An electron beam lithography three-dimensional development simulation calculation method

Abstract

This invention provides a method for 3D development simulation calculation in electron beam lithography. The method includes: S1 classifying photoresist types and establishing a unified mesh; S2 calculating the 3D electron beam energy deposition density field; S3 calculating the initial photoacid concentration distribution, performed only on chemically amplified photoresists; S4 calculating the 3D material state field; S5 calculating the 3D development rate field; S6 solving the 3D equation using a fast scanning method; S7 extracting the 3D development region and development contour; and S8 calibrating material parameters and performing independent verification. This invention uses Monte Carlo electron beam simulation results to fit a depth-varying double Gaussian point diffusion function, converting the 2D electron beam exposure dose distribution into a 3D energy deposition density field within the photoresist. It then calculates the 3D development rate field and developer arrival time field based on the material response relationship of chemically amplified or non-chemically amplified photoresists. The most significant feature of this invention is that it couples electron beam energy deposition, photoresist material state changes, and three-dimensional development processes within a unified three-dimensional mesh. It employs a rapid scanning method to solve the equations and obtain the three-dimensional development region and development profile at a specified development time. This method is applicable to electron beam three-dimensional development simulation of both chemically amplified and non-chemically amplified photoresists, and the model parameters can be calibrated and verified using experimental profile data.

Description

Technical Field

[0001] This invention specifically relates to a simulation calculation method for predicting three-dimensional development contours in electron beam lithography. This method is applicable to both chemically amplified and non-chemically amplified resists of various compositions. By combining Monte Carlo simulation, material reaction-diffusion models, and fast scanning algorithms, it achieves high-precision simulation of everything from three-dimensional exposure dose and three-dimensional inhibitor dose concentration distribution to three-dimensional development morphology. This method belongs to the fields of micro / nano fabrication, computational lithography, and electronic design automation technologies. Background Technology

[0002] Electron beam lithography (EBL) uses a focused electron beam to directly pattern photoresist, offering extremely high resolution and serving as a key technology for nanofabrication, mask fabrication, and cutting-edge physics research. As integrated circuit feature sizes continue to shrink, the three-dimensional effects of photolithography become increasingly significant. The physicochemical reactions occurring in the photoresist during exposure, post-exposure baking (PEB), and development exhibit strong spatial inhomogeneity, and the resulting three-dimensional development profile directly determines the device's sidewall morphology, linewidth roughness, and critical dimension (CD) accuracy. Therefore, accurately simulating the three-dimensional development profile of the photoresist is crucial for process window optimization and defect control.

[0003] Existing electron beam lithography simulation techniques mainly focus on proximity correction (PEC) or energy deposition distribution calculations in two-dimensional planes. In three-dimensional development simulation, while traditional cellular automata or ray tracing methods can simulate the development process, they often suffer from low computational efficiency, poor numerical stability, or difficulty in handling complex anisotropic development rate fields. Particularly when considering both the post-exposure diffusion of chemically amplified resists and the molecular chain breaking mechanism of non-chemically amplified resists (such as PMMA), a unified and efficient computational framework is lacking. Furthermore, the propagation of the developer in a non-homogeneous medium is essentially a problem of solving an eigenfunction equation. Existing algorithms for solving this equation exhibit superlinear computational time increases with the number of grid cells when dealing with large-scale three-dimensional meshes, making it difficult to meet the demands of rapid iteration and parameter calibration in practical processes.

[0004] To address the issues of low computational efficiency and difficulty in unifying the modeling of chemically amplified and non-chemically amplified photoresists in existing electron beam lithography 3D simulations, this invention proposes a highly efficient simulation method for 3D development contour simulation in electron beam lithography. This method constructs a 3D point diffusion function based on Monte Carlo simulation, combines it with a photoresist type-adaptive material reaction-diffusion model, and employs a block-parallel fast scanning method to solve the 3D equations. While maintaining the accuracy of the 3D morphology simulation, it significantly reduces the computation time of development simulation, exhibits high scalability, and features high computational accuracy, high computational efficiency, and strong process adaptability. Summary of the Invention

[0005] This invention is an algorithm for simulating the three-dimensional development profile of electron beam lithography, applicable to both chemically amplified and non-chemically amplified photoresists. The algorithm takes as input two-dimensional electron beam exposure dose distribution, electron beam and material parameters, photoresist thickness, development time, and developer parameters. Combined with a three-dimensional PSF function obtained from Monte Carlo simulation, it calculates the energy deposition density, material state, development rate, and developer arrival time at the center of each unit cell within the photoresist. Based on a specified development time, it determines the developed area and the remaining photoresist area, outputting the three-dimensional development profile. The computation time of this algorithm is proportional to the number of three-dimensional computational grids, and efficiency is improved through block-based parallel computation.

