CN113568278B - Curve type reverse photoetching method based on rapid covariance matrix self-adaptive evolution strategy - Google Patents

Abstract

An Inverse curve Lithography (IL) method based on Fast Covariance Matrix adaptive evolution strategy (Fast CMA-ES). The method characterizes the mask pattern in pixels, each pixel representing the mask transmittance at that location. And (3) optimizing the mask pattern by adopting a rapid covariance matrix adaptive evolution strategy by taking weighted superposition of pattern errors between the photoresist pattern and the target pattern under different exposure dose deviations and defocus conditions as an evaluation function. The method approximates the covariance matrix representing the solution space distribution to a set of simple models only composed of two evolution paths, learns the main solution search direction and variable correlation by means of the low-rank approximation of the covariance matrix, adaptively adjusts the search step length, improves the convergence efficiency and the optimization capability, and effectively improves the photoetching imaging quality and the process robustness.

Description

Curve type reverse photoetching method based on rapid covariance matrix self-adaptive evolution strategy

Technical Field

The invention belongs to the technical field of photoetching resolution enhancement, and particularly relates to a curvilinear reverse photoetching method based on a rapid covariance matrix adaptive evolution strategy.

Background

Photolithography is one of the key technologies in very large scale integrated circuit fabrication, and the photolithography resolution determines the Critical Dimension (CD) of the integrated circuit pattern. As the feature size of integrated circuit patterns is continuously reduced, the mask diffraction effect becomes increasingly non-negligible, resulting in the degradation of the lithographic imaging quality, and therefore a series of lithographic Resolution Enhancement Techniques (RETs) have been proposed in the art. Inverse Lithography Technology (ILT) was first used for 65nm node integrated circuit fabrication, and has been developed, and has become one of the resolution enhancement technologies essential for the fabrication of 22nm and below technology node integrated circuits. The reverse lithography technique utilizes a lithography imaging model to reversely calculate the mask pattern with the best imaging quality under given process conditions. The search space of the optimal solution of the reverse photoetching is large, and the mask optimization process is not limited by the target pattern. Because Sub-Resolution Assist Feature (SRAF) can be generated flexibly and optimization of the main Feature and the Assist Feature can be realized at the same time, the optimal mask pattern calculated by the reverse lithography technique can obtain the pattern fidelity and process window that Optical Proximity Correction (OPC) and the Sub-Resolution Assist Feature cannot achieve.

Early reverse lithography techniques suffered from inefficient optimization, poor manufacturability of the optimized mask, and the like. In order to avoid the loss of imaging performance caused by the regularization method to improve the Mask manufacturability, techniques such as Curvilinear Mask Process Correction (CLMPC), Curvilinear Mask Rule Check (CLMC), Model-Based Mask Data Preparation (MBMDP), etc. are proposed in succession in the industry to generate Curvilinear Mask patterns by means of the reverse lithography technique. Due to the limiting factors of the electron beam shape, the sensitivity of photoresist, the resolution of a lithography machine and the like, the real mask pattern and the pattern transferred to the silicon wafer are both curved. The imaging quality of the curvilinear mask pattern is better than that of a manhattan type mask pattern produced by optical proximity correction. However, in order to precisely manufacture the curved mask pattern, more electron beam bombardment times are required, increasing mask write-through time and mask manufacturing costs. The Multi Beam Mask Writer (MBMW) can manufacture a Mask pattern with any shape by a single bombardment of electron beams with a large number of independent control switches, so that the Mask write time only depends on the Mask area and is not influenced by the shape of the Mask pattern. The introduction of multi-electron beam mask direct writing is considered by the industry to greatly improve the efficiency of curve type mask direct writing and clear the biggest obstacle of mask mass production. In recent years, the development of the full-chip reverse lithography technology is promoted by the introduction of a Graphics Processing Unit (GPU), and the scheme of mask block optimization, optimization result integration, global verification and multiple iterative adjustment and correction as in the conventional reverse lithography technology is not required any more, so that the efficiency of the full-chip reverse lithography is improved. Therefore, it is important to perform reverse lithography by using an efficient core optimization algorithm.

The optimization of the Mask pattern was guided by calculating the gradient of the evaluation function based on the gradient reverse lithography method (prior art 1, w.lv, q.xia, and s.liu, "Mask-filtering-based inversion lithography," j.micro/nanolith.mems MOEMS,12(4),043003 (2013)). Since the gradient calculation process involves frequent calling of the lithography imaging module, when the complexity of the lithography imaging model and the evaluation function expression is increased, the time consumption of the gradient calculation is obviously increased, and the mask optimization efficiency is reduced. The mask optimization method based on the heuristic optimization algorithm does not need to master the priori knowledge of photoetching, and any imaging model and optimization target can be selected. Reverse lithography pixelates the mask pattern with a small-size grid, which is essentially a non-convex (multi-peaked), inseparable high-dimensional nonlinear mask optimization problem. The mask optimization method based on the Covariance Matrix adaptive Evolution Strategy (CMA-ES) algorithm (prior art 2, G.Chen, S.Li, and X.Wang, "Source mask optimization using the Covariance Matrix adaptive Evolution Strategy," Opt.express 28(22), "33371-. However, when the dimension of the optimized variable is increased to thousands or even more than tens of thousands, the eigenvalue decomposition efficiency of the large covariance matrix is extremely low, and the generation efficiency of the candidate solution vector and the mask optimization performance are greatly reduced. In addition, the variable dimension in reverse lithography is high, which results in too low learning rate factor of the covariance matrix adaptive evolution strategy algorithm and too low adaptive adjustment speed of the covariance matrix and the search step length. Therefore, the covariance matrix adaptive evolution strategy is obviously not suitable for the inverse lithography technology with huge optimization variable dimension. The mask Optimization method based on the Social Learning Particle Swarm (SL-PSO) algorithm (prior art 3, z.zhang, s.li, x.wang, w.cheng, and y.qi, "Source mask Optimization for extreme-analysis based on a program mask model and a Social Learning Particle Swarm Optimization algorithm," operation.express 29(4),5448-5465(2021)) requires the construction of a population in which the number of individuals and the number of Optimization variables are linearly related, i.e., the Social Learning of the individuals is completed by the large population in reverse lithography, so that the number of calls of the evaluation function is greatly increased, and the mask Optimization efficiency is reduced.

In summary, the existing reverse lithography method has the defects of high gradient calculation cost, low convergence efficiency of the optimization algorithm due to overhigh variable dimension and the like.

