Photoetching simulation method and system based on circular sampling function decomposition and superposition pupil shift matrix

Abstract

The invention discloses a photoetching simulation method and system for decomposing a superposition pupil shift matrix based on a circular sampling function, and the method comprises the steps: carrying out the sampling of a shape function and a pupil function of an extended light source, and obtaining a corresponding superposition pupil shift matrix; processing the superposed pupil shift matrix, the extended light source and the frequency domain circle sampling function matrix of the pupil plane to obtain a frequency domain cross transmission coefficient matrix and a projection matrix; performing singular value decomposition processing on the projection matrix to obtain a singular value decomposition result; processing the spatial domain circular sampling function matrix based on a singular vector to obtain a convolution kernel matrix; constructing a spatial domain image simulation model based on the singular value decomposition result, the convolution kernel matrix and the initial Hopkinson model; and obtaining a spatial domain image simulation result based on the spatial domain image simulation model. According to the method, direct calculation and storage of the TCC matrix can be reduced by using a pupil shift matrix superposition method and analytic circle sampling function decomposition, and calculation consumption required for obtaining the kernel is remarkably reduced.

Description

Technical Field

[0001] The present invention relates to the field of photolithography technology, and in particular to a photolithography simulation method and system based on circular sampling function decomposition and superposition pupil shift matrix. Background Art

[0002] In an optical system, pupil function usually refers to pupil function, which indicates the distribution of light beams on pupil plane when passing through an optical system. Pupil plane is the collection of all light rays, indicating the entrance of light from a sample or object to an imaging system, or the exit of light from an imaging system to an eye. The shape and size of pupil plane have an important influence on the resolution and beam quality of the imaging system. Pupil plane is usually determined by the aperture stop, which is a component that limits the imaging beam of an optical system. The image formed by the aperture stop in the object space is called the entrance pupil, and the image formed in the image space is called the exit pupil. The entrance pupil and the exit pupil are a pair of conjugate surfaces, and they control the size of the aperture angles of the incident and exit beams, respectively. Pupil aberration refers to the imaging error caused by the irregularity or imperfection of the pupil plane. In general, pupil function and pupil plane are important concepts in optical systems, which can affect the imaging quality and performance of optical systems. By analyzing pupil function, the optical system can be optimized to improve imaging quality and resolution.

[0003] The Hopkins model is an important theoretical model in the field of computational lithography. It is used to describe the partially coherent imaging system in lithography and calculate the electric field intensity distribution on the wafer, that is, the light intensity distribution. The core assumption of the Hopkins model is "spectral shift invariance", which means that the diffraction field of plane waves incident on the mask at different angles is the same after passing through the mask, except that the light of different diffraction orders has an offset in the coordinates of the pupil plane. In the Hopkins model, the spatial domain is expressed as follows:

[0004]

[0005] in, Represents the spatial image, represents the scaled mask near field, represents the complex coherence, is the point spread function, is its conjugate function, are the coordinate variables in the image plane.

[0006] In the Hopkins model, only a single TCC function is required, and the calculated TCC function is used to calculate the aerial image under different masks, thereby reducing the calculation cost. However, after research, it was found that each time the aerial image is calculated, it is necessary to process the The calculation process is relatively complicated and is currently solved in the following way: Applying singular value decomposition to the TCC function, the TCC function expression is expressed as:

[0007] Then replace it into the Hopkins model and use replace , which is expressed as follows:

[0008] symbol represents matrix convolution, represents the singular vector of the convolution kernel. The weighted summation of the coherent systems obtains the spatial image of the partially coherent system. This process is called the sum of coherent systems algorithm (SOCS algorithm).

[0009] Although the SOCS algorithm can effectively reduce the calculation process and amount of space image, it is still a difficult problem to decompose the matrix of TCC function. Since the TCC function requires four independent variables, assuming that the number of samples of each variable is N, it is necessary to calculate The computational complexity of the singular value decomposition operation on a two-dimensional matrix is , which is bound to lead to very low computational efficiency. Summary of the invention

[0010] In view of the shortcomings of the prior art, the present invention provides a lithography simulation method and system based on circular sampling function decomposition and superposition pupil shift matrix.

