A mask wafer collaborative optimization method for improving mask exposure efficiency

Abstract

This invention is a mask wafer co-optimization method to improve mask exposure efficiency. The steps include: S1 calculating optical proximity correction to obtain the target mask pattern; S2 initially fracturing the target mask pattern and initializing the mask rectangle exposure basis function set; S3 simulating variable electron beam lithography forward exposure and development; S4 correcting the variable electron beam exposure mode; and S5 setting convergence conditions and outputting the optimized variable electron beam exposure mode. The technical feature of this invention is that by calculating optical proximity correction to obtain the target mask pattern, initially fracturing the target mask pattern, and initializing the mask rectangle exposure basis function set, the linear combination of these basis functions and a threshold function represent the variable electron beam exposure lens. After simulating electron beam forward exposure and development, while ensuring the accuracy of the mask pattern after lithography, the variable electron beam exposure mode is optimized, reducing the number of variable electron beam exposures, thereby improving lithography efficiency. This method features high computational efficiency and high computational accuracy.

Description

Technical Field

[0001] This invention relates to a mask-wafer collaborative optimization method to improve mask exposure efficiency. This method can reduce the number of mask exposures and improve variable electron beam exposure efficiency while optimizing optical proximity effect and electron beam secondary effect, and belongs to the field of computational lithography. Background Technology

[0002] Lithography is a crucial step in chip manufacturing, where optical lithography transfers different feature patterns onto a wafer using a mask. Due to optical diffraction, the optical proximity effect severely impacts wafer pattern resolution, making optical proximity correction (OPC) an essential mask patterning technique. Traditional model-based OPC produces Manhattan patterns with straight edges, while the most advanced OPC technology is inverse lithography (ILT), which generates complex mask patterns with many curved shapes. Currently, mask fabrication primarily utilizes variable shape beam (VSB) lithography, a direct-write electron beam lithography technique. Similarly, during electron beam exposure, the scattering of the electron beam in the photoresist leads to the electron beam proximity effect, as well as fogging, loading, charging, and temperature effects. These secondary effects reduce the resolution of the mask pattern after OPC. Electron beam secondary effect correction is an essential step in the electron beam exposure process for mask pattern fabrication.

[0003] Currently, the optical lithography (OPC) process and the secondary effect correction process in electron beam lithography are simulated using two independent process flows. However, with the development of ILT technology, while improving wafer pattern resolution, the exposure count for VSB writing curve shapes has increased, resulting in extremely low exposure efficiency for direct writing of curve shapes. There is an urgent need to co-optimize the ILT and PEC processes to obtain an overlayable VSB layout mesh with low exposure counts while ensuring the accuracy of the mask pattern after lithography. Therefore, researching a mask-wafer co-optimization (MWCO) method to improve mask exposure efficiency is urgently needed.

[0004] The technical feature of this invention is that it obtains the target mask pattern by calculating optical proximity effect correction, initially fragments the target mask pattern, initializes the mask rectangle exposure basis function set, and uses the linear combination of this basis function set and threshold function to represent the VSB exposure lens. After simulating electron beam forward exposure and development, it optimizes the VSB exposure method and reduces the number of VSB exposures while ensuring the accuracy of the mask pattern after photolithography, thereby improving photolithography efficiency. Summary of the Invention

[0005] This invention is a mask wafer co-optimization method to improve mask exposure efficiency. The aim is to reduce the number of mask exposures and improve exposure efficiency while optimizing the optical proximity effect.

[0006] The technical solution of this invention is: a mask wafer co-optimization method to improve mask exposure efficiency, the invention steps are as follows:

[0007] Step S1: Calculate optical proximity correction and obtain the target mask pattern;

[0008] Based on the optical lithography target pattern, the optical proximity correction is calculated, and the mask pattern H(x,y) after optical proximity correction is expressed as:

[0009]

[0010] In the formula, T{I(x,y)} represents the result of applying an optically lithographic forward model T{·} to a mask pattern I(x,y) without optical proximity correction; t (x,y) represents the optical lithography target pattern.

