CN115469555B - Space image prediction and image quality optimization method for sensor chip projection lithography machine - Google Patents
Space image prediction and image quality optimization method for sensor chip projection lithography machine Download PDFInfo
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Abstract
The invention discloses a space 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 lithography system space image imaging model is based on an Abbe imaging method, and the calculation of space image intensity distribution is completed by extracting mask effective diffraction spectrum information. The light source S consists of four symmetrical subregions, and effective units of the subregions are extracted to be used as variables for optimizing the light source. The mask M is composed of symmetrical regular patterns, and cells near the edges of the sub-region patterns are extracted to be used as variables for mask optimization. Using the figure error and the edge placement error as an objective function F 1 And F 2 And performing Gaussian filtering operation on the optimized light source, and performing binary processing on the optimized gray mask by a threshold method. The invention provides a method for a photoetching system space image imaging model and provides a rapid light source mask optimization method, which provides effective help for improving the working efficiency of a sensor chip projection photoetching machine.
Description
Technical Field
The invention belongs to the field of projection lithography, and particularly relates to a space image prediction and image quality optimization method for a sensor chip projection lithography machine.
Background
Projection lithography is the dominant technology in the manufacture of very large scale integrated circuits. At present, the performance of very large scale integrated circuits is improved and miniaturized by reducing the feature size of a single transistor and increasing the number of transistors in the same area. According to Rayleigh criterion, the exposure wavelength is shortened, the numerical aperture of the objective lens is increased, and the photoetching imaging resolution ratio can be effectively improved. The continuous reduction of the critical dimension leads to the aggravation of the optical diffraction effect, so that in the imaging process, a more obvious optical proximity effect is introduced, and the quality of the photoetching imaging is reduced. Therefore, how to improve the lithography imaging performance has become a problem to be solved urgently.
The key of the lithography reverse optimization model based on the pixilated light source mask optimization lies in a forward imaging model and a reverse optimization model of lithography. The forward imaging model mainly comprises a light source model, a mask model and a pupil model. According to the Abbe imaging theory and the frequency spectrum relation among the Abbe imaging theory and the Abbe imaging theory, a forward forming model is established to obtain the intensity distribution of the photoetching space image. In the inverse lithography optimization model, in order to meet the optimization rule of the iterative algorithm, the sum of absolute values of differences of each element between the photoresist pattern and the ideal pattern is used as a cost function, namely a pattern error. Wherein, the photoresist pattern can approximately represent the photoresist effect by a sigmoid function. In the light source optimization model, light source effective units are marked and used as optimization variables of the iterative model. According to the characteristic that the illumination light source is symmetrical about the optical axis, only a quarter of optimization variables are needed, the complexity of an optimization model is reduced, and the optimization efficiency is improved. In the mask optimization model, an edge optimization strategy is adopted, namely, a unit near the edge of the feature pattern is used as an optimization variable, and the variable value is continuously updated through iteration.
In the inverse optimization model, the obtained effect is different according to different optimization algorithms. However, for the same feature pattern, the optimized light source intensity distribution has similar trends, and the optimization result of the mask pattern is different according to different optimization strategies. Prior art 1 (Yao Pen, jinyu Zhang, yan Wang, and Zhiping Yu, "Gradient-Based Source and Mask Optimization in Optical Lithography," IEEE trans. On Image Process. 20 (10), 2856-2864 (2011)) proposes a light Source Mask Optimization method of a Gradient descent method. The method adopts an Abbe imaging model to complete light source optimization, and adopts the sum of coherent systems (SOCS) to complete mask optimization. In the light source mask optimization model, the value range of an optimization variable is constrained by a cosine function, and meanwhile, a threshold function is adopted to carry out binary operation according to the value of a mask variable. Prior art 2 (x, ma, c, han, y, li, l, dong, and g.r. Area, "pixel source and mask optimization for imaging," j. Opt. Soc. Am. A30 (1), 112 (2013)), proposes a lithography light source mask optimization model based on a gradient method of pixel characterization. The model establishes a photoetching imaging model by a vector Abbe imaging method, and provides a synchronous light source mask optimization model and a sequence light source mask optimization model to optimize light source intensity distribution and mask pattern layout. In prior art 3 (c, yang, s, li, and x, wang, "Efficient source mask optimization using multiple source reconstruction," j, micro/nanolith, MEMS MOEMS 13 (4), 043001 (2014)), a genetic algorithm-based light source mask optimization method is proposed. The method adopts a polar coordinate mode to mark the distribution of the variable of the effective unit of the light source.