Disclosure of Invention

The invention provides a curve type reverse photoetching method based on a rapid covariance matrix self-adaptive evolution strategy. The mask pattern is characterized by pixels, each pixel in the mask pattern representing the transmittance at that location. And (3) taking weighted superposition of graphic errors between the photoresist graphic and the target graphic under different exposure dose deviations and defocusing amounts as an evaluation function, and optimizing the mask graphic by adopting a rapid covariance matrix adaptive evolution strategy. The method approximates the covariance matrix representing the solution space distribution to a set of simple models only composed of two evolution paths, learns the main solution search direction and variable correlation by means of the low-rank approximation of the covariance matrix, adaptively adjusts the search step length, improves the convergence efficiency and the optimization capability, and effectively improves the photoetching imaging quality and the process robustness.

The technical solution of the invention is as follows:

the curve type reverse photoetching method based on the fast covariance matrix self-adaptive evolution strategy comprises the following specific steps:

1. initializing light source pattern J ₀Pupil function H₀Photoresist sensitivity alpha and photoresist threshold t_rMask threshold t_mDeveloping threshold t_devThe value of the exposure dose deviation and the corresponding weight, and the value of the defocus amount and the corresponding weight. (in the case where no additional description is given, the bold variables or numbers are vectors or matrices in this context)

Initializing T values of exposure dose deviation T, wherein the corresponding weight is p_tInitializing H values of defocus H, and setting the corresponding weight as p_h. Initializing a light source graph J according to the value of the defocusing amount h₀And pupil function H₀And (3) calculating TCC cores corresponding to the defocusing amount h in the Hopkins imaging model in advance, wherein TCC (Transmission Cross coefficient) represents a transmission Cross coefficient, and the first K TCC cores are reserved.

2. Initializing mask pattern M₀A target pattern TP formed by initializing a mask pattern M₀Obtaining a mask code x_M。

Initializing mask pattern M₀Is of size N_V×N_HWherein N is_VAnd N_HRespectively representing initialization mask patterns M₀Each column and each row of bagsThe number of the contained elements is odd. Setting initialization mask pattern M₀The transmittance of the upper light-transmitting pixel is 1, and the transmittance of the light-shielding pixel is 0. Initializing target pattern TP ═ M₀。

The mask pattern coding mode is selected according to the symmetry of the mask pattern, and common mask patterns comprise an asymmetric mask pattern and an axisymmetric mask pattern.

When the mask pattern M is initialized₀For asymmetric mask pattern, the initial mask pattern M is scanned column by column point₀And carrying out mask coding by using all pixel values obtained by scanning:

x_M＝(M₀(1,1),…,M₀(N_V,1),…,M₀(i,j),…,M₀(1,N_H),…,M₀(N_V,N_H)).

wherein M is₀(i, j) represents the initialization mask pattern M₀(ii) a mask pixel transmittance at the middle index position of (i, j),

and i is more than or equal to 1 and less than or equal to N_V，

And j is more than or equal to 1 and less than or equal to N_H，M₀(i, j) is e {0,1}, and the variable dimension D_M＝N_V×N_H。

When the mask pattern M is initialized₀When the horizontal axis symmetry and the vertical axis symmetry are satisfied simultaneously, the initialization mask pattern M is scanned column by column point₀Middle row number range from 1 to NH_VColumn number ranging from 1 to NH_HThe sub-block of (2) is mask-encoded using the pixel values obtained by the scanning:

x_M＝(M₀(1,1),…,M₀(NH_V,1),…,M₀(i,j),…,M₀(1,NH_H),…,M₀(NH_V,NH_H)).

wherein NH_V＝(1+N_V)/2，NHH＝(1+N_H)/2，M₀(i, j) represents the initialization mask pattern M₀Middle index(ii) mask pixel transmittance at position (i, j),

and i is more than or equal to 1 and less than or equal to NH_V，

And j is more than or equal to 1 and less than or equal to NH_H，M₀(i, j) is e {0,1}, and the variable dimension D_M＝NH_V×NH_H。

Mask patterns that satisfy only horizontal axis symmetry or only vertical axis symmetry may be encoded in a similar manner and will not be described in detail herein. 3. Coding x according to a mask_MDecoding is carried out, and a binary mask M is obtained by mask filtering and binarization processing_B。

The mask pattern decoding method is selected according to the symmetry of the mask pattern.

When the mask pattern M is initialized₀When the mask pattern is asymmetric, the expression is used

Coding a mask x_MIs arranged into a size of N_V×N_HThe matrix M of (a).

When the mask pattern M is initialized₀When the horizontal axis symmetry and the vertical axis symmetry are simultaneously satisfied, the expression is utilized

Coding a mask x_MIs finished into NH_V×NH_HSub-block M of_qUsing subblock M_qFilling size of N_V×N_HThe line number range of the mask pattern M with the element values all being 0 is 1 to NH_VColumn number ranging from 1 to NH_HPart (c) of (a). According to sub-block M_qNH th of mask patterns M, respectively_VRow and NH th_HAnd (4) listing as a symmetry axis, carrying out symmetric assignment on other elements in the mask pattern M, and dividing the value of the element on the corresponding symmetry axis by 2 after each symmetric assignment is finished to obtain the symmetric mask pattern M.

Whether or not the mask pattern isSymmetry can reduce the complexity of the mask pattern by a mask filtering method or a regularization method, thereby improving the manufacturability of the mask pattern. The invention adopts Gaussian filtering processing to the mask pattern to obtain the fuzzified mask pattern M_blur，

Wherein the content of the first and second substances,

representing the convolution symbol, r₀Represents the center position, | | r-r₀I represents point r to point r₀Distance of (a)_GFIs the standard deviation of the gaussian function and Ω represents the number of elements contained in the gaussian convolution kernel.

Using a mask threshold t_mBlurred mask pattern M _blurBinary processing is carried out to obtain a decoded binary mask M_BI.e. M_B＝Γ(M_blur-t_m)。Γ(x)＝{1|x≥0∪0|x<0} and the function Γ (x) will be M_blurMiddle transmittance is greater than or equal to mask threshold t_mAssigns M to 1_blurMedium transmittance less than mask threshold t_mThe pixel of (a) is assigned a value of 0.

