagation matrix is ​​divided into blocks to obtain convolution kernel blocks. Mask sub-regions corresponding to the image blocks are extracted from the mask matrix based on the second matrix side length. The convolutional kernel block is convolved in the frequency domain to obtain a region convolution result. The target imaging pattern is determined based on the effective region corresponding to the region convolution result. A global gradient is determined based on the difference between the target imaging pattern and the target imaging pattern. The accompanying kernel corresponding to the convolutional kernel block is determined. The region gradient corresponding to the mask sub-region is determined based on the global gradient and the accompanying kernel. The region gradients are summed to obtain the mask gradient matrix. The mask matrix is ​​updated using the mask gradient matrix to obtain a new mask matrix. The process then jumps to the step of extracting the mask sub-region corresponding to the image block from the mask matrix based on the side length of the second matrix, until the target convergence condition is met to obtain the target mask matrix. The target mask pattern on the mask plate is determined based on the target mask matrix.

[0016] As can be seen from the above, this application constructs a mask matrix based on the light transmission probability and a propagation matrix based on the spherical propagation characteristics, fully preserving the physical laws of light diffraction and interference. The matrix size is precisely calculated using propagation angle, propagation distance, and pixel size to ensure that edge pixels of the target image receive illumination at complete angles. The target imaging pattern is divided into blocks, breaking down the global imaging problem into local block problems, avoiding memory overflow when processing the entire image at once. The propagation matrix block division splits the large kernel into independent small kernel blocks, loading only a single kernel block and its corresponding mask sub-region at a time, completely breaking through the single-card memory bottleneck. Frequency domain convolution is used to improve efficiency while preserving the linear superposition property of convolution. The effective regions in the convolution results are accumulated to obtain the image pattern to be tested. Then, the global gradient is calculated based on the difference between the image pattern to be tested and the target pattern. By convolving the adjoint kernel with the global gradient, the local gradients of each mask sub-region are obtained. The local gradients are accumulated and summed to obtain the complete mask gradient matrix, ensuring global consistency of the gradient. The mask matrix is ​​iteratively updated using the gradient to continuously reduce imaging errors. In this way, based on the target mask matrix that meets the target convergence condition, the corresponding lithographic imaging result can accurately match the target imaging pattern, realize the reverse optimization target of the mask pattern, support the real-time computing needs of large-scale iterative optimization, and greatly improve the optimization efficiency. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0018] Figure 1 This is a flowchart of a photolithography mask optimization method based on linear convolution disclosed in this application; Figure 2 This is a schematic diagram of a photolithographic imaging method disclosed in this application; Figure 3 This is a side view of the propagation angle disclosed in this application; Figure 4 This is a schematic diagram illustrating the relationship between mask size and target imaging pattern disclosed in this application; Figure 5 This is a schematic diagram of a photolithography mask optimization device based on linear convolution disclosed in this application; Figure 6 This is a structural diagram of an electronic device disclosed in this application. Detailed Implementation

[0019] 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.

[0020] Currently, traditional HPC implementations, such as those in geophysics, do not fully utilize the high parallel scheduling capabilities of GPU clusters, resulting in extremely low computational efficiency for large-scale convolutions. Furthermore, the computation process generally employs approximate pruning strategies, such as truncating the propagation matrix and reducing numerical precision, leading to outputs that are approximate simulations, which cannot meet the stringent imaging accuracy requirements of lithography scenarios. While large model training and optimization techniques involve independent inter-layer relationships in large models, the propagation matrix in high-precision physical convolution scenarios is globally coupled, requiring convolution computation and gradient aggregation to be completed as a whole, making it impossible to reduce the scale of a single computation through parallel processing of multiple batches of data. Therefore, this application provides a lithography mask optimization method based on linear convolution. Based on a target mask matrix that satisfies the target convergence condition, the corresponding lithography imaging result can accurately match the target imaging pattern, achieving the inverse optimization objective of the mask layout. This supports the real-time computational needs of large-scale iterative optimization, significantly improving optimization efficiency.

[0021] See Figure 1As shown, this embodiment of the invention discloses a photolithography mask optimization method based on linear convolution, including: Step S11: Determine the mask matrix based on the light transmittance probability of each physical pixel in the photolithography image, and determine the propagation matrix based on the spherical propagation characteristics of light passing through the mask.

[0022] In this embodiment, by Figure 2 As shown, each transparent pixel on the photomask is considered an ideal point light source. Each point light source propagates along an ideal sphere, illuminating the photoresist (i.e., the imaging surface). Phase interference between the point light sources forms the target imaging pattern. The physical process of photolithography is abstracted into mathematical language, that is, the physical process of photolithographic interference imaging is transformed into a linear convolution of the mask matrix A and the propagation matrix W. The mask is stored as a logit(p) matrix to represent the point transparency probability, thus obtaining the mask matrix. Based on the spherical propagation characteristics of light passing through the photomask, a propagation matrix characterizing the light propagation law is generated using the point spread function.

