A calculation method for energy deposition of a layout in proximity effect correction of large-scale parallel electron beam lithography

Abstract

The present invention is a method for calculating the energy deposition of a layout in proximity effect correction of large-scale parallel electron beam lithography. The purpose is to solve the memory and computing power bottlenecks of a single computer, expand the size limit of the layout to be calculated, and improve the calculation speed of the layout energy deposition, ultimately improving the efficiency of proximity effect correction of electron beam lithography, while ensuring accuracy. The present invention is divided into six steps: Step S1: Reading in the exposure layout and dividing it into sub-layouts; Step S2: Determining the edge regions of the sub-layouts; Step S3: Communicating between adjacent sub-layouts; Step S4: Calculating the energy deposition in large-scale parallel; Step S5: Developing and measuring the mean error; Step S6: Updating the exposure dose of the layout.

Description

Technical Field

[0001] The present invention is a method for calculating energy deposition of a layout for proximity effect correction in large-scale parallel electron beam lithography. Under the premise of ensuring accuracy, this method solves the limitation of the memory bottleneck of a single computer on the layout size of electron beam lithography, breaks through the limitation of the computing power bottleneck on the calculation time of proximity effect correction in electron beam lithography, greatly improves the calculation speed, has high scalability, and has the characteristics of high calculation accuracy and high calculation efficiency. It belongs to the field of computational lithography. Background Art

[0002] Electron Beam Lithography (EBL) technology has high resolution, capable of reaching below sub-10 nanometers. It has a wide range of applications and plays an important role in fields such as micro-nano structures and optical mask manufacturing. Electron beam lithography is a maskless lithography technology. On a wafer coated with an electron resist, circuit patterns are directly drawn using an electron beam. Since the electron resist is sensitive to electrons, the chemical properties of the resist change after being irradiated by the electron beam, and its solubility in the developer also changes. By immersing it in the developer, the unexposed or exposed areas can be removed. However, due to the inevitable physical phenomena of forward scattering and backward scattering of electrons in the photoresist and the substrate, the electrons change their trajectories, resulting in uneven exposure energy distribution, and ultimately causing the obtained layout to be inconsistent with the expectation. This phenomenon that has a serious negative impact on the final resolution of the layout is called the proximity effect (Proximity Effect, PE).

[0003] The proximity effect can be used to convolve the layout exposure dose with the point spread function (Point Spread Function, PSF) obtained through Monte Carlo simulation, which describes the influence of the incident point of electrons on the photoresist on the energy distribution of the surrounding area, to obtain the energy deposition of the exposure layout. Through a correction algorithm, different exposure doses are reset for different regions of the layout, so that the final exposure result can achieve a relatively uniform energy deposition, improving the actual resolution of electron beam lithography. This process is called proximity effects correction (Proximity Effects Correction, PEC).

[0004] In the proximity effect correction of electron beam lithography based on layout pixelization, calculating the energy deposition of the exposure layout is a computationally intensive and memory-intensive process. A single computer cannot meet the requirements for proximity effect correction of large exposure layouts. On the one hand, after layout pixelization, a large amount of memory is required, but the memory of a single computer is limited. Therefore, a single computer can only be used for proximity effect correction of small layouts. On the other hand, a large layout has a large amount of data that needs to be calculated, and the computing power of a single computer is limited. Under an acceptable computing time, it is only suitable for calculating small layouts with a small amount of data. To solve these two major problems, the present invention proposes a method for calculating the energy deposition of a layout in large-scale parallel proximity effect correction of electron beam lithography. This method is based on the large-scale parallel technology of the Message Pass Interface (MPI) and the Fast Fourier Transform (FFT). On the premise of ensuring accuracy, by dividing the exposure layout into multiple sub-layouts, each computing node processes the PEC of a sub-layout, solves the memory bottleneck of a single computer for the layout size limitation of electron beam lithography, breaks through the limitation of the computing power bottleneck on the computing time of proximity effect correction of electron beam lithography, greatly improves the computing speed, has high scalability, and has the characteristics of high computing accuracy and high computing efficiency. Summary of the Invention

[0005] The present invention is a method for calculating the energy deposition of a layout in large-scale parallel proximity effect correction of electron beam lithography. The purpose is to solve the memory and computing power bottlenecks of a single computer on the premise of ensuring accuracy, expand the size limitation of the layout to be calculated, and improve the computing speed of the energy deposition of the layout, and finally improve the PEC efficiency of electron beam lithography.

