Lithography simulation method and system based on decomposition of superposition pupil shift matrix by circular sampling function
By decomposing the superimposed pupil shift matrix using a circular sampling function, the lithography simulation process was optimized, reducing computational complexity and storage requirements, improving lithography simulation efficiency, and achieving more efficient image quality and resolution optimization.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- ZJU HANGZHOU GLOBAL SCI & TECH INNOVATION CENT
- Filing Date
- 2024-12-20
- Publication Date
- 2026-06-09
AI Technical Summary
In existing lithography simulation methods, the quadruple integral of the TCC function is complex and inefficient, resulting in high computational complexity in the lithography simulation process and making it difficult to effectively optimize imaging quality and resolution.
A method based on circular sampling function decomposition and superimposed pupil shift matrix is adopted. By sampling the extended light source and pupil function, a frequency domain cross-transmission coefficient matrix is constructed and singular value decomposition is performed to obtain the convolution kernel matrix, thereby constructing a spatial domain image simulation model.
It significantly reduces the direct computation and storage requirements of the TCC matrix, improves computational efficiency, allows for flexible adjustment of the convolution kernel matrix grid size, and enhances the computational speed and memory utilization efficiency of the lithography simulation process.
Smart Images
Figure CN119596647B_ABST
Abstract
Description
Technical Field
[0001] This 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 of pupil shift matrix. Background Technology
[0002] In optical systems, the pupil function typically refers to the distribution of a light beam across the pupil plane as it passes through the optical system. The pupil plane is the collection of all light rays, representing the light entry point from the sample or object to the imaging system, or the light exit point from the imaging system to the eye. The shape and size of the pupil plane significantly influence the resolution and beam quality of the imaging system. The pupil plane is usually determined by the aperture stop, which is the element that confines the imaging beam of the optical system. The image formed by the aperture stop in object space is called the entrance pupil, and the image formed in image space is called the exit pupil. The entrance and exit pupils are a pair of conjugate planes, controlling the aperture angles of the incident and exit beams, respectively. Pupil aberration refers to the imaging errors caused by irregularities or imperfections in the pupil plane. In summary, the pupil function and pupil plane are crucial concepts in optical systems, affecting their imaging quality and performance. Analyzing the pupil function allows for optimized design of the optical system to improve imaging quality and resolution.
[0003] The Hopkins model is an important theoretical model in computational lithography, used to describe partially coherent imaging systems in lithography and to calculate the electric field intensity distribution, i.e., the light intensity distribution, on a wafer. The core assumption of the Hopkins model is "spectral translation invariance," which means that plane waves incident on a mask at different angles result in the same diffraction field after passing through the mask; only the coordinates of different diffraction orders are offset at the pupil plane. In the Hopkins model, the spatial domain expression is as follows:
[0004]
[0005]
[0006] in, Represents a spatial image. This represents the near field of the scaled mask. Indicates the degree of complex coherence. Let be the point spread function. Let it be its conjugate function. These are the coordinate variables within the image plane.
[0007] In the Hopkins model, only a single TCC function is needed, and the calculated TCC function is used to calculate spatial images under different masks, thus reducing computational costs. However, research has revealed that each calculation of the spatial image requires processing information related to… The quadruple integral. The calculation process is quite complex, and it is currently solved using the following method:
[0008] Applying singular value decomposition to the TCC function makes the TCC function expression as follows:
[0009]
[0010] Then replace it in the Hopkins model and use it. replace , means as follows:
[0011]
[0012] symbol Represents matrix convolution. The convolution kernel represents singular vectors. By... The spatial image of a partially coherent system is obtained by weighted summation of several coherent systems. This process is called the Coherent System Sum Algorithm (SOCS algorithm).
[0013] Although the SOCS algorithm effectively reduces the computational process and amount of data for spatial images, decomposing the matrix of the TCC function remains a challenge. Since the TCC function requires four independent variables, assuming each variable has N samples, it requires computation... The computational complexity of performing singular value decomposition on a two-dimensional matrix is O(n log n). This will inevitably lead to very low computational efficiency. Summary of the Invention
[0014] This invention addresses the shortcomings of existing technologies by providing a lithography simulation method and system based on circular sampling function decomposition and superposition of pupil shift matrices.