[0011] Step S2: Initialize the target mask pattern and initialize the mask rectangle exposure basis function set;

[0012] The initial fractured optical proximity effect corrected mask pattern H(x,y) is represented by multiple mask rectangular exposure basis functions. Each rectangular exposure basis function is defined as follows:

[0013]

[0014] In the formula, (x p ,y p ) represents the coordinates of the center point of the mask rectangle exposure basis functions in a two-dimensional matrix (p = 1, 2, ..., P, where P is the total number of basis functions), w p and l p Let be the width and length of the rectangle represented by the basis functions. A linear combination of the basis functions is expressed as:

[0015]

[0016] In the formula, αp It is the p-th basis function S p The coefficient, w p and l p The three coefficients, representing the width and length of the rectangle in the basis function representation, determine the exposure method of the variable electron beam, and different mask rectangle exposure basis functions allow for regional overlap.

[0017] Using this set of basis functions, the entire exposure mask pattern is defined and initialized as follows:

[0018]

[0019] In the formula, c is the pattern threshold. The differentiable threshold function Γ(ψ) is defined as:

[0020]

[0021] In the formula, ψ is a floating-point value, and ε is the slope control value.

[0022] Step S3: Variable electron beam lithography forward exposure and development simulation;

[0023] The mask pattern H, represented by the exposure basis function set of the mask rectangle in the k-th iteration (k≥0, k represents the iteration number), is used. k The energy deposition distribution of the simulated exposure is obtained by directly convolving (x,y) with the electron beam point spread function PSF(x,y). The electron beam point spread function includes the combined effects of secondary effects such as electron beam proximity effect, fogging effect, loading effect, charge effect, and temperature effect.

[0024] Development simulation was performed based on the energy deposition distribution of the exposure to obtain the developed exposure pattern M. k The developing function (x,y) needs to be differentiable in both first-order and second-order forms.

[0025] Step S4: Correct the variable electron beam exposure method;

[0026] Define the cost function E(α) k ,w k ,l k )for:

[0027]

[0028] In the formula, H(x,y) is the mask pattern after optical proximity correction, and M... k (x,y) is the exposure pattern after variable electron beam proximity effect correction obtained through the k-th mask-wafer co-optimization iteration.

[0029] After simulating the forward exposure and development of variable electron beam lithography, the variable electron beam exposure mode is corrected by solving the Gauss-Newton iterative algorithm. The algorithm optimizes the coefficient matrix of the rectangular exposure basis function and the length and width of the exposure rectangle iteratively. The algorithm flow is as follows:

[0030] The iteration direction vector δ of the k-th Gauss-Newton iteration algorithm k for:

[0031]

[0032] In the formula, α k =[α1 α2…α p ] T w k =[w1 w2…w p ] T and l k =[l1 l2…l p ] T Let G(α) represent the coefficient vector, width, and height of the basis function rectangle in the k-th iteration, respectively; α represents the variable G(α). k ,w k ,l k ) is represented as:

[0033]

[0034] G'(α k ,w k ,l k ) represents G(α) k ,w k ,l k ) in (α k ,w k ,l k The first derivative at point M. k (x,y) is the exposure pattern after variable electron beam proximity effect correction obtained through the k-th mask-wafer co-optimization iteration.

[0035] The exposure rectangle coefficient α of the (k+1)th Gaussian-Newton iteration algorithm k Exposure rectangle length l k Width w k Updated to:

[0036]

[0037] In the formula, δ k This indicates the iteration direction of the (k+1)th Gaussian-Newton iteration algorithm.

[0038] Optionally, the modified variable electron beam exposure method is solved using a particle swarm optimization algorithm, the algorithm flow of which is as follows:

[0039] The rectangular basis function coefficients α of the kth particle swarm algorithm k The iterative velocity vector V k for:

[0040] V k =ωV k-1 +c1r1(α_pbest k -α k-1 )+c2r2(α_gbest k -α k-1 (10)

[0041] In the formula, ω is the inertia factor, c1 and c2 are learning factors, r1 and r2 are random numbers between (0,1), and α_pbest k α_gbest is the local optimum of the coefficients of the rectangular basis function in the k-th iteration. k This represents the globally optimal solution for the coefficients of the rectangular basis function in the k-th iteration.