[0023] Specifically, determining the mask matrix based on the transmittance probability of each physical pixel in the photolithography image and determining the propagation matrix based on the spherical propagation characteristics of light passing through the mask includes: using the logit function to store the transmittance probability corresponding to each physical pixel in the photolithography image as a two-dimensional matrix to obtain the mask matrix; the elements in the mask matrix have a one-to-one correspondence with the physical pixels of the mask; and generating the propagation matrix based on the spherical propagation characteristics of light passing through the mask and using the point spread function.

[0024] Step S12: Determine the first matrix side length of the propagation matrix based on the propagation angle, the pixel size of the target imaging pattern formed on the photoresist, and the propagation distance from the mask to the photoresist; determine the second matrix side length of the mask matrix based on the first matrix side length and the side length of the target imaging pattern; the propagation angle is the maximum angle at which the light emitted from the light-transmitting point deviates from the vertical direction.

[0025] In this embodiment, in order to limit the actual process light propagation, a propagation angle is defined, such as... Figure 3 As shown, the side length of the propagation matrix is... Where α is the propagation angle, z is the propagation distance, and the side length of the propagation matrix is ​​[number of pixels]. Where α is the propagation angle, z is the propagation distance, and p is the pixel size of the target imaging pattern formed on the photoresist. In practical engineering, the number of pixels is rounded up to a multiple of 2N, i.e., KN, meaning the propagation angle, the propagation distance, and the pixel size determine the value of K. In one specific embodiment, if p = 4 nanometers, α = 25 degrees, and z = 1500 micrometers, the corresponding propagation matrix size is close to 1TB, which cannot be supported by a single graphics memory card, meaning that the linear convolution of the mask matrix A and the propagation matrix W (equivalent to the convolution kernel) cannot be directly calculated.

[0026] It is understandable that defining the propagation angle and propagation distance indirectly defines the relationship between the mask size and the target imaging pattern, such as... Figure 4 As shown. To ensure that the edge pixels of the target image receive complete propagation angle illumination, the mask needs to extend outwards. The side length. Valid rules based on linear convolution operations: The input size is derived in reverse, that is, the side length of the mask matrix is ​​the side length of the target imaging pattern + the side length of the propagation matrix - 1.

[0027] Specifically, determining the first matrix side length of the propagation matrix based on the propagation angle, the pixel size of the target imaging pattern formed on the photoresist, and the propagation distance from the mask to the photoresist, and determining the second matrix side length of the mask matrix based on the first matrix side length and the side length of the target imaging pattern, includes: determining the propagation length based on the propagation angle and the propagation distance from the mask to the photoresist; determining the number of pixels based on the propagation length and the pixel size of the target imaging pattern formed on the photoresist; rounding up the number of pixels based on the block length of the target imaging pattern to obtain the first matrix side length of the propagation matrix; and determining the second matrix side length of the mask matrix based on the first matrix side length and the side length of the target imaging pattern and using the valid rule in linear convolution.

[0028] Step S13: Divide the target imaging pattern into blocks to obtain image blocks, and divide the propagation matrix into blocks to obtain convolution kernel blocks. Extract the mask sub-regions corresponding to the image blocks from the mask matrix based on the side length of the second matrix. Perform frequency domain convolution based on the mask sub-regions and the convolution kernel blocks to obtain region convolution results. Determine the imaging pattern to be tested based on the effective region corresponding to the region convolution results.

[0029] In this embodiment, to handle large-scale convolution, the target imaging pattern is first divided into several small blocks of length N, i.e., each image block. The side length of the mask region corresponding to each image block is: image block side length N + propagation matrix side length KN-1 = N + K N-1 = (K+1) N-1; Convolve each mask region and the propagation matrix, and take the effective part to obtain the output of the image block. If the propagation matrix is ​​too large, that is, greater than the corresponding target propagation matrix threshold, further splitting is required, and the propagation matrix is ​​split into... The convolutional kernel blocks are loaded one at a time, along with the corresponding input sub-region. These are then accumulated after local convolution in the frequency domain to obtain the output. Specifically, the final pattern is initialized to 0, i.e., the output imaging matrix. The propagation matrix is ​​divided into M There are M convolutional kernel blocks, each with a size of M. Then M= KN is the propagation matrix; for each convolutional kernel block Perform a traversal and extract convolution kernel blocks. ,in, , , , ;in, , These are the row and column indices (from 0 to M-1) of the current convolutional kernel block, respectively. , These are the start and end indices of the current kernel block in the row direction of W (i.e., the propagation matrix); , These are the start and end indices of the current kernel block in the W column direction, respectively; KN is the side length of the propagation matrix.