[0011] In order to solve the above technical problems, the present invention is solved by the following technical solutions: A lithography simulation method based on decomposing and superimposing pupil shift matrix by circular sampling function comprises the following steps: The shape function and pupil function of the extended light source are sampled, and the corresponding superimposed pupil shift matrix is ​​calculated; Processing the superimposed pupil shift matrix, the frequency domain circular sampling function matrix of the extended light source and the frequency domain circular sampling function matrix of the pupil plane to obtain a frequency domain cross transmission coefficient matrix and obtaining a projection matrix based on the frequency domain cross transmission coefficient matrix; Performing singular value decomposition processing on the projection matrix to obtain a singular value decomposition result, wherein the singular value decomposition result includes singular values ​​and singular vectors; The spatial domain circular sampling function matrix is ​​processed based on the singular vectors to obtain the convolution kernel matrix; Based on the singular value decomposition results, convolution kernel matrix and initial Hopkins model, a spatial domain image simulation model is constructed; Based on the spatial domain image simulation model, the spatial domain image simulation result is obtained.

[0012] As an implementable method, sampling the shape function and pupil function of the extended light source and calculating the corresponding superimposed pupil shift matrix includes the following steps: Acquire a plurality of source coordinates and a plurality of pupil coordinates of the extended light source, and determine a source coordinate grid and a pupil coordinate grid respectively; Obtain a first circle sampling function grid based on the source coordinate grid, and obtain a second circle sampling function grid based on the pupil coordinate grid; The frequency domain circular sampling function is modified based on the first circular sampling function grid, and the space domain circular sampling function is modified based on the second circular sampling function grid. The shape function and the pupil function are sampled respectively by the modified frequency domain circular sampling function and the space domain circular sampling function, and an initial frequency domain circular sampling function is calculated. The initial frequency domain circular sampling function is processed to obtain an initial pupil matrix and then modified to obtain a corresponding superimposed pupil shift matrix.

[0013] As an implementable method, the method of processing the superimposed pupil shift matrix, the frequency domain circular sampling function matrix of the extended light source, and the frequency domain circular sampling function matrix of the pupil plane to obtain a frequency domain cross transmission coefficient matrix and obtaining a projection matrix based on the frequency domain cross transmission coefficient matrix includes the following steps: The superimposed pupil shift matrix, the frequency domain circular sampling function matrix of the extended light source and the frequency domain circular sampling function matrix of the pupil plane are multiplied to obtain a frequency domain cross transmission coefficient matrix; A projection matrix is ​​obtained based on the frequency domain cross transmission coefficient matrix and the conjugate transpose of the frequency domain cross transmission coefficient matrix; The frequency domain cross-transmission coefficient matrix is ​​expressed as follows: ; in, represents the frequency domain cross-transmission coefficient matrix, is the superimposed pupil shift matrix, , , Complex coherence The Fourier transform result is, Point spread function The Fourier transform result is, , represent the source coordinates, , , , They represent pupil coordinates respectively.

[0014] As an implementable method, performing singular value decomposition processing on the projection matrix to obtain a singular value decomposition result includes the following steps: when or When , the corresponding element in the superimposed pupil shift matrix is ​​0; The superimposed pupil shift matrix is ​​decomposed by the frequency domain circular sampling function to obtain the frequency domain circular sampling function decomposition result, which is expressed as follows:

[0015] Among them, the coefficients of the frequency domain circular sampling function decomposition result are calculated based on the orthogonality of the circular sampling function, which is expressed as follows:

[0016] The coefficients of the frequency domain circular sampling function decomposition result are replaced into the frequency domain cross transmission coefficient matrix to obtain the decomposition result of the frequency domain cross transmission coefficient matrix, which is expressed as follows:

[0017] in, represents the decomposition result of the frequency domain cross-transmission coefficient matrix, is the projection matrix, and * represents the conjugate transformation of the corresponding function.

[0018] As an implementable method, the spatial domain circle sampling function is expressed as follows: ,in,

[0019] The frequency domain circular sampling function is expressed as follows: ,in,

[0020] in, , , Indicates Bessel function of order, Indicates The first order Bessel function Zero point, , Respectively represent arrays ( , ), in the equation for superimposing the pupil shift matrix, the coordinates of the circular sampling function are expressed as Changed to Cartesian coordinates, The total number of items is set to , The total number of items is set to ,in, and , represents the frequency domain kernel of the cross-transmission coefficients, Indicates a subscript mark, used to distinguish and , , represents the normalized coefficient of the corresponding orthogonal function, represents the frequency domain circular sampling function with respect to the pupil coordinates as the independent variable, represents the frequency domain circular sampling function with respect to the source coordinates as the independent variable, Represents polar coordinates in polar coordinates.