In the prior art 1 and the prior art 2, a model for optimizing a light source mask is established by a gradient-based method, although the convergence rate of the method is high, the derivation process of the cost function is complex, and the optimization model is prone to be in a locally optimal condition. In the prior art 3, a genetic algorithm is used as a kernel for optimizing the intensity distribution of the light source and the layout of the mask pattern, and the genetic algorithm is used as a heuristic algorithm for global optimization, so that the method has the advantages of simpler optimization structure, high search speed and the like. However, the photoetching imaging model and the photoetching model are complex, so that the dimension of the variable matrix is large, the method is easy to generate a state of premature convergence, and the convergence efficiency of the algorithm is reduced.
Disclosure of Invention
In order to solve the technical problem, the invention provides a space image prediction and image quality optimization method for a sensor chip projection lithography machine. The method realizes the space image imaging process of the photoetching system by adopting a mode of extracting effective characteristic pattern frequency spectrum information, reduces the calculation complexity of the process, and simultaneously improves the accuracy of an imaging model. The global light source mask optimization method is suitable for various objective functions F such as graphic errors, edge placement errors and the like, and effectively improves the imaging performance of a photoetching system while ensuring low complexity of a mask optimization result.
In order to achieve the purpose, the technical solution adopted by the invention is as follows:
a space image prediction and image quality optimization method for a sensor chip projection lithography machine is a hybrid method of tabu search-genetic algorithm, and comprises the following steps:
step 1: initializing space image imaging model parameters of photoetching system, inputting light sourceSAnd mask patternM；
And 2, step: coding the light source and the mask effective unit as target function variables;
and step 3: randomly generating a group variable whole matrix to be optimized according to a heuristic optimization algorithm structureP(ii) a Therefore, in the light source mask optimization model, a light source and mask initial population-light source variable population matrix is randomly generatedP S And mask variable population matrixP M The light source variable group matrixP S And mask variable population matrixP M Are respectively asP S =[S 1 ,S 2 ,S 3 ,…,S P ]，P M =[M 1 ,M 2 ,M 3 ,…,M P ]；
And 4, step 4: according to the initial light source variable matrixP S Calculating the intensity distribution of the space image generated by each individual through the space image imaging model of the photoetching systemI S The spatial image prediction under different imaging conditions is realized; and according to an objective function F 1 And F 2 Calculating adaptive value, and selecting current optimum initial light source variable individual by comparison
And an adapted value->
(ii) a Wherein it is present>
Expressed in the space image imaging model of the lithography system, the group matrix is formed according to different light source variablesP S Of (2)S P The resulting aerial image intensity distribution matrixI S I.e. based on>
，/>
；
And 5: the current optimal initial light source variable obtained in the step 4 is taken as an individual
As an input condition of a tabu search-genetic algorithm optimization model, iteratively updating the light source variable individuals until iteration is stopped;
and 6: according to the light source variable individuals after iteration is stopped, matrix inversion mirror image and Gaussian filtering manipulation are executed, and the appearance of the light source is recovered;
and 7: using the obtained light source as the light source condition of the mask optimization model; population matrix according to mask variablesP M Calculating and recording current best initial mask variable individual
And an adapted value->
；
And 8: the current best initial mask variable obtained in the step 7 is taken as an individual
Performing iterative update on mask variable individuals until iteration stops as an input condition of a tabu search-genetic algorithm optimization model;
and step 9: outputting the optimal light source intensity distribution and the mask pattern layout.