[0042] Similarly, the width w of the basis function rectangle in the k-th particle swarm optimization algorithm k The iterative velocity vector V k for:

[0043] V k =ωV k-1 +c1r1(w_pbest k -w k-1 )+c2r2(w_gbest k -w k-1 (11)

[0044] In the formula, w_pbest k w_gbest is the local optimum of the width of the basis function rectangle in the k-th iteration. k This is the globally optimal solution for the width of the basis function rectangle in the k-th iteration.

[0045] Similarly, the length l of the basis function rectangle in the k-th particle swarm optimization algorithm k The iterative velocity vector V k for:

[0046] V k =ωV k-1 +c1r1(l_pbest k -l k-1 )+c2r2(l_gbest k -l k-1 (12)

[0047] In the formula, l_pbest k l_gbest is the local optimum of the height of the basis function rectangle in the k-th iteration. kIt is the globally optimal solution for the height of the basis function rectangle in the k-th iteration.

[0048] The exposure rectangle coefficient α of the (k+1)th particle swarm optimization algorithm k Exposure rectangle length l k Width w k Updated to:

[0049]

[0050] In the formula, V k This represents the iteration speed of the (k+1)th particle swarm optimization algorithm.

[0051] Optionally, the modified variable electron beam exposure method is solved using a genetic algorithm, the algorithm flow of which is as follows:

[0052] Initialize and set multiple electron beam exposure modes (one exposure mode corresponds to one set of α). k w k l k The fitness of each variable is calculated using the cost function of formula (6) as the evaluation criterion. The smaller the cost function, the higher the fitness of the exposure method.

[0053] 1) Perform selection operations as follows:

[0054] Some groups α are determined based on fitness levels. k w k l k Variables can be retained, and the greater the fitness, the greater the likelihood of them being retained.

[0055] 2) Perform crossover operations as follows:

[0056] The remaining multiple α groups k w k l k Variables are randomly paired, and each group α k w k l k The variables are cross-probability P c Swap some of the variables between them.

[0057] 3) Perform mutation operations as follows:

[0058] For each group of α that was retained k w k l k The variable has a probability of variation P m Change the values ​​of certain variables to other random values ​​within the range of possible values.

[0059] Execute step S5 to calculate the fitness of all exposure methods again. If the convergence criteria are met, output the result; otherwise, iterate and execute 1) selection operation, 2) crossover operation, and 3) mutation operation again.

[0060] Step S5: Set convergence conditions and output the optimized variable electron beam exposure mode.

[0061] Set convergence conditions, using the cost function of formula (6) as the standard. When the convergence error is less than or equal to the preset accuracy, the optimized variable electron beam exposure mode is output. When the convergence error is greater than the preset accuracy, the iterative operation is still performed until convergence, and the optimized variable electron beam exposure mode is output.

[0062] Similarly, the convergence criteria can also be set as the key dimensions of the pattern, edge error prevention, and other convergence criteria. Attached Figure Description

[0063] Figure 1 This is a flowchart of the operation of the present invention; Detailed Implementation

[0064] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0065] This invention relates to a mask wafer co-optimization method to improve mask exposure efficiency. The aim is to reduce the number of mask exposures and improve exposure efficiency while optimizing the optical proximity effect.

[0066] This invention is a mask wafer co-optimization method to improve mask exposure efficiency. The steps include: S1 calculating optical proximity correction to obtain the target mask pattern; S2 initially fracturing the target mask pattern and initializing the mask rectangle exposure basis function set; S3 simulating variable electron beam lithography forward exposure and development; S4 correcting the variable electron beam exposure mode; and S5 setting convergence conditions and outputting the optimized variable electron beam exposure mode. The technical feature of this invention is that by calculating optical proximity correction to obtain the target mask pattern, initially fracturing the target mask pattern, and initializing the mask rectangle exposure basis function set, the linear combination of these basis functions and a threshold function are used to represent the variable electron beam exposure lens. After simulating electron beam forward exposure and development, while ensuring the accuracy of the mask pattern after lithography, the variable electron beam exposure mode is optimized, reducing the number of variable electron beam exposures, thereby improving lithography efficiency. This method features high computational efficiency and high computational accuracy. The steps of this method are as follows: Figure 1 As shown, the specific embodiments of the present invention are as follows:

[0067] Step S1: Calculate optical proximity correction and obtain the target mask pattern;

[0068] Based on the optical lithography target pattern, the optical proximity correction is calculated, and the mask pattern H(x,y) after optical proximity correction is expressed as:

[0069]

[0070] In the formula, T{I(x,y)} represents the result of applying an optically lithographic forward model T{·} to a mask pattern I(x,y) without optical proximity correction; t (x,y) represents the optical lithography target pattern.