[0021] As an implementable method, performing singular value decomposition processing on the projection matrix to obtain a singular value decomposition result includes the following steps: The projection matrix is ​​subjected to singular value decomposition to obtain the decomposed projection matrix, which is expressed as follows: ; Based on the correspondence between the frequency domain circular sampling function and the space domain circular sampling function, the singular value decomposition result of the TCC frequency matrix is ​​converted into the decomposed singular value of the TCC space domain matrix, which is expressed as follows:

[0022] in, are the singular vectors of the TCC space domain matrix, represents the singular values ​​corresponding to the singular vectors, represents the TCC space domain matrix, represents singular values, represents the singular vectors, , They represent the coordinate variables in the image plane respectively.

[0023] As an implementable method, performing singular value decomposition processing on the projection matrix to obtain a singular value decomposition result includes the following steps: The projection matrix is ​​subjected to singular value decomposition to obtain the decomposed projection matrix, which is expressed as follows: ; Based on the correspondence between the frequency domain circular sampling function and the space domain circular sampling function, the singular value decomposition result of the TCC frequency matrix is ​​converted into the decomposed singular value of the TCC space domain matrix, which is expressed as follows:

[0024] in, are the singular vectors of the TCC space domain matrix, represents the singular values ​​corresponding to the singular vectors, Represents the TCC space domain matrix.

[0025] As an implementable method, the spatial domain image simulation model is expressed as follows:

[0026] in, represents matrix convolution, represents the spatial domain image, represents the singular vectors of the TCC space domain matrix, represents the mask near field, represents singular values, represents the ordinal number of the singular value, They represent the coordinate variables in the image plane respectively.

[0027] A lithography simulation system based on decomposing and superimposing pupil shift matrix by circular sampling function, comprising: The sampling conversion module samples the shape function and pupil function of the extended light source and calculates the corresponding superimposed pupil shift matrix; The first processing module processes the superimposed pupil shift matrix, the frequency domain circular sampling function matrix of the extended light source and the frequency domain circular sampling function matrix of the pupil plane to obtain a frequency domain cross transmission coefficient matrix and obtain a projection matrix based on the frequency domain cross transmission coefficient matrix; A decomposition processing module performs singular value decomposition processing on the projection matrix to obtain a singular value decomposition result, wherein the singular value decomposition result includes a singular value and a singular vector; The second processing module processes the spatial domain circular sampling function matrix based on the singular vectors to obtain a convolution kernel matrix; The model building module builds a spatial domain image simulation model based on the singular value decomposition results, the convolution kernel matrix and the initial Hopkins model; The result simulation module obtains the spatial domain image simulation result based on the spatial domain image simulation model.

[0028] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the following method is implemented: The shape function and pupil function of the extended light source are sampled, and the corresponding superimposed pupil shift matrix is ​​calculated; Processing the superimposed pupil shift matrix, the frequency domain circular sampling function matrix of the extended light source and the frequency domain circular sampling function matrix of the pupil plane to obtain a frequency domain cross transmission coefficient matrix and obtaining a projection matrix based on the frequency domain cross transmission coefficient matrix; Performing singular value decomposition processing on the projection matrix to obtain a singular value decomposition result, wherein the singular value decomposition result includes singular values ​​and singular vectors; The spatial domain circular sampling function matrix is ​​processed based on the singular vectors to obtain the convolution kernel matrix; Based on the singular value decomposition results, convolution kernel matrix and initial Hopkins model, a spatial domain image simulation model is constructed; Based on the spatial domain image simulation model, the spatial domain image simulation result is obtained.

[0029] A lithography simulation device based on circular sampling function decomposition and superposition pupil shift matrix comprises a memory, a processor and a computer program stored in the memory and running on the processor, wherein the processor implements the following method when executing the computer program: The shape function and pupil function of the extended light source are sampled, and the corresponding superimposed pupil shift matrix is ​​calculated; Processing the superimposed pupil shift matrix, the frequency domain circular sampling function matrix of the extended light source and the frequency domain circular sampling function matrix of the pupil plane to obtain a frequency domain cross transmission coefficient matrix and obtaining a projection matrix based on the frequency domain cross transmission coefficient matrix; Performing singular value decomposition processing on the projection matrix to obtain a singular value decomposition result, wherein the singular value decomposition result includes singular values ​​and singular vectors; The spatial domain circular sampling function matrix is ​​processed based on the singular vectors to obtain the convolution kernel matrix; Based on the singular value decomposition results, convolution kernel matrix and initial Hopkins model, a spatial domain image simulation model is constructed; Based on the spatial domain image simulation model, the spatial domain image simulation result is obtained.