Further, in step 1, the mask pattern M and the input light source S are gridded, effective characteristic information of the mask pattern is extracted by an effective spectrum extraction method, and an aerial image generated by the lithography optical system is represented by the following mathematical model in combination with an Abbe imaging method:
wherein the content of the first and second substances,Irepresenting the spatial image intensity distribution, i.e. the result of partially coherent imaging;N ' S representing the number of effective point light sources in the pixelated light source;CCI i the coherent imaging results produced by a single point source are represented by the following mathematical model:
wherein the content of the first and second substances, (ii) (x i ,y i ) Representing a coherent image plane spatial coordinate system; (f,g) Representing a pupil plane spectral coordinate system; (f',g') denotes the mask spectral coordinate system;Hrepresents the optical transfer function, i.e. the pupil function, of the imaging system;H i representing the position of the light source according to points: (S x ,S y ) A pupil after translation;Mrepresenting a mask spectrum;
the coherent imaging model was discretized and represented by the following mathematical model:
wherein the content of the first and second substances,
representing a discretized coherent image plane spatial coordinate system; (j,k) Representing a discretized pupil plane spectral coordinate system; (j',k') denotes the discretized mask spectral coordinate system;N ext representing the number of extracted valid spectral samples,
；
according to Abbe's method, aerial image obtained by partially coherent imaging processI ext Is represented by the following mathematical model:
wherein, in the followingm, nAnd establishing a photoetching system illumination light source model for the index-mode coordinate system.S(m,n) Is shown in the light source model coordinate system at (m,n) Point light source at the position, the size of the illumination light source model matrix of the photoetching system isN S ×N S ，m,n=1,2,3,…,N S 。
Further, in the step 4, the sum of absolute values of the differences between the photoresist pattern matrix and each unit of the ideal pattern is defined as a pattern error, and the pattern error is taken as an objective function F 1 (ii) a Marking the areas of the inner and outer pixel points near the boundary of the mask pattern, and calculating the edge placement error, taking the edge prevention error as an objective function F 2 (ii) a Objective function F 1 And F 2 Are respectively provided withIs represented as the following mathematical model:
wherein the content of the first and second substances,RP(x i ,y i ) A photoresist pattern is represented and,M * (x i ,y i ) Representing an ideal graph;ICC Edge representing a matrix formed by the extracted edge pixel points;S ext representing the extracted light source matrix;M ' ext representing a matrix formed by extracting ideal graph edge pixel points according to the index positions;minimizethe method is characterized in that in a tabu search-genetic iteration optimization-based model, the numerical value of an objective function is guaranteed to be minimum when iteration stops.
Compared with the prior art, the invention has the following advantages:
1. the invention provides a hybrid genetic algorithm, improves the convergence efficiency of the genetic algorithm and ensures that a photoetching system has better imaging performance.
2. According to the optical characteristics of the photoetching illumination system, the light source appearance is divided into four identical parts, effective light source variables are encoded, and the light source intensity distribution gradient is improved by a Gaussian filtering method.
3. The optimization method provided by the invention is suitable for various objective functions, such as graphic errors, edge prevention errors and the like.
Drawings
FIG. 1 is a schematic flow chart of a method for spatial image prediction and image quality optimization for a sensor chip projection lithography machine according to the present invention;
FIG. 2 is a schematic diagram of a mask used in the present invention;
FIG. 3 is a schematic diagram of a mask effective feature spectrum extraction method according to the present invention;
FIG. 4 is a schematic view of a lithography system aerial image imaging method employed in the present invention;
FIG. 5 is a schematic diagram of a light source encoding and Gaussian filtering method according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may 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 invention discloses an aerial image prediction and image quality optimization method for a sensor chip projection lithography machine through the following embodiments.