4. Constructing an evaluation function of a reverse lithography problem

And taking weighted superposition of graphic errors between the photoresist graph and the target graph under different exposure dose deviations and defocus conditions as an evaluation function. The specific calculation process of the evaluation function is as follows:

4.1 decoding the mask x_MBinary mask M obtained by decoding_BSubstituting the space image into a Hopkins imaging model, calculating an aerial image AI when the defocusing amount is h,

wherein the content of the first and second substances,

is a binary mask M_BThe mask diffraction spectrum calculated by fourier transform, (x, y) is the spatial coordinates of the mask pattern, and (f ', g') is the normalized spatial frequency coordinates of the mask diffraction spectrum. Phi_i(f ', g'; h) denotes the ith frequency domain TCC kernel, S, with defocus h_iAnd the coefficients corresponding to the ith TCC core are shared by K TCC cores. IFFT { } denotes an inverse fourier transform.

4.2 calculating the photoresist image RI when the defocusing amount is h and the exposure dose deviation is t according to the space image AI and the sigmoid photoresist model,

where α is the photoresist sensitivity, t _rIs the photoresist threshold. Besides the sigmoid photoresist model, a constant threshold photoresist model, a variable threshold photoresist model, a three-dimensional photoresist model and the like can be selected according to actual needs.

4.3 in the Positive developing process, if the RI of the photoresist image is greater than or equal to the developing threshold t_devThen the photoresist at that location is removed; conversely, if the photoresist image RI is less than the development threshold t_devThe photoresist at that location is retained. Thus, a developed resist pattern RC is obtained, that is, RC (x, y; h, t) ═ Γ (RI (x, y; h, t) -t_dev)。

4.4 constructing an evaluation function f by utilizing the weighted superposition of the graphic errors between the photoresist graph and the target graph under the conditions of different exposure dose deviations t and defocus amounts h,

5. optimizing mask patterns using fast covariance matrix adaptive evolution strategy

5.1 initializing the evolution algebra g of the fast covariance matrix self-adaptive evolution strategy, the current minimum evaluation function value tmpBestF, the optimal mask code bestX, the population mean vector m, the search step sigma, the search step adjustment factor s, the evolution path P of the covariance matrix, periodically storing and updating the low-rank matrix P of the evolution path, the iteration termination condition of the optimization process and the like.

The variable dimension N of the optimization problem is an important parameter, and a plurality of parameters in the fast covariance matrix self-adaptive evolution strategy are obtained through calculation according to N. In a reverse lithography method, the optimization variable dimension N ═ D _M. Setting the initial evolution algebra g to 0, setting the current minimum evaluation function value tmpBestF to a larger value, and coding x by using the mask corresponding to the target graph TP_MInitializing best mask code bestX and population mean vector m⁽⁰⁾Initial search step size σ⁽⁰⁾Setting the length of the variable interval to be one third, and initializing a search step length adjustment factor to be s ⁽⁰⁾0. The evolution path of the covariance matrix is initialized to p⁽⁰⁾The low rank matrix is initialized to P0.

In addition, the iteration termination condition of the reverse lithography includes: the minimum value of the evaluation function stopFitness, the maximum calling times of the evaluation function stopExval, and the variation range of the evaluation function values in the continuous iteration process is too small (the variation range of continuous nLimit generations is smaller than tolerance).

5.2 setting relevant parameters of the fast covariance matrix adaptive evolution strategy:

population comprises number of individuals:

the number of parents in the recombination is:

the weight corresponding to the ith individual in the recombination is:

satisfy omega₁≥…≥ω_μIs not less than 0 and

effective variance selection quality:

cumulative time constant of covariance matrix evolution path: c is 2/(N +5).

Generating a learning rate of the mutation according to the evolution path:

cumulative time constant of search step: c. C_σ＝0.3.

Target rate of search step adjustment: q. q.s ^*＝0.27.

Searching the damping factor of step adjustment: d is a radical of_σ＝1.

The number of search directions contained in the low-rank matrix: n ═ λ.

Algebraic interval of low rank matrix update: Δ g ═ 50.

5.3 according to the standard normal distribution

Covariance matrix evolution path p of current generation (g generation)^(g)Current low rank matrix P^(g)Generating random mutation, combining with population mean vector m of current generation^(g)Generating candidate solutions of the next generation (g +1 th generation), each candidate solution corresponding to a mask code, the steps are as follows:

5.3.1 random mutations were generated for the ith individual,

wherein

Is a low rank matrix P^(g)Ith column in (1), corresponding to low rank matrix P^(g)The ith search direction of (1).

5.3.2 population binding to Current GenerationMean vector m^(g)Random mutation with the i-th individual to generate the i-th individual of the next generation

5.4 updating the mean vector

After the evaluation function values of lambda individuals in the g +1 th generation population are arranged in ascending order, the individuals corresponding to the evaluation function values in the ith position are sorted, namely

f denotes the evaluation function constructed in step 4.4, which is to be called individually each time

Decoding as mask code to obtain binary mask M_B. Selecting the first mu individuals with the minimum fitness value in the g +1 generation for recombination to generate a mean vector of the g +1 generation

The updated mean may be considered a weighted maximum likelihood estimate of the population distribution mean.

5.5 updating evolution Path and Low rank matrix by cumulative learning

The evolution path performs cumulative learning on the continuous movement of the distribution mean in the iteration process, as shown in the following formula:

the evolutionary path cumulatively learns successive search directions in an iterative process, reducing oscillations between these search directions. The opposite search directions cancel out and the consistent direction is accumulated into the evolution path. Thus, the current evolutionary path represents one of the most potential search directions.

Every time a fixed algebra delta g is passed, the earliest searching direction in the low-rank matrix P is replaced by the current evolution path, and in other algebras, the low-rank matrix P of the previous generation is directly used, namely

if g％Δg＝0，P^(g+1)＝P^(g).

5.6 Using sort-based success rules for step size adjustment

Respectively extracting the minimum mu evaluation function values F of the g generation and the g +1 generation^(g)And F^(g+1)The union of the two is F ═ F^(g)∪F^(g+1). Then the union set F is arranged in ascending order to obtain F_mix. Calculating the difference of the two generations of populations by comparing the weighted rank sums of the two adjacent generations of populations:

and

the ith-smallest evaluation function of the g-th generation and the g +1 th generation, respectively, is expressed in F_mixThe order in (1). In an iterative process by means of a target rate q^*Q is smoothed to eliminate randomness. The search step adjustment factor is updated to s ^(g+1)＝(1-c_σ)s^(g)+c_σ(q-q^*) The search step is updated to σ^(g+1)＝σ^(g)·exp(s^(g+1)/d_σ)。

5.7 judging iteration termination Condition

And if the minimum evaluation function value of the current population is less than the minimum value stopFitness of the evaluation function, the number of times of calling the evaluation function reaches the maximum number of times of calling stopEval or the variation range of the continuous nLimit generation of the evaluation function is less than tolerance, then the step 5.8 is carried out.

