Prediction method and system for electron beam exposure long-range deposition energy
By using ring filtering and Gaussian stacking to piecewise fit the parameters of the long-range deposition energy density function, the problem of accuracy in predicting long-range deposition energy in electron beam exposure was solved, achieving efficient and accurate prediction of long-range deposition energy.
Patent Information
- Application Number
- CN202511070501.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-31
- Publication Date
- 2025-11-25
AI Technical Summary
Existing technologies struggle to accurately predict long-range deposition energy during electron beam exposure, and traditional filtering methods are ineffective against random fluctuations. Furthermore, parameter fitting algorithms suffer from performance degradation under high degrees of freedom, resulting in large prediction errors.
A data dimensionality reduction method based on ring filtering is adopted, combined with the area approximation method and the Gaussian stacking method, to fit the parameters of the long-range deposition energy density function piecewise and construct a long-range deposition energy prediction model.
It improves the accuracy and efficiency of long-range depositional energy prediction, reduces data noise, and ensures the accuracy of parameter fitting across different distance segments.
Smart Images
Figure CN121009687A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application mainly relates to the field of electron beam technology, and in particular to a prediction method and system for electron beam exposure long-range deposition energy. BACKGROUND
[0002] In the electron beam exposure process, proximity effect is a ubiquitous negative effect, which is caused by the forward scattering and back scattering of the electron beam after entering the photoresist. The forward scattering refers to the scattering of the electron beam when it enters the photoresist from top to bottom, and the included angle between the scattering direction and the incident direction is less than 90 degrees. The back scattering refers to the scattering of the electron beam after entering the photoresist due to the reflection of the photoresist or the substrate, and the included angle between the scattering direction and the incident direction is greater than 90 degrees. The forward scattering causes a relatively large deposition energy, but the diffusion range is relatively short, usually between 10 nm and 100 nm. The back scattering causes a relatively small deposition energy, but the diffusion range is relatively far, usually between 10 μm and 100 μm, which belongs to long-range deposition energy. Accurate prediction of long-range deposition energy plays an important role in electron beam proximity effect correction.
[0003] The deposited energy prediction usually uses a point spread function (PSF) to construct a deposited energy density function (DEDF), and then uses the deposited energy density function and the beam spot pattern binary function to construct a convolution prediction model. However, the long-range deposition energy value is relatively small, and is greatly disturbed by random fluctuations, and the diffusion range is relatively far, resulting in a large amount of data. Therefore, it is difficult to fit the parameters of the long-range deposition energy density function by calculating the error between the convolution prediction model output and the two-dimensional plane deposition energy data. In addition, due to the relatively far diffusion range of the long-range deposition energy, the physical action is relatively complex, and it is necessary to construct the deposited energy density function based on a multi-order Gaussian point spread function, which results in a large number of parameters to be fitted. If all parameters are searched at the same time, it may lead to too high search freedom, and it is difficult to search for ideal parameters.
[0004] If the error between the convolution prediction model output and the long-range backscattering energy is directly used for deposited energy density function parameter fitting, it will face the problem of too large calculation cost due to too large amount of data. In addition, the long-range backscattering deposition energy is relatively small in value, so it is greatly disturbed by random fluctuations. Therefore, the filtering effect of traditional filtering methods such as Gaussian filtering, mean filtering and median filtering is poor. Therefore, first of all, a data processing method is needed to realize data smoothing and dimension reduction; then the convolution prediction model needs to be approximated to reduce the calculation amount of the deposited energy prediction value.
[0005] Traditional parameter fitting algorithms, such as genetic algorithm, particle swarm algorithm, gradient descent method and the like, when the number of parameters to be fitted is large, due to the large degree of freedom of search, the performance of parameter search is reduced, and the parameter fitting is not accurate. And due to the exponential decay characteristics of the deposition energy with distance, the use of mean absolute error will lead to better fitting effect of the deposition energy at a short distance, and the use of mean logarithmic absolute error will lead to better fitting effect of the deposition energy at a long distance. Therefore, a parameter fitting method for multi-order Gaussian deposition energy density function is needed, which can segmentally select appropriate error indicators to fit the parameters of each Gaussian term in the function. SUMMARY
[0006] In view of the technical problems existing in the prior art, the present application provides a prediction method and system for long-range deposition energy of electron beam exposure with high prediction accuracy.