As shown in FIG. 1, the space image prediction and image quality optimization method for sensor chip projection lithography machine of the present invention is a hybrid tabu search-genetic algorithm, wherein the space image prediction is performed in step 4, and the objective function is F 1 And F 2 The method comprises the following steps:
step 1: initializing space image imaging model parameters of photoetching system, inputting light sourceSAnd mask patternM；
Step 2: taking the coded light source and the mask effective unit as target function variables;
and step 3: according to the heuristic optimization algorithm structure, all matrixes of group variables to be optimized need to be randomly generatedP. Therefore, in the light source mask optimization model, a light source and mask initial population-light source variable population matrix is randomly generatedP S And mask variable population momentsMatrix ofP M The light source variable group matrixP S And mask variable population matrixP M Are respectively asP S =[S 1 ,S 2 ,S 3 ,…,S P ]，P M =[M 1 ,M 2 ,M 3 ,…,M P ]；
And 4, step 4: according to the initial light source variable matrixP S Calculating the intensity distribution of the space image generated by each individual through the space image imaging model of the photoetching systemI S And space image prediction under different imaging conditions is realized. And according to an objective function F 1 And F 2 Calculating adaptive value, and selecting current optimum initial light source variable individual by comparison
And an adaptive value>
(ii) a Wherein it is present>
Expressed in the space image imaging model of the lithography system, the group matrix is formed according to different light source variablesP S Of (2)S P The resulting aerial image intensity distribution matrixI S I.e. is->
，/>
；
And 5: the current optimal initial light source variable obtained in the step 4 is taken as an individual
As input conditions of a tabu search-genetic algorithm optimization modelIteratively updating the light source variable individual until iteration is stopped;
step 6: according to the light source variable individuals after iteration is stopped, matrix inversion mirror image and Gaussian filtering manipulation are executed, and the appearance of the light source is recovered;
and 7: the light source obtained above was used as the light source condition for the mask optimization model. Population matrix according to mask variablesP M Calculating and recording current best initial mask variable individual
And an adapted value->
；
And 8: the current best initial mask variable obtained in the step 7 is taken as an individual
Performing iterative update on mask variable individuals until iteration stops as an input condition of a tabu search-genetic algorithm optimization model;
and step 9: outputting the aerial image intensity distribution, the optimal light source intensity distribution and the mask pattern layout.
In this embodiment, the number of horizontal sampling points of the aerial image imaging model of the lithography system is setN=521, physical size of pixel point is 5.625nm×5.625nm. Then, the number of horizontal sampling points of the light sourceN S =41, coherence factor of annular illumination sourceσ inner =0.68 andσ outer =0.95. The mask feature pattern has a line width of 45 nm and a spacing of 45 nm as shown in fig. 2. The lithography system aerial image imaging model adopts an effective spectrum extraction method, as shown in FIG. 3. Wherein, step 301 represents the raster array pattern as the input pattern of the schematic diagram. Step 302 represents representing the feature information in the form of a frequency spectrum by using a fast fourier transform operation for the feature pattern, step 303 represents the feature information in the form of a three-dimensional frequency spectrum representation, step 304 represents an effective spectrum extraction operation, i.e. a spectrum information for the mask pattern according to a cut-off frequency rangeExtracting, wherein step 305 shows that in a lithography system space image imaging model, an effective three-dimensional spectrum of a characteristic graph can be obtained according to the relation between an effective spectrum and a cut-off spectrum which participate in imaging, and step 306 shows that the effective spectrum of the characteristic graph is represented by a two-dimensional distribution graph, wherein DC represents the radiusR f The circular region of (a), which is the effective cut-off spectral range.
