Electron beam exposure deposition energy prediction method and system based on improved point spread function

Abstract

The invention discloses an electron beam exposure deposition energy prediction method and system based on an improved point spread function, and the method comprises the steps: S1, obtaining two-dimensional deposition energy distribution data generated by electron beam exposure, and processing the two-dimensional deposition energy distribution data into one-dimensional data according to the axial symmetry of the two-dimensional deposition energy distribution data; s2, on the basis of the one-dimensional data characteristics generated in the step S1, constructing a sedimentary energy prediction model taking an inverse proportion point spread function as a core; s3, performing parameter preliminary estimation on the sedimentary energy prediction model in the step S2 based on a least square method, and determining a reasonable search range of parameters; and then global optimization is carried out in a reasonable search range based on a particle swarm algorithm, and accurate parameter fitting is realized by taking minimization of a prediction error as a target. The method has the advantages of improving model prediction precision and the like.

Description

Technical Field

[0001] The present invention mainly relates to the technical field of electron beam, and particularly relates to a method and system for predicting electron beam exposure deposition energy based on an improved point spread function. Background Art

[0002] Electron beam exposure is a widely used semiconductor processing technology, commonly used in high-precision chip manufacturing and chip pre-research scenarios. During the electron beam exposure process, due to the scattering and transmission effects of the electron beam in the photoresist and substrate, the exposure dose at the pattern edge will be affected, thus resulting in the proximity effect. The proximity effect is a negative effect that seriously affects the accuracy of the exposure pattern during electron beam lithography. In order to reduce the influence of the proximity effect, it is necessary to perform dose correction on the exposure process, and to achieve high-precision dose correction, it is necessary to achieve high-accuracy prediction of electron beam exposure deposition energy.

[0003] Predicting electron beam exposure deposition energy means predicting the deposition energy at different positions on a two-dimensional plane in the same layer of photoresist with uniform thickness by using a deposition energy prediction model. The deposition energy prediction model usually adopts a mathematical function with an analytical expression, and is generally constructed based on the point spread function (PSF). When the exposure dose changes, the deposition energy changes proportionally to the exposure dose, and the point spread function remains unchanged. Therefore, to achieve accurate deposition energy prediction, the following conditions need to be met:

[0004] (1) Determine the appropriate form of the PSF function;

[0005] (2) Accurately fit the parameters in the deposition energy prediction model by using deposition energy data.

[0006] However, predicting the deposition energy generated by electron beam exposure faces the following difficulties:

[0007] (1) The form of the PSF function is complex. The currently widely used PSF functions in the field of deposition energy prediction are the double Gaussian PSF or the triple Gaussian PSF. The above functions can predict the deposition energy distribution to a certain extent; however, the form is relatively complex and there are many parameters, so the parameter fitting is difficult, and it also causes the inability to use parameter fitting methods such as the least squares method that rely on the function form.

[0008] (2) The accuracy of the parameter fitting algorithm for the deposition energy prediction model needs to be improved. Among the currently commonly used PSF fitting algorithms, the genetic algorithm will discretize the continuous numerical space, reducing the search accuracy; the Newton iteration method and the gradient descent method are extremely prone to falling into local optima and do not meet the requirements of the field for the robustness of the algorithm; the particle swarm algorithm has a good global search effect and can achieve relatively accurate parameter fitting. However, its convergence speed and accuracy depend on the selection of the optimization range. Summary of the Invention

[0009] In view of the technical problems existing in the prior art, the present invention provides an electron beam exposure deposition energy prediction method and system based on an improved point spread function, which can improve the accuracy of parameter fitting and thus enhance the prediction accuracy of the model.

[0010] To solve the above technical problems, the technical solution proposed by the present invention is as follows:

[0011] An electron beam exposure deposition energy prediction method based on an improved point spread function, comprising the steps of:

[0012] S1. Obtain two-dimensional deposition energy distribution data generated by electron beam exposure, and process it into one-dimensional data according to the axial symmetry of the two-dimensional deposition energy distribution data;

[0013] S2. Based on the characteristics of the one-dimensional data generated in step S1, construct a deposition energy prediction model with an inverse point spread function as the core;

[0014] S3. Based on the least squares method, perform a preliminary estimation of the parameters of the deposition energy prediction model in step S2 to determine a reasonable search range for the parameters; subsequently, perform global optimization within the reasonable search range based on the particle swarm algorithm, with the goal of minimizing the prediction error, to achieve accurate fitting of the parameters.