[0030] It is understandable that the current convolutional kernel block is flipped to obtain the flipped convolutional kernel block, and the corresponding formula is as follows: ; in, This is the flipped convolution kernel block; This is a flip operation; The current convolutional kernel block is defined; then, the mask sub-region corresponding to the current convolutional kernel block is extracted from the mask matrix, using the following formula: ; in, The mask sub-region; The mask matrix; , These are the start and end indices of the current kernel block in the row direction of W (i.e., the propagation matrix); , These are the start and end indices of the current kernel block in the W column direction, respectively; N is the side length of the output matrix.

[0031] Furthermore, linear convolution is achieved using the Fast Fourier Transform, and the corresponding formula is as follows: result = IFFT(FFT(I)) FFT(F)); Wherein, result is the result of the region convolution; The mask sub-region; The convolution kernel is flipped; FFT is Fast Fourier Transform; IFFT is Inverse Fast Fourier Transform. The effective region from the convolution result is extracted and added to the initial Y matrix to obtain the final output matrix, as shown in the following formula: ; Where Y is the output matrix, i.e. the imaging pattern to be measured; result is the region convolution result; is the side length of the convolution kernel block; This is the side length of the output matrix.

[0032] Specifically, the steps of segmenting the target imaging pattern into image blocks and segmenting the propagation matrix into convolution kernel blocks, extracting mask sub-regions corresponding to the image blocks from the mask matrix based on the side length of the second matrix, performing frequency domain convolution on the mask sub-regions and the convolution kernel blocks to obtain region convolution results, and determining the imaging pattern to be tested based on the effective regions corresponding to the region convolution results include: segmenting the target imaging pattern into image blocks using the overlap-preserving method of linear convolution, and splitting the propagation matrix into convolution kernels with preset side lengths. The image blocks are processed as follows: Using the side length of the second matrix as a constraint, mask sub-regions corresponding to each image block are extracted from the mask matrix; Fast Fourier Transform is performed on the mask sub-regions and the convolution kernel blocks respectively to obtain transformed sub-regions and transformed convolution kernel blocks; Frequency domain dot product is performed on the transformed sub-regions and the transformed convolution kernel blocks, and inverse Fast Fourier Transform is performed on the obtained dot product results to obtain region convolution results; Effective regions are extracted from the region convolution results, and all-reduce communication is used to accumulate and fuse each effective region to obtain the image pattern to be tested.

[0033] In this embodiment, starting from the original definition of linear convolution, it is proven that block accumulation equals the global convolution result. The valid formula for linear convolution is as follows: ; in, To output the element in the i-th row and j-th column of matrix Y, and , ; The input matrix is ​​the mask matrix. Let m be the propagation matrix; m and n are the summation variables. Let K be the side length of the output matrix; KN is the side length of the propagation matrix. To transform linear convolution into a form that can be directly implemented using the Fast Fourier Transform, the following definition is used: ; in, The convolution kernel block is flipped; m and n are the summation variables; Let KN be the propagation matrix; KN is the side length of the propagation matrix. This is a flip operation. Accordingly, the aforementioned formula can be simplified to: ; in, To output the element in the i-th row and j-th column of matrix Y; The convolution kernel block is flipped; m and n are the summation variables; KN is the side length of the propagation matrix; Let be the mask matrix.

[0034] It is understandable that the convolution kernel is arranged according to... After being divided into blocks, it can be further broken down into the sum of the results of each convolutional kernel block, and the corresponding formula is as follows: ; in, To output the element in the i-th row and j-th column of matrix Y; The convolution kernel block is flipped; m and n are the summation variables; , These are the start and end indices of the current kernel block in the row direction of W (i.e., the propagation matrix); , These are the start and end indexes of the current kernel block in the W column direction, respectively; This is the result of a region convolution for a single kernel block. The calculation is performed using the overlap-preserving method of linear convolution. The total size of the frequency domain convolution is... The index of the valid portion of the region convolution result is... .

[0035] Step S14: Determine the global gradient based on the difference between the target imaging pattern and the imaging pattern to be tested, determine the adjoint kernel corresponding to the convolution kernel block, determine the region gradient corresponding to the mask sub-region based on the global gradient and the adjoint kernel, sum the region gradients to obtain the mask gradient matrix, update the mask matrix using the mask gradient matrix to obtain a new mask matrix, and jump to the step of extracting the mask sub-region corresponding to the image block from the mask matrix based on the side length of the second matrix, until the target convergence condition is met to obtain the target mask matrix, and determine the target mask pattern on the mask based on the target mask matrix.