[0015] To solve the above-mentioned technical problems, the present invention provides the following technical solution:
[0016] A lithography simulation method based on circular sampling function decomposition and superposition of pupil shift matrices includes the following steps:
[0017] The shape function and pupil function of the extended light source are sampled, and the corresponding superimposed pupil shift matrix is calculated.
[0018] 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 surface are processed to obtain the frequency domain cross-transmission coefficient matrix, and the projection matrix is obtained based on the frequency domain cross-transmission coefficient matrix.
[0019] The projection matrix is subjected to singular value decomposition to obtain the singular value decomposition result, wherein the singular value decomposition result includes singular values and singular vectors;
[0020] The convolution kernel matrix is obtained by processing the spatial domain circular sampling function matrix based on singular vectors;
[0021] Based on the singular value decomposition results, convolution kernel matrix, and initial Hopkins model, a spatial domain image simulation model is constructed.
[0022] Based on the spatial domain image simulation model, spatial domain image simulation results are obtained.
[0023] As one possible implementation, sampling the shape function and pupil function of the extended light source and calculating the corresponding superimposed pupil shift matrix includes the following steps:
[0024] Obtain several source coordinates and several pupil coordinates of the extended light source, and determine the source coordinate grid and pupil coordinate grid respectively;
[0025] The first circular sampling function grid is obtained based on the source coordinate grid, and the second circular sampling function grid is obtained based on the pupil coordinate grid.
[0026] The frequency domain circular sampling function is modified based on the first circular sampling function grid, and the spatial domain circular sampling function is modified based on the second circular sampling function grid. The shape function and pupil function are sampled by the modified frequency domain circular sampling function and spatial domain circular sampling function respectively, and the initial frequency domain circular sampling function is calculated.
[0027] The initial frequency domain circular sampling function is processed to obtain the initial pupil matrix, which is then modified to obtain the corresponding superimposed pupil shift matrix.
[0028] As one possible implementation, 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 the frequency domain cross-transmission coefficient matrix, and then obtaining the projection matrix based on the frequency domain cross-transmission coefficient matrix, includes the following steps:
[0029] Multiply 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 surface to obtain the frequency domain cross-transmission coefficient matrix.
[0030] The projection matrix is obtained based on the frequency domain cross-transmission coefficient matrix and its conjugate transpose.
[0031] The frequency domain cross-transmission coefficient matrix is represented as follows:
[0032] ;
[0033] in, Represents the frequency domain cross-transmission coefficient matrix. To superimpose the pupil shift matrix, , , Indicates complex coherence The Fourier transform result, Point spread function The Fourier transform result, , These represent the source coordinates, , , , These represent the pupil coordinates.
[0034] As one possible implementation, the process of performing singular value decomposition on the projection matrix to obtain the singular value decomposition result includes the following steps:
[0035] when or When the time is right, the corresponding element in the superimposed pupil shift matrix is 0;
[0036] The superimposed pupil shift matrix is decomposed using a frequency-domain circular sampling function, and the frequency-domain circular sampling function decomposition result is expressed as follows:
[0037]
[0038] The coefficients of the frequency domain circular sampling function decomposition result are obtained by calculating the orthogonality of the circular sampling function, as shown below:
[0039]
[0040] By replacing the coefficients of the frequency domain circular sampling function decomposition result with those of the frequency domain cross-transmission coefficient matrix, the decomposition result of the frequency domain cross-transmission coefficient matrix is obtained, as shown below:
[0041]
[0042] in, This represents the decomposition result of the frequency domain cross-transmission coefficient matrix. Let be the projection matrix, and * denote the conjugate transformation of the corresponding function.
