CN115469555B - Spatial image prediction and image quality optimization method for sensor chip projection lithography machine - Google Patents

Abstract

The invention discloses a spatial image prediction and image quality optimization method for a sensor chip projection lithography machine, which is a hybrid method of tabu search and genetic algorithm. The spatial image imaging model of the lithography system is based on the Abbe imaging method, and the calculation of the spatial image intensity distribution is completed by extracting the effective diffraction spectrum information of the mask. The light source S is composed of four symmetrical sub-regions, and the effective units of the sub-regions are extracted as variables for light source optimization. The mask M is composed of symmetrical regular graphics, and the cells near the edge of the sub-region graphics are extracted as variables for mask optimization. Taking the graphic error and edge placement error as the objective functions F ₁ and F ₂ , the optimized light source is subjected to Gaussian filter operation, and the optimized gray mask is binary processed by the threshold method. The invention provides a method for the spatial image imaging model of the lithography system, and proposes a fast light source mask optimization method, which provides effective help for improving the working efficiency of the sensor chip projection lithography machine.

Description

Spatial image prediction and image quality optimization method for sensor chip projection lithography machine

Technical Field

The present invention belongs to the field of projection lithography, and in particular relates to a method for predicting a spatial image and optimizing image quality for a projection lithography machine for a sensor chip.

Background Art

Projection lithography is the mainstream technology for VLSI manufacturing. At present, the performance improvement and miniaturization of VLSI are achieved by reducing the characteristic size of a single transistor and increasing the number of transistors in the same area. According to the Rayleigh criterion, shortening the exposure wavelength and increasing the numerical aperture of the objective lens can effectively improve the resolution of lithography imaging. However, the continuous reduction of the critical size leads to the intensification of the optical diffraction effect, which introduces a more obvious optical proximity effect during the imaging process, resulting in a decrease in the quality of lithography imaging. Therefore, how to improve the performance of lithography imaging has become an urgent problem to be solved.

The key to the inverse optimization model of lithography based on pixelated light source mask optimization lies in the forward imaging model and inverse optimization model of lithography. Among them, the forward imaging model mainly includes the light source model, the mask model and the pupil model. According to the Abbe imaging theory, according to the spectral relationship between the three, a forward molding model is established to obtain the lithography space image intensity distribution. In the inverse lithography optimization model, in order to meet the optimization rules of the iterative algorithm, the sum of the absolute values of the difference between each element of the photoresist pattern and the ideal pattern is used as the cost function, that is, the pattern error. Among them, the photoresist pattern can be approximated by the sigmoid function to represent the photoresist effect. In the light source optimization model, the effective units of the light source are marked and used as the optimization variables of the iterative model. According to the symmetric characteristics of the illumination light source about the optical axis, only one quarter of the optimization variables are needed, which reduces the complexity of the optimization model and improves the optimization efficiency. In the mask optimization model, the edge optimization strategy is adopted, that is, the units near the edge of the feature pattern are used as optimization variables, and the variable values are continuously updated through iteration.

In the inverse optimization model, different optimization algorithms can produce different results. However, for the same feature graph, the optimized light source intensity distribution has a similar trend, while the optimization results of the mask graph vary depending on the optimization strategy. Prior art 1 (Yao Peng, Jinyu Zhang, Yan Wang, and Zhiping Yu, "Gradient-Based Source and Mask Optimization in Optical Lithography," IEEE Trans. onImage Process. 20(10), 2856–2864 (2011).) proposed a light source mask optimization method using a gradient descent method. This method uses the Abbe imaging model to optimize the light source and the sum of coherent systems (SOCS) to optimize the mask. In the light source mask optimization model, the value range of the optimization variable is constrained by a cosine function, and a threshold function is used to perform binary operations based on the value of the mask variable. Prior art 2 (X. Ma, C. Han, Y. Li, L. Dong, and G. R. Arce, "Pixelated source and mask optimization for immersion lithography," J. Opt.Soc. Am. A 30(1), 112 (2013).) proposed a lithography light source mask optimization model based on a gradient method with pixel representation. The model established a lithography imaging model based on the vector Abbe imaging method, and proposed a synchronous light source mask optimization model and a sequential light source mask optimization model to optimize the light source intensity distribution and mask pattern layout. Prior art 3 (C. Yang,S. Li, and X. Wang, "Efficient source mask optimization using multipolesource representation," J. Micro/Nanolith. MEMS MOEMS 13(4), 043001 (2014).) proposed a light source mask optimization method based on a genetic algorithm. The method uses polar coordinates to mark the distribution of light source effective unit variables.