[0030] The present invention has significant technical effects due to the adoption of the above technical solution: The present invention utilizes the superposition pupil shift matrix method and analytical circle sampling function decomposition to reduce the direct calculation and storage of the TCC matrix and significantly reduce the computational consumption required to obtain the kernel; the present invention has a flexible calculation method and can arbitrarily change the grid size of the convolution kernel matrix according to the analytical characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0032] Figure 1 It is a schematic diagram of the overall process of the method of the present invention; Figure 2 It is a schematic diagram of the overall structure of the system of the present invention; Figure 3 Figure a shows an input schematic diagram of the present invention, and Figure b shows a schematic diagram of generating aberrations; Figure 4 Schematic diagram comparing the singular values ​​output by the present invention and the singular values ​​output by the traditional algorithm; Figure 5 Schematic diagram of comparison between the first four convolution kernel matrices output by the present invention and the traditional method; Figure 6 It is a schematic diagram comparing the running time of the present invention and other methods; Figure 7 It is a schematic diagram comparing the memory consumption of the present invention and other methods. DETAILED DESCRIPTION

[0033] The present invention is further described in detail below in conjunction with embodiments. The following embodiments are for explanation of the present invention but the present invention is not limited to the following embodiments.

[0034] Embodiment 1: A lithography simulation method based on decomposing and superimposing pupil shift matrix based on circular sampling function, such as Figure 1 As shown, the following steps are included: S100, sampling the shape function and pupil function of the extended light source, and calculating and obtaining a corresponding superimposed pupil shift matrix; S200, processing the superimposed pupil shift matrix, the frequency domain circular sampling function matrix of the extended light source, and the frequency domain circular sampling function matrix of the pupil plane to obtain a frequency domain cross transmission coefficient matrix and obtain a projection matrix based on the frequency domain cross transmission coefficient matrix; S300, performing singular value decomposition processing on the projection matrix to obtain a singular value decomposition result, wherein the singular value decomposition result includes singular values ​​and singular vectors; S400, processing the spatial domain circular sampling function matrix based on the singular vector to obtain a convolution kernel matrix; S500, constructing a spatial domain image simulation model based on the singular value decomposition result, the convolution kernel matrix and the initial Hopkins model; S600: Obtain a spatial domain image simulation result based on the spatial domain image simulation model.

[0035] The present invention utilizes the superposition pupil shift matrix method and analytical circle sampling function decomposition to reduce the direct calculation and storage of the TCC matrix and significantly reduce the computational consumption required to obtain the kernel; the present invention has a flexible calculation method and can arbitrarily change the grid size of the convolution kernel matrix according to the analytical characteristics.

[0036] In one embodiment, the step of sampling the shape function and pupil function of the extended light source and calculating the corresponding superimposed pupil shift matrix comprises the following steps: Acquire a plurality of source coordinates and a plurality of pupil coordinates of the extended light source, and determine a source coordinate grid and a pupil coordinate grid respectively; Obtain a first circle sampling function grid based on the source coordinate grid, and obtain a second circle sampling function grid based on the pupil coordinate grid; The frequency domain circular sampling function is modified based on the first circular sampling function grid, and the space domain circular sampling function is modified based on the second circular sampling function grid. The shape function and the pupil function are sampled respectively by the modified frequency domain circular sampling function and the space domain circular sampling function, and an initial frequency domain circular sampling function is calculated. The initial frequency domain circular sampling function is processed to obtain an initial pupil matrix and then modified to obtain a corresponding superimposed pupil shift matrix.

[0037] During the acquisition process, the initial frequency domain circular sampling function usually represents the circular sampling of the signal of the extended light source in the frequency domain, which can be understood as including the frequency domain circular sampling function and the space domain circular sampling function. and The number of samples is set to , pupil coordinates and The number of samples is set to According to the superposition pupil shift matrix method, the frequency domain Hopkins model is first discretized and converted into the product of two superposition pupil shift matrices. Here, the spatial domain circular sampling function is expressed as: ,in,

[0038] The frequency domain circular sampling function is expressed as: ,in,

[0039] in, , , Indicates Bessel function of order, Indicates The first order Bessel function Zero point, , Respectively represent arrays ( , ), in the equation for superimposing the pupil shift matrix, the coordinates of the circular sampling function are expressed as Changed to Cartesian coordinates, The total number of items is set to , The total number of items is set to ,in, and .