[0071] Step S2: Initialize the target mask pattern and initialize the mask rectangle exposure basis function set;

[0072] The initial fractured optical proximity effect corrected mask pattern H(x,y) is represented by multiple mask rectangle exposure basis functions. Each mask rectangle exposure basis function is defined as follows:

[0073]

[0074] In the formula, (x p ,y p ) represents the coordinates of the center point of the mask rectangle exposure basis functions in a two-dimensional matrix (p = 1, 2, ..., P, where P is the total number of basis functions), w p and l p Let be the width and length of the rectangle represented by the basis functions. A linear combination of the basis functions is expressed as:

[0075]

[0076] In the formula, α p It is the p-th basis function S p The coefficient, w p and l p The three coefficients, representing the width and length of the rectangle in the basis function representation, determine the exposure method of the variable electron beam, and different mask rectangle exposure basis functions allow for regional overlap.

[0077] Using this set of basis functions, the entire exposure mask pattern is defined and initialized as follows:

[0078]

[0079] In the formula, c is the pattern threshold. The differentiable threshold function Γ(ψ) is defined as:

[0080]

[0081] In the formula, ψ is a floating-point value, and ε is the slope control value.

[0082] Step S3: Variable electron beam lithography forward exposure and development simulation;

[0083] The mask pattern H, represented by the exposure basis function set of the mask rectangle in the k-th iteration (k≥0, k represents the iteration number), is used. k The energy deposition distribution of the simulated exposure is obtained by directly convolving (x,y) with the electron beam point spread function PSF(x,y). The electron beam point spread function includes the combined effects of secondary effects such as electron beam proximity effect, fogging effect, loading effect, charge effect, and temperature effect.

[0084] Development simulation was performed based on the energy deposition distribution of the exposure to obtain the developed exposure pattern M. k The developing function (x,y) needs to be differentiable in both first-order and second-order forms.

[0085] Step S4: Correct the variable electron beam exposure method;

[0086] Define the cost function E(α) k ,w k ,l k )for:

[0087]

[0088] In the formula, H(x,y) is the mask pattern after optical proximity correction, and M... k (x,y) is the exposure pattern after variable electron beam proximity effect correction obtained through the k-th mask-wafer co-optimization iteration.

[0089] After simulating the forward exposure and development of variable electron beam lithography, the variable electron beam exposure mode is corrected by solving the Gauss-Newton iterative algorithm. The algorithm optimizes the coefficient matrix of the rectangular exposure basis function and the length and width of the exposure rectangle iteratively. The algorithm flow is as follows:

[0090] The iteration direction vector δ of the k-th Gauss-Newton iteration algorithm k for:

[0091]

[0092] In the formula, α k =[α1 α2…α p ] T w k =[w1 w2…w p ] T and l k =[l1 l2…l p ] T Let G(α) represent the coefficient vector, width, and height of the basis function rectangle in the k-th iteration, respectively; α represents the variable G(α). k ,wk ,l k ) is represented as:

[0093]

[0094] G'(α k ,w k ,l k ) represents G(α) k ,w k ,l k ) in (α k ,w k ,l k The first derivative at point M. k (x,y) is the exposure pattern after variable electron beam proximity effect correction obtained through the k-th mask-wafer co-optimization iteration.

[0095] The exposure rectangle coefficient α of the (k+1)th Gaussian-Newton iteration algorithm k Exposure rectangle length l k Width w k Updated to:

[0096]

[0097] In the formula, δ k This indicates the iteration direction of the (k+1)th Gaussian-Newton iteration algorithm.