[0007] To solve the above technical problems, the technical solution provided by the present application is: A prediction method for long-range deposition energy of electron beam exposure, comprising the steps of: S1, data dimensionality reduction based on ring filtering: generating a ring filtering data set through deposition energy data acquisition, ring region division and ring filtering calculation, wherein the ring region division divides a two-dimensional plane into a plurality of ring regions based on a set of concentric circles, and the ring filtering calculation performs average processing on the deposition energy data in each ring region to realize data dimensionality reduction and noise suppression; S2, long-range deposition energy prediction model construction based on area approximation method: using the distance information in the ring filtering data set, constructing a long-range deposition energy density function, and based on the product approximation of the beam spot area and the long-range deposition energy density function, generating a long-range deposition energy prediction model; S3, parameter fitting based on Gaussian stacking method: using the ring filtering data set and the long-range deposition energy prediction model, fitting the parameters in the long-range deposition energy density function step by step to obtain an optimized long-range deposition energy prediction model; S4, predicting the long-range deposition energy of electron beam exposure based on the optimized long-range deposition energy prediction model.
[0008] Preferably, the specific process of step S1 is: S101, deposition energy data acquisition: dividing a two-dimensional plane into a square deposition energy collection grid through Monte Carlo simulation software to obtain the distribution data of deposition energy density in the two-dimensional plane; S102, ring region division: constructing a set of concentric circles as follows :
[0009] whereinR 0 represents the radius of the innermost concentric circle, indicating the distance from which the deposition energy is first counted; N represents the number of concentric circles; (x, y) represents the coordinates of any point on a concentric circle; n represents the index of the concentric circle. Then use The concentric circles in the diagram divide the two-dimensional plane into N annular regions. The specific expression is as follows:
[0010] S103. Data dimensionality reduction based on ring filtering: First, the collected depositional energy data is divided into several datasets according to the coordinate position. The expression is as follows:
[0011] in Represents the deposition energy harvesting grid The depositional energy density in Represents the dataset The number of data points in the data; Then to The data in the dataset is subjected to ring filtering calculations to obtain a ring-filtered dataset, which is used for fitting the parameters of the long-range deposition energy density function.
[0012] Preferably, the formula for calculating the ring filter is as follows:
[0013] in This represents the distance between the i-th annular region and the origin. Represents the depositional energy density of the i-th annular region. This represents the area of the deposition energy harvesting grid.
[0014] Preferably, in step S2, the specific process of constructing the long-range deposition energy density function using the distance information in the ring filter dataset is as follows: First, construct the long-range point spread function. :
[0015] Where M is the number of Gaussian terms; Then, a long-range deposition energy density function is constructed based on the long-range point diffusion function. The expression is as follows:
[0016] Where K is the proportionality coefficient and D is the beam spot dose; the parameters to be fitted are K and the parameters in the long-range point spread function.
[0017] Preferably, in step S2, the expression for the long-range depositional energy prediction model is:
[0018] Where S is the area of the beam spot, (x,y) represents the offset of the coordinates relative to the centroid of the beam spot, and the output of the long-range sedimentary energy prediction model is the predicted value of the sedimentary energy density at (x,y).
[0019] Preferably, in step S3, the parameters in the long-range deposition energy density function are fitted step by step by calculating the deposition energy segment points, calculating the error loss function segment points, and fitting the Gaussian term parameters by segment stacking.
[0020] Preferably, in step S3, the specific process for calculating the deposition energy segmentation points is as follows: a total of M+1 deposition energy segmentation points are needed. The deposition energy diffusion distance is divided into M segments according to the logarithm, with each segment corresponding to one Gaussian term; the farthest deposition energy diffusion distance is... R 0 +d Then the m-th segment point rs m The calculation formula is as follows:
[0021] in ; R 0 represents the radius of the innermost concentric circle in the annular region division; d represents the distance between the farthest distance of long-range depositional energy diffusion and the innermost concentric circle.