[0015] Preferably, in step S1, the specific process of obtaining the two-dimensional deposition energy distribution data generated by electron beam exposure is as follows:

[0016] In the simulation software, build a simulation scenario according to the actual exposure process and configure the process parameters;

[0017] Then, according to the data acquisition requirements, configure the data acquisition parameters;

[0018] Finally, run the simulation software to perform Monte Carlo simulation to obtain the deposition energy data generated by a single small-sized beam spot in the two-dimensional plane.

[0019] Preferably, in step S1, the specific process of processing the two-dimensional deposition energy distribution data into one-dimensional data according to the axial symmetry is as follows:

[0020] Establish a rectangular coordinate system Oxy with the center of gravity of the exposure beam spot as the origin, and count the deposition energy data outside the beam spot in the positive x-axis direction, negative x-axis direction, positive y-axis direction, and negative y-axis direction;

[0021] Then calculate the average value of the deposition energy data in the four directions to obtain a one-dimensional data set D = {(r, e)|(r, e) = ((M + i - 1)d, e i), where \(1\leq i\leq K\) and \(i, K\) are positive integers; where \(r\) is the distance between the grid and the centroid of the beam spot, \(e\) is the deposited energy in the grid; \(d\) is the grid size in nanometers; \(M\) and \(K\) are positive integers, and \(M\) satisfies \((M - 1)d < R\leq Md\); where \(R\) is the maximum distance from any point in the beam spot to the centroid of the beam spot, and \(K\) is the number of data samples in \(D\).

[0022] Preferably, in step S2, according to the data characteristic that the deposited energy gradually decreases with the increase of distance, an inverse proportional point spread function is constructed, and the expression is as follows:

[0023]

[0024] where \(m\) is the power exponent and satisfies \(m > 0\); \(P\) is the normalization coefficient used to ensure that the integral of the PSF within the two-dimensional plane deposited energy distribution range is 1; \(x\) and \(y\) are the offsets of any point relative to the centroid of the exposure beam spot.

[0025] Preferably, in step S2, the expression of the deposited energy density function is constructed as follows:

[0026]

[0027] where \(Q\) is the proportionality coefficient and \(N\) is the number of electrons in the beam spot.

[0028] Preferably, in step S2, a grid deposited energy function is constructed, specifically:

[0029]

[0030] When the grid size \(d\) is small enough, the following approximate calculation is performed:

[0031]

[0032] Let \(E = P\cdot Q\cdot N\cdot d\) 2 , then the expression of the grid deposited energy function is as follows:

[0033]

[0034] The obtained grid deposited energy function is the deposited energy prediction model to be constructed.

[0035] Preferably, in step S3, based on the least squares method, a preliminary parameter estimation of the deposited energy prediction model in step S2 is performed, and the specific process of determining the reasonable search range of the parameters is as follows:

[0036] Take the logarithm of the grid deposited energy to convert it into a form that can be used for parameter fitting by the least squares method, and the expression is as follows:

[0037]

[0038] Then, using the data set D, the parameters m and E are fitted based on the least squares method, and the fitted values are set as m0 and E0 respectively;

[0039] Finally, [0.5m0, 1.5m0] and [0.5E0, 1.5E0] are used as the parameter search ranges respectively.

[0040] Preferably, in step S3, global optimization is performed within a reasonable search range based on the particle swarm algorithm, with the goal of minimizing the prediction error. The specific process for achieving accurate parameter fitting is as follows:

[0041] First, an optimization objective function is constructed based on the mean absolute error, and the expression is as follows:

[0042]

[0043] where (M + i - 1, e i ) is the i-th data sample in the data set D;

[0044] Considering that the deposition energy in each direction of the small-sized beam spot is approximately the same, x = M + i - 1 and y = 0 are directly substituted into the grid deposition energy function for calculation;

[0045] Then, the particle swarm algorithm is run to search within the parameter search range to achieve accurate fitting of the parameter values.

[0046] The present invention also discloses a computer-readable storage medium, on which a computer program is stored. The computer program, when run by a processor, executes the steps of the method described above.

[0047] The present invention further discloses an electron beam exposure deposition energy prediction system based on an improved point spread function, including a memory and a processor connected to each other. A computer program is stored on the memory, and the computer program, when run by the processor, executes the steps of the method described above.