[0006] The technical solution of the present invention is as follows: Based on the MPI large-scale parallel technology and FFT, multiple computing nodes are used. By dividing the layout into multiple sub-layouts, each computing node obtains all the data within a sub-layout, and exchanges the data at the edges of adjacent sub-layouts through MPI. On the premise of ensuring accuracy, each computing node calculates the energy deposition of its sub-layout according to the obtained data, uses the energy deposition to develop the layout after exposure, adjusts the exposure dose, and finally completes the proximity effect correction of the layout. The steps of the invention are as follows:

[0007] Step S1: Read in the exposure layout and divide it into sub-layouts;

[0008] Read in the original layout of electron beam lithography to obtain the maximum and minimum coordinates of the part of the layout that needs to be exposed. As Figure 2As shown, the layout is pixelated into a square grid with a width of w nm at equal intervals. Each grid is a pixel (which can also be called an exposure point), and the initial exposure dose of each exposure point is the exposure dose of the center of the exposure point in the original layout. The exposure layout is divided into m rows and n columns, with a total of m×n sub-layouts. According to the number of computing nodes npes, m×n = npes. There are W×W exposure points in each sub-layout, and each computing node obtains the layout data within a sub-layout and uses a computing process P i (i ∈ [0, npes)) to process this data.

[0009] Step S2: Determine the edge region of the sub-layout;

[0010] The PSF of electron beam lithography can be fitted by a double Gaussian function, expressed as:

[0011]

[0012]

[0013] In the formula, the physical parameter α is the forward scattering range, β is the backward scattering range, η is the energy ratio of forward scattering to backward scattering. In formula (1), x is the distance from the exposure point, and in formula (2), x 2 +y 2 is the square of the distance from the exposure point in two-dimensional form.

[0014] The total exposure energy deposition E(x0, y0) at the exposure point (x0, y0) is expressed as:

[0015] E(x0, y0) = ∫∫PSF(x - x0, y - y0)σ(x, y)dxdy (3)

[0016] In the formula, let the dose distribution of the layout be σ(x, y), and the integration region is the entire exposure layout.

[0017] Assume that the exposure area of the layout is infinite, and the maximum exposure dose of the layout is σ max , for a certain exposure point (x0, y0), when x > x0 + d, y > y0 + d, the contribution of the region to the energy deposition of the exposure point (x0, y0) is expressed as:

[0018]

[0019] In the formula, d is a width constant of the edge overlap region. By comparing inequality (4) with the standard normal distribution, it can be seen that when only calculating the influence of other exposure points within a certain region around the central exposure point on the central exposure point, under a certain accuracy, it can represent the energy deposition of the central exposure point.

[0020] The width constant d of the edge overlap region of the sub-layout in the present invention is expressed as:

[0021]

[0022] Wherein, max(α, β) represents the larger one of α and β.

[0023] Each process P i (i≥0&&i<npes) The calculated sub-layout only needs a part of the layout data at the edge of the adjacent sub-layout to meet the accuracy requirements for calculating the energy deposition of the exposure points within the sub-layout. For example Figure 3 As shown, for any sub-layout P i , P i has at most 8 adjacent sub-layouts, which are P i-n-1 , P i-n , P i-n+1 , P i-1 , P i+1 , P i+n-1 , P i+n , P i+n+1 .