[0036] In this embodiment, after the forward block computation is completed, all GPUs obtain the complete output Y through all-reduce communication to obtain the image pattern to be tested. Then, the error between the target image pattern and the image pattern to be tested is determined, and the gradient of the error with respect to the image pattern to be tested is calculated. , i.e., global gradient, where L is the error between the target imaging pattern and the imaging pattern to be measured; Y is the imaging error to be measured; for each convolutional kernel block The formula for calculating its associated kernel is as follows: ; in, The convolutional kernel is the accompanying kernel of the convolutional kernel block; The convolution kernel block; This represents a flipping operation; the horizontal line above indicates complex conjugation. Then, convolution is performed using the gradient and the accompanying kernel to obtain the region gradient corresponding to the mask sub-region, as shown in the following formula: ; in, The region gradient corresponding to the mask sub-region; For global gradient; is the accompanying kernel of the convolution kernel block.

[0037] Specifically, determining the global gradient based on the difference between the target imaging pattern and the imaging pattern to be tested, determining the accompanying kernel corresponding to the convolutional kernel block, and determining the regional gradient corresponding to the mask sub-region based on the global gradient and the accompanying kernel includes: determining the pixel difference between the target imaging pattern and the imaging pattern to be tested, and determining the imaging error based on the pixel difference; determining the global gradient based on the gradient of the imaging pattern to be tested based on the imaging error; flipping and complex conjugating each of the convolutional kernel blocks to obtain the corresponding accompanying kernel, and convolving the gradient and the accompanying kernel to obtain the regional gradient corresponding to the mask sub-region.

[0038] Understandably, based on the multi-chain principle, The summation of overlapping gradients in each block yields the complete gradient of A (the mask matrix). This involves accumulating the gradients from all regions into the mask gradient matrix and updating the parameters of the mask matrix using these gradients to obtain a new mask matrix. This process of forward and backward convolution is repeated until the error is less than a target error threshold, yielding the target mask matrix. The target error threshold can be determined based on specific circumstances.

[0039] Specifically, the step of summing the gradients of each region to obtain a mask gradient matrix, updating the mask matrix using the mask gradient matrix to obtain a new mask matrix, and then proceeding to the step of extracting the mask sub-regions corresponding to the image blocks from the mask matrix based on the side length of the second matrix, until the target convergence condition is met to obtain the target mask matrix, includes: summing the gradients of each region to obtain a mask gradient matrix; the mask gradient matrix is ​​used to characterize the optimization direction of each element in the mask matrix; optimizing and updating the mask matrix based on the mask gradient matrix to obtain a new mask matrix, and then proceeding to the step of extracting the mask sub-regions corresponding to the image blocks from the mask matrix based on the side length of the second matrix, until the imaging error is less than the target error threshold to obtain the target mask matrix.

[0040] Furthermore, the target mask layout is determined by using the gumbel_sigmoid function with an annealing mechanism to obtain the target mask matrix that meets the target convergence condition. Specifically, determining the target mask layout on the mask based on the target mask matrix includes: converting the target mask matrix into a target binary matrix using a target activation function; the target activation function is a function based on the sigmoid function and Gumbel noise combined with the annealing mechanism; and mapping the target binary matrix to the physical pixels on the mask to obtain the target mask layout.

[0041] In this embodiment, regarding The forward and reverse calculations are broken down into The size of the block, where N and Both are configurable. If the size of the convolution kernel (i.e., the propagation matrix) is small, the output target imaging pattern is divided into blocks, and gradient calculations are performed on each block separately; if the size of the convolution kernel is large, it is split into a group. This method, which divides convolutional data into blocks of varying sizes and adds a single communication step, supports computation of any convolutional kernel. The mask matrix, mask gradient matrix, and optimizer state are all stored in CPU memory; GPU memory does not store any state data. Furthermore, I / O time is masked within computation time to reduce waiting time and improve GPU utilization.

[0042] Understandably, during the reverse engineering process, PyTorch's transfer function can be rewritten to leverage the property that the gradient of the all-reduce summation is 1, eliminating the need for additional inter-GPU communication. If the convolutional kernel is too large to fit in all GPU memory on a single node, the reverse computation can be separated, thus avoiding caching the entire convolutional kernel and saving GPU memory. Furthermore, considering multi-node parallel acceleration, the target output is split into multiple blocks, with each node responsible for the forward and reverse computation of one block. After one iteration, the gradients of the overlapping parts are synchronized across nodes using all-reduce, and the mask is updated locally. It's worth noting that this method can be applied not only to optical physics but also to other fields such as acoustics and fluid dynamics, as long as it involves the forward and reverse computation and optimization of large-scale convolutional kernels.