[0098] Optionally, the modified variable electron beam exposure method is solved using a particle swarm optimization algorithm, the algorithm flow of which is as follows:

[0099] The rectangular basis function coefficients α of the kth particle swarm algorithm k The iterative velocity vector V k for:

[0100] V k =ωV k-1 +c1r1(α_pbest k -α k-1 )+c2r2(α_gbest k -α k-1 (10)

[0101] In the formula, ω is the inertia factor, c1 and c2 are learning factors, r1 and r2 are random numbers between (0,1), and α_pbest k α_gbest is the local optimum of the coefficients of the rectangular basis function in the k-th iteration. k This represents the globally optimal solution for the coefficients of the rectangular basis function in the k-th iteration.

[0102] Similarly, the width w of the basis function rectangle in the k-th particle swarm optimization algorithm kThe iterative velocity vector V k for:

[0103] V k =ωV k-1 +c1r1(w_pbest k -w k-1 )+c2r2(w_gbest k -w k-1 (11)

[0104] In the formula, w_pbest k w_gbest is the local optimum of the width of the basis function rectangle in the k-th iteration. k This is the globally optimal solution for the width of the basis function rectangle in the k-th iteration.

[0105] Similarly, the length l of the basis function rectangle in the k-th particle swarm optimization algorithm k The iterative velocity vector V k for:

[0106] V k =ωV k-1 +c1r1(l_pbest k -l k-1 )+c2r2(l_gbest k -l k-1 (12)

[0107] In the formula, l_pbest k l_gbest is the local optimum of the height of the basis function rectangle in the k-th iteration. k It is the globally optimal solution for the height of the basis function rectangle in the k-th iteration.

[0108] The exposure rectangle coefficient α of the (k+1)th particle swarm optimization algorithm k Exposure rectangle length l k Width w k Updated to:

[0109]

[0110] In the formula, V k This represents the iteration speed of the (k+1)th particle swarm optimization algorithm.

[0111] Optionally, the modified variable electron beam exposure method is solved using a genetic algorithm, the algorithm flow of which is as follows:

[0112] Initialize and set multiple electron beam exposure modes (one exposure mode corresponds to one set of α). k w k l kThe fitness of each variable is calculated using the cost function of formula (6) as the evaluation criterion. The smaller the cost function, the higher the fitness of the exposure method.

[0113] 1) Perform selection operations as follows:

[0114] Some groups α are determined based on fitness levels. k w k l k Variables can be retained, and the greater the fitness, the greater the likelihood of them being retained.

[0115] 2) Perform crossover operations as follows:

[0116] The remaining multiple α groups k w k l k Variables are randomly paired, and each group α k w k l k The variables are cross-probability P c Swap some of the variables between them.

[0117] 3) Perform mutation operations as follows:

[0118] For each group of α that was retained k w k l k The variable has a probability of variation P m Change the values ​​of certain variables to other random values ​​within the range of possible values.

[0119] Execute step S5 to calculate the fitness of all exposure methods again. If the convergence criteria are met, output the result; otherwise, iterate and execute 1) selection operation, 2) crossover operation, and 3) mutation operation again.

[0120] Step S5: Set convergence conditions and output the optimized variable electron beam exposure mode.

[0121] Set convergence conditions, using the cost function of formula (6) as the standard. When the convergence error is less than or equal to the preset accuracy, the optimized variable electron beam exposure mode is output. When the convergence error is greater than the preset accuracy, the iterative operation is still performed until convergence, and the optimized variable electron beam exposure mode is output.

[0122] Similarly, the convergence criteria can also be set as the key dimensions of the pattern, edge error prevention, and other convergence criteria.

[0123] This invention synergistically optimizes two independent process flows: the optical lithography correction process and the secondary effect correction process of electron beam lithography. This improves the wafer pattern resolution while reducing the number of exposures for variable electron beam writing curve shapes, thereby greatly improving the efficiency of mask exposure while ensuring the accuracy of the mask pattern after lithography.

[0124] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the present invention. Referring to the description of these embodiments, those skilled in the art should be able to understand and make relevant modifications or substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention.