[0024] Step S3: Communication between adjacent sub-layouts;

[0025] After determining d, each calculation process only needs to obtain part of the data of the adjacent sub-layout, and then, under the condition of meeting a certain accuracy, it can calculate the energy deposition of the sub-layout of the original layout it controls, so as to obtain the energy deposition of the entire layout. For example Figure 4 As shown, the sub-layout P i needs a part of the layout information of the adjacent sub-layout P j (j≥0&&j<npes) to make the calculation of the energy deposition of the layout of the sub-layout P i meet a certain accuracy. For example Figure 4 As shown, A i,j represents that calculating the energy deposition of the sub-layout P i requires part of the layout information of the adjacent sub-layout P i of P j . The sub-layout P i needs to receive from the adjacent sub-layouts P i-n-1 , P i-n , P i-n+1 , P i-1 , P i+1 , P i+n-1 , P i+n , P i+n+1 respectively receive A i,i-n-1 , A i,i-n , A i,i-n+1 , A i,i-1 , A i,i+1 , A i,i+n-1 , A i,i+n , A i,i+n+1The size of the area is d×d, d×W, d×d, W×d, W×d, d×d, d×W, d×d. i The adjacent sub-pattern P j Sub-layout P is also required i The above receiving and sending processes can be performed simultaneously using MPI non-blocking communication mode. i Once all the above information is received, the sub-pattern P can be calculated independently i Energy deposition, no longer required for communication.

[0026] Step S4: large-scale parallel computing energy deposition;

[0027] S4.1 Circular convolution instead of linear convolution: Circular convolution replaces the linear convolution shown in equation (3), and FFT is used to accelerate the convolution operation to obtain the energy deposition of the sub-layout P i The original layout information and the layout information of the adjacent sub-layouts form a matrix. Each position in the matrix represents an exposure point. The value of the matrix is the exposure dose. The matrix is expanded to twice its original length in both directions, and the expanded area is filled with 0 to obtain the matrix M. pattern , the number of elements in the rows and columns of the matrix are r and c respectively. Figure 5 Represents the matrix M pattern , Figure 5 The A1 area in represents the original two-dimensional matrix, and the rest of the area is filled with 0. The process of expanding and filling the original two-dimensional matrix can be carried out simultaneously with the communication in step S3, so as to achieve the purpose of overlapping communication and calculation and improve efficiency. When the communication in step S3 is completed, the received layout information of the adjacent sub-layout is stored in the corresponding position of the matrix.

[0028] S4.2 For the calculation data described in S4.1, first calculate the matrix M pattern The row where the original data is located ( Figure 6 (a) A2) Perform 1D-FFT, using FFT based on Discrete Cosine Transform (DCT), relative to the entire matrix M pattern Performing a discrete Fourier transform (DFT) based FFT can save 75% of the computing time. Then use a cache-independent algorithm to take full advantage of the cache hierarchy of modern computing to quickly and efficiently convert the matrix M pattern Transpose( Figure 6 (b) A3 is the area where the data is not all zero), and then the matrix M pattern All rows ( Figure 6 (c) The row where area A4 is located) performs a 1D-FFT operation based on DCT.

[0029] S4.3 Dot - product the matrix M after performing FFT in S4.2 pattern with the PSF after Fourier transform, then perform 1D - IFFT (1D - Inverse FFT) based on DCT for all rows, use cache - oblivious algorithms to efficiently utilize the cache hierarchy of modern computing to quickly transpose the matrix, and then perform 1D - IFFT on pattern half of the rows of matrix M.

[0030] S4.4 Divide the data at the original data position in S4.3 by r×c to obtain the exposure dose of each exposure point.

[0031] Step S5: Development and measurement of mean error;

[0032] After the layout energy deposition calculation is completed, the actual exposed layout shape can be obtained through development. The threshold development model used in the present invention is expressed as:

[0033]

[0034] where E thr is the development threshold related to the substrate solubility, and H(x, y) is the developed layout shape.

[0035] The quality of the developed layout can be measured by the mean - square error (MSE) from the target exposure shape of the layout, expressed as:

[0036]

[0037] where N is the number of exposure points of the layout, and D(x, y) is the target exposure shape of the layout.

[0038] Step S6: Update the layout exposure dose.