[0043] Furthermore, to reduce I / O operations, a sliding window of the input mask matrix A is scheduled using a serpentine pattern, utilizing the overlap between two gradient calculations to reduce redundant I / O. Adjacent convolutional kernel blocks are assigned to the same GPU, ensuring continuous access to the input sub-regions and reducing random I / O. BF16 can be used for storage and computation instead of F32, reducing storage and I / O overhead without affecting result accuracy. However, due to the large size of the complete propagation matrix and the high accuracy requirements, storage space cannot be reduced, making storage and I / O issues problematic. Therefore, the propagation matrix is ​​not pre-calculated; it is generated temporarily when calculating the corresponding block. The kernel block is released after use.

[0044] It should be noted that the propagation matrix is ​​a spherical propagation model of an ideal point light source, possessing axisymmetric properties, and can be arbitrarily chosen from convolutional kernel blocks. Both have 3 convolutional kernel blocks and B are flipped and paired. Definition ,in, The result of the linear convolution of I and B (only the valid part is retained), where I is the mask sub-region and B is the convolution kernel block; FFT is the Fast Fourier Transform; IFFT is the Inverse Fast Fourier Transform; based on the above definitions, there are three equations: ; ; ; in, This is the result of a linear convolution; Indicates vertical flip; Indicates horizontal flip; This indicates a double flip, i.e., a 180-degree rotation; I represents the mask sub-region, and B represents the convolutional kernel block. In the original block-based process, each convolutional kernel block (including 3 symmetric convolutional kernel blocks) requires 4 steps. The operation, using the above equation, only requires one calculation of the original convolution kernel block B. This allows for convolution operations with other symmetric convolution kernels. Similarly, in the reverse process, only one computation is needed. The gradients of the other three symmetric convolution kernels can also be obtained by flipping them.

[0045] As can be seen from the above, this application constructs a mask matrix based on the light transmission probability and a propagation matrix based on the spherical propagation characteristics, fully preserving the physical laws of light diffraction and interference. The matrix size is precisely calculated using propagation angle, propagation distance, and pixel size to ensure that edge pixels of the target image receive illumination at complete angles. The target imaging pattern is divided into blocks, breaking down the global imaging problem into local block problems, avoiding memory overflow when processing the entire image at once. The propagation matrix block division splits the large kernel into independent small kernel blocks, loading only a single kernel block and its corresponding mask sub-region at a time, completely breaking through the single-card memory bottleneck. Frequency domain convolution is used to improve efficiency while preserving the linear superposition property of convolution. The effective regions in the convolution results are accumulated to obtain the image pattern to be tested. Then, the global gradient is calculated based on the difference between the image pattern to be tested and the target pattern. By convolving the adjoint kernel with the global gradient, the local gradients of each mask sub-region are obtained. The local gradients are accumulated and summed to obtain the complete mask gradient matrix, ensuring global consistency of the gradient. The mask matrix is ​​iteratively updated using the gradient to continuously reduce imaging errors. In this way, based on the target mask matrix that meets the target convergence condition, the corresponding lithographic imaging result can accurately match the target imaging pattern, realize the reverse optimization target of the mask pattern, support the real-time computing needs of large-scale iterative optimization, and greatly improve the optimization efficiency.

[0046] Accordingly, see Figure 5 As shown, this application also provides a photolithography mask optimization device based on linear convolution, comprising: The matrix determination module 11 is used to determine the mask matrix based on the transmittance probability of each physical pixel of the mask in photolithography imaging, and to determine the propagation matrix based on the spherical propagation characteristics of light passing through the mask. The matrix side length determination module 12 is used to determine the first matrix side length of the propagation matrix based on the propagation angle, the pixel size of the target imaging pattern formed on the photoresist, and the propagation distance from the mask to the photoresist, and to determine the second matrix side length of the mask matrix based on the first matrix side length and the side length of the target imaging pattern; the propagation angle is the maximum angle at which the light emitted from the light-transmitting point deviates from the vertical direction; The test pattern determination module 13 is used to divide the target imaging pattern into blocks to obtain image blocks, and divide the propagation matrix into blocks to obtain convolution kernel blocks. Based on the side length of the second matrix, it extracts the mask sub-regions corresponding to the image blocks from the mask matrix, performs frequency domain convolution based on the mask sub-regions and the convolution kernel blocks to obtain region convolution results, and determines the test imaging pattern based on the effective region corresponding to the region convolution results. The mask layout determination module 14 is used to determine the global gradient based on the difference between the target imaging pattern and the imaging pattern to be tested, determine the adjoint kernel corresponding to the convolution kernel block, determine the region gradient corresponding to the mask sub-region based on the global gradient and the adjoint kernel, sum the region gradients to obtain the mask gradient matrix, update the mask matrix using the mask gradient matrix to obtain a new mask matrix, and jump to the step of extracting the mask sub-region corresponding to the image block from the mask matrix based on the side length of the second matrix, until the target convergence condition is met to obtain the target mask matrix, and determine the target mask layout on the mask based on the target mask matrix.