Claims

1. A mask-wafer collaborative optimization method for improving mask exposure efficiency, characterized in that, Includes the following steps: Step S1: Based on the optical proximity effect correction results, generate a binary target mask pattern H(x,y); Step S2: Divide the target mask pattern H(x,y) into rectangular exposure units, and construct the exposure basis function based on the rectangular exposure units. In the formula ( , Let be the coordinates of the center point of the mask rectangle exposure basis functions in the two-dimensional matrix, p be the basis function index (p=1,2,…,P), and P be the total number of basis functions. The symbols #imgpt4# represent the width and length of the rectangle; Step S3, simulated forward exposure and development of variable electron beam lithography; Step S4, with the cost function: As an evaluation criterion, k represents the number of iterations, and α k w is a coefficient k and l k Let H(x,y) represent the width and length of the rectangle, and let M represent the mask pattern after optical proximity correction. k (x,y) represents the exposure pattern after the kth mask-wafer collaborative optimization iteration. The cost function (2) satisfies the preset convergence condition as the convergence criterion. If the convergence criterion is not satisfied, the Gauss-Newton method, particle swarm algorithm or genetic algorithm is used to correct the variable electron beam exposure method. Step S5, with the cost function: For the standard, k represents the number of iterations, and α k w is a coefficient k and l k H(x,y) represents the width and length of the rectangle. The mask pattern after optical proximity correction, M k (x,y) represents the exposure pattern after the kth mask-wafer co-optimization iteration. Based on the cost function (3) as the convergence criterion, the optimized variable electron beam exposure mode is output.

2. The mask-wafer collaborative optimization method for improving mask exposure efficiency as described in claim 1, characterized in that: In step S1, optical proximity correction is calculated based on the optical lithography target pattern. The mask pattern H(x,y) after optical proximity correction is expressed as: In the formula, T{I(x,y)} represents the result of applying an optically lithographic forward model T{·} to a mask pattern I(x,y) without optical proximity correction; t (x,y) represents the optical lithography target pattern.

3. The mask-wafer collaborative optimization method for improving mask exposure efficiency as described in claim 1, characterized in that: In step S2, the initial fractured optical proximity effect corrected mask pattern H(x,y) is represented by multiple mask rectangle exposure basis functions. Each mask rectangle exposure basis function is defined as follows: In the formula, (x p ,y p Let be the coordinates of the center point of the mask rectangle exposure basis functions in the two-dimensional matrix, p be the basis function index, p = 1, 2, ..., P, and P be the total number of basis functions. p and l p Let be the width and length of the rectangle represented by the basis functions; The linear combination of basis functions is expressed as: In the formula, α p It is the p-th basis function S p The coefficient, w p and l p The width and length of the rectangle represented by the basis function, these three coefficients determine the exposure mode of the variable electron beam, and different mask rectangle exposure basis functions allow for regional overlap; Using this set of basis functions, the entire exposure mask pattern is defined and initialized as follows: In the formula, c is the pattern threshold; the differentiable threshold function Γ(ψ) is defined as: In the formula, ψ is a floating-point value, and ε is the slope control value.

4. The mask wafer collaborative optimization method for improving mask exposure efficiency as described in claim 1, characterized in that: In step S3, the mask pattern H represented by the mask rectangle of the k-th iteration is exposed to the basis function set. k The energy deposition distribution of the simulated exposure is obtained by directly convolving (x,y) with the electron beam point spread function PSF(x,y), where k is the iteration number and k≥0; the electron beam point spread function includes the combined effects of electron beam proximity effect, fogging effect, loading effect, charge effect and temperature effect. Development simulation was performed based on the energy deposition distribution of the exposure to obtain the developed exposure pattern M. k The developing function (x,y) needs to be differentiable in both first-order and second-order forms.