Prior art 1 and 2 both use a gradient-based method to establish a model for optimizing the light source mask. Although this method can converge very quickly, the derivation process of its cost function is relatively complex, and the optimization model is prone to fall into a local optimal situation. Prior art 3 uses a genetic algorithm as the core for optimizing the light source intensity distribution and mask pattern layout. As a heuristic algorithm for global optimization, the genetic algorithm has the advantages of a relatively simple optimization structure and high search speed. However, due to the complexity of the lithography imaging model and the lithography model, the variable matrix dimension is large, which makes this method prone to premature convergence, resulting in a decrease in the convergence efficiency of the algorithm.

Summary of the invention

In order to solve the above technical problems, the present invention provides a method for predicting and optimizing the spatial image quality of a sensor chip projection lithography machine. The method realizes the spatial image imaging process of the lithography system by extracting effective characteristic pattern spectrum information, reduces the computational complexity of the process, and improves the accuracy of the imaging model. The global light source mask optimization method is applicable to a variety of objective functions F such as pattern error and edge placement error. This method effectively improves the imaging performance of the lithography system while ensuring the low complexity of the mask optimization result.

To achieve the above purpose, the technical solutions adopted by the present invention are as follows:

A method for spatial image prediction and image quality optimization for a sensor chip projection lithography machine is a hybrid method of taboo search and genetic algorithm, and the method comprises the following steps:

Step 1: Initialize the parameters of the lithography system spatial image model, input the light source S and the mask pattern M ;

Step 2: Encode the light source and mask effective units as objective function variables;

Step 3: According to the heuristic optimization algorithm structure, randomly generate the matrix P of all population variables to be optimized; therefore , in the light source _{mask optimization model, randomly generate the initial population of light sources and masks, namely, the light source variable population matrix PS and the mask variable population matrix PM, wherein the light source variable population matrix PS and the mask variable population matrix PM are PS} = [ _{S1 , S2 , S3 , …} , SP ] and _PM = [ _M1 , _{M2 ,} M3 , … _{, MP} ] respectively ;

及适应值

；其中，

表示在该光刻系统空间像成像模型中，根据不同光源变量群体矩阵P _S 的个体S _P 所得空间像强度分布矩阵I _S ，即

，

；Step 4: According to the initial light source variable matrix P _S , the spatial image intensity distribution I ^S generated by each individual is calculated through the above-mentioned lithography system spatial image imaging model to achieve spatial image prediction under different imaging conditions; and the fitness value is calculated according to the objective functions F ₁ and F ₂ , and the current best initial light source variable individual is selected by comparison.

and fitness value

;in,

It means that in the lithography system aerial image imaging model, the aerial image intensity distribution _matrix IS is obtained according to _{the individual SP} of _the different light source variable group matrix PS , that is,

,

;

作为禁忌搜索-遗传算法优化模型的输入条件，进行迭代更新光源变量个体至迭代停止；Step 5: The current optimal initial light source variable individual obtained in step 4

As the input condition of the taboo search-genetic algorithm optimization model, iteratively update the light source variable individuals until the iteration stops;

Step 6: According to the individual light source variables after the iteration, perform matrix inversion mirroring and Gaussian filtering operations to restore the light source shape;

及适应值

；Step 7: Use the light source obtained above as the light source condition of the mask optimization model; calculate and record the current best initial mask _variable individual according to the mask variable population matrix PM

and fitness value

;

作为禁忌搜索-遗传算法优化模型的输入条件，进行迭代更新掩模变量个体至迭代停止；Step 8: The current best initial mask variable individual obtained in step 7

As the input condition of the taboo search-genetic algorithm optimization model, the mask variable individuals are iteratively updated until the iteration stops;

Step 9: Output the optimal light source intensity distribution and mask pattern layout.