[0040] In one embodiment, the process of processing the superimposed pupil shift matrix, the frequency domain circular sampling function matrix of the extended light source, and the frequency domain circular sampling function matrix of the pupil plane to obtain a frequency domain cross transmission coefficient matrix and obtaining a projection matrix based on the frequency domain cross transmission coefficient matrix includes the following steps: The superimposed pupil shift matrix, the frequency domain circular sampling function matrix of the extended light source and the frequency domain circular sampling function matrix of the pupil plane are multiplied to obtain a frequency domain cross transmission coefficient matrix; A projection matrix is ​​obtained based on the frequency domain cross transmission coefficient matrix and the conjugate transpose of the frequency domain cross transmission coefficient matrix; The frequency domain cross-transmission coefficient matrix is ​​expressed as follows: ; in, represents the frequency domain cross-transmission coefficient matrix, is the superimposed pupil shift matrix, , , Complex coherence The Fourier transform result is, Point spread function The Fourier transform result is, , They represent the source coordinates, , , , represent pupil coordinates respectively.

[0041] In one embodiment, performing singular value decomposition processing on the projection matrix to obtain a singular value decomposition result includes the following steps: when or When , the corresponding element in the superimposed pupil shift matrix is ​​0; The superimposed pupil shift matrix is ​​decomposed by the frequency domain circular sampling function to obtain the frequency domain circular sampling function decomposition result, which is expressed as follows:

[0042] Among them, the coefficients of the frequency domain circular sampling function decomposition result are calculated based on the orthogonality of the circular sampling function, which is expressed as follows:

[0043] The coefficients of the frequency domain circular sampling function decomposition result are replaced into the frequency domain cross transmission coefficient matrix to obtain the decomposition result of the frequency domain cross transmission coefficient matrix, which is expressed as follows:

[0044] in, represents the decomposition result of the frequency domain cross-transmission coefficient matrix, is the projection matrix, and * represents the conjugate transformation of the corresponding function.

[0045] In step S300, the projection matrix is ​​subjected to singular value decomposition processing to obtain a singular value decomposition result, including the following steps: The projection matrix is ​​subjected to singular value decomposition to obtain the decomposed projection matrix, which is expressed as follows: ; Based on the correspondence between the frequency domain circular sampling function and the space domain circular sampling function, the singular value decomposition result of the TCC frequency matrix is ​​converted into the decomposed singular value of the TCC space domain matrix, which is expressed as follows:

[0046] in, are the singular vectors of the TCC space domain matrix, represents the singular values ​​corresponding to the singular vectors, Represents the TCC space domain matrix.

[0047] Finally, after the above steps, the spatial domain image simulation model is obtained:

[0048] in, represents matrix convolution, represents the spatial domain image, represents the singular vectors of the TCC space domain matrix, represents the mask near field, represents singular values, represents the ordinal number of the singular value, They represent the coordinate variables in the image plane respectively.

[0049] In order to evaluate the computational efficiency of the whole process, the environment used is a system equipped with an Intel i5-13400 processor (main frequency 2.5GHz), 64GB memory and running Windows 10. MATLAB is used to compare the calculation process and calculation results of three methods. The three algorithms are: a method of directly performing singular value decomposition (SVD) on the TCC matrix; a circular sampling function TCC method that uses a circular sampling function to project the spatial TCC matrix into a smaller projection matrix and then perform singular value decomposition; and the method proposed in the present invention. The comparison results of the three methods are shown in Figure 2. Figure 6 and Figure 7As shown in Figure 2, the direct singular value decomposition (SVD) method is the least efficient in terms of computational time and memory consumption. As the pupil sampling rate increases, its time and memory requirements are several orders of magnitude larger than those of the other two methods. The circular sampling function TCC method has a significant reduction in computational time compared to the direct SVD method, but is still inferior to the method proposed in this invention, and its complexity is , and the complexity of the present invention is And because the circle sampling function TCC method needs to calculate the TCC matrix, it also requires a lot of memory, resulting in its memory consumption being similar to that of the direct singular value decomposition (SVD) method.