[0048] Compared with the prior art, the advantages of the present invention are as follows:

[0049] The present invention preprocesses the deposition energy generated by the beam spot. Under the condition of comprehensively considering the deposition energy distribution in multiple directions, the two-dimensional deposition energy data is converted into one-dimensional data, reducing the difficulty of data fitting. Through mathematical and physical theoretical analysis, a method for constructing a grid energy function based on the PSF is proposed, thereby realizing the construction of a deposition energy prediction model. A deposition energy prediction model based on the inverse proportional PSF is constructed, which simplifies the PSF mathematical expression while ensuring the same function trend, reduces the difficulty of parameter fitting, and expands the optional range of parameter fitting methods. The least squares method is used to determine the parameter search range of the particle swarm algorithm, and then the particle swarm algorithm is used for parameter fitting, improving the global search ability of the parameters and the accuracy of parameter fitting. Brief Description of the Drawings

[0050] Figure 1 It is a flowchart of the deposition energy prediction method of the present invention in an embodiment. Detailed Embodiments

[0051] The present invention will be further described below in conjunction with the specification drawings and specific embodiments.

[0052] As Figure 1 shown, the electron beam exposure deposition energy prediction method based on the improved point spread function provided by the embodiment of the present invention includes the steps:

[0053] Step S1: Data acquisition and preprocessing

[0054] Use simulation software to obtain the distribution data outside the small-sized beam spot in the two-dimensional plane, and process it into one-dimensional data according to the axial symmetry of the deposition energy distribution of the small-sized beam spot, specifically including the following steps:

[0055] S1.1. Simulation data acquisition;

[0056] In the simulation software, build a simulation scenario according to the actual exposure process, and configure process parameters such as acceleration voltage, beam spot size, substrate material parameters, and photoresist material parameters;

[0057] Then, according to the data acquisition requirements, configure data acquisition parameters such as grid size and data acquisition range;

[0058] Finally, run the simulation software to perform Monte Carlo simulation to obtain the deposition energy data generated by a single small-sized beam spot in the two-dimensional plane. Among them, the data statistically obtained is the total deposition energy in each grid; the grid size is the coordinate accuracy of the data distribution.

[0059] S1.2. Data preprocessing;

[0060] Taking the centroid of the exposure beam spot as the origin, establish a rectangular Oxy coordinate system, and statistically analyze the deposited energy data outside the beam spot in the positive x-axis direction, negative x-axis direction, positive y-axis direction, and negative y-axis direction;

[0061] Then calculate the average value of the deposited energy data in the four directions to obtain a one-dimensional data set D, specifically:

[0062] D = {(r, e)|(r, e) = ((M + i - 1)d, e i ), 1 ≤ i ≤ K and i, K are positive integers}.

[0063] Where r is the distance between the grid and the centroid of the beam spot, e is the deposited energy in the grid; d is the grid size, with the unit of nm; M and K are positive integers, and M satisfies (M - 1)d < R ≤ Md; where R is the maximum distance from any point in the beam spot to the centroid of the beam spot, and K is the number of data samples in D.

[0064] Through the above data preprocessing, the two-dimensional plane deposited energy distribution data is converted into one-dimensional data.

[0065] Step S2: Construction of the deposited energy prediction model

[0066] According to the data characteristics and physical meaning, construct a deposited energy prediction model based on the inverse proportional PSF, specifically:

[0067] S2.1, Construction of PSF (Point Spread Function);

[0068] Based on the data characteristic that the deposited energy gradually decreases with the increase of distance, construct an inverse proportional PSF, and the expression is as follows:

[0069]

[0070] Where m is the power exponent, satisfying m > 0; P is the normalization coefficient, used to ensure that the integral of the PSF within the two-dimensional plane deposited energy distribution range is 1; x, y are the offsets of any point relative to the centroid of the exposure beam spot.

[0071] S2.2, Construction of the Deposited Energy Density Function (DEDF);

[0072] Based on the physical meaning of the PSF, construct the deposited energy density function, with the unit of keV / nm 2 . The expression of the deposited energy density function is as follows:

[0073]

[0074] Where Q is the proportionality coefficient and N is the number of electrons in the beam spot.