[0043] As one possible implementation method, the spatial domain circular sampling function is expressed as follows:
[0044] ,in,
[0045] The frequency domain circular sampling function is expressed as follows:
[0046] ,in,
[0047] in, , , Indicates the first Bessel function of order 1, Indicates the first The first order of the Bessel function One zero point, , They represent arrays ( , The arrangement of ) in the equation of the superimposed pupil shift matrix, and the coordinate representation of the circular sampling function. It has been changed to Cartesian coordinates. The total number of items is set to , The total number of items is set to ,in, and , The frequency domain kernel representing the cross-transmission coefficients, Indicates a subscript marker, used to distinguish... and , , Represents the normalized coefficients of the corresponding orthogonal functions. This represents the frequency domain circular sampling function with respect to the pupil coordinates. This represents a frequency domain circular sampling function with respect to the source coordinates. This represents the polar radius coordinate in polar coordinates.
[0048] As one possible implementation, the process of performing singular value decomposition on the projection matrix to obtain the singular value decomposition result includes the following steps:
[0049] The projection matrix is subjected to singular value decomposition to obtain the decomposed projection matrix, as shown below:
[0050] ;
[0051] Based on the correspondence between the frequency domain circular sampling function and the spatial domain circular sampling function, the singular value decomposition result of the TCC frequency matrix is transformed into the singular value decomposition of the TCC spatial domain matrix, as shown below:
[0052]
[0053] in, Let be a singular vector of the TCC space field matrix. This represents the singular value corresponding to the singular vector. Represents the TCC space field matrix. Represents singular values, Represents singular vectors, , These represent the coordinate variables within the image plane.
[0054] As one possible implementation, the process of performing singular value decomposition on the projection matrix to obtain the singular value decomposition result includes the following steps:
[0055] The projection matrix is subjected to singular value decomposition to obtain the decomposed projection matrix, as shown below:
[0056] ;
[0057] Based on the correspondence between the frequency domain circular sampling function and the spatial domain circular sampling function, the singular value decomposition result of the TCC frequency matrix is transformed into the singular value decomposition of the TCC spatial domain matrix, as shown below:
[0058]
[0059] in, Let be a singular vector of the TCC space field matrix. This represents the singular value corresponding to the singular vector. This represents the TCC spatial domain matrix.
[0060] As one possible implementation method, the spatial domain image simulation model is represented as follows:
[0061]
[0062] in, Represents matrix convolution. Representing spatial domain images, Describes the singular vectors of the TCC space field matrix. Indicates the near field of the mask. Represents singular values, Ordinal numbers representing singular values These represent the coordinate variables within the image plane.
[0063] A lithography simulation system based on circular sampling function decomposition and superposition of pupil shift matrices includes:
[0064] The sampling conversion module samples the shape function and pupil function of the extended light source and calculates the corresponding superimposed pupil shift matrix;
[0065] 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 surface to obtain the frequency domain cross-transmission coefficient matrix and obtain the projection matrix based on the frequency domain cross-transmission coefficient matrix.
[0066] The decomposition processing module performs singular value decomposition on the projection matrix to obtain the singular value decomposition result, wherein the singular value decomposition result includes singular values and singular vectors.
[0067] The second processing module processes the spatial domain circular sampling function matrix based on singular vectors to obtain the convolution kernel matrix;
[0068] The model building module constructs a spatial domain image simulation model based on the singular value decomposition results, convolution kernel matrix, and initial Hopkins model.
[0069] The results simulation module, based on the spatial domain image simulation model, obtains spatial domain image simulation results.
[0070] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the following method:
[0071] The shape function and pupil function of the extended light source are sampled, and the corresponding superimposed pupil shift matrix is calculated.
[0072] 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 surface are processed to obtain the frequency domain cross-transmission coefficient matrix, and the projection matrix is obtained based on the frequency domain cross-transmission coefficient matrix.
[0073] The projection matrix is subjected to singular value decomposition to obtain the singular value decomposition result, wherein the singular value decomposition result includes singular values and singular vectors;
[0074] The convolution kernel matrix is obtained by processing the spatial domain circular sampling function matrix based on singular vectors;
[0075] Based on the singular value decomposition results, convolution kernel matrix, and initial Hopkins model, a spatial domain image simulation model is constructed.
[0076] Based on the spatial domain image simulation model, spatial domain image simulation results are obtained.
[0077] A photolithography simulation device based on circular sampling function decomposition and superimposed pupil shift matrix includes a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the following method:
[0078] The shape function and pupil function of the extended light source are sampled, and the corresponding superimposed pupil shift matrix is calculated.