[0039] When the MSE in step S5 is less than the preset error limit ∈, PEC is completed and the algorithm proposed in the present invention ends. Otherwise, update the dose and iterate steps S3 - S6 until the MSE meets the requirements. The dose update is expressed as:

[0040]

[0041] where σ k (x, y) is the input dose of the exposure layout in the k - th iteration, and D T is the preset target energy deposition value of the layout. Description of the Drawings

[0042] Figure 1 is the operation flowchart of the present invention;

[0043] Figure 2 It is a schematic diagram of the calculation node division;

[0044] Figure 3 It is a schematic diagram of the relative position of the sub-layouts;

[0045] Figure 4 It is a schematic diagram of the overlapping area of the edges of the sub-layouts;

[0046] Figure 5 It is a schematic diagram of the position of the original data in the calculation matrix;

[0047] Figure 6 It is a schematic diagram of the FFT calculation area; Specific implementation manners

[0048] The present invention will be further described in detail below in conjunction with the accompanying drawings of the specification and specific embodiments.

[0049] The present invention is a method for calculating the energy deposition of a layout for proximity effect correction in large-scale parallel electron beam lithography. The purpose is to solve the memory and computing power bottlenecks of a single computer, expand the size limit of the layout to be calculated, and improve the calculation speed of the layout energy deposition on the premise of ensuring accuracy, and finally improve the PEC efficiency of electron beam lithography. The steps of the present invention are as Figure 1 shown, and are divided into six steps in total: reading in the exposure layout and dividing it into sub-layouts; determining the edge areas of the sub-layouts; communicating between adjacent sub-layouts; calculating the energy deposition in large-scale parallel; developing and measuring the mean error; updating the exposure dose of the layout. The technical solution of the present invention is: based on the MPI large-scale parallel technology and FFT, using multiple computing nodes, by dividing the layout into multiple sub-layouts, each computing node obtains all the data within a sub-layout, and exchanges the data at the edges of adjacent sub-layouts through MPI. On the premise of ensuring accuracy, each computing node calculates the energy deposition of its sub-layout according to the obtained data, uses the energy deposition to develop the exposed layout, adjusts the exposure dose, and finally completes the proximity effect correction of the layout. The specific implementation steps are as follows:

[0050] Step S1: Reading in the exposure layout and dividing it into sub-layouts;

[0051] Read in the original layout of the electron beam lithography to obtain the maximum and minimum coordinates of the part of the layout that needs to be exposed. As Figure 2As shown in the figure, the layout image is pixelated into a square grid with an equal interval width of w nm. Each grid is a pixel (which can also be called an exposure point), and the initial exposure dose of each exposure point is the exposure dose of the center of the exposure point in the original layout. The exposure layout is divided into m rows and n columns, with a total of m×n sub-layouts. According to the number of computing nodes npes, m×n = npes. There are W×W exposure points in each sub-layout, and each computing node obtains the layout data within a sub-layout and uses a computing process P i (i ∈ [0, npes)) to process this data.

[0052] Step S2: Determine the edge region of the sub-layout;

[0053] The PSF of electron beam lithography can be fitted by a double Gaussian function, expressed as:

[0054]

[0055]

[0056] In the formula, the physical parameter α is the forward scattering range, β is the backward scattering range, η is the energy ratio of forward scattering to backward scattering. In formula (1), x is the distance from the exposure point, and in formula (2), x 2 +y 2 is the square of the distance from the exposure point in two-dimensional form.

[0057] The total exposure energy deposition E(x0, y0) at the exposure point (x0, y0) is expressed as:

[0058] E(x0, y0) = ∫∫PSF(x - x0, y - y0)σ(x, y)dxdy (3)

[0059] In the formula, let the dose distribution of the layout be σ(x, y), and the integration region is the entire exposure layout.

[0060] Assume that the exposure area of the layout is infinite and the maximum exposure dose of the layout is σ max , for a certain exposure point (x0, y0), when x > x0 + d, y > y0 + d, the contribution of the region to the energy deposition of the exposure point (x0, y0) is expressed as:

[0061]

[0062] In the formula, d is a constant width of the edge overlap region. By comparing inequality (4) with the standard normal distribution, it can be seen that when only calculating the influence of other exposure points within a certain region around the central exposure point on the central exposure point, under a certain accuracy, it can represent the energy deposition of the central exposure point.