Furthermore, in step 1, the mask pattern M and the input light source S are gridded, and the effective spectrum extraction method is used to extract the effective feature information of the mask pattern. Combined with the Abbe imaging method, the spatial image generated by the lithography optical system is represented by the following mathematical model:

Wherein, I represents the spatial image intensity distribution, i.e., the result of partial coherent imaging; N ^'S represents the number of effective point light sources in the pixelated light source; CCI _i represents the coherent imaging result generated by a single _point light source, which is represented by the following mathematical model:

,

,

Wherein, ( xi _, yi ) represents the spatial coordinate system of the coherent image plane; ( f , _g ) represents the pupil plane spectrum coordinate system; ( f ', g ' ) represents the mask spectrum coordinate system; H _represents the optical transfer function of the imaging system, i.e., the pupil function; Hi _represents the pupil after translation according to the position of the point light source ( Sx _{, Sy} ) ; M represents the mask spectrum;

The coherent imaging model is discretized and expressed by the following mathematical model:

表示离散化相干像平面空间坐标系；(j,k)表示离散化光瞳面频谱坐标系；(j',k')表示离散化掩模频谱坐标系；N _ext 表示被提取的有效频谱采样点数，

；in,

represents the discretized coherent image plane spatial coordinate system; ( j , k ) represents the discretized pupil plane _spectrum coordinate system; ( j ', k ') represents the discretized mask spectrum coordinate system; Next represents the number of effective spectrum sampling points extracted,

;

According to the Abbe method, the spatial image I _ext obtained by the partial coherence imaging process is represented by the following mathematical model:

Among them, the lithography system illumination source model is established in a coordinate system with m , n as the index. S ( m , n ) represents a point light source located at the position ( m , n ) in the light source model coordinate system, and the lithography system illumination source model matrix size is N _S × N _S , m , n = 1,2,3,…, N _S.

Furthermore, in the step 4, the sum of the absolute values of the differences between the photoresist pattern matrix and each unit of the ideal pattern is defined as the pattern error, and the image error is used as the objective function _F1 ; the area of two inner and outer pixel points near the boundary of the mask pattern is marked and used to calculate the edge placement error, and the edge prevention error is used as the objective function _F2 ; the objective functions _F1 and _F2 are respectively expressed as the following mathematical models:

，

,

，

,

Among them, RP ( xi , yi ₎ represents the photoresist pattern, M ^* ( xi , yi ₎ represents the ideal pattern; ICC _Edge represents _the matrix composed of the extracted edge pixels; Sext represents the extracted light source matrix; _{M'ext represents} the _matrix composed of the edge pixels of the ideal pattern extracted according to the index position; minimize means that in the taboo search-genetic iterative optimization model, the value of the objective function is guaranteed to be the ^minimum when the iteration stops.

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

1. The present invention proposes a hybrid genetic algorithm to improve the convergence efficiency of the genetic algorithm and ensure that the lithography system has good imaging performance.

2. The present invention divides the light source morphology into four identical parts according to the optical characteristics of the lithography illumination system, encodes the effective light source variables, and improves the gradient distribution of the light source intensity through the Gaussian filtering method.

3. The optimization method proposed in the present invention is applicable to a variety of objective functions, such as graphic error, edge prevention error, etc.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic flow chart of a method for spatial image prediction and image quality optimization for a sensor chip projection lithography machine proposed by the present invention;

FIG2 is a schematic diagram of a mask used in the present invention;

FIG3 is a schematic diagram of a method for extracting effective characteristic spectrum of a mask proposed in the present invention;

FIG4 is a schematic diagram of a method for imaging an aerial image of a lithography system used in the present invention;

FIG. 5 is a schematic diagram of the light source coding and Gaussian filtering method used in the present invention.