[0079] 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 surface are processed to obtain the frequency domain cross-transmission coefficient matrix, and the projection matrix is obtained based on the frequency domain cross-transmission coefficient matrix.
[0080] The projection matrix is subjected to singular value decomposition to obtain the singular value decomposition result, wherein the singular value decomposition result includes singular values and singular vectors;
[0081] The convolution kernel matrix is obtained by processing the spatial domain circular sampling function matrix based on singular vectors;
[0082] Based on the singular value decomposition results, convolution kernel matrix, and initial Hopkins model, a spatial domain image simulation model is constructed.
[0083] Based on the spatial domain image simulation model, spatial domain image simulation results are obtained.
[0084] This invention, by adopting the above technical solutions, has significant technical effects:
[0085] This invention utilizes the superimposed pupil shift matrix method and analytical circular sampling function decomposition to reduce the direct calculation and storage of the TCC matrix, significantly reducing the computational cost required to obtain the kernel. The calculation method of this invention is flexible and can arbitrarily change the grid size of the convolution kernel matrix according to the analytical characteristics. Attached Figure Description
[0086] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0087] Figure 1 This is a schematic diagram of the overall process of the method of the present invention;
[0088] Figure 2 This is a schematic diagram of the overall structure of the system of the present invention;
[0089] Figure 3 Figure a shows the input diagram of the present invention, and Figure b shows the diagram of the aberration generation;
[0090] Figure 4 This is a schematic diagram comparing the singular values output by the present invention with those output by the traditional algorithm;
[0091] Figure 5 This is a schematic diagram comparing the first four convolution kernel matrices output by this invention with those of the traditional method;
[0092] Figure 6 This is a schematic diagram comparing the running time of the present invention with that of other methods;
[0093] Figure 7This is a schematic diagram comparing the memory consumption of the present invention with other methods. Detailed Implementation
[0094] The present invention will be further described in detail below with reference to the embodiments. The following embodiments are explanations of the present invention, but the present invention is not limited to the following embodiments.
[0095] Example 1:
[0096] A lithographic simulation method based on circular sampling function decomposition and superposition of pupil shift matrices, such as Figure 1 As shown, it includes the following steps:
[0097] S100. Sample the shape function and pupil function of the extended light source and calculate the corresponding superimposed pupil shift matrix;
[0098] S200. 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 surface are processed to obtain the frequency domain cross-transmission coefficient matrix, and the projection matrix is obtained based on the frequency domain cross-transmission coefficient matrix.
[0099] S300. Perform singular value decomposition on the projection matrix to obtain the singular value decomposition result, wherein the singular value decomposition result includes singular values and singular vectors.
[0100] S400. Based on the singular vector, the circular sampling function matrix in the spatial domain is processed to obtain the convolution kernel matrix;
[0101] S500, based on the singular value decomposition results, convolution kernel matrix and initial Hopkins model, constructs a spatial domain image simulation model;
[0102] S600, based on the spatial domain image simulation model, obtains spatial domain image simulation results.
[0103] This invention utilizes the superimposed pupil shift matrix method and analytical circular sampling function decomposition to reduce the direct calculation and storage of the TCC matrix, significantly reducing the computational cost required to obtain the kernel. The calculation method of this invention is flexible and can arbitrarily change the grid size of the convolution kernel matrix according to the analytical characteristics.
[0104] In one embodiment, sampling the shape function and pupil function of the extended light source and calculating the corresponding superimposed pupil shift matrix includes the following steps:
[0105] Obtain several source coordinates and several pupil coordinates of the extended light source, and determine the source coordinate grid and pupil coordinate grid respectively;
[0106] The first circular sampling function grid is obtained based on the source coordinate grid, and the second circular sampling function grid is obtained based on the pupil coordinate grid.
[0107] The frequency domain circular sampling function is modified based on the first circular sampling function grid, and the spatial domain circular sampling function is modified based on the second circular sampling function grid. The shape function and pupil function are sampled by the modified frequency domain circular sampling function and spatial domain circular sampling function respectively, and the initial frequency domain circular sampling function is calculated.