[0063] The width constant d of the edge overlap region of the sub-layout in the present invention is expressed as:

[0064]

[0065] In the formula, max(α, β) represents the larger value between α and β.

[0066] Each process P i (i≥0 && i < npes), the sub-layout calculated only requires a part of the layout data at the edge of the adjacent sub-layouts to meet the accuracy requirements for calculating the energy deposition of the exposure points within the sub-layout. As Figure 3 shown, for any sub-layout P i , P i has at most 8 adjacent sub-layouts, which are P i-n-1 , P i-n , P i-n+1 , P i-1 , P i+1 , P i+n-1 , P i+n , P i+n+1 .

[0067] Step S3: Communication between adjacent sub-layouts;

[0068] After determining d, each computing process only needs to obtain part of the data of the adjacent sub-layouts, and then, under the condition of meeting a certain accuracy, it can calculate the energy deposition of the sub-layouts of the original layout it controls, thereby obtaining the energy deposition of the entire layout. As Figure 4 shown, the sub-layout P i requires a part of the layout information of the adjacent sub-layout P j (j≥0 && j < npes) to make the calculation of the energy deposition of the layout of the sub-layout P i meet a certain accuracy. As Figure 4 shown, A i,j represents that calculating the energy deposition of the sub-layout P i requires part of the layout information of the adjacent sub-layout P i of P j . The sub-layout P i needs to receive A i-n-1 , P i-n , P i-n+1 , P i-1 , P i+1 , P i+n-1 , P i+n , P i+n+1 respectively from A i,i-n-1 , A i,i-n , A i,i-n+1 , A i,i-1 , A i,i+1 , A i,i+n-1 , A i,i+n , A i,i+n+1The size of the area is d×d, d×W, d×d, W×d, W×d, d×d, d×W, d×d. i The adjacent sub-pattern P j Sub-layout P is also required i The above receiving and sending processes can be performed simultaneously using MPI non-blocking communication mode. i Once all the above information is received, the sub-pattern P can be calculated independently i Energy deposition, no longer required for communication.

[0069] Step S4: large-scale parallel computing energy deposition;

[0070] S4.1 Circular convolution instead of linear convolution: Circular convolution replaces the linear convolution shown in equation (3), and FFT is used to accelerate the convolution operation to obtain the energy deposition of the sub-layout P i The original layout information and the layout information of the adjacent sub-layouts form a matrix. Each position in the matrix represents an exposure point. The value of the matrix is the exposure dose. The matrix is expanded to twice its original length in both directions, and the expanded area is filled with 0 to obtain the matrix M. pattern , the number of elements in the rows and columns of the matrix are r and c respectively. Figure 5 Represents the matrix M pattern , Figure 5 The A1 area in represents the original two-dimensional matrix, and the rest of the area is filled with 0. The process of expanding and filling the original two-dimensional matrix can be carried out simultaneously with the communication in step S3, so as to achieve the purpose of overlapping communication and calculation and improve efficiency. When the communication in step S3 is completed, the received layout information of the adjacent sub-layout is stored in the corresponding position of the matrix.

[0071] S4.2 For the calculation data described in S4.1, first calculate the matrix M pattern The row where the original data is located ( Figure 6 (a) A2) Perform 1D-FFT, using FFT based on Discrete Cosine Transform (DCT), relative to the entire matrix M pattern Performing a discrete Fourier transform (DFT) based FFT can save 75% of the computing time. Then use a cache-independent algorithm to take full advantage of the cache hierarchy of modern computing to quickly and efficiently convert the matrix M pattern Transpose( Figure 6 (b) A3 is the area where the data is not all zero), and then the matrix M pattern All rows ( Figure 6 (c) The row where area A4 is located) performs a 1D-FFT operation based on DCT.