5. The mask wafer co-optimization method for improving mask exposure efficiency as described in claim 1, characterized in that: In step S4, using the cost function (3) as the evaluation function, after calculating the variable electron beam lithography forward exposure and development simulation, the variable electron beam exposure method is corrected by solving the Gauss-Newton iterative algorithm, and the exposure rectangle basis function coefficient matrix and the length and width of the exposure rectangle are iteratively optimized. The algorithm flow is as follows: The iteration direction vector δ of the k-th Gauss-Newton iteration algorithm k for: In the formula, α k =[α1 α2 … α p ]T、w k =[w1 w2 … w p T and l k =[l1 l2 … l p ]T, representing the coefficient vector, width, and height of the basis function rectangle in the k-th iteration, respectively; variable G(α k ,w k ,l k ) is represented as: G'(α k ,w k ,l k ) represents G(α) k ,w k ,l k ) in (α k ,w k ,l k The first derivative at point M; k (x,y) is the exposure pattern after variable electron beam proximity effect correction obtained through the kth mask-wafer co-optimization iteration; The exposure rectangle coefficient α of the (k+1)th Gaussian-Newton iteration algorithm k Exposure rectangle length l k Width w k Updated to: In the formula, δ k This indicates the iteration direction of the (k+1)th Gaussian-Newton iteration algorithm.

6. A mask wafer collaborative optimization method for improving mask exposure efficiency as described in claim 1. Its features are: In step S4, the variable electron beam exposure method is corrected using the cost function (3) as the evaluation function. The algorithm flow is as follows: The rectangular basis function coefficients α of the kth particle swarm algorithm k The iterative velocity vector V k for: In the formula, ω is the inertia factor, c1 and c2 are learning factors, r1 and r2 are random numbers between (0,1), and α_pbest k α_gbest is the local optimum of the coefficients of the rectangular basis function in the k-th iteration. k This represents the globally optimal solution for the coefficients of the rectangular basis function in the k-th iteration. Similarly, the width w of the basis function rectangle in the k-th particle swarm optimization algorithm k The iterative velocity vector V k for: In the formula, w_pbest k w_gbest is the local optimum of the width of the basis function rectangle in the k-th iteration. k This is the globally optimal solution for the width of the basis function rectangle in the k-th iteration; Similarly, the length l of the basis function rectangle in the k-th particle swarm optimization algorithm k The iterative velocity vector V k for: In the formula, l_pbest k l_gbest is the local optimum of the height of the basis function rectangle in the k-th iteration. k The globally optimal solution for the height of the basis function rectangle in the k-th iteration; The exposure rectangle coefficient α of the (k+1)th particle swarm optimization algorithm k Exposure rectangle length l k Width w k Updated to: In the formula, V k This represents the iteration speed of the (k+1)th particle swarm algorithm.

7. The mask wafer co-optimization method for improving mask exposure efficiency as described in claim 1, characterized in that: In step S4, the cost function (3) is used as the evaluation function, and the genetic algorithm is used to correct the variable electron beam exposure method. The algorithm flow is as follows: The initial settings include multiple electron beam exposure modes, with one mode corresponding to a set of α values. k w k l k The fitness of each variable is calculated using the S5 cost function as the evaluation criterion. The smaller the cost function, the higher the fitness of the exposure method. 1) Perform selection operations as follows: Some groups α are determined based on fitness levels. k w k l k Variables can be retained, and the greater the fitness, the greater the likelihood of them being retained. 2) Perform crossover operations as follows: The remaining multiple α groups k w k l k Variables are randomly paired, and each group α k w k l k The variables are cross-probability P c Swap some of the variables between them; 3) Perform mutation operations as follows: For each group of α that was retained k w k l k The variable has a probability of variation P m Change the values ​​of certain variables to other random values ​​within the range of possible values; Execute step S5 to calculate the fitness of all exposure methods again. If the convergence criteria are met, output the result; otherwise, iterate and execute 1) selection operation, 2) crossover operation, and 3) mutation operation again.

8. The mask wafer co-optimization method for improving mask exposure efficiency as described in claim 1, characterized in that: In step S5, the convergence condition is set, and the exposure pattern after variable electron beam proximity effect correction is obtained through cost function co-optimization iteration. When the convergence error is less than or equal to the preset accuracy, the optimized variable electron beam exposure method is used; when the convergence error is greater than the preset accuracy, the iterative operation is still performed until convergence, and the optimized variable electron beam exposure method is output. The convergence criteria can also be set as the key dimensions of the pattern and the convergence criteria for edge placement errors.

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