[0022] Preferably, in step S3, the specific process of piecewise stacked fitting of the Gaussian term parameters is as follows: First, calculate the proportionality coefficient in the long-range deposition energy density function. K ; Then for any distance segment [ R 0 ,rs m ), 1≤m≤M Construct an m-order long-range depositional energy prediction model ; Finally, Gaussian parameter stacking fitting is performed.
[0023] Preferably, the specific process of Gaussian term parameter stacking fitting is as follows: To minimize Output predicted values and distance segments [ R 0 ,rs m The error of the ring filter data in the model is used as the optimization objective. The parameters of the m-th Gaussian term in the long-range deposition energy prediction model are fitted using an optimization method. and ; The loss function adopts a segmented function form, when the deposition energy diffusion distance is in the interval [ R 0 ,fs ), the loss function adopts the average absolute error function; when the deposition energy diffusion distance is in the interval [ fs,R 0 +d ), the loss function adopts the average logarithmic absolute error, and the logarithmic function characteristics are considered, and the data with the deposition energy of 0 is not involved in the calculation of the average logarithmic absolute error.
[0024] The application also discloses a prediction system for long-range deposition energy of electron beam exposure, which comprises a memory and a processor connected with each other, and the memory stores a computer program, and the computer program performs the steps of the method when the processor runs.
[0025] Compared with the prior art, the application has the following advantages: The application proposes a data dimension reduction method based on ring filtering according to the data characteristics of long-range deposition energy, and compared with the traditional filtering method, the filtering range is larger, the data noise can be effectively suppressed while reducing the data dimension, and the characteristics of the deposition energy data changing with the distance are retained, thereby providing a data basis for parameter fitting.
[0026] The application constructs a long-range deposition energy prediction model based on the area approximation method, avoids complex convolution calculation, and ensures the accuracy of long-range deposition energy prediction.
[0027] The application calculates the deposition energy segmentation point based on the logarithmic segmentation idea, provides a segmentation mode conforming to the data exponential decay characteristics with the distance for the segmentation point calculation of the error loss function and the segmented stacking fitting of the Gaussian term parameters.
[0028] The application constructs a segmented error loss function according to the characteristics of the deposition energy exponentially decaying with the distance, and can ensure high parameter fitting accuracy in different distance segments.
[0029] The application proposes a parameter fitting method based on the Gaussian stacking method according to the characteristics of the multiple Gaussian function parameters, can segmentally and item-by-item fit the parameters in the multiple Gaussian function, avoids simultaneously fitting multiple parameters, and improves the parameter fitting accuracy. BRIEF DESCRIPTION OF DRAWINGS
[0030] Figure 1 The flowchart of the prediction method for long-range deposition energy of electron beam exposure of the application in the embodiment.
[0031] Figure 2 The flowchart of the Gaussian term parameter stacking fitting in the application. DETAILED DESCRIPTION
[0032] The application will be further described below in conjunction with the accompanying drawings and specific embodiments.
[0033] As shown in the drawings, the embodiment of the application provides a prediction method for electron beam exposure long-range deposition energy, comprising the steps of: Figure 1 S1, data dimensionality reduction based on ring filtering, the specific steps are as follows: S101, deposition energy data acquisition. Through Monte Carlo simulation software, a two-dimensional plane is divided into small-size square deposition energy collection grids to obtain the distribution data of deposition energy density in the two-dimensional plane.
[0034] S102, ring area division. A set of concentric circles is constructed as follows :
[0035] Wherein R 0 is the radius of the innermost concentric circle, representing the distance to start counting deposition energy; the interval between the innermost concentric circle and any point on the beam spot edge is greater than α, and α is the electron beam front scattering diffusion distance; N is the number of concentric circles; (x, y) represents the coordinates of any point on the concentric circle; n represents the serial number of the concentric circle.