[0072] S4.3 Dot-product the matrix M after FFT in S4.2 pattern with the PSF after Fourier transform, then perform 1D-IFFT (1D-Inverse FFT) based on DCT on all rows, use cache-oblivious algorithms to make full use of the cache hierarchy of modern computing to quickly and efficiently transpose the matrix, and then perform 1D-IFFT on half of the rows of matrix M pattern

[0073] S4.4 Divide the data at the original data location in S4.3 by r×c to obtain the exposure dose of each exposure point.

[0074] Step S5: Development and measurement of mean error;

[0075] After the layout energy deposition calculation is completed, the actual exposed layout shape can be obtained through development. The threshold development model used in the present invention is expressed as:

[0076]

[0077] where E thr is the development threshold related to the substrate solubility, and H(x, y) is the developed layout shape.

[0078] The quality of the developed layout can be measured by the mean-square error (MSE) from the target exposure shape of the layout, expressed as:

[0079]

[0080] where N is the number of exposure points of the layout, and D(x, y) is the target exposure shape of the layout.

[0081] Step S6: Update the layout exposure dose.

[0082] When the MSE in Step S5 is less than the preset error limit ∈, PEC is completed and the algorithm proposed in the present invention ends. Otherwise, update the dose and iterate Steps S3 to S6 until the MSE meets the requirements. The dose update is expressed as:

[0083]

[0084] where σ k (x, y) is the input dose of the exposure layout for the k-th iteration, and D T is the preset target energy deposition value of the layout.

[0085] ​As shown in Table 1, for a method of calculating energy deposition in a layout for proximity effect correction in large-scale parallel electron beam lithography according to the present invention, when the PSF parameters represented by Equation (2) are α = 14.98, β = 197.48, η = 1.66, the layout grid size is w = 1 nm, the number of grids N = 5,045 × 5,092 = 25,689,140, and the width d of the overlapping region at the edge of the sub-layout is 625, calculations are performed using the present invention. The calculation times for single-node, dual-node, and four-node are shown in Table 1. Table 1 proves that the calculation time of the present invention decreases nearly linearly with the increase in the number of calculation nodes. Therefore, the present invention can be well applied in practice.

[0086] Table 1

[0087] Number of nodes Single node Double node Four nodes FFT calculation time (s) 92.45 46.52 22.66

[0088] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than limiting the protection scope of the present invention. With reference to the description of this embodiment, those of ordinary skill in the art should be able to understand and make relevant modifications or substitutions to the technical solutions of the present invention without departing from the essence and scope of the present invention.