[0108] The initial frequency domain circular sampling function is processed to obtain the initial pupil matrix, which is then modified to obtain the corresponding superimposed pupil shift matrix.
[0109] During the acquisition process, the initial frequency domain circular sampling function typically represents the circular sampling of the signal from the extended light source in the frequency domain. This can be understood as including both the frequency domain circular sampling function and the spatial domain circular sampling function, with source coordinates... and The number of samples is set to Pupil coordinates and The number of samples is set to According to the superimposed pupil shift matrix method, the frequency domain form of the Hopkins model is first discretized and converted into the product of two superimposed pupil shift matrices. Here, the spatial domain circular sampling function is expressed as:
[0110] ,in,
[0111] The frequency domain circular sampling function is expressed as:
[0112] ,in,
[0113] in, , , Indicates the first Bessel function of order 1, Indicates the first The first order of the Bessel function One zero point, , They represent arrays ( , The arrangement of ) in the equation of the superimposed pupil shift matrix, and the coordinate representation of the circular sampling function. It has been changed to Cartesian coordinates. The total number of items is set to , The total number of items is set to ,in, and .
[0114] 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 the frequency domain cross-transmission coefficient matrix, and obtaining the projection matrix based on the frequency domain cross-transmission coefficient matrix, includes the following steps:
[0115] Multiply 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 surface to obtain the frequency domain cross-transmission coefficient matrix.
[0116] The projection matrix is obtained based on the frequency domain cross-transmission coefficient matrix and its conjugate transpose.
[0117] The frequency domain cross-transmission coefficient matrix is represented as follows:
[0118] ;
[0119] in, Represents the frequency domain cross-transmission coefficient matrix. To superimpose the pupil shift matrix, , , Indicates complex coherence The Fourier transform result, Point spread function The Fourier transform result, , These represent the source coordinates, , , , These represent the pupil coordinates.
[0120] In one embodiment, performing singular value decomposition on the projection matrix to obtain the singular value decomposition result includes the following steps:
[0121] when or When the time is right, the corresponding element in the superimposed pupil shift matrix is 0;
[0122] The superimposed pupil shift matrix is decomposed using a frequency-domain circular sampling function, and the frequency-domain circular sampling function decomposition result is expressed as follows:
[0123]
[0124] The coefficients of the frequency domain circular sampling function decomposition result are obtained by calculating the orthogonality of the circular sampling function, as shown below:
[0125]
[0126] By replacing the coefficients of the frequency domain circular sampling function decomposition result with those of the frequency domain cross-transmission coefficient matrix, the decomposition result of the frequency domain cross-transmission coefficient matrix is obtained, as shown below:
[0127]
[0128] in, This represents the decomposition result of the frequency domain cross-transmission coefficient matrix. Let be the projection matrix, and * denote the conjugate transformation of the corresponding function.
[0129] In step S300, performing singular value decomposition on the projection matrix to obtain the singular value decomposition result includes the following steps:
[0130] The projection matrix is subjected to singular value decomposition to obtain the decomposed projection matrix, as shown below:
[0131] ;
[0132] Based on the correspondence between the frequency domain circular sampling function and the spatial domain circular sampling function, the singular value decomposition result of the TCC frequency matrix is transformed into the singular value decomposition of the TCC spatial domain matrix, as shown below:
[0133]
[0134] in, Let be a singular vector of the TCC space field matrix. This represents the singular value corresponding to the singular vector. This represents the TCC spatial domain matrix.
[0135] Finally, after the above steps, the resulting spatial domain image simulation model is as follows:
[0136]
[0137] in, Represents matrix convolution. Representing spatial domain images, Describes the singular vectors of the TCC space field matrix. Indicates the near field of the mask. Represents singular values, Ordinal numbers representing singular values These represent the coordinate variables within the image plane.