[0036] Assuming that the farthest distance of long-range deposition energy diffusion is R 0 +d , the calculation formula of N uses the upward rounding function, which is as follows:
[0037] Then the two-dimensional plane is divided into N ring areas using the concentric circles in , the specific expression is as follows:
[0038] S103, data dimensionality reduction based on ring filtering. First, according to the coordinate position, the collected deposition energy data is divided into several data sets , the expression is as follows:
[0039] Wherein represents the deposition energy density in the deposition energy collection grid , represents the number of data in the data set ; Then the data in is calculated by ring filtering, the formula is as follows:
[0040] where represents the distance between the i-th annular region and the origin, represents the deposited energy density of the i-th annular region, represents the area of the deposited energy collection grid; Finally, the annular filtering data set is obtained for long-range deposited energy density function parameter fitting.
[0041] S2, long-range deposited energy prediction model construction based on area approximation method S201, long-range deposited energy density function construction. First, the long-range point spread function (LRPSF) is constructed. Since the prediction object is long-range backscattered deposited energy, the point spread function does not need the forward scattering term in the traditional method, and its specific expression is as follows:
[0042] where M is the number of Gaussian terms; and is the parameter of the m-th Gaussian term; Then, based on the long-range point spread function, the long-range deposited energy density function (LRDEDF) is constructed, and its expression is as follows:
[0043] where K is the proportionality coefficient, and D is the spot dose; the parameters to be fitted are K and the parameters in the long-range point spread function.
[0044] S202, long-range deposited energy prediction model construction. The product of the spot area and the long-range point spread function is used to approximate the convolution result of the spot and the long-range point spread function, and the long-range deposited energy prediction is realized. The expression of the long-range deposited energy prediction model is as follows:
[0045] where is the spot area, (x, y) represents the coordinate offset relative to the spot barycenter, and the output of the long-range deposited energy prediction model is the deposited energy density prediction value at (x, y).
[0046] S3, parameter fitting based on Gaussian stacking method. The parameters to be fitted are K in the long-range deposited energy density function and the Gaussian term parameters, and the fitting method is as follows: S301. Calculation of sedimentation energy segmentation points. A total of M+1 sedimentation energy segmentation points are needed. The sedimentation energy diffusion distance is divided into M segments logarithmically, with each segment corresponding to one Gaussian term. The farthest sedimentation energy diffusion distance is... R 0 +d Then the m-th segment point rs m The calculation formula is as follows:
[0047] in .
[0048] S302. Calculation of the piecewise point of the error loss function. Only one piecewise point is needed for the error loss function, denoted as... fs The calculation method for the piecewise points fs of the error loss function is as follows: If M is even, then:
[0049] If M is odd, then:
[0050] S303, piecewise stacked fitting of Gaussian parameters. First, calculate the proportionality coefficient K in the long-range deposition energy density function, as shown in the following formula:
[0051] Then for any distance segment [ R 0 ,rs m ()( 1≤m≤M Construct an m-order long-range sedimentary energy prediction model. The formula is as follows:
[0052] In this formula, only the first m Gaussian terms of the long-range deposition energy prediction model are retained, reducing the number of parameters to be fitted.
[0053] Finally, Gaussian parameter stacking fitting is performed. The specific steps and process are as follows: Figure 2 As shown: 1. Let m = 1; 2. Construction The parameters of the first m-1 Gaussian terms are obtained from the previous fitting results, while the parameters of the m-th Gaussian term need to be fitted. 3. To minimize Output predicted values and distance range [R0, rs] m The error of the ring filter data in the model is used as the optimization objective. The parameters of the m-th Gaussian term in the long-range deposition energy prediction model are fitted using an optimization method. and wherein the parameter search range needs to satisfy , .
[0054] The loss function adopts the form of a segmented function, when the deposition energy diffusion distance is in the interval [ R 0 ,fs ), the loss function adopts the mean absolute error function;When the deposition energy diffusion distance is in the interval [ fs,R 0 +d ), the loss function adopts the average logarithmic absolute error, and considering the logarithmic function characteristics, for the data with 0 deposition energy, it is not involved in the calculation of the average logarithmic absolute error; 4.If m=M, end fitting, otherwise, let m=m+1, return to step 2.
[0055] S4, based on the optimized long-range deposition energy prediction model, the long-range deposition energy of electron beam exposure is predicted.