[0006] The technical solution of the present invention is as follows:

[0007] First, the material response branch is selected based on the photoresist type. For chemically amplified photoresists, calculations are performed in the order of 3D energy deposition, photoacid generation, post-exposure drying reaction diffusion, normalized material state, and development rate. For non-chemically amplified photoresists, the photoacid generation and post-exposure drying steps are omitted; instead, the inhibitor state or polymer molecular weight is directly calculated based on the 3D energy deposition, and then the development rate is calculated. The 3D development rate fields obtained from both branches are substituted into the 3D functional equation, and the developer arrival time field is solved using the Fast Scan Method (FSM). Finally, the 3D development profile is extracted according to the specified development time. The material model parameters can be calibrated using experimental profile data and the least squares method, and the model is evaluated using validation data independent of the training data.

[0008] The steps of the invention are as follows:

[0009] Step S1: Classification of photoresist types and establishment of a unified mesh

[0010] The system reads the photoresist type, electron beam parameters, photoresist thickness, substrate type, development time, and grid resolution from the simulation instructions to determine whether the current photoresist is a chemically amplified photoresist or a non-chemically amplified photoresist. Chemically amplified photoresists enter the photoacid generation and post-exposure baking branches; non-chemically amplified photoresists enter the inhibitor attenuation or polymer chain breakage branches.

[0011] A three-dimensional unit center grid is established so that the energy deposition density field, material state field, development rate field, and developer arrival time field use the same coordinates. Preferably, a uniform grid step size is used in all three directions.

[0012]

[0013] in, This is the grid step size. The depth direction is... The center coordinates of each unit are This avoids half-grid misalignment between different physical fields.

[0014] Step S2: Calculate the three-dimensional electron beam energy deposition density field

[0015] A Monte Carlo electron transport simulation model was established based on the current photoresist, substrate, and electron beam conditions. The electron beam accelerating voltage, beam radius, number of primary electrons, material density, photoresist thickness, and substrate structure were set. The deposition energy of incident electrons in the three-dimensional source voxel was statistically analyzed to obtain the Monte Carlo three-dimensional energy distribution. This three-dimensional data is preserved. , and Information from three directions is not summed along the horizontal direction.

[0016] A three-dimensional point spread function is constructed using the three-dimensional energy distribution obtained from Monte Carlo simulation as the fitting target. Let... The radial distance from the central axis of the electron beam is used to characterize the contributions of forward scattering and backscattering using a double Gaussian function:

[0017]

[0018] in, and These are the lateral scales of forward scattering and backscattering, respectively. For backscattering weights, The value represents the longitudinal energy distribution coefficient; the parameters of the above function are determined by fitting the three-dimensional energy distribution using Monte Carlo methods.

[0019] After fitting, for each depth layer, the two-dimensional exposure dose distribution is convolved with the corresponding depth PSF in the lateral plane to obtain the three-dimensional energy deposition field:

[0020]

[0021] Received The same three-dimensional grid coordinates are used as those for the subsequent material state field and development rate field. When the Monte Carlo source grid and the target grid are inconsistent, three-dimensional resampling is performed first, followed by PSF fitting.

[0022] Step S3: Calculate the initial photoacid concentration distribution (perform only for chemically amplified gels)

[0023] For chemically amplified photoacid generators, the remaining proportion of the photoacid generator after exposure and the initial normalized concentration of the photoacid are calculated based on the three-dimensional energy deposition density. The following relationship is preferred:

[0024]

[0025] in, This represents the normalized residual concentration of the photoacid generator after exposure. The photoresist's sensitivity coefficient to the electron beam deposition energy is denoted as . This represents the initial photoacid normalized concentration at the end of the exposure.