Otherwise, recording the minimum evaluation function value of the current population

And best mask code bestX: if the minimum evaluation function value of the current population

If the current minimum evaluation function value tmpBestF is less than the current minimum evaluation function value tmpBestF, the current minimum evaluation function value tmpBestF is updated to the minimum evaluation function value of the current population

Updating the best mask code bestX to the best individual of the current population

Otherwise, the current minimum evaluation function value tmpBestF remains unchanged, the best mask code bestX remains unchanged, and the process returns to step 5.3.

5.8 terminate the optimization process and output the optimal binary mask pattern M according to the optimal mask code bestX decoding_B。

Compared with the prior art, the invention has the following advantages:

the method approximates the covariance matrix representing the solution space distribution to a set of a simple model only consisting of two evolution paths, learns the main solution search direction and variable correlation by means of low-rank approximation of the covariance matrix, adaptively adjusts the search step length, avoids time-consuming eigenvalue decomposition operation of a large covariance matrix by adopting an efficient solution vector generation mode, can realize optimization of high-dimensional variables in reverse photoetching without learning among large groups of individuals, improves the convergence efficiency and the optimization searching capability, and effectively improves the photoetching imaging quality and the process robustness.

Drawings

FIG. 1 is a schematic diagram of a target mask pattern used in the present invention

FIG. 2 is a schematic diagram of a photoresist pattern generated under different process conditions using an initial mask pattern according to the present invention

FIG. 3 is a schematic diagram of a mask pattern optimized by the method of the present invention

FIG. 4 is a schematic diagram of a mask pattern optimized by the SL-PSO algorithm

FIG. 5 is a schematic diagram of a photoresist pattern produced under different process conditions using an optimized mask pattern of the present invention

FIG. 6 is a schematic diagram of a photoresist pattern generated under different process conditions by using a mask pattern optimized by the SL-PSO algorithm

FIG. 7 is a schematic diagram comparing the convergence curves of the inverse lithography by the method of the present invention and SL-PSO algorithm

FIG. 8 is a flow chart of reverse photolithography using the method of the present invention

Detailed Description

The present invention will be further described with reference to the following examples and drawings, but the present invention should not be limited by these examples. FIG. 1 is a diagram of a target mask pattern used in the present invention, the mask pattern size is 1215nm, which includes 405X 405 pixels, and the feature size is 45 nm. The mask pattern is a binary mask satisfying both horizontal axis symmetry and vertical axis symmetry, and has a white region transmittance of 1 and a black region transmittance of 0.

The invention provides a curve type reverse photoetching method based on a rapid covariance matrix self-adaptive evolution strategy, which comprises the following steps:

1. initializing light source pattern J₀Pupil function H₀Photoresist sensitivity alpha and photoresist threshold t_rMask threshold t_mDeveloping threshold t_devThe value of the exposure dose deviation and the corresponding weight, and the value of the defocus amount and the corresponding weight.

In the present embodiment, the illumination wavelength of the lithography machine is 193.368nm, and the partial coherence factor sigma is adopted_in＝0.7、σ_outThe ring light source is 0.9, the polarization type of the light source is tPol, the numerical aperture NA of the projection objective is 1.35, the zoom magnification R is 4, and the refractive index of the immersion liquid is 1.44. T is 3, the exposure dose deviation T has 3 values of { -10%, 0, 10% }, the corresponding weights are {1.5,1,1.5}, H is 2, and the defocus amount H has a value of { -10%, 0, 10% }{0nm, 60nm }, with corresponding weights {1,1.1}, respectively. Initializing a light source graph J according to the value of the defocusing amount h₀And pupil function H₀The TCC kernel corresponding to the defocus amount h in the Hopkins imaging model is calculated in advance, and the first 10 TCC kernels are reserved, i.e., the number of TCC kernels is K10.

2. Initializing mask pattern M₀A target pattern TP formed by initializing a mask pattern M₀Obtaining a mask code x_M。

Initializing mask pattern M ₀Has a size of 405X 405, i.e. N_V＝N_H405. Setting an initialization mask pattern M₀The transmittance of the upper light-transmitting pixel is 1, and the transmittance of the light-shielding pixel is 0. Initializing target pattern TP ═ M₀。

The mask pattern coding mode is selected according to the symmetry of the mask pattern, and common mask patterns comprise an asymmetric mask pattern and an axisymmetric mask pattern.

When the mask pattern M is initialized₀For asymmetric mask pattern, the initial mask pattern M is scanned column by column point₀And carrying out mask coding by using all pixel values obtained by scanning:

x_M＝(M₀(1,1),…,M₀(N_V,1),…,M₀(i,j),…,M₀(1,N_H),…,M₀(N_V,N_H)).

wherein M is₀(i, j) represents the initialization mask pattern M₀(ii) a mask pixel transmittance at the middle index position of (i, j),

and i is more than or equal to 1 and less than or equal to N_V，

And j is more than or equal to 1 and less than or equal to N_H，M₀(i, j) is e {0,1}, and the variable dimension D_M＝N_V×N_H。

When the mask pattern M is initialized₀When the horizontal axis symmetry and the vertical axis symmetry are satisfied simultaneously, the initialization mask pattern M is scanned column by column point₀Middle row number range from 1 to NH_VColumn number ranging from 1 to NH_HThe sub-block of (2) is mask-encoded using the pixel values obtained by the scanning:

x_M＝(M₀(1,1),…,M₀(NH_V,1),…,M₀(i,j),…,M₀(1,NH_H),…,M₀(NH_V,NH_H)).

wherein NH_V＝(1+N_V)/2，NH_H＝(1+N_H)/2，M₀(i, j) represents the initialization mask pattern M₀(ii) a mask pixel transmittance at the middle index position of (i, j),

and i is more than or equal to 1 and less than or equal to NH_V，

And j is more than or equal to 1 and less than or equal to NH_H，M₀(i, j) is e {0,1}, and the variable dimension D_M＝NH_V×NH_H。

Mask patterns that satisfy only horizontal axis symmetry or only vertical axis symmetry may be encoded in a similar manner and will not be described in detail herein. 3. Coding x according to a mask _MDecoding is carried out, and a binary mask M is obtained by mask filtering and binarization processing_B。

The mask pattern decoding method is selected according to the symmetry of the mask pattern.