[0056] The present application proposes a data dimension reduction method based on ring filtering according to the characteristics of long-range deposition energy data, compared with the traditional filtering method, the filtering range is larger, which can effectively suppress the data noise while reducing the data dimension, and the characteristics of the deposition energy data changing with the distance are retained, providing a data basis for parameter fitting.
[0057] The present application constructs a long-range deposition energy prediction model based on the area approximation method, avoids complex convolution calculation, and at the same time ensures the accuracy of long-range deposition energy prediction.
[0058] The present application calculates the deposition energy segmentation point based on the idea of logarithmic segmentation, provides a segmentation method conforming to the exponential decay characteristics of data with distance for the segmentation point calculation of error loss function and the segmented stacking fitting of Gaussian term parameters.
[0059] The present application constructs a segmented error loss function according to the characteristics of the exponential decay of deposition energy with distance, which can ensure high parameter fitting accuracy in different distance segments.
[0060] The present application proposes a parameter fitting method based on Gaussian stacking method according to the characteristics of multiple Gaussian function parameters, which can segment and itemize the parameters in the multiple Gaussian function, avoid fitting multiple parameters at the same time, and improve the parameter fitting accuracy.
[0061] The present application also discloses a prediction system for long-range deposition energy of electron beam exposure, comprising a memory and a processor connected to each other, the memory stores a computer program, and the computer program executes the steps of the above-mentioned method when the processor runs. The prediction system of the present application corresponds to the above-mentioned prediction method, and also has the advantages of the above-mentioned prediction method.
[0062] The present application can realize all or part of the processes in the above-mentioned embodiment methods, and can also be completed by computer program instruction related hardware. The computer program can be stored in a computer readable storage medium, and the computer program can realize the steps of the above-mentioned method embodiments when executed by a processor. The computer program includes computer program code, which can be in the form of source code, object code, executable files or some intermediate forms, etc. The computer readable storage medium includes any entity or device capable of carrying computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal and software distribution medium, etc. The memory is used to store computer programs and / or modules, and the processor realizes various functions by running or executing the computer programs and / or modules stored in the memory, and calling the data stored in the memory. The memory can include high-speed random access memory, and can also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one magnetic disk storage device, flash memory device, or other volatile solid-state storage device, etc.
[0063] Noun explanation: PSF (Point Spread Function): point spread function; DEDF (Deposited Energy Density Function): deposited energy density function; LRPSF (Long Range Point Spread Function): long-range point spread function; LRDEDF (Long Range Deposited Energy Density Function): long-range deposited energy density function.
[0064] The above is only the preferred embodiment of the present application, and the protection scope of the present application is not limited to the above-mentioned embodiments. Any technical solution falling within the concept of the present application shall fall within the protection scope of the present application. It should be noted that, for ordinary skilled persons in the art, some improvements and refinements without departing from the principles of the present application shall be considered as the protection scope of the present application.
Claims
1. A method of predicting electron beam exposure long-range deposition energy, characterized by, The method comprises the steps of: S1, ring filter-based data dimension reduction: generating a ring filter data set through deposition energy data acquisition, ring region division based on a set of concentric circles to divide a two-dimensional plane into a plurality of ring regions, and ring filter calculation to average deposition energy data in each ring region, thereby achieving data dimension reduction and noise suppression; S2, long-range deposition energy prediction model construction based on area approximation method: constructing a long-range deposition energy density function using distance information in the ring filter data set, and generating a long-range deposition energy prediction model based on the product approximation of beam spot area and the long-range deposition energy density function; S3, parameter fitting based on Gaussian stacking method: step-by-step fitting of parameters in the long-range deposition energy density function using the ring filter data set and the long-range deposition energy prediction model, to obtain an optimized long-range deposition energy prediction model; S4, predicting electron beam exposure long-range deposition energy based on the optimized long-range deposition energy prediction model.