As shown in the schematic diagram of the process of imaging the lithography system aerial image in fig. 4, assuming that the light source in the model of imaging the lithography system aerial image is the annular illumination light source S, step 401 represents representing the light source as the annular illumination light source S by using the discretization matrix, i.e. the intensity distribution of the illumination light source is represented by pixelization. Step 402 represents the extraction of the effective light source points and the matrix transformation operation. The matrix conversion operation converts the effective light source matrix from a multi-dimensional matrix to a column vectorS ext . Step 403 represents representing the active light sources by a one-dimensional column vector. According to the coherent imaging theory, in the discretized annular illumination light source S, each point light source can generate a coherent imageCCI i . Step 404 represents each partially coherent image to be extractedCCI i The edge pixels form an illumination cross coefficient matrixICC ext Each column of the matrix represents the intensity distribution of the coherent image produced by each point source. Step 405 represents a matrix transformation operation, which represents the transformation of the result of the product of the multi-dimensional matrix into a column vector and an illumination cross coefficient matrix, and the intensity of the spatial image of the lithography system can be obtainedI ext . Step 406 represents segmenting the aerial image intensityI ext And (4) discretizing expression. According to the size ofN M ×N M The mask pattern of (2) can be known as the size of the aerial image intensity distribution matrix obtained by the aerial image imaging model of the lithography system isN M ×N M Step 408 is required to operate. Said step 408 represents the acquisition of the complete aerial image intensity distribution by interpolationI. Step 409 represents the resulting standard aerial image intensity distributionI. Step 407 and step 410 represent the aerial image intensity portions to be extractedI ext AndIthe matrix of (2) is represented by local information amplification. According to the Abbe imaging method, the imaging model can be represented by the following mathematical model:
wherein the content of the first and second substances,Irepresenting the spatial image intensity distribution, i.e. the result of partially coherent imaging.N ' S Representing the number of effective point sources in the pixelated light source.CCI i Represents the coherent imaging results produced by a single point source, which can be represented by the following mathematical model:
wherein the content of the first and second substances, (ii) (x i ,y i ) Representing a coherent image plane spatial coordinate system; (f,g) Representing a pupil plane spectral coordinate system; (f',g') denotes a mask spectral coordinate system;Hrepresents the optical transfer function, i.e. the pupil function, of the imaging system;H i representing the position of the light source according to points: (S x ,S y ) A pupil after translation;Mrepresenting the mask spectrum.
According to the theory of lithographic imaging, the lithographic imaging system is a strictly optical diffraction limited system with a cut-off frequency approximately equal to the numerical apertureNAAnd wavelength of illuminationλRatio of (i) to (ii)NA/λ. In the lithography imaging model, the pupil function corresponds to a circular low-pass filter with a radius of the cutoff frequency of the optical system.
The lithographic imaging process being classical partially coherent imaging, the light source thereofCan be defined as the radius of the illumination sourcer S Radius of pupilr H Ratio of (i) to (ii)σ=r S /r H . Thus, in the partially coherent imaging model, the light source has a radius ofσ NA/λThe circle of (c). According to the Hopkins imaging method, the pupil matrix center is shifted according to the spot light source position. Thus, the maximum shift in the center of the pupil matrix is at a radius ofr S +r H Is circular. In the photoetching imaging process, the mask frequency spectrum participating in the process is the effective frequency spectrum, and the coverage area of the mask frequency spectrum is a radiusr S +2r H The circular area DC (as shown in fig. 3), only this part is also involved in the imaging process. Discretizing the coherent imaging model can be represented by the following mathematical model:
wherein, the first and the second end of the pipe are connected with each other,
representing a discretized coherent image plane spatial coordinate system; (j,k) Representing a discretized pupil plane spectral coordinate system; (j',k') represents a discretized mask spectral coordinate system;N ext indicating the number of extracted active spectral sample points,
；
according to Abbe's method, aerial image obtained by partially coherent imaging processI ext Is represented by the following mathematical model:
wherein, in the followingm, nAnd establishing a photoetching system illumination light source model for the index-mode coordinate system.S(m,n) Is shown in the light source model coordinate system at (m,n) Point light source at the position, the size of the illumination light source model matrix of the photoetching system isN S ×N S ，m,n=1,2,3,…,N S 。
Amplifying the mathematical model by interpolation method to obtain standard spatial image intensity distributionI。
The objective function F 1 And F 2 Defining the sum of absolute values of differences between each unit of photoresist pattern matrix and ideal pattern as pattern error, and using the pattern error as target function F 1 . Marking the areas of the inner and outer pixel points near the boundary of the mask pattern, and calculating the edge placement error, taking the edge prevention error as an objective function F 2 . Objective function F 1 And F 2 Are represented as the following mathematical models, respectively:
wherein the content of the first and second substances,RP(x i ,y i ) A photoresist pattern is represented and,M * (x i ,y i ) Representing an ideal figure.ICC Edge And representing a matrix formed by the extracted edge pixel points.S ext Representing the extracted light source matrix.M ' ext And representing a matrix formed by extracting the edge pixel points of the ideal graph according to the index position.minimizeThe method is characterized in that in a tabu search-genetic iteration optimization-based model, the numerical value of an objective function is guaranteed to be minimum when iteration stops.
FIG. 5 is a schematic diagram of a light source encoding and Gaussian filtering method used in an imaging model of a lithography system. The light source can be divided into four identical parts according to the special optical symmetry of the illumination light source, namely a ring-shaped illumination light sourceSThe first part of (1)J 1 A second partJ 2 Third partJ 3 Fourth sectionJ 4 . In the optimization model, only one quarter of the light source points are required as optimization variables. Step 501 represents extracting the light source S quarter active area as an optimized area, marking the position of each active point by encoding, and performing a matrix transformation operation. Encoding the active source points into column vectors by encoding and matrix conversion operationsS ' Of matrix size ofmX 1. Step 502 represents randomly generating an optimized variable group in an initialization stage according to the number of variables in the optimized areaS r I.e. light source variable population matrixP S . Step 503 represents selecting the current best light source variable individual according to the objective function valueS opt . Step 504 represents obtaining the complete intensity distribution of the discrete light sources by matrix conversion and the like. Since the light source intensity distribution in the photolithography system is in continuous gradient change, the discrete light source is subjected to gaussian filtering operation in step 505 to obtain the illumination light source with continuously changing gray scaleS * 。
The application is described in detail above with reference to specific embodiments and the description of the drawings. The method carries out local extraction processing on the mask characteristic diffraction spectrum information, and reduces the calculation complexity of the space image imaging model. Quarter coding and optimization are carried out on the illumination light source and the mask, and the optimizing speed of the optimization model is improved. The taboo search algorithm is combined with the genetic algorithm, the global convergence expressive property of the genetic algorithm is improved, the target function graph error and the edge prevention error are combined, and the imaging expressive property of the photoetching system is effectively improved.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (1)
1. A space image prediction and image quality optimization method for a sensor chip projection lithography machine is a hybrid method of tabu search-genetic algorithm, and is characterized by comprising the following steps:
step 1: initializing photoetching system space image imaging model parameters in photoetching light source mask optimization model based on tabu search-genetic algorithm, inputting light sourceSAnd mask patternM(ii) a Carrying out gridding processing on the mask pattern M and the input light source S, extracting effective characteristic information of the mask pattern by adopting an effective frequency spectrum extraction method, and representing a space image generated by a photoetching optical system by using the following mathematical model by combining an Abbe imaging method:
wherein, the first and the second end of the pipe are connected with each other,Irepresenting the spatial image intensity distribution, i.e. the result of partially coherent imaging;N ' S representing the number of effective point light sources in the pixelated light source;CCI i the coherent imaging results produced by a single point source are represented by the following mathematical model:
wherein the content of the first and second substances, (ii) (x i ,y i ) Representing a coherent image plane spatial coordinate system; (f,g) Representing a pupil plane spectral coordinate system; (f',g') denotes a mask spectral coordinate system;Hrepresents the optical transfer function, i.e. the pupil function, of the imaging system;H i representing the position of the light source according to points: (S x ,S y ) A pupil after translation;Mrepresenting a mask spectrum;
the coherent imaging model was discretized and represented by the following mathematical model:
wherein the content of the first and second substances,
representing a discretized coherent image plane spatial coordinate system; (j,k) Representing a discretized pupil plane spectral coordinate system; (j',k') represents a discretized mask spectral coordinate system;N ext representing the number of extracted valid spectral samples,
；
according to Abbe's method, aerial images obtained by partially coherent imaging processI ext Is represented by the following mathematical model:
wherein, in the followingm, nEstablishing a photoetching system illumination light source model for an index-mode coordinate system,S(m,n) Is shown in the light source model coordinate system at (m,n) Point light source at the position, the size of the illumination light source model matrix of the photoetching system isN S ×N S ，m,n=1,2,3,…,N S ；
Step 2: coding the light source and the mask effective unit as target function variables;
and step 3: randomly generating a group variable whole matrix to be optimized according to a heuristic optimization algorithm structureP(ii) a Therefore, in the light source mask optimization model, a light source and mask initial population-light source variable population matrix is randomly generatedP S And mask variable population matrixP M The light source variable group matrixP S And mask variable population matrixP M Are respectively asP S =[S 1 ,S 2 ,S 3 ,…,S P ]，P M =[M 1 ,M 2 ,M 3 ,…,M P ]；
And 4, step 4: according to the initial light source variable matrixP S Calculating the intensity distribution of the space image generated by each individual through the space image imaging model of the photoetching system
The spatial image prediction under different imaging conditions is realized,i=1,2, …,p(ii) a And according to an objective function F 1 And F 2 Calculating an adaptation value and selecting the currently best initial light source variable individual by comparison>
And an adapted value->
(ii) a Wherein it is present>
A group matrix formed in the space image imaging model of the lithography system according to different light source variablesP S Of (2)S P The resulting aerial image intensity distribution matrixI S I.e. is->
，/>
；/>
Defining the sum of absolute values of the difference values of each unit of the photoresist pattern matrix and the ideal pattern as a pattern error, and taking the pattern error as a target function F 1 (ii) a Marking areas of inner and outer pixel points near the boundary of the mask pattern, calculating edge placement error, and taking the edge placement error as an objective function F 2 (ii) a Objective function F 1 And F 2 Are represented as the following mathematical models, respectively:
wherein the content of the first and second substances,RP(x i ,y i ) A photoresist pattern is represented and,M * (x i ,y i ) Representing an ideal graph;ICC Edge representing a matrix formed by the extracted edge pixel points;S ext representing the extracted light source matrix;M ' ext representing a matrix formed by extracting ideal graph edge pixel points according to the index positions;minimizeexpressed in a tabu search-genetic iteration-based optimization modelWhen iteration stops, the numerical value of the objective function is ensured to be minimum;
and 5: the current optimal initial light source variable obtained in the step 4 is used as an individual
Performing iterative updating on the light source variable individuals until iteration stops as an input condition of a taboo search-genetic algorithm optimization model;
step 6: according to the light source variable individual after iteration is stopped, matrix inversion mirror image and Gaussian filtering operation are executed, and the appearance of the light source is recovered;
and 7: using the obtained light source as the light source condition of the mask optimization model; population matrix according to mask variablesP M Calculating and recording current best initial mask variable individual
And an adapted value->
；
And step 8: the current best initial mask variable obtained in the step 7 is used as an individual
Performing iterative update on mask variable individuals until iteration stops as an input condition of a tabu search-genetic algorithm optimization model;
and step 9: outputting the optimal light source intensity distribution and the mask pattern layout.
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