When the mask pattern M is initialized₀When the mask pattern is asymmetric, the expression is used

Coding a mask x_MIs arranged to be N in size_V×N_HThe matrix M of (a).

When the mask pattern M is initialized₀When the horizontal axis symmetry and the vertical axis symmetry are simultaneously satisfied, the expression is utilized

Coding a mask x_MIs finished into NH_V×NH_HSub-block M of_qUsing subblock M_qFilling size of N_V×N_HThe line number range of the mask pattern M with the element values all being 0 is 1 to NH_VColumn number ranging from 1 to NH_HPart (c) of (a). According to sub-block M_qNH th of mask patterns M, respectively_VRow and NH th_HAnd (4) listing as a symmetry axis, carrying out symmetric assignment on other elements in the mask pattern M, and dividing the value of the element on the corresponding symmetry axis by 2 after each symmetric assignment is finished to obtain the symmetric mask pattern M.

Whether the mask pattern is symmetrical or not, the complexity of the mask pattern can be reduced by a mask filtering method or a regularization method, thereby improving the manufacturability of the mask pattern. The invention adopts Gaussian filtering processing to the mask pattern to obtain the fuzzified mask pattern M_blur，

Wherein the content of the first and second substances,

Represents the convolution symbol, r₀Represents the center position, | | r-r₀| | denotes point r to point r₀Distance of (a)_GFIs the standard deviation of the gaussian function and Ω represents the number of elements contained in the gaussian convolution kernel. In this embodiment, the Gaussian convolution kernel is a 21 × 21 matrix, σ_GF＝18nm。

Using a mask threshold t_mBlurred mask pattern M_blurBinary processing is carried out to obtain a decoded binary mask M_BI.e. M_B＝Γ(M_blur-t_m)。Γ(x)＝{1|x≥0∪0|x<0} and the function Γ (x) will be M_blurMiddle transmittance is greater than or equal to mask threshold t_mAssigns M to 1_blurMedium transmittance less than mask threshold t_mThe pixel of (a) is assigned a value of 0.

Mask patterns that satisfy only horizontal axis symmetry or vertical axis symmetry can be decoded in a similar manner and will not be described in detail here. 4. Constructing an evaluation function of a reverse lithography problem

And taking weighted superposition of graphic errors between the photoresist graph and the target graph under different exposure dose deviations and defocus conditions as an evaluation function. The specific calculation process of the evaluation function is as follows:

4.1 decoding the mask x_MBinary mask M obtained by decoding_BSubstituting the space image into a Hopkins imaging model, calculating an aerial image AI when the defocusing amount is h,

wherein the content of the first and second substances,

is a binary mask M_BThe mask diffraction spectrum calculated by fourier transform, (x, y) is the spatial coordinates of the mask pattern, and (f ', g') is the normalized spatial frequency coordinates of the mask diffraction spectrum. Phi _i(f ', g'; h) denotes the ith frequency-domain TCC core, S, at defocus h_iAnd the coefficient corresponding to the ith TCC core is shared to K which is 10 TCC cores. IFFT { } denotes an inverse fourier transform.

4.2 calculating the photoresist image RI when the defocusing amount is h and the exposure dose deviation is t according to the space image AI and the sigmoid photoresist model,

wherein, alpha is the sensitivity of the photoresist, t_rIs the photoresist threshold. Besides the sigmoid photoresist model, a constant threshold photoresist model, a variable threshold photoresist model, a three-dimensional photoresist model and the like can be selected according to actual needs.

4.3 in the Positive developing process, if the RI of the photoresist image is greater than or equal to the developing threshold t_devThen the photoresist at that location is removed; conversely, if the photoresist image RI is less than the development threshold t_devThe photoresist at that location is retained. Thereby obtaining a developed photoresistThe pattern RC, RC (x, y; h, t) ═ Γ (RI (x, y; h, t) -t_dev)。

4.4 constructing an evaluation function f by utilizing the weighted superposition of the graphic errors between the photoresist graph and the target graph under the conditions of different exposure dose deviations t and defocus amounts h,

5. optimizing mask patterns using fast covariance matrix adaptive evolution strategy

5.1 initializing the evolution algebra g of the fast covariance matrix self-adaptive evolution strategy, the current minimum evaluation function value tmpBestF, the optimal mask code bestX, the population mean vector m, the search step sigma, the search step adjustment factor s, the evolution path P of the covariance matrix, periodically storing and updating the low-rank matrix P of the evolution path, the iteration termination condition of the optimization process and the like.

The variable dimension N of the optimization problem is an important parameter, and a plurality of parameters in the fast covariance matrix adaptive evolution strategy are obtained through calculation according to N. In the reverse lithography method, the optimization variable dimension N ═ D_M. The initial evolution algebra g is 0, and the current minimum evaluation function value tmpbesf is set to a larger value, which is 10 in this embodiment⁶Coding x with a mask corresponding to the target pattern TP_MInitializing best mask code bestX and population mean vector m⁽⁰⁾Initial search step size σ⁽⁰⁾Set to one third of the variable interval length, taken as 0.33 in this example, the search step adjustment factor is initialized to s ⁽⁰⁾0. The evolution path of the covariance matrix is initialized to p⁽⁰⁾The low rank matrix is initialized to P0.

In addition, the iteration termination condition of the reverse lithography includes: the minimum value of the evaluation function stopFitness, the maximum calling times of the evaluation function stopExval, and the variation range of the evaluation function values in the continuous iteration process is too small (the variation range of continuous nLimit generations is smaller than tolerance). In this embodiment, stopperiod is 200, stopinterval 15000, nLimit 100, and tolerance 10.

5.2 setting relevant parameters of the fast covariance matrix adaptive evolution strategy:

Population comprises number of individuals:

the number of parent individuals in the recombination was:

the weight corresponding to the ith individual in the recombination is:

satisfy omega₁≥…≥ω_μNot less than 0 and

effective variance selection quality:

cumulative time constant of covariance matrix evolution path: c is 2/(N +5).

Generating a learning rate of the mutation according to the evolution path:

cumulative time constant of search step: c. C_σ＝0.3.

Target rate of search step adjustment: q. q.s^*＝0.27.

Searching for damping factor of step adjustment: d_σ＝1.

The number of search directions contained in the low rank matrix is: n ═ λ.