Claims

1. A calculation method for energy deposition in a layout for proximity effect correction in large-scale parallel electron beam lithography, characterized in that The following steps are involved: Step S1, reading in the original electron beam lithography layout to obtain the maximum and minimum coordinates of the portion of the layout that needs to be exposed; The layout is pixelated into equally spaced square grids with a width of w nm. Each grid is a pixel. The initial exposure dose of each exposure point is the exposure dose of the center of the exposure point in the original layout. The exposure layout is divided into m rows and n columns, with a total of m×n sub-layouts. According to the number of calculated nodes npes, m×n=npes; There are W×W exposure points in each sub-layout, and each computing node obtains the layout data within a sub-layout and uses a computing process P i (i ∈ [0, npes)) processes this data; Step S2, the PSF of electron beam lithography can be fitted by a double Gaussian function, expressed as: In the formula, the physical parameter α is the forward scattering range, β is the backscattering range, η is the ratio of forward scattering to backscattering energy, and x in formula (1) is is the distance from the exposure point, and \(x\) in Equation (2) 2 + \(y\) 2 is the square of the distance from the exposure point in two-dimensional form; The total exposure energy deposition E(x0,y0) at the exposure point (x0,y0) is expressed as: E(x0,y0)=∫∫PSF(x-x0,y-y0)σ(x,y)dxdy (3) In the formula, let the dose distribution of the layout be σ(x,y), and the integration area be the entire exposure layout; Assume that the exposure area of the layout is infinitely large and the maximum exposure dose of the layout is σ max , for a certain exposure point (x0, y0), the contribution of the area where x > x0 + d and y > y0 + d to the energy deposition at the exposure point (x0, y0) is expressed as: In the formula, d is a constant of the width of the edge overlap area. By comparing inequality (4) with the standard normal distribution, it can be seen that when only the influence of other exposure points in a certain area around the central exposure point on the central exposure point is calculated, the energy deposition of the central exposure point can be represented under a certain accuracy. The sub-layout edge overlap region width constant d in the present invention is expressed as: In the formula, max(α,β) represents the larger of α and β; Each process P i (i≥0&&i<npes) For the sub-layout calculated, only a part of the layout data at the edge of adjacent sub-layouts is required to meet the accuracy requirements for calculating the energy deposition of exposure points within the sub-layout. Step S3, after determining d, each computing process only needs to obtain partial data of adjacent sub-layouts, and then, under the condition of meeting a certain accuracy, it can calculate the energy deposition of the sub-layouts of the original layout it controls, so as to obtain the energy deposition of the entire layout; sub-layout P i requires a part of the layout information of adjacent sub-layout P j (j≥0&&j<npes) to make the calculation of the energy deposition of the layout of sub-layout P i meet a certain accuracy; sub-layout P i Once receiving the layout information of adjacent sub-layouts, it can calculate the energy deposition of sub-layout P alone i without the need for communication anymore; Step S4, large-scale parallel computing energy deposition; S4.1 Replace linear convolution with circular convolution: Replace the linear convolution shown in Equation (3) with circular convolution, and use FFT to accelerate the convolution operation to obtain the energy deposition of the layout; sub-layout P i The original layout information and the layout information of adjacent sub-layouts form a matrix. Each position in the matrix represents an exposure point, and the value of the matrix is the exposure dose. The matrix is expanded to twice its original length in both directions, and the expanded area is filled with 0 to obtain matrix M pattern , where the number of row and column elements of the matrix are r and c respectively; The process of expanding and filling the original two-dimensional matrix can be carried out simultaneously with the communication in step S3, so as to achieve the purpose of overlapping communication and calculation and improve efficiency. When the communication in step S3 is completed, the received layout information of the adjacent sub-layout is stored in the corresponding position of the matrix. S4.2 For the calculated data described in S4.1, first for the matrix M pattern perform 1D-FFT on the row where the original data is located. Use FFT based on Discrete Cosine Transform (DCT). Compared with performing FFT based on Discrete Fourier Transform (DFT) on the entire matrix M pattern it can save 75% of the calculation time. Then use cache-oblivious algorithms to make full use of the cache hierarchy of modern computing to quickly and efficiently transpose the matrix M pattern and then perform 1D-FFT operations based on DCT on all rows of the matrix M pattern ; S4.3 Dot the matrix M after FFT in S4.2 pattern with the PSF after Fourier transform, then perform 1D-IFFT (1D-Inverse FFT) based on DCT on all rows, use cache-oblivious algorithms to fully utilize the cache hierarchy of modern computing to quickly and efficiently transpose the matrix, and then for half of the rows of matrix M pattern perform 1D-IFFT; S4.4 divides the data at the location of the original data in S4.3 by r×c to obtain the exposure dose at each exposure point; Step S5, in step S5, the mean error of development and measurement is performed. After the layout energy deposition calculation is completed, the actual exposed layout shape can be obtained by development. The threshold development model used in the present invention is expressed as: where E thr is the development threshold related to the substrate solubility, and H(x, y) is the layout shape after development; The quality of the developed layout can be measured by the mean-square error (MSE) of the target exposure shape of the layout, expressed as: Where N is the number of exposure points of the layout, and D(x,y) is the target exposure shape of the layout; Step S6: In step S6, when the MSE in step S5 is less than the preset error limit ∈, PEC is completed and the algorithm proposed by the present invention ends. Otherwise, the dose is updated and steps S3 to S6 are iterated until the MSE meets the requirement. The dose update is expressed as: where σ k (x, y) is the input dose of the exposure layout for the k-th iteration, and D T is the preset target energy deposition value of the layout.

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