[0138] To evaluate the computational efficiency of the entire process, the environment used was a system equipped with an Intel i5-13400 processor (2.5GHz), 64GB of memory, and running Windows 10. MATLAB was used to compare the computational processes and results of three methods: a method of directly performing Singular Value Decomposition (SVD) on the TCC matrix; a circular sampling function TCC method that projects the spatial TCC matrix onto a smaller projection matrix using a circular sampling function before performing Singular Value Decomposition; and the method proposed in this invention. The comparison results of the three methods are as follows: Figure 6 and Figure 7 As shown, the direct singular value decomposition (SVD) method is the least efficient in terms of computation time and memory consumption. With increasing pupil sampling rate, its time and memory requirements increase by several orders of magnitude compared to the other two methods. The circular sampling function TCC method significantly reduces computation time compared to the direct SVD method, but it is still inferior to the method proposed in this invention, with a complexity of [missing information]. The complexity of this invention is Furthermore, since the circular sampling function TCC method requires the computation of the TCC matrix, it also requires a large amount of memory, resulting in a memory consumption similar to that of the direct singular value decomposition (SVD) method.
[0139] For a detailed calculation process, please refer to the specific implementation examples. Figure 3 : Input the shape function of the extended light source One of the circular lights is like Figure 3 As shown in Figure a. And the pupil function. The pupil function may have random aberrations, examples of which are as follows: Figure 3 As shown in b, here, Figure 3 (a) The X-axis and Y-axis are the cosines of the angle between the light source illumination direction and the X-axis, and the cosines of the angle between the light source illumination direction and the Y-axis, respectively. Figure 3 (b) The X-axis and Y-axis represent the relative spatial frequencies of the pupils in the X and Y directions.
[0140] First, generate The two 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. The matrix; then The superimposed pupil shift matrix is multiplied by 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 by its conjugate transpose to obtain the projection matrix; then singular value decomposition is applied to the projection matrix to obtain a diagonal matrix and an orthogonal matrix; finally, the orthogonal matrix is multiplied by the spatial domain circular sampling function matrix to generate a convolution kernel matrix, and finally the singular values and convolution kernel matrix are output.
[0141] like Figure 4 The diagram shows a comparison between the singular values obtained by the method of this invention and those obtained by the traditional method. The X-axis represents the ordinal number of the singular value (i.e., which singular value), and the Y-axis represents the normalized singular value magnitude.
[0142] like Figure 5 , Figure 5 The X and Y axes are the X and Y coordinates of the spatial image 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 traditional methods, giving the weighted relative errors between them.
[0143] in addition, Figure 6 and Figure 7 The presentation also includes a comparison chart of the running time and memory consumption of the method used in this invention with other methods. The comparison reveals that the method proposed in this invention has a shorter running time and lower memory consumption. Figure 6 The X-coordinate represents the pupil sampling rate, and the Y-coordinate represents the algorithm running time. Figure 7 The X-coordinate represents the sampling rate of the pupil, and the Y-coordinate represents the memory required by the algorithm.
[0144] In summary, the method proposed in this invention is superior to other existing methods in all respects.
[0145] Example 2:
[0146] A lithography simulation system based on circular sampling function decomposition and superposition of pupil shift matrices, such as Figure 2 As shown, it includes:
[0147] The sampling conversion module 100 samples the shape function and pupil function of the extended light source and calculates the corresponding superimposed pupil shift matrix;
[0148] 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 surface to obtain the frequency domain cross-transmission coefficient matrix and obtain the projection matrix based on the frequency domain cross-transmission coefficient matrix.
[0149] The decomposition processing module 300 performs singular value decomposition on the projection matrix to obtain the singular value decomposition result, wherein the singular value decomposition result includes singular values and singular vectors.
[0150] The second processing module 400 processes the spatial domain circular sampling function matrix based on singular vectors to obtain the convolution kernel matrix;
[0151] Model building module 500 constructs a spatial domain image simulation model based on singular value decomposition results, convolution kernel matrix, and initial Hopkins model;
[0152] The simulation module 600, based on the spatial domain image simulation model, obtains spatial domain image simulation results.
[0153] Various changes and modifications made without departing from the spirit and scope of this invention, and all equivalent technical solutions, also fall within the scope of this invention.
[0154] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.
[0155] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, apparatus, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied 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.