Algebraic interval of low rank matrix update: Δ g ═ 50.

5.3 Normal distribution according to the Standard

Of the current generation (g-th generation)Covariance matrix evolution path p^(g)Current low rank matrix P^(g)Generating random mutation, combining with population mean vector m of current generation^(g)Generating candidate solutions of the next generation (g +1 th generation), each candidate solution corresponding to a mask code, the steps are as follows:

5.3.1 random mutations were generated for the ith individual,

wherein

Is a low rank matrix P^(g)Ith column in (1), corresponding to low rank matrix P^(g)The ith search direction of (1).

5.3.2 population mean vector m in combination with the current generation^(g)Random mutation with the i-th individual to generate the i-th individual of the next generation

5.4 updating the mean vector

After the evaluation function values of lambda individuals in the g +1 th generation population are arranged in ascending order, the individuals corresponding to the evaluation function values in the ith position are sorted, namely

f denotes the evaluation function constructed in step 4.4, which is to be called each time

Decoding as a mask code to obtain a binary mask M_B. Selecting the first mu individuals with the minimum fitness value in the g +1 generation for recombination to generate a mean vector of the g +1 generation

The updated mean may be considered a weighted maximum likelihood estimate of the population distribution mean.

5.5 updating evolution Path and Low rank matrix by cumulative learning

The evolution path performs cumulative learning on the continuous movement of the distribution mean in the iteration process, as shown in the following formula:

the evolutionary path cumulatively learns successive search directions in an iterative process, reducing oscillations between these search directions. The opposite search directions cancel out and the consistent direction is accumulated into the evolution path. Thus, the current evolutionary path represents one of the most potential search directions.

Every time a fixed algebra delta g is passed, the earliest searching direction in the low-rank matrix P is replaced by the current evolution path, and in other algebras, the low-rank matrix P of the previous generation is directly used, namely

if g％Δg＝0，P^(g+1)＝P^(g).

5.6 Using sort-based success rules for step size adjustment

Respectively extracting the minimum mu evaluation function values F of the g generation and the g +1 generation^(g)And F^(g+1)The union of the two is F ═ F ^(g)∪F^(g+1). Then the union set F is arranged in ascending order to obtain F_mix. Calculating the difference of the two generations of populations by comparing the weighted rank sums of the two adjacent generations of populations:

and

f for individuals with a small i-th evaluation function representing the g-th generation and the g + 1-th generation, respectively_mixOf (3). In an iterative process by means of a target rate q^*Q is smoothed to eliminate randomness. Updating the search step adjustment factor to s^(g+1)＝(1-c_σ)s^(g)+c_σ(q-q^*) The search step is updated to σ^(g+1)＝σ^(g)·exp(s^(g+1)/d_σ)。

5.7 judging the iteration termination condition

And if the minimum evaluation function value of the current population is less than the minimum evaluation function value stopFitness, the number of times of calling the evaluation function reaches the maximum number of times of calling stopExval, or the variation amplitude of the continuous nLimit generation of the evaluation function is less than tolerance, entering step 5.8.

Otherwise, recording the minimum evaluation function value of the current population

And best mask code bestX: if the minimum evaluation function value of the current population

If the current minimum evaluation function value tmpBestF is less than the current minimum evaluation function value tmpBestF, the current minimum evaluation function value tmpBestF is updated to the minimum evaluation function value of the current population

Updating the best mask code bestX to the best individual of the current population

Otherwise, the current minimum evaluation function value tmpBestF remains unchanged, the best mask code bestX remains unchanged, and the process returns to step 5.3.

5.8 terminate the optimization process and output the optimal binary mask pattern M based on the optimal mask code bestX decoding_B。

FIG. 2 is a schematic diagram of a photoresist pattern generated under different process conditions by using an initial mask pattern according to the present invention, wherein when the mask is not optimized, the photoresist pattern under different process conditions has an obvious difference from a target pattern, and the pattern fidelity is very poor. FIG. 3 is a schematic diagram of a mask pattern obtained by optimization using the method of the present invention, an auxiliary pattern is generated in a pattern sparse region, and the main pattern and the auxiliary pattern after optimization have smooth outlines without too small pattern width and pattern interval. The SL-PSO algorithm shows better optimization performance in the mask optimization problem, so that the reverse photoetching method provided by the invention is compared with the reverse photoetching method based on the SL-PSO algorithm. Relevant parameters of the SL-PSO algorithm are set as follows: stopperiod ═ 200, stoperval ═ 60000, nLimit ═ 50, tolerance ═ 10, and population size nPop ═ 306. Apart from the differences in these parameters, the other conditions of both reverse lithographic methods are unchanged. FIG. 4 is a schematic diagram of a mask pattern obtained by optimization using the SL-PSO algorithm. Obviously, the reverse photoetching method based on the SL-PSO algorithm does not generate auxiliary patterns in sparse areas like the method of the invention, but adjusts the outline of the main pattern. FIGS. 5 and 6 are schematic diagrams of photoresist patterns generated under different process conditions by using the mask pattern optimized by the SL-PSO algorithm and the method of the present invention, respectively. Obviously, the result of reverse photoetching by adopting the method of the invention shows better process robustness. Comparing fig. 5(c) with fig. 6(c), it can be found that the reverse photolithography method based on the SL-PSO algorithm causes the soft bridging phenomenon at the line end when the exposure dose is large, but the method of the present invention does not have such a problem. Comparing fig. 5(d) with fig. 6(d), it can be found that the reverse photolithography method based on the SL-PSO algorithm can cause an obvious soft shrinkage phenomenon when the exposure dose is small and the defocus is out of focus, and there is a risk of pattern fracture. Fig. 7 is a schematic diagram comparing the convergence curves of the reverse photolithography by using the method of the present invention and the SL-PSO algorithm, and it can be seen that the method of the present invention reaches convergence after 12670 times of evaluation function calls, and terminates iteration, the final evaluation function value is 5307.31, and the whole process takes 547.92 s. In contrast, the reverse photolithography method based on the SL-PSO algorithm still does not converge after 60000 evaluation function calls, the final evaluation function value is 5965.61, and the whole process takes 2804.16 s. The reverse lithography method based on the SL-PSO algorithm has larger evaluation function values compared with the method of the invention, which is consistent with the comparison results of FIG. 5 and FIG. 6. The method has the advantages of less number of times of calling the evaluation function required by convergence, shorter running time and smaller final evaluation function value, which shows that the optimization performance of the method is better, the convergence speed is higher, and the photoetching imaging quality and the process robustness are effectively improved. FIG. 8 is a flow chart of reverse photolithography using the method of the present invention.