[0047] In some specific embodiments, the matrix determination module 11 may specifically include: The mask matrix determination unit is used to store the light transmission probability corresponding to each physical pixel of the mask in photolithography imaging as a two-dimensional matrix using the logit function to obtain the mask matrix; the elements in the mask matrix have a one-to-one correspondence with the physical pixels of the mask. The propagation matrix generation unit is used to generate a propagation matrix based on the spherical propagation characteristics of light passing through the mask and using a point spread function.

[0048] In some specific embodiments, the matrix side length determination module 12 may specifically include: A pixel count determination unit is used to determine the propagation length based on the propagation angle and the propagation distance from the mask to the photoresist, and to determine the pixel count based on the propagation length and the pixel size of the target imaging pattern formed on the photoresist. The first side length determination unit is used to round up the number of pixels based on the block length of the target imaging pattern to obtain the first matrix side length of the propagation matrix; The second side length determination unit is used to determine the second matrix side length of the mask matrix based on the side length of the first matrix and the side length of the target imaging pattern, and using the valid rule in linear convolution.

[0049] In some specific embodiments, the pattern determination module 13 may specifically include: The matrix splitting unit is used to divide the target imaging pattern into blocks using the overlap-preserving method of linear convolution to obtain image blocks, and to split the propagation matrix into convolution kernel blocks of a preset side length. The sub-region extraction unit is used to extract the mask sub-regions corresponding to each image block from the mask matrix, with the side length of the second matrix as a constraint. The kernel transformation unit is used to perform fast Fourier transform on the mask sub-region and the kernel block respectively to obtain the transformed sub-region and the transformed kernel block. The convolution result determination unit is used to perform frequency domain dot product on the transformed sub-region and the transformed convolution kernel block, and to perform inverse fast Fourier transform on the obtained dot product result to obtain the region convolution result. The effective region accumulation unit is used to extract the effective regions from the region convolution result, and to accumulate and fuse each effective region using all-reduce communication to obtain the imaging pattern to be tested.

[0050] In some specific embodiments, the mask layout determination module 14 may specifically include: An error determination unit is used to determine the pixel difference between the target imaging pattern and the imaging pattern to be tested, and to determine the imaging error based on the pixel difference; A global gradient determination unit is used to determine the global gradient based on the gradient of the imaging pattern to be measured by the imaging error; The region gradient determination unit is used to flip and conjugate each of the convolution kernel blocks to obtain the corresponding adjoint kernel, and to convolve the gradient and the adjoint kernel to obtain the region gradient corresponding to the mask sub-region.

[0051] In some specific embodiments, the mask layout determination module 14 may specifically include: A gradient accumulation unit is used to accumulate and sum the gradients of each region to obtain a mask gradient matrix; the mask gradient matrix is ​​used to characterize the optimization direction of each element in the mask matrix; The target matrix determination unit is used to optimize and update the mask matrix based on the mask gradient matrix to obtain a new mask matrix, and then jump to the step of extracting the mask sub-region corresponding to the image block from the mask matrix based on the side length of the second matrix, until the imaging error is less than the target error threshold to obtain the target mask matrix.

[0052] In some specific embodiments, the mask layout determination module 14 may specifically include: The target matrix transformation unit is used to convert the target mask matrix into a target binary matrix using a target activation function; the target activation function is a function based on the Sigmoid function and Gumbel noise combined with an annealing mechanism. The matrix mapping unit is used to map the target binary matrix to the physical pixels on the mask to obtain the target mask pattern.

[0053] Furthermore, embodiments of this application also disclose an electronic device, Figure 6This is a structural diagram of an electronic device 20 according to an exemplary embodiment. The content of the diagram should not be construed as limiting the scope of this application. Specifically, the electronic device 20 may include: at least one processor 21, at least one memory 22, a power supply 23, a communication interface 24, an input / output interface 25, and a communication bus 26. The memory 22 stores a computer program, which is loaded and executed by the processor 21 to implement the relevant steps in the linear convolution-based photolithography mask optimization method disclosed in any of the foregoing embodiments. Furthermore, the electronic device 20 in this embodiment may specifically be an electronic computer.

[0054] In this embodiment, the power supply 23 is used to provide operating voltage for each hardware device on the electronic device 20; the communication interface 24 can create a data transmission channel between the electronic device 20 and external devices, and the communication protocol it follows can be any communication protocol applicable to the technical solution of this application, and is not specifically limited here; the input / output interface 25 is used to acquire external input data or output data to the outside world, and its specific interface type can be selected according to specific application needs, and is not specifically limited here.