[0050] In conjunction with the specific embodiment, the specific calculation process can be found in Figure 3 : Input the shape function of the extended light source , where one of the rings is illuminated as Figure 3 As shown in a. And the pupil function , the pupil function may have random aberrations, examples of which are Figure 3 As shown in b, here, Figure 3 (a) The X-axis and Y-axis are the cosine of the angle between the light source illumination direction and the X-axis and the cosine of the angle between the light source illumination direction and the Y-axis respectively; Figure 3 (b) The X-axis and Y-axis are the relative spatial frequencies of the pupil in the X-direction and Y-direction.

[0051] First, generate The mutually orthogonal two-dimensional frequency domain circular sampling functions can be understood as the initial frequency domain circular sampling function, which is modified based on the circular sampling function as The matrix of The superimposed pupil shift matrix is ​​multiplied with the frequency domain circular sampling function matrix of the extended light source and the frequency domain circular sampling function matrix of the pupil plane to form a coefficient matrix; the coefficient matrix is ​​multiplied with its conjugate transpose to obtain a projection matrix; the singular value decomposition is then applied to the projection matrix to obtain a diagonal matrix and an orthogonal matrix; finally, the orthogonal matrix is ​​multiplied with the spatial domain circular sampling function matrix to generate a convolution kernel matrix, and finally the singular values ​​and convolution kernel matrix are output.

[0052] like Figure 4 As shown, a schematic diagram comparing the singular values ​​obtained by the method of the present invention with the singular values ​​obtained by the traditional method is shown, where the X-axis represents the ordinal number of the singular value (i.e., the number of the singular value), and the Y-axis represents the normalized singular value size.

[0053] like Figure 5 , Figure 5 The X-axis and Y-axis are the spatial image X-coordinate and Y-coordinate of the convolution kernel. Figure 5 Figures a, b, c, and d show the first four convolution kernels of the output convolution kernel matrix, and compare them with the traditional method, giving the weighted relative error between them.

[0054] in addition, Figure 6 and Figure 7 A comparison chart of the running time and memory consumption of the method adopted by the present invention and other methods is also shown. Through the comparison, it is found that the method proposed by the present invention has a short running time and low memory consumption, among which, Figure 6 The X coordinate is the sampling rate of the pupil, and the Y coordinate is the algorithm running time. Figure 7 The X coordinate is the sampling rate of the pupil, and the Y coordinate is the memory required by the algorithm.

[0055] In summary, the method proposed in the present invention is superior to other existing methods in all aspects.

[0056] Embodiment 2: A lithography simulation system based on circular sampling function decomposition and superposition pupil shift matrix, such as Figure 2 As shown, including: The sampling and conversion module 100 samples the shape function and pupil function of the extended light source and calculates and obtains the corresponding superimposed pupil shift matrix; The first processing module 200 processes the superimposed pupil shift matrix, the frequency domain circular sampling function matrix of the extended light source and the frequency domain circular sampling function matrix of the pupil plane to obtain a frequency domain cross transmission coefficient matrix and obtain a projection matrix based on the frequency domain cross transmission coefficient matrix; The decomposition processing module 300 performs singular value decomposition processing on the projection matrix to obtain a singular value decomposition result, wherein the singular value decomposition result includes singular values ​​and singular vectors; A second processing module 400 processes the space domain circular sampling function matrix based on the singular vectors to obtain a convolution kernel matrix; A model building module 500 builds a spatial domain image simulation model based on the singular value decomposition result, the convolution kernel matrix and the initial Hopkins model; The result simulation module 600 obtains the space domain image simulation result based on the space domain image simulation model.

[0057] Various changes and modifications can be made without departing from the spirit and scope of the present invention, and all equivalent technical solutions also belong to the scope of the present invention.

[0058] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0059] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, devices or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0060] The present invention is described with reference to the flowcharts and / or block diagrams of the method, terminal device (system), and computer program product according to the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of the processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing terminal device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing terminal device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0061] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing terminal device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured product including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0062] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal device so that a series of operating steps are executed on the computer or other programmable terminal device to produce a computer-implemented process, thereby providing instructions for executing on the computer or other programmable terminal device to implement the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0063] It should be noted that: The "one embodiment" or "embodiment" mentioned in the specification means that the specific features, structures or characteristics described in conjunction with the embodiment are included in at least one embodiment of the present invention. Therefore, the phrases "one embodiment" or "embodiment" appearing in various places throughout the specification do not necessarily refer to the same embodiment.