[0075] S2.3, Construction of Grid Deposited Energy Function (GDEF);

[0076] The grid deposited energy function describes the total amount of deposited energy contained in a single grid, with the unit of keV, and the expression is as follows:

[0077]

[0078] When the grid size d is small enough, the following approximate calculation is carried out:

[0079]

[0080] Let E = P·Q·N·d 2 , then the expression of the grid deposited energy function is as follows:

[0081]

[0082] The obtained grid deposited energy function is the deposition energy prediction model to be constructed.

[0083] Step S3: Fitting of deposition energy prediction model parameters

[0084] First, perform formula form conversion, make a preliminary estimate of the parameter range based on the least squares method, then set the optimization objective function, and perform accurate fitting of the parameter values based on the particle swarm algorithm, so as to achieve relatively accurate deposition energy prediction. Specifically:

[0085] S3.1, Preliminary estimate of parameter range.

[0086] Take the logarithm of the grid deposited energy to convert it into a form that can be used for parameter fitting by the least squares method, and the expression is as follows:

[0087]

[0088] Then use the dataset D to fit the parameters m and E based on the least squares method, and let the fitting values be m0 and E0 respectively;

[0089] Finally, take [0.5m0, 1.5m0] and [0.5E0, 1.5E0] as the parameter search ranges respectively.

[0090] S3.2, Accurate fitting of parameter values.

[0091] First, construct the optimization objective function based on the mean absolute error, and the expression is as follows:

[0092]

[0093] Among them, (M + i - 1, e i ) is the i-th group of data samples in the data set D.

[0094] Considering that the deposition energy in each direction of the small-sized beam spot is approximately the same, x = M + i - 1 and y = 0 can be directly substituted into the grid deposition energy function for calculation;

[0095] Then run the particle swarm optimization algorithm to search within the parameter search range to achieve accurate fitting of parameter values.

[0096] The present invention preprocesses the deposition energy generated by the beam spot. Under the condition of comprehensively considering the deposition energy distribution in multiple directions, the two-dimensional deposition energy data is converted into one-dimensional data, reducing the difficulty of data fitting; through mathematical and physical theoretical analysis, a method for constructing a grid energy function based on PSF is proposed, thereby realizing the construction of a deposition energy prediction model; a deposition energy prediction model based on inverse PSF is constructed, simplifying the PSF mathematical expression while ensuring the same function trend, reducing the difficulty of parameter fitting, and expanding the optional range of parameter fitting methods; the least squares method is used to determine the parameter search range of the particle swarm optimization algorithm, and then the particle swarm optimization algorithm is used for parameter fitting, improving the global search ability of parameters and the accuracy of parameter fitting.

[0097] The present invention also discloses a computer-readable storage medium, on which a computer program is stored. When the computer program is run by a processor, it executes the steps of the method described above. The present invention further discloses an electron beam exposure deposition energy prediction system based on an improved point spread function, including a memory and a processor connected to each other. A computer program is stored on the memory. When the computer program is run by the processor, it executes the steps of the method described above. The medium and system of the present invention, corresponding to the above method, also have the advantages described in the above method. Implementing all or part of the processes in the method of the above embodiments of the present invention can also be completed by hardware related to computer program instructions. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, it can implement the steps of the method embodiments described above. Among them, the computer program includes computer program code, and the computer program code can be in the form of source code, object code, executable file or some intermediate form, etc. The computer-readable storage medium includes: any entity or device capable of carrying computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disc, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electrical carrier signal, telecommunication signal, and software distribution medium, etc. The memory is used to store computer programs and / or modules. 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 may include high-speed random access memory, and may 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 device, or other volatile solid-state storage devices, etc.

[0098] The above are only the preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the idea of the present invention belong to the protection scope of the present invention. It should be pointed out that for those of ordinary skill in the art of the present technology, several improvements and refinements made without departing from the principle of the present invention should be regarded as within the protection scope of the present invention.

Claims

1. An electron beam exposure deposition energy prediction method based on an improved point spread function, characterized in that Including the steps: S1. Obtain the two-dimensional deposition energy distribution data generated by electron beam lithography, and process it into one-dimensional data according to the axial symmetry of the two-dimensional deposition energy distribution data; S2. Based on the characteristics of the one-dimensional data generated in step S1, construct a deposition energy prediction model with an inverse point spread function as the core; S3. Based on the least squares method, perform a preliminary parameter estimation on the deposition energy prediction model in step S2 to determine a reasonable search range for the parameters; subsequently, perform global optimization within the reasonable search range based on the particle swarm algorithm, with the goal of minimizing the prediction error, to achieve precise parameter fitting.