[0055] In addition, the memory 22, as a carrier for resource storage, can be a read-only memory, random access memory, disk or optical disk, etc. The resources stored thereon can include operating system 221, computer program 222, etc., and the storage method can be temporary storage or permanent storage.

[0056] The operating system 221 is used to manage and control the various hardware devices on the electronic device 20 and the computer program 222, which may be Windows Server, Netware, Unix, Linux, etc. In addition to including a computer program capable of performing the linear convolution-based photolithography mask optimization method executed by the electronic device 20 as disclosed in any of the foregoing embodiments, the computer program 222 may further include computer programs capable of performing other specific tasks.

[0057] Furthermore, this application also discloses a computer-readable storage medium for storing a computer program; wherein, when the computer program is executed by a processor, it implements the aforementioned photolithography mask optimization method based on linear convolution. Specific steps of this method can be found in the corresponding content disclosed in the foregoing embodiments, and will not be repeated here.

[0058] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0059] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0060] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0061] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0062] The technical solutions provided in this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A photolithography mask optimization method based on linear convolution, characterized in that, include: The mask matrix is ​​determined based on the transmittance probability of each physical pixel of the mask in photolithography imaging, and the propagation matrix is ​​determined based on the spherical propagation characteristics of light passing through the mask. The first matrix side length of the propagation matrix is ​​determined based on the propagation angle, the pixel size of the target imaging pattern formed on the photoresist, and the propagation distance from the mask to the photoresist. The second matrix side length of the mask matrix is ​​determined based on the first matrix side length and the side length of the target imaging pattern. The propagation angle is the maximum angle at which the light emitted from the light-transmitting point deviates from the vertical direction; The target imaging pattern is divided into blocks to obtain image blocks, and the propagation matrix is ​​divided into blocks to obtain convolution kernel blocks. The mask sub-regions corresponding to the image blocks are extracted from the mask matrix based on the side length of the second matrix. Frequency domain convolution is performed based on the mask sub-regions and the convolution kernel blocks to obtain region convolution results. The imaging pattern to be tested is determined based on the effective region corresponding to the region convolution results. The global gradient is determined based on the difference between the target imaging pattern and the imaging pattern to be tested. The adjoint kernel corresponding to the convolution kernel block is determined. The region gradient corresponding to the mask sub-region is determined based on the global gradient and the adjoint kernel. The region gradients are accumulated and summed to obtain the mask gradient matrix. The mask matrix is ​​updated using the mask gradient matrix to obtain a new mask matrix. Then, the process jumps to the step of extracting the mask sub-region corresponding to the image block from the mask matrix based on the side length of the second matrix, until the target convergence condition is met to obtain the target mask matrix. The target mask pattern on the mask plate is determined based on the target mask matrix.

2. The photolithography mask optimization method based on linear convolution according to claim 1, characterized in that, The determination of the mask matrix based on the transmittance probability of each physical pixel in the photolithography image, and the determination of the propagation matrix based on the spherical propagation characteristics of light passing through the mask, include: The light transmittance probability corresponding to each physical pixel of the photomask in photolithography imaging is stored as a two-dimensional matrix using the logit function to obtain the mask matrix; the elements in the mask matrix have a one-to-one correspondence with the physical pixels of the photomask. The propagation matrix is ​​generated based on the spherical propagation characteristics of light passing through the mask and using the point spread function.

3. The photolithography mask optimization method based on linear convolution according to claim 1, characterized in that, The determination of the first matrix side length of the propagation matrix based on the propagation angle, the pixel size of the target imaging pattern formed on the photoresist, and the propagation distance from the mask to the photoresist, and the determination of the second matrix side length of the mask matrix based on the first matrix side length and the side length of the target imaging pattern, includes: The propagation length is determined based on the propagation angle and the propagation distance from the mask to the photoresist, and the number of pixels is determined based on the propagation length and the pixel size of the target imaging pattern formed on the photoresist. The first matrix side length of the propagation matrix is ​​obtained by rounding up the number of pixels based on the block length of the target imaging pattern. The second matrix side length of the mask matrix is ​​determined based on the side length of the first matrix and the side length of the target imaging pattern, using the valid rule in linear convolution.