[0156] This invention is described with reference to flowchart illustrations and / or block diagrams of the method, terminal device (system), and computer program product according to the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0157] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0158] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal equipment, causing a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0159] It should be noted that:
[0160] The phrase "an embodiment" or "an embodiment" used in this specification means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. Therefore, the phrase "an embodiment" or "an embodiment" appearing in various places throughout the specification does not necessarily refer to the same embodiment.
[0161] Furthermore, it should be noted that the shapes and names of the parts and components described in the specific embodiments described in this specification may differ. All equivalent or simple variations made to the structure, features, and principles described in this patent concept are included within the protection scope of this patent. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, as long as they do not depart from the structure of this invention or exceed the scope defined in these claims, all of which should fall within the protection scope of this invention.
Claims
1. A lithographic simulation method based on circular sampling function decomposition and superposition of pupil shift matrices, characterized in that, Includes 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. 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 surface are processed to obtain the frequency domain cross-transmission coefficient matrix, and the projection matrix is obtained based on the frequency domain cross-transmission coefficient matrix. The projection matrix is subjected to singular value decomposition to obtain the singular value decomposition result, wherein the singular value decomposition result includes singular values and singular vectors; The convolution kernel matrix is obtained by processing the spatial domain circular sampling function matrix based on singular vectors; 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, spatial domain image simulation results are obtained; The step of sampling the shape function and pupil function of the extended light source and calculating the corresponding superimposed pupil shift matrix includes the following steps: Obtain several source coordinates and several pupil coordinates of the extended light source, and determine the source coordinate grid and pupil coordinate grid respectively; The first circular sampling function grid is obtained based on the source coordinate grid, and the second circular sampling function grid is obtained based on the pupil coordinate grid. The frequency domain circular sampling function is modified based on the first circular sampling function grid, and the spatial domain circular sampling function is modified based on the second circular sampling function grid. The shape function and pupil function are sampled by the modified frequency domain circular sampling function and spatial domain circular sampling function respectively, and the initial frequency domain circular sampling function is calculated. The initial frequency domain circular sampling function is processed to obtain the initial pupil matrix, which is then modified to obtain the corresponding superimposed pupil shift matrix.
2. The lithography simulation method based on circular sampling function decomposition and superposition of pupil shift matrices according to claim 1, characterized in that, 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 the frequency domain cross-transmission coefficient matrix, and then obtaining the projection matrix based on the frequency domain cross-transmission coefficient matrix, includes the following steps: Multiply 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 surface to obtain the frequency domain cross-transmission coefficient matrix. The projection matrix is obtained based on the frequency domain cross-transmission coefficient matrix and its conjugate transpose. The frequency domain cross-transmission coefficient matrix is represented as follows: ； in, Represents the frequency domain cross-transmission coefficient matrix. To superimpose the pupil shift matrix, , , Represents complex coherence The Fourier transform result, Point spread function The Fourier transform result, , These represent the source coordinates, , , , These represent the pupil coordinates.
3. The lithography simulation method based on circular sampling function decomposition and superposition of pupil shift matrices according to claim 1, characterized in that, The process of performing singular value decomposition on the projection matrix to obtain the singular value decomposition result includes the following steps: when or When the time is right, the corresponding element in the superimposed pupil shift matrix is 0; The superimposed pupil shift matrix is decomposed using a frequency-domain circular sampling function, and the frequency-domain circular sampling function decomposition result is expressed as follows: The coefficients of the frequency domain circular sampling function decomposition result are obtained by calculating the orthogonality of the circular sampling function, as shown below: By replacing the coefficients of the frequency domain circular sampling function decomposition result with those of the frequency domain cross-transmission coefficient matrix, the decomposition result of the frequency domain cross-transmission coefficient matrix is obtained, as shown below: The spatial domain circular sampling function is expressed as follows: ,in, The frequency domain circular sampling function is expressed as follows: ,in, in, The coefficients represent the results of the frequency domain circular sampling function decomposition. This represents the decomposition result of the frequency domain cross-transmission coefficient matrix. Let be the projection matrix. This represents the conjugate transformation of the corresponding function. To superimpose the pupil shift matrix, , These represent the source coordinates, , , , These represent the pupil coordinates, , , , , They represent arrays ( , The number of terms in ) , , Indicates the first Bessel function of order 1, Indicates the first The first order of the Bessel function The coordinate representation of the circular sampling function in the equation of the superimposed pupil shift matrix, with zeros. It has been changed to Cartesian coordinates. The total number of items is set to , The total number of items is set to ,in, and , The frequency domain kernel representing the cross-transmission coefficients, Indicates a subscript marker, used to distinguish... and , , Represents the normalized coefficients of the corresponding orthogonal functions. This represents the frequency domain circular sampling function with respect to the pupil coordinates. This represents a frequency domain circular sampling function with respect to the source coordinates. This represents the polar radius coordinate in polar coordinates.