[0064] In addition, it should be noted that the shapes and names of the parts and components of the specific embodiments described in this specification may be different. Any equivalent or simple changes made based on the structure, features and principles described in the patent concept of the present invention are included in the protection scope of the patent of the present invention. The technicians in the technical field of the present invention can make various modifications or supplements to the specific embodiments described or replace them in a similar manner, as long as they do not deviate from the structure of the present invention or exceed the scope defined by the claims, they should all fall within the protection scope of the present invention.

Claims

1. A lithography simulation method based on decomposing and superimposing pupil shift matrix by circular sampling function, characterized in that: The following steps are involved: The shape function and pupil function of the extended light source are sampled, and the corresponding superimposed pupil shift matrix is ​​calculated; Processing the superimposed pupil shift matrix, the frequency domain circular sampling function matrix of the extended light source and the frequency domain circular sampling function matrix of the pupil plane to obtain a frequency domain cross transmission coefficient matrix and obtaining a projection matrix based on the frequency domain cross transmission coefficient matrix; Performing singular value decomposition processing on the projection matrix to obtain a singular value decomposition result, wherein the singular value decomposition result includes singular values ​​and singular vectors; The spatial domain circular sampling function matrix is ​​processed based on the singular vectors to obtain the convolution kernel matrix; Based on the singular value decomposition results, convolution kernel matrix and initial Hopkins model, a spatial domain image simulation model is constructed; Based on the spatial domain image simulation model, the spatial domain image simulation result is obtained.

2. The lithography simulation method based on decomposition and superposition of pupil shift matrix by circular sampling function according to claim 1, characterized in that: The step of sampling the shape function and pupil function of the extended light source and calculating the corresponding superimposed pupil shift matrix comprises the following steps: Acquire a plurality of source coordinates and a plurality of pupil coordinates of the extended light source, and determine a source coordinate grid and a pupil coordinate grid respectively; Obtain a first circle sampling function grid based on the source coordinate grid, and obtain a second circle sampling function grid based on the pupil coordinate grid; The frequency domain circular sampling function is modified based on the first circular sampling function grid, and the space domain circular sampling function is modified based on the second circular sampling function grid. The shape function and the pupil function are sampled respectively by the modified frequency domain circular sampling function and the space domain circular sampling function, and an initial frequency domain circular sampling function is calculated. The initial frequency domain circular sampling function is processed to obtain an initial pupil matrix and then modified to obtain a corresponding superimposed pupil shift matrix.

3. The lithography simulation method based on decomposition and superposition of pupil shift matrix by circular sampling function according to claim 1, characterized in that: The method of processing the superimposed pupil shift matrix, the frequency domain circular sampling function matrix of the extended light source and the frequency domain circular sampling function matrix of the pupil plane to obtain a frequency domain cross transmission coefficient matrix and obtaining a projection matrix based on the frequency domain cross transmission coefficient matrix comprises the following steps: The superimposed pupil shift matrix, the frequency domain circular sampling function matrix of the extended light source and the frequency domain circular sampling function matrix of the pupil plane are multiplied to obtain a frequency domain cross transmission coefficient matrix; A projection matrix is ​​obtained based on the frequency domain cross transmission coefficient matrix and the conjugate transpose of the frequency domain cross transmission coefficient matrix; The frequency domain cross-transmission coefficient matrix is ​​expressed as follows: ； in, represents the frequency domain cross-transmission coefficient matrix, is the superimposed pupil shift matrix, , , Complex coherence The Fourier transform result is, Point spread function The Fourier transform result is, , They represent the source coordinates, , , , represent pupil coordinates respectively.