2. The method for predicting the deposition energy of electron beam lithography based on the improved point spread function according to claim 1, wherein In step S1, the specific process of obtaining the two-dimensional deposition energy distribution data generated by electron beam lithography is as follows: In the simulation software, build a simulation scenario according to the actual exposure process and configure the process parameters; Then, according to the data acquisition requirements, configure the data acquisition parameters; Finally, run the simulation software to perform Monte Carlo simulation to obtain the deposition energy data generated by a single small-sized beam spot in the two-dimensional plane.

3. The method for predicting the deposition energy of electron beam lithography based on the improved point spread function according to claim 2, wherein In step S1, the specific process of processing the two-dimensional deposition energy distribution data into one-dimensional data according to the axial symmetry of the two-dimensional deposition energy distribution data is as follows: Establish a right-handed Oxy coordinate system with the centroid of the exposure beam spot as the origin, and count the deposition energy data outside the beam spot in the positive x-axis direction, negative x-axis direction, positive y-axis direction, and negative y-axis direction; Then calculate the average value of the deposition energy data in four directions to obtain a one-dimensional data set D = {(r, e)|(r, e) = ((M + i - 1)d, e i ), 1 ≤ i ≤ K and i, K are positive integers}; where r is the distance between the grid and the centroid of the beam spot, e is the deposition energy in the grid; d is the grid size, in nm; M and K are positive integers, M satisfies (M - 1)d < R ≤ Md; where R is the maximum distance from any point in the beam spot to the centroid of the beam spot, and K is the number of data samples in D.

4. The method for predicting the deposition energy of electron beam exposure based on the improved point spread function according to claim 1 or 2 or 3, characterized in that, In step S2, based on the data characteristic that the deposition energy gradually decreases with the increase of distance, construct an inverse point spread function, and the expression is as follows: where m is the power exponent, satisfying m>0; P is the normalization coefficient, which is used to ensure that the integral of the PSF within the two-dimensional plane deposition energy distribution range is 1; x and y are the offsets of any point relative to the centroid of the exposure beam spot.

5. The method for predicting the deposition energy of electron beam exposure based on the improved point spread function according to claim 4, characterized in that, In step S2, the expression of the deposition energy density function is constructed as follows: where Q is the proportionality coefficient and N is the number of electrons within the beam spot.

6. The method for predicting the deposition energy of electron beam lithography based on the improved point spread function according to claim 5, characterized in that, In step S2, construct the grid deposition energy function, specifically: When the grid size d is small enough, perform the following approximate calculation: Let E = P·Q·N·d 2 , then the expression of the grid deposition energy function is as follows: The obtained grid deposition energy function is the deposition energy prediction model that needs to be constructed.

7. The method for predicting the deposition energy of electron beam exposure based on the improved point spread function according to claim 6, wherein In step S3, the specific process of performing a preliminary parameter estimation on the deposition energy prediction model in step S2 based on the least squares method to determine a reasonable search range for the parameters is as follows: Take the logarithm of the grid deposition energy to convert it into a form that can use the least squares method for parameter fitting, and the expression is as follows: Then use the data set D to fit the parameters m and E based on the least squares method, and assume the fitting values are m0 and E0 respectively; Finally, use [0.5m0, 1.5m0] and [0.5E0, 1.5E0] as the parameter search ranges respectively.

8. The method for predicting the deposition energy of electron beam lithography based on the improved point spread function according to claim 7, characterized in that, In step S3, the specific process of performing global optimization within the reasonable search range based on the particle swarm algorithm with the goal of minimizing the prediction error to achieve precise parameter fitting is as follows: First, construct an optimization objective function based on the mean absolute error, and the expression is as follows: where (M + i - 1, e i ) is the i-th data sample in the data set D; Considering that the deposition energy in each direction of the small-sized beam spot is approximately the same, directly substitute x = M + i - 1, y = 0 into the grid deposition energy function for calculation; Then run the particle swarm algorithm to search within the parameter search range to achieve precise fitting of the parameter values.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, The computer program, when run by a processor, performs the steps of the method according to any one of claims 1-8.

10. An electron beam exposure deposition energy prediction system based on an improved point spread function, comprising a memory and a processor connected to each other, wherein a computer program is stored on the memory, and is characterized in that The computer program, when run by a processor, performs the steps of the method according to any one of claims 1-8.

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