4. The lithography simulation method based on circular sampling function decomposition and superposition of pupil shift matrices according to claim 1, characterized in that, The process of performing singular value decomposition on the projection matrix to obtain the singular value decomposition result includes the following steps: The projection matrix is subjected to singular value decomposition to obtain the decomposed projection matrix, as shown below: ； Based on the correspondence between the frequency domain circular sampling function and the spatial domain circular sampling function, the singular value decomposition result of the TCC frequency matrix is transformed into the singular value decomposition of the TCC spatial domain matrix, as shown below: in, Let be a singular vector of the TCC space field matrix. This represents the singular value corresponding to the singular vector. Represents the TCC space field matrix. Represents singular values, Represents singular vectors, , These represent the coordinate variables within the image plane.
5. The lithography simulation method based on circular sampling function decomposition and superposition of pupil shift matrices according to claim 1, characterized in that, The spatial domain image simulation model is represented as follows: in, Represents matrix convolution. Representing spatial domain images, Describes the singular vectors of the TCC space field matrix. Indicates the near field of the mask. Represents singular values, Ordinal numbers representing singular values These represent the coordinate variables within the image plane.
6. A lithography simulation system based on circular sampling function decomposition and superposition of pupil shift matrices, 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 surface to obtain the frequency domain cross-transmission coefficient matrix and obtain the projection matrix based on the frequency domain cross-transmission coefficient matrix. The decomposition processing module performs singular value decomposition on the projection matrix to obtain the singular value decomposition result, wherein the singular value decomposition result includes singular values and singular vectors. The second processing module processes the spatial domain circular sampling function matrix based on singular vectors to obtain the convolution kernel matrix; The model building module constructs a spatial domain image simulation model based on the singular value decomposition results, convolution kernel matrix, and initial Hopkins model. The results simulation module, based on the spatial domain image simulation model, obtains spatial domain image simulation results; The step of sampling the shape function and pupil function of the extended light source and calculating the corresponding superimposed pupil shift matrix includes the following steps: Obtain several source coordinates and several pupil coordinates of the extended light source, and determine the source coordinate grid and pupil coordinate grid respectively; The first circular sampling function grid is obtained based on the source coordinate grid, and the second circular sampling function grid is obtained based on the pupil coordinate grid. The frequency domain circular sampling function is modified based on the first circular sampling function grid, and the spatial domain circular sampling function is modified based on the second circular sampling function grid. The shape function and pupil function are sampled by the modified frequency domain circular sampling function and spatial domain circular sampling function respectively, and the initial frequency domain circular sampling function is calculated. The initial frequency domain circular sampling function is processed to obtain the initial pupil matrix, which is then modified to obtain the corresponding superimposed pupil shift matrix.
7. The photolithography simulation system based on circular sampling function decomposition and superposition of pupil shift matrices according to claim 6, characterized in that, The first processing module is configured as follows: Multiply 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 surface to obtain the frequency domain cross-transmission coefficient matrix. The projection matrix is obtained based on the frequency domain cross-transmission coefficient matrix and its conjugate transpose. The frequency domain cross-transmission coefficient matrix is represented as follows: ； in, Represents the frequency domain cross-transmission coefficient matrix. To superimpose the pupil shift matrix, , , Represents complex coherence The Fourier transform result, Point spread function The Fourier transform result, , These represent the source coordinates, , , , These represent the pupil coordinates.
8. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 5.
9. A photolithography simulation apparatus based on circular sampling function decomposition and superposition of pupil shift matrices, 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, it implements the method as described in any one of claims 1 to 5.