2. The method of claim 1, wherein the method is a method of predicting electron beam exposure long-range deposition energy. The specific process of step S1 is as follows: S101, deposition energy data acquisition: dividing a two-dimensional plane into a square deposition energy acquisition grid through Monte Carlo simulation software to obtain deposition energy density distribution data in the two-dimensional plane; S102, annular region division: construct a set of concentric circles as follows : wherein R 0 is the radius of the innermost concentric circle, representing the distance at which the deposition energy is started to be counted; N is the number of concentric circles; (x, y) represents the coordinates of an arbitrary point on the concentric circle; n represents the serial number of the concentric circle; Then the two-dimensional plane is divided into N annular regions using the concentric circles in , and the specific expression is as follows: S103, data dimensionality reduction based on ring filtering: first, according to the coordinate position, the collected deposition energy data is divided into several data sets The expression is as follows: wherein represents the deposited energy density in the deposited energy collection grid, represents the number of data in the data set The data in is then circularly filtered to obtain a circularly filtered data set, which is used for long-range sedimentary energy density function parameter fitting.
3. The method of claim 2, wherein the method is a method of predicting electron beam exposure long-range deposition energy, the method comprising: The formula for ring filter calculation is as follows: wherein represents the distance of the i-th annular region from the origin, represents the deposition energy density of the i-th annular region, denotes the area of the deposition energy collection grid.
4. The method of claim 1 or 2 or 3, wherein, In step S2, the specific process of constructing a long-range deposition energy density function using distance information in the ring filter data set is as follows: First, a long-range point spread function is constructed : where M is the number of Gaussian terms; and are parameters of the mth Gaussian term; A long-range deposition energy density function is then constructed based on the long-range point spread function , expressed as follows: where K is a proportional coefficient, and D is a beam spot dose; the parameters to be fitted are K and parameters in the long-range point spread function.
5. The method of claim 4, wherein the method is a method of predicting electron beam exposure long-range deposition energy, characterized by, In step S2, the expression of the long-range deposition energy prediction model is as follows: where S is the beam spot area, (x, y) represents the coordinate offset relative to the beam spot barycenter, and the output of the long-range deposition energy prediction model is the deposition energy density prediction value at (x, y).
6. The method of claim 1 or 2 or 3, wherein, In step S3, the parameters in the long-range deposition energy density function are step-by-step fitted through deposition energy segmented point calculation, error loss function segmented point calculation, and Gaussian term parameter segmented stacking fitting.
7. The method of claim 6, wherein the method is a method of predicting electron beam exposure long-range deposition energy. In step S3, the specific process of deposition energy segmented point calculation is as follows: M+1 deposition energy segmented points are needed, and the deposition energy diffusion distance is divided into M segments according to the logarithm, with one Gaussian term corresponding to each segment; The deposition energy diffuses the farthest distance of R 0 +d The mth segment point rs m The calculation formula is as follows: wherein ; R 0 is the radius of the innermost concentric circle in the annular region division; d is the distance between the farthest distance of long-range deposition energy diffusion and the innermost concentric circle.
8. The method of claim 7, wherein the method is a method of predicting electron beam exposure long-range deposition energy, the method comprising: In step S3, the specific process of Gaussian term parameter segmented stacking fitting is as follows: First, the proportionality coefficient in the long-range deposition energy density function is calculated K ; Then for any distance segment R 0 ,rs m ), 1≤m≤M , construct m order long-range deposition energy prediction model ; Finally, Gaussian term parameter stacking fitting is performed.
9. The method for predicting long-range deposition energy for electron beam exposure according to claim 8, characterized in that, The specific process of Gaussian term parameter stacking fitting is as follows: To minimize The output prediction value and the distance segment[ R 0 ,rs m The error of the annular filter data in the mth Gaussian term in the long-range sedimentary energy prediction model is taken as the optimization target, and an optimization method is used to fit the parameters of the mth Gaussian term And ; The loss function adopts a segmented function form, when the deposition energy diffusion distance is in the interval [ R 0 ,fs ), the loss function adopts the mean absolute error function; when the deposition energy diffusion distance is in the interval [ fs,R 0 +d ), the loss function adopts the mean logarithmic absolute error, and considering the logarithmic function characteristics, for the data with the deposition energy of 0, it is not involved in the calculation of the mean logarithmic absolute error.
10. A system for predicting e-beam exposure long-range deposition energy, comprising a memory and a processor connected to each other, wherein the memory has stored thereon a computer program, characterized in that, The computer program, when executed by a processor, performs the steps of the method of any one of claims 1-9.