DETAILED DESCRIPTION

In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

In order to improve the imaging performance of the aerial image of the lithography system, the present invention discloses a method for predicting the aerial image and optimizing the image quality for a sensor chip projection lithography machine through the following embodiments.

As shown in FIG1 , the method for predicting the spatial image and optimizing the image quality of the sensor chip projection lithography machine of the present invention is a hybrid method of taboo search and genetic algorithm, wherein the spatial image prediction is completed in step 4, the objective functions are F ₁ and F ₂ , and the method comprises the following steps:

Step 1: Initialize the parameters of the lithography system spatial image model, input the light source S and the mask pattern M ;

Step 2: Use the coded light source and mask effective units as objective function variables;

Step 3: According to the structure of the heuristic optimization algorithm, it is necessary to randomly generate the matrix P of all the population _variables to be optimized. Therefore, in the light source mask optimization model, the initial population of light sources and masks _, namely, _{the light source variable population matrix PS and the mask variable population matrix PM, are randomly generated. The light source variable population matrix PS} and _{the mask variable population matrix PM are PS = [S1, S2 ,} S3 _, … , _SP ] , PM = _{[ M1 ,} M2 _, M3 _{, …, MP} ] respectively ;

及适应值

；其中，

表示在该光刻系统空间像成像模型中，根据不同光源变量群体矩阵P _S 的个体S _P 所得空间像强度分布矩阵I _S ，即

，

；Step 4: Based on the initial light source variable matrix P _S , the above-mentioned lithography system spatial image imaging model is used to calculate the spatial image intensity ^{distribution IS} generated by each individual, and the spatial image prediction under different imaging conditions is realized. The fitness value is calculated based on the objective functions F ₁ and F ₂ , and the current best initial light source variable individual is selected by comparison.

and fitness value

;in,

It means that in the lithography system aerial image imaging model, the aerial image intensity distribution _matrix IS is obtained according to _{the individual SP} of _the different light source variable group matrix PS , that is,

,

;

作为禁忌搜索-遗传算法优化模型的输入条件，进行迭代更新光源变量个体至迭代停止；Step 5: The current optimal initial light source variable individual obtained in step 4

As the input condition of the taboo search-genetic algorithm optimization model, iteratively update the light source variable individuals until the iteration stops;

Step 6: According to the individual light source variables after the iteration, perform matrix inversion mirroring and Gaussian filtering operations to restore the light source shape;

及适应值

；Step 7: Use the light source obtained above as the light source condition of the mask optimization model. Calculate and record the current best initial mask variable individual according to the mask _variable population matrix PM

and fitness value

;

作为禁忌搜索-遗传算法优化模型的输入条件，进行迭代更新掩模变量个体至迭代停止；Step 8: The current best initial mask variable individual obtained in step 7

As the input condition of the taboo search-genetic algorithm optimization model, the mask variable individuals are iteratively updated until the iteration stops;

Step 9: Output the spatial image intensity distribution, the optimal light source intensity distribution and the mask pattern layout.

In this embodiment, the number of lateral sampling points of the spatial image imaging model of the lithography system is N = 521, and the physical size of the pixel is 5.625 nm × 5.625 nm . Then, the number of lateral sampling points of the light source is N _S = 41, and the coherence factors of the annular illumination light source are σ _inner = 0.68 and σ _outer = 0.95. The line width of the mask feature pattern is 45 nm and the interval is 45 nm, as shown in Figure 2. The spatial image imaging model of the lithography system adopts the method of effective spectrum extraction, as shown in Figure 3. Among them, step 301 represents the input pattern of the grating array pattern as the schematic diagram. Step 302 indicates that the characteristic information of the characteristic pattern is represented in the form of a spectrum by adopting a fast Fourier transform operation, step 303 indicates that the characteristic pattern is represented by a three-dimensional spectrum diagram, step 304 indicates an effective spectrum extraction operation, that is, the spectrum information of the mask pattern is extracted and processed according to the cutoff frequency range, step 305 indicates that in the spatial image imaging model of the lithography system, the effective three-dimensional spectrum of the characteristic pattern can be obtained according to the relationship between the effective spectrum involved in the imaging and the cutoff spectrum, step 306 indicates that the effective spectrum of the characteristic pattern is represented by a two-dimensional distribution diagram, wherein DC represents a circular area with a radius of R _f , which is the effective cutoff spectrum range.