4. The lithography simulation method based on decomposition and superposition of pupil shift matrix by circular sampling function according to claim 1, characterized in that: The process of performing singular value decomposition on the projection matrix to obtain a singular value decomposition result comprises the following steps: when or When , the corresponding element in the superimposed pupil shift matrix is ​​0; The superimposed pupil shift matrix is ​​decomposed by the frequency domain circular sampling function to obtain the frequency domain circular sampling function decomposition result, which is expressed as follows: Among them, the coefficients of the frequency domain circular sampling function decomposition result are calculated based on the orthogonality of the circular sampling function, which is expressed as follows: The coefficients of the frequency domain circular sampling function decomposition result are replaced into the frequency domain cross transmission coefficient matrix to obtain the decomposition result of the frequency domain cross transmission coefficient matrix, which is expressed as follows: Among them, the spatial domain circle sampling function is expressed as follows: ,in, The frequency domain circular sampling function is expressed as follows: ,in, in, represents the coefficients of the decomposition result of the frequency domain circular sampling function, represents the decomposition result of the frequency domain cross-transmission coefficient matrix, is the projection matrix, * represents the conjugate transformation of the corresponding function, is the superimposed pupil shift matrix, , They represent the source coordinates, , , , represent the pupil coordinates, , , , , Respectively represent arrays ( , ), , , Indicates Bessel function of order, Indicates The first order Bessel function zero points, in the equation for the superimposed pupil shift matrix, the coordinates of the circular sampling function are expressed as Changed to Cartesian coordinates, The total number of items is set to , The total number of items is set to ,in, and , represents the frequency domain kernel of the cross-transmission coefficients, Indicates a subscript mark, used to distinguish and , , represents the normalized coefficient of the corresponding orthogonal function, represents the frequency domain circular sampling function with respect to the pupil coordinates as the independent variable, represents the frequency domain circular sampling function with respect to the source coordinates as the independent variable, Represents polar coordinates in polar coordinates.

5. The lithography simulation method based on decomposing and superimposing pupil shift matrix based on circular sampling function according to claim 1, characterized in that: The process of performing singular value decomposition on the projection matrix to obtain a singular value decomposition result comprises the following steps: The projection matrix is ​​subjected to singular value decomposition to obtain the decomposed projection matrix, which is expressed as follows: ； Based on the correspondence between the frequency domain circular sampling function and the space domain circular sampling function, the singular value decomposition result of the TCC frequency matrix is ​​converted into the decomposed singular value of the TCC space domain matrix, which is expressed as follows: in, are the singular vectors of the TCC space domain matrix, represents the singular values ​​corresponding to the singular vectors, represents the TCC space domain matrix, represents singular values, represents the singular vectors, , They represent the coordinate variables in the image plane respectively.

6. The lithography simulation method based on decomposing and superimposing pupil shift matrix based on circular sampling function according to claim 1, characterized in that: The spatial domain image simulation model is expressed as follows: in, represents matrix convolution, represents the spatial domain image, represents the singular vectors of the TCC space domain matrix, represents the mask near field, represents singular values, represents the ordinal number of the singular value, They represent the coordinate variables in the image plane respectively.

7. A lithography simulation system based on circular sampling function decomposition and superposition of pupil shift matrix, characterized in that: include: The sampling conversion module samples the shape function and pupil function of the extended light source and calculates the corresponding superimposed pupil shift matrix; The first processing module processes the superimposed pupil shift matrix, the frequency domain circular sampling function matrix of the extended light source and the frequency domain circular sampling function matrix of the pupil plane to obtain a frequency domain cross transmission coefficient matrix and obtain a projection matrix based on the frequency domain cross transmission coefficient matrix; A decomposition processing module performs singular value decomposition processing on the projection matrix to obtain a singular value decomposition result, wherein the singular value decomposition result includes a singular value and a singular vector; The second processing module processes the spatial domain circular sampling function matrix based on the singular vectors to obtain a convolution kernel matrix; The model building module builds a spatial domain image simulation model based on the singular value decomposition results, the convolution kernel matrix and the initial Hopkins model; The result simulation module obtains the spatial domain image simulation result based on the spatial domain image simulation model.

8. The lithography simulation system based on circular sampling function decomposition and superposition of pupil shift matrix according to claim 7, characterized in that: The first processing module is configured to: The superimposed pupil shift matrix, the frequency domain circular sampling function matrix of the extended light source and the frequency domain circular sampling function matrix of the pupil plane are multiplied to obtain a frequency domain cross transmission coefficient matrix; A projection matrix is ​​obtained based on the frequency domain cross transmission coefficient matrix and the conjugate transpose of the frequency domain cross transmission coefficient matrix; The frequency domain cross-transmission coefficient matrix is ​​expressed as follows: ； in, represents the frequency domain cross-transmission coefficient matrix, is the superimposed pupil shift matrix, , , Complex coherence The Fourier transform result is, Point spread function The Fourier transform result is, , They represent the source coordinates, , , , represent pupil coordinates respectively.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

10. A lithography simulation device based on circular sampling function decomposition and superposition pupil shift matrix, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the processor executes the computer program, the method according to any one of claims 1 to 6 is implemented.

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