4. The photolithography mask optimization method based on linear convolution according to claim 1, characterized in that, The process of dividing the target imaging pattern into blocks to obtain image blocks, dividing the propagation matrix into blocks to obtain convolution kernel blocks, extracting mask sub-regions corresponding to the image blocks from the mask matrix based on the side length of the second matrix, performing frequency domain convolution based on the mask sub-regions and the convolution kernel blocks to obtain region convolution results, and determining the imaging pattern to be tested based on the effective region corresponding to the region convolution results includes: The target imaging pattern is divided into blocks using the overlap-preserving method of linear convolution to obtain image blocks, and the propagation matrix is ​​split into convolution kernel blocks of a preset side length. Using the side length of the second matrix as a constraint, extract the mask sub-regions corresponding to each image block from the mask matrix; The mask sub-region and the convolution kernel block are subjected to Fast Fourier Transform to obtain the transformed sub-region and the transformed convolution kernel block respectively; The transformed sub-region and the transformed convolution kernel block are multiplied in the frequency domain, and the resulting multiplication is subjected to inverse fast Fourier transform to obtain the region convolution result. The effective regions are extracted from the region convolution results, and the effective regions are accumulated and fused using all-reduce communication to obtain the imaging pattern to be tested.

5. The photolithography mask optimization method based on linear convolution according to claim 1, characterized in that, The step of determining the global gradient based on the difference between the target imaging pattern and the imaging pattern to be measured, determining the accompanying kernel corresponding to the convolutional kernel block, and determining the region gradient corresponding to the mask sub-region based on the global gradient and the accompanying kernel includes: The pixel difference between the target imaging pattern and the imaging pattern to be tested is determined, and the imaging error is determined based on the pixel difference; The global gradient is determined based on the gradient of the imaging pattern to be measured according to the imaging error; Each of the convolutional kernel blocks is flipped and reconjugated to obtain a corresponding adjoint kernel. The gradient and the adjoint kernel are convolved to obtain the region gradient corresponding to the mask sub-region.

6. The photolithography mask optimization method based on linear convolution according to claim 5, characterized in that, The process of summing the gradients of each region to obtain a mask gradient matrix, updating the mask matrix using the mask gradient matrix to obtain a new mask matrix, and then proceeding to the step of extracting the mask sub-regions corresponding to the image blocks from the mask matrix based on the side length of the second matrix, continues until the target convergence condition is met to obtain the target mask matrix, including: The gradients of each region are summed to obtain the mask gradient matrix; the mask gradient matrix is ​​used to characterize the optimization direction of each element in the mask matrix; The mask matrix is ​​optimized and updated based on the mask gradient matrix to obtain a new mask matrix, and then the process jumps to the step of extracting the mask sub-regions corresponding to the image blocks from the mask matrix based on the side length of the second matrix, until the imaging error is less than the target error threshold to obtain the target mask matrix.

7. The photolithography mask optimization method based on linear convolution according to any one of claims 1 to 6, characterized in that, Determining the target mask pattern on the mask based on the target mask matrix includes: The target mask matrix is ​​converted into a target binary matrix using a target activation function; the target activation function is a function based on the Sigmoid function and Gumbel noise combined with an annealing mechanism. The target binary matrix is ​​mapped to the physical pixels on the mask to obtain the target mask pattern.

8. A photolithography mask optimization device based on linear convolution, characterized in that, include: The matrix determination module is used to determine the mask matrix based on the transmittance probability of each physical pixel of the mask in photolithography imaging, and to determine the propagation matrix based on the spherical propagation characteristics of light passing through the mask. The matrix side length determination module is used to determine the first matrix side length of the propagation matrix based on the propagation angle, the pixel size of the target imaging pattern formed on the photoresist, and the propagation distance from the mask to the photoresist, and to determine the second matrix side length of the mask matrix based on the first matrix side length and the side length of the target imaging pattern. The propagation angle is the maximum angle at which the light emitted from the light-transmitting point deviates from the vertical direction; The test pattern determination module is used to divide the target imaging pattern into blocks to obtain image blocks, and divide the propagation matrix into blocks to obtain convolution kernel blocks. Based on the side length of the second matrix, it extracts the mask sub-regions corresponding to the image blocks from the mask matrix, performs frequency domain convolution based on the mask sub-regions and the convolution kernel blocks to obtain region convolution results, and determines the test imaging pattern based on the effective region corresponding to the region convolution results. The mask layout determination module is used to determine the global gradient based on the difference between the target imaging pattern and the imaging pattern to be tested, determine the adjoint kernel corresponding to the convolution kernel block, determine the region gradient corresponding to the mask sub-region based on the global gradient and the adjoint kernel, sum the region gradients to obtain the mask gradient matrix, update the mask matrix using the mask gradient matrix to obtain a new mask matrix, and jump to the step of extracting the mask sub-region corresponding to the image block from the mask matrix based on the side length of the second matrix, until the target convergence condition is met to obtain the target mask matrix, and determine the target mask layout on the mask based on the target mask matrix.

9. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the linear convolution-based photolithography mask optimization method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, Used to store a computer program, wherein the computer program, when executed by a processor, implements the linear convolution-based photomask optimization method as described in any one of claims 1 to 7.

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