As shown in FIG4 , the schematic diagram of the process of the lithography system aerial image imaging is assumed to be a ring-shaped illumination source S. Step 401 represents the light source being represented as a ring-shaped illumination source S by a discretized matrix, that is, pixel-characterizing the intensity distribution of the illumination source. Step 402 represents the extraction of effective light source points and matrix conversion operations. The matrix conversion operation converts the effective light source matrix from a multidimensional matrix into a column vector S _ext . Step 403 represents the representation of the effective light source by a one-dimensional column vector. According to the coherent imaging theory, in the discretized ring-shaped illumination source S, each point light source can generate a coherent image CCI _i . Step 404 represents the formation of an illumination cross coefficient matrix ICC _ext from the edge pixel points of each part of the extracted coherent image CCI _i , and each column of the matrix represents the intensity distribution of the coherent image generated by each point light source. Step 405 represents the matrix conversion operation, which means converting the multidimensional matrix into a column vector and the result of the product of the illumination cross coefficient matrix to obtain the lithography system aerial image intensity part I _ext . Step 406 represents the discretization of the aerial image intensity part I _ext . According to the mask pattern of size N _M × N _M , it can be known that the size of the spatial image intensity distribution matrix obtained through the photolithography system spatial image imaging model is N _M × N _M , and step 408 needs to be operated. The step 408 represents obtaining the complete spatial image intensity distribution I through interpolation operation. Step 409 represents finally obtaining the standard spatial image intensity distribution I. Steps 407 and 410 represent the matrices of the extracted spatial image intensity parts I _ext and I using local information amplification. According to the Abbe imaging method, the imaging model can be represented by the following mathematical model:

Where, I represents the spatial image intensity distribution, i.e., the result of partial coherent imaging. N ^'S represents the number of effective point light sources in the pixelated light source. CCI _i represents the coherent imaging result generated by a single _point light source, which can be represented by the following mathematical model:

,

,

_Among them, ( xi _, yi ) represents the coherent image plane spatial coordinate system; ( f , g ) represents the pupil plane spectrum coordinate system; ( f ', g ') represents the mask spectrum coordinate system; H _represents the optical transfer function of the imaging system, that is, the pupil function; Hi _represents the pupil after translation according to the position of the point light source ( Sx _{, Sy} ) ; M represents the mask spectrum.

According to the theory of photolithography, the imaging system of photolithography is a strict optical diffraction-limited system, and its cutoff frequency is approximately equal to the ratio of the numerical aperture NA to the illumination wavelength λ , that is, NA / λ . In the photolithography imaging model, the pupil function is equivalent to a circular low-pass filter, whose radius is the cutoff frequency of the optical system.

The photolithography imaging process is a classic partially coherent imaging, and the partial coherence factor of its light source can be defined as the ratio of the radius of the illumination light source r _S to the radius of the pupil r _H , that is, σ = r _S / r _H. Therefore, in the partial coherence imaging model, the light source is a circle with a radius of σ NA / λ . According to the Hopkins imaging method, the center of the pupil matrix is offset according to the position of the point light source. Therefore, the area with the largest offset of the center of the pupil matrix is a circle with a radius of r _S + r _H. In the photolithography imaging process, the mask spectrum participating in the process is the effective spectrum, and its coverage area is a circular area DC with a radius of r _S +2 r _H (as shown in Figure 3), and only this part participates in the imaging process. Discretizing the coherent imaging model can be represented by the following mathematical model:

表示离散化相干像平面空间坐标系；(j,k)表示离散化光瞳面频谱坐标系；(j',k')表示离散化掩模频谱坐标系；N _ext 表示被提取的有效频谱采样点数，

；in,

represents the discretized coherent image plane spatial coordinate system; ( j , k ) represents the discretized pupil plane _spectrum coordinate system; ( j ', k ') represents the discretized mask spectrum coordinate system; Next represents the number of effective spectrum sampling points extracted,

;

According to the Abbe method, the spatial image I _ext obtained by the partial coherence imaging process is represented by the following mathematical model:

Among them, the lithography system illumination source model is established in a coordinate system with m , n as the index. S ( m , n ) represents a point light source located at the position ( m , n ) in the light source model coordinate system, and the lithography system illumination source model matrix size is N _S × N _S , m , n = 1,2,3,…, N _S.

By using the interpolation method to enlarge the above mathematical model, the standard spatial image intensity distribution I can be obtained.

The objective functions _F1 and _F2 are functions of the spatial image intensity distribution I. The sum of the absolute values of the differences between the photoresist pattern matrix and each unit of the ideal pattern is defined as the pattern error, and the image error is used as the objective function _F1 . The area of two inner and outer pixel points near the boundary of the mask pattern is marked and used to calculate the edge placement error, and the edge prevention error is used as the objective function _F2 . The objective functions _F1 and _F2 are respectively expressed as the following mathematical models:

，

,

，

,

Wherein, RP ( xi , yi ₎ represents the photoresist pattern , M ^* ( xi , yi ₎ represents the ideal pattern. ICC _Edge represents _the matrix of extracted edge pixels. Sext represents the extracted light source matrix. _{M'ext represents} the matrix of ideal edge pixels extracted according to the index _position . minimize represents the value of the objective function to be minimized when the ^iteration stops in the taboo search-genetic iterative optimization model.

FIG5 is a schematic diagram of the light source encoding and Gaussian filtering method used in the imaging model of the lithography system. According to the special optical symmetry of the illumination light source, the light source can be divided into four identical parts, namely the _first part J1 , _the second part J2 , the third part J3 , and _the fourth part J4 of the annular illumination light source S. In the optimization model, only one quarter of the light source points are needed as optimization variables. Step ₅₀₁ represents extracting one quarter of the effective area of the light source S as the optimization area, marking the position of each effective point by encoding, and performing a matrix conversion operation. Through the encoding and matrix conversion operations, the effective light source points are encoded into a column vector S ^' , and its matrix size is m ×1. Step 502 represents randomly generating an optimization variable group Sr , that is, a light source variable group matrix Ps _, according to the number of variables in the optimization area in the initialization stage. Step 503 represents selecting the current best light source variable _{individual Sopt} according _to the objective function value. Step 504 represents obtaining a complete discrete light source intensity distribution through operations such as matrix conversion. Since the intensity distribution of the light source in the photolithography system varies in a continuous gradient, the discrete light source is subjected to a Gaussian filter operation in step 505 to obtain an illumination light source S ^* with a continuously varying grayscale.

The above application is described in detail in combination with the specific implementation methods and the accompanying drawings. The present invention performs local extraction and processing on the mask feature diffraction spectrum information to reduce the computational complexity of the aerial image imaging model. The illumination light source and the mask are quarter-encoded and optimized to improve the optimization speed of the optimization model. The taboo search algorithm is combined with the genetic algorithm to improve the global convergence performance of the genetic algorithm, and combined with the objective function graphic error and edge prevention error, the imaging performance of the lithography system is effectively improved.

It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. A method for spatial image prediction and image quality optimization for a sensor chip projection lithography machine, which is a hybrid method of taboo search and genetic algorithm, characterized in that the method comprises the following steps: Step 1: In the lithography light source mask optimization model based on taboo search-genetic algorithm, initialize the parameters of the lithography system aerial image imaging model, input the light source S and the mask pattern M ; grid the mask pattern M and the input light source S, and use the effective spectrum extraction method to extract the effective feature information of the mask pattern. Combined with the Abbe imaging method, the aerial image generated by the lithography optical system is represented by the following mathematical model:

Wherein, I represents the spatial image intensity distribution, i.e., the result of partial coherent imaging; N ^'S represents the number of effective point light sources in the pixelated light source; CCI _i represents the coherent imaging result generated by a single _point light source, which is represented by the following mathematical model:

,

Wherein, ( xi _, yi ) represents the spatial coordinate system of the coherent image plane; ( f , _g ) represents the pupil plane spectrum coordinate system; ( f ', g ' ) represents the mask spectrum coordinate system; H _represents the optical transfer function of the imaging system, i.e., the pupil function; Hi _represents the pupil after translation according to the position of the point light source ( Sx _{, Sy} ) ; M represents the mask spectrum; The coherent imaging model is discretized and expressed by the following mathematical model:

in,

represents the discretized coherent image plane spatial coordinate system; ( j , k ) represents the discretized pupil plane _spectrum coordinate system; ( j ', k ') represents the discretized mask spectrum coordinate system; Next represents the number of effective spectrum sampling points extracted,

; According to the Abbe method, the spatial image I _ext obtained by the partial coherence imaging process is represented by the following mathematical model:

Wherein, the lithography system illumination source model is established in a coordinate system with m , n as the index, S ( m , n ) represents a point light source located at the position ( m , n ) in the light source model coordinate system, and the lithography system illumination source model matrix size is N _S × N _S , m , n = 1, 2, 3, …, N _S ; Step 2: Encode the light source and mask effective units as objective function variables; Step 3: According to the heuristic optimization algorithm structure, randomly generate the matrix P of all population variables to be optimized; therefore, in the light source _{mask optimization model, randomly generate the initial population of light sources and masks, namely, the light source variable population matrix PS and the mask variable population matrix PM, wherein the light source variable population matrix PS and the mask variable population matrix PM are PS} = [ S1 _{, S2 , S3 ,} … _, SP ] and PM ₌ [ _M1 , _M2 , _{M3 ,} … , MP ] _{respectively ;} Step 4: Based on the initial light source variable matrix P _S , the spatial image intensity distribution generated by each individual is calculated using the above-mentioned lithography system spatial image imaging model.

, realize spatial image prediction under different imaging conditions, i =1,2, …, p ; and calculate the fitness value according to the objective function _F1 and _F2 , and select the current best initial light source variable individual by comparison

and fitness value

;in,

In the lithography system aerial image imaging model, the aerial image intensity distribution _matrix IS is obtained according to the individual SP _{of the} different light source variable group matrix PS , that is,

,

; The sum of the absolute values of the differences between the photoresist pattern matrix and each unit of the ideal pattern is defined as the pattern error, and the pattern error is used as the objective function _F1 ; the area of two inner and outer pixel points near the boundary of the mask pattern is marked and used to calculate the edge placement error, and the edge placement error is used as the objective function _F2 ; the objective functions _F1 and _F2 are respectively expressed as the following mathematical models:

Wherein, RP ( xi , yi ₎ represents the photoresist pattern , M ^* ( xi , yi ₎ represents ^the ideal pattern; ICC _{Edge represents the} matrix composed of the extracted edge pixels; Sext represents the extracted light source matrix; _M'ext represents the matrix composed of the edge pixels of the ideal pattern extracted according to the index position _; minimize represents the value of the objective function to be minimized when the iteration stops in the taboo search-genetic iterative optimization model; Step 5: The current optimal initial light source variable individual obtained in step 4

As the input condition of the taboo search-genetic algorithm optimization model, iteratively update the light source variable individuals until the iteration stops; Step 6: According to the individual light source variables after the iteration, perform matrix inversion mirroring and Gaussian filtering operations to restore the light source shape; Step 7: Use the light source obtained above as the light source condition of the mask optimization model; calculate and record the current best initial mask _variable individual according to the mask variable population matrix PM

and fitness value

; Step 8: The current best initial mask variable individual obtained in step 7

As the input condition of the taboo search-genetic algorithm optimization model, the mask variable individuals are iteratively updated until the iteration stops; Step 9: Output the optimal light source intensity distribution and mask pattern layout.

Images