In addition, the method can be expanded to the computing lithography technologies such as Source Mask Optimization (SMO), Source Mask projection objective joint Optimization (SMPO) and the like, and the lithography imaging quality is further improved by increasing the degree of freedom of Optimization.

The present invention is not limited to the embodiments shown in the drawings, and various other embodiments are possible. Various corresponding changes, substitutions and alterations can be made herein by those skilled in the art without departing from the spirit and scope of the invention, and it is intended that all such changes, substitutions and alterations be considered as within the scope of the appended claims.

Claims (2)

1. A curve type reverse photoetching method based on a fast covariance matrix self-adaptive evolution strategy is characterized by comprising the following specific steps of:

step 1. initialize light source graph J₀Pupil function H₀Photoresist sensitivity alpha and photoresist threshold t_rMask threshold t_mDeveloping threshold t_devThe value of the exposure dose deviation and the corresponding weight, the value of the defocus amount and the corresponding weight;

initializing T values of exposure dose deviation T, wherein the corresponding weight is p _tInitializing H values of the defocusing amount H, wherein the corresponding weight is p_h(ii) a Initializing a light source graph J according to the value of the defocusing amount h₀And pupil function H₀Precalculating TCC (TCC) (Transmission Cross Cooffience) corresponding to the defocusing amount h in the Hopkins imaging model, wherein the TCC (Transmission Cross Cooffience) represents a transmission Cross coefficient, and reserving the first K TCC cores;

step 2. initialize mask pattern M₀A target pattern TP formed by initializing a mask pattern M₀Obtaining a mask code x_M：

Setting initialization mask pattern M₀Is N_V×N_HWherein N is_VAnd N_HRespectively representing initialization mask patterns M₀The number of elements contained in each column and each row is odd; setting initialization mask pattern M₀The transmittance of the upper light-transmitting pixel is 1, and the transmittance of the light-shielding pixel is 0; initializing target pattern TP ═ M₀；

When the mask pattern M is initialized₀For asymmetric mask pattern, the initial mask pattern M is scanned column by column point₀And carrying out mask coding by using all pixel values obtained by scanning:

x_M＝(M₀(1,1),…,M₀(N_V,1),…,M₀(i,j),…,M₀(1,N_H),…,M₀(N_V,N_H))

wherein M is₀(i, j) represents the initialization mask pattern M₀(ii) a mask pixel transmittance at the middle index position of (i, j),

and i is more than or equal to 1 and less than or equal to N_V，

And j is more than or equal to 1 and less than or equal to N_H，M₀(i, j) is e {0,1}, and the variable dimension D_M＝N_V×N_H；

When the mask pattern M is initialized₀When the horizontal axis symmetry and the vertical axis symmetry are satisfied simultaneously, the initialization mask pattern M is scanned column by column point ₀Middle row number ranging from 1 to NH_VHaving a column number in the range of 1 to NH_HThe sub-block of (2) is mask-encoded using the pixel values obtained by the scanning:

x_M＝(M₀(1,1),…,M₀(NH_V,1),…,M₀(i,j),…,M₀(1,NH_H),…,M₀(NH_V,NH_H))

wherein NH_V＝(1+N_V)/2，NH_H＝(1+N_H)/2，M₀(i, j) represents the initialization mask pattern M₀(ii) a mask pixel transmittance at the middle index position of (i, j),

and i is more than or equal to 1 and less than or equal to NH_V，

And j is more than or equal to 1 and less than or equal to NH_H，M₀(i, j) is e {0,1}, and the variable dimension D_M＝NH_V×NH_H；

Step 3. encode x according to the mask_MDecoding is carried out to obtain a decoded binary mask M by mask filtering and binarization processing_B：

When the mask pattern M is initialized₀When the mask pattern is asymmetric, the expression is used

Coding a mask x_MIs arranged to be N in size_V×N_HA matrix M of (A);

when the mask pattern M is initialized₀When the horizontal axis symmetry and the vertical axis symmetry are simultaneously satisfied, the expression is utilized

Coding a mask x_MIs finished into NH_V×NH_HSub-block M of_qUsing subblock M_qFilling size of N_V×N_HThe line number range of the mask pattern M with the element values all being 0 is 1 to NH_VColumn number ranging from 1 to NH_HA moiety of (a); according to sub-block M_qNH th of mask patterns M, respectively_VLine and NH th_HArranging the mask pattern M as a symmetry axis, symmetrically assigning other elements in the mask pattern M, and dividing the value of the element on the corresponding symmetry axis by 2 after each symmetric assignment is finished to obtain a symmetric mask pattern M;

adopting Gaussian filtering processing to the mask pattern to obtain the fuzzified mask pattern M _blurThe formula is as follows:

wherein, the first and the second end of the pipe are connected with each other,

represents the convolution symbol, r₀Represents the center position, | | r-r₀| | denotes point r to point r₀Distance of σ_GFIs the standard deviation of the gaussian function, Ω represents the number of elements contained in the gaussian convolution kernel;

using a mask threshold t_mBlurred mask pattern M_blurBinary processing is carried out to obtain a decoded binary mask M_BThe formula is as follows:

M_B＝Γ(M_blur-t_m)；

wherein the function Γ (x) means that M is represented by_blurMiddle transmittance is greater than or equal to mask threshold t_mAssigns M to 1_blurMedium transmittance less than mask threshold t_mIs assigned a value of 0, i.e. Γ (x) ═ 1| x ≧ 0| x<0}；

And 4, constructing an evaluation function of the reverse photoetching problem by weighted superposition of graphic errors between the photoresist graphic and the target graphic under different exposure dose deviations and defocus conditions:

step 4.1 decode the mask x_MBinary mask M obtained by decoding_BSubstituting the space image into a Hopkins imaging model, calculating an aerial image AI when the defocusing amount is h,

wherein the content of the first and second substances,

is a binary mask M_BThe mask diffraction spectrum obtained by Fourier transform calculation, (x, y) is the space coordinate of the mask pattern, and (f ', g') is the normalized space frequency coordinate of the mask diffraction spectrum; phi_i(f ', g'; h) denotes the ith frequency domain TCC kernel, S, with defocus h_iThe coefficient corresponding to the ith TCC core is shared by K TCC cores; IFFT { } denotes inverse fourier transform;

Step 4.2, calculating the photoresist image RI when the defocusing amount is h and the exposure dose deviation is t according to the space image AI and the sigmoid photoresist model,

wherein, alpha is the sensitivity of the photoresist, t_rIs the photoresist threshold;

step 4.3 in the positive developing process, if the RI of the photoresist image is greater than or equal to the developing threshold t_devThen the photoresist at the position is removed; conversely, if the RI of the photoresist image is less than the developing threshold t_devThe photoresist at the position is reserved; thus, a developed resist pattern RC is obtained, that is, RC (x, y; h, t) ═ Γ (RI (x, y; h, t) -t-_dev)；

Step 4.4, an evaluation function f is constructed by utilizing the weighted superposition of the graphic errors between the photoresist graph and the target graph under the conditions of different exposure dose deviations t and defocus h,

step 5, optimizing a mask graph by adopting a fast covariance matrix self-adaptive evolution strategy:

step 5.1, initializing an evolution algebra g of a fast covariance matrix self-adaptive evolution strategy, a current minimum evaluation function value tmpBestF, an optimal mask code bestX, a population mean vector m, a search step sigma, a search step adjustment factor s, an evolution path P of a covariance matrix, a low-rank matrix P for periodically storing and updating the evolution path, an iteration termination condition of an optimization process and the like;

In the reverse lithography method, the optimization variable dimension N ═ D_MThe initial evolution algebra g is 0, the current minimum evaluation function value tmpbesf is set to a larger value, and the mask code x corresponding to the target graph TP is used_MInitializing best mask code bestX and population mean vector m⁽⁰⁾Initial search step size σ⁽⁰⁾Setting the length of the variable interval to be one third, and initializing a search step length adjustment factor to be s⁽⁰⁾0; the evolution path of the covariance matrix is initialized to p⁽⁰⁾Initializing the low-rank matrix to be P-0;

setting a minimum value stopFittness of an evaluation function, a maximum calling time stoperval of the evaluation function, wherein the variation amplitude of the evaluation function value in the continuous nLimit generation is smaller than tolerance;

step 5.2, setting relevant parameters of the fast covariance matrix adaptive evolution strategy:

population comprises number of individuals:

the number of parents in the recombination is:

the weight corresponding to the ith individual in the recombination is:

satisfy omega₁≥…≥ω_μIs not less than 0 and

effective variance selection quality:

cumulative time constant of covariance matrix evolution path: c 2/(N +5)

Generating a learning rate of the mutation according to the evolution path:

cumulative time constant of search step: c. C_σ＝0.3

Target rate of search step adjustment: q. q.s^*＝0.27

Searching for damping factor of step adjustment: d _σ＝1

The number of search directions contained in the low-rank matrix: n ═ λ

Algebraic interval of low rank matrix update: Δ g ═ 50

Step 5.3 according to the standard normal distribution

Covariance matrix evolution path p of current generation (g-th generation)^(g)Current low rank matrix P^(g)Generating random mutation, combining with population mean vector m of current generation^(g)Generating candidate solutions of the next generation (g +1 th generation), each candidate solution corresponding to a mask code, the steps are as follows:

step 5.3.1 random mutations were generated for the ith individual,

wherein

Is a low rank matrix P^(g)Ith column in (1), corresponding to low rank matrix P^(g)The ith search direction of (a);

step 5.3.2 combine the population mean vector m of the current generation^(g)Random mutation with respect to the i-th individual,generating the ith individual of the next generation

Step 5.4 update mean vector

After the evaluation function values of lambda individuals in the g +1 th generation population are arranged in ascending order, the individuals corresponding to the evaluation function values in the ith position are sorted, namely

f denotes the evaluation function constructed in step 4.4, which is to be called individually each time

Decoding as mask code to obtain binary mask M_B(ii) a Selecting the first mu individuals with the minimum fitness value in the g +1 generation for recombination to generate a mean vector of the g +1 generation

The updated mean value can be regarded as the weighted maximum likelihood estimation of the population distribution mean value;

Step 5.5 update the evolution path and the low rank matrix by cumulative learning

The evolution path cumulatively learns the continuous movement of the distribution mean in the iterative process, as shown in the following formula:

every time a fixed algebra delta g is passed, the earliest searching direction in the low-rank matrix P is replaced by the current evolution path, and in other algebras, the low-rank matrix P of the previous generation is directly used, namely

Step 5.6 Using success rules based on ranking to make step size adjustments

Respectively extracting the minimum mu evaluation function values F of the g generation and the g +1 generation^(g)And F^(g+1)The union of the two is F ═ F^(g)∪F^(g+1)(ii) a Then the union set F is arranged in ascending order to obtain F_mix；

Calculating the difference of the two generations of populations by comparing the weighted rank sums of the two adjacent generations of populations:

and

the ith-smallest evaluation function of the g-th generation and the g +1 th generation, respectively, is expressed in F_mixThe ordering of (1); in an iterative process by means of a target rate q^*Smoothing q, thereby eliminating randomness;

updating the search step adjustment factor to s^(g+1)＝(1-c_σ)s^(g)+c_σ(q-q^*) The search step is updated to σ^(g+1)＝σ^(g)·exp(s^(g+1)/d_σ)；

Step 5.7 judging iteration termination conditions

If the minimum evaluation function value of the current population is less than the minimum evaluation function value stopFitness, the number of times of calling the evaluation function reaches the maximum number of times of calling stopExval or the variation amplitude of the continuous nLimit generation of the evaluation function is less than tolerance, entering step 5.8;

Otherwise, recording the minimum evaluation of the current populationFunction value

And best mask code bestX: i.e. the minimum evaluation function value of the current population

If the minimum evaluation function value tmpBestF is smaller than the current minimum evaluation function value tmpBestF, the current minimum evaluation function value tmpBestF is updated to be the minimum evaluation function value of the current population

Updating the best mask code bestX to the best individual of the current population

Otherwise, keeping the current minimum evaluation function value tmpBestF unchanged, keeping the optimal mask code bestX unchanged, and returning to the step 5.3;

step 5.8 terminate the optimization process, outputting the optimal binary mask pattern M according to the optimal mask code bestX decoding_B。

2. The curvilinear reverse photoetching method based on the fast covariance matrix adaptive evolution strategy according to claim 1, wherein a constant threshold photoresist model, a variable threshold photoresist model and a three-dimensional photoresist model are selected according to actual needs to replace the sigmoid photoresist model in step 4.2.

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