[0026] Step S4: Calculate the three-dimensional material state field

[0027] For chemically amplified resists, calculate photoacid diffusion, quencher diffusion, acid-base neutralization, and photoacid-catalyzed deprotection reactions during the post-exposure baking process. To normalize the state of materials that have not been deprotected or inhibited, This represents the normalized concentration of photoacid. Given the normalized concentration of the quencher, the reaction-diffusion equation is:

[0028]

[0029] in, The coefficient of photoacid-catalyzed deprotection reaction, The coefficient of the acid-base neutralization reaction. and These are the diffusion coefficients of the photoacid and the quencher, respectively. The initial conditions are:

[0030]

[0031] The baking time after exposure can be calculated using the finite element method or the finite difference method. To obtain the three-dimensional material state before chemical magnification and development. .

[0032] For non-chemically amplified photoresists containing inhibitors, the post-exposure drying-diffusion step is not performed; the normalized inhibitor state is directly calculated based on the three-dimensional energy deposition density.

[0033]

[0034] in, The response coefficient is for non-chemically amplified photoresist materials. For PMMA positive photoresist, the actual number-average molecular weight field is calculated based on the electron beam-induced molecular chain breakage relationship:

[0035]

[0036] in, The initial number-average molecular weight of PMMA before exposure. This represents the chain breakage yield per unit deposition energy. For PMMA density, is Avogadro's constant.

[0037] Step S5: Calculate the three-dimensional development rate field

[0038] For normalized inhibitory material states For chemically amplified or non-chemically amplified gels, the development rate was calculated using the MACK model:

[0039]

[0040] in, Based on the development rate, The development rate is the standard. This is the material state threshold. This is the contrast ratio for development. For PMMA, it can be set to... Alternatively, the MACK model can be used, or the Greeneich molecular weight development rate model can be used directly:

[0041]

[0042] in, Based on the development rate, For reference development rate coefficient, For reference molecular weight, This is an exponential parameter relating molecular weight to development rate. This leads to the three-dimensional development rate field co-located with the energy deposition field. .

[0043] Step S6: Solve the three-dimensional equations using the fast sweep method

[0044] The propagation of the developer in a spatially non-uniform developing rate field satisfies a three-dimensional equation:

[0045]

[0046] in, For the developer to reach the center of the cell from the initial contact boundary The time. Using the top surface of the photoresist as the initial boundary; for the current grid point, respectively obtain... , , The minimum arrival times of adjacent values ​​along the three coordinate axes are used to solve the corresponding one-dimensional, two-dimensional, or three-dimensional local quadratic equations in ascending order, and the minimum candidate arrival time is selected.

[0047] Using the FSM algorithm sequentially along , , , , , , and The 3D mesh is scanned in eight directions. The mesh is divided into spatial blocks, and parallel updates are performed on blocks that satisfy dependencies. The scan stops when the maximum arrival time variation of a complete eight-direction scan is less than the preset tolerance, or when the maximum number of scan rounds is reached.

[0048] Step S7: Extract the 3D developing area and developing contour

[0049] Given a specified development time The development state of each three-dimensional unit is determined based on the arrival time field:

[0050]

[0051] in, This indicates that the unit has been reached by the developer within the specified time. This indicates that the cell still contains residual photoresist. (Based on isosurfaces) As a continuous three-dimensional development boundary, it outputs a three-dimensional mesh contour.

[0052] Step S8: Calibrate material parameters and perform independent verification.

[0053] Data with experimentally developed outlines or linewidths are divided into training data and validation data. Let the vector of parameters to be calibrated be... , No. The experimental measurement linewidth is The simulated linewidth under the same dose, depth, and development conditions is: Construction residuals:

[0054]

[0055] Solve using a nonlinear least squares method with upper and lower bound constraints:

[0056]

[0057] For parameters that must be positive and span multiple orders of magnitude, optimization in logarithmic coordinates is preferred; the sensitivity of the residuals to the parameters is calculated using finite difference or automatic differentiation. After training, the parameters are frozen, and the validation error is calculated using only the validation data; the parameters are not updated using the validation data. The root mean square error of the training or validation set is:

[0058]

[0059] The final output includes the calibrated material parameters, training error, verification error, comparison of experimental and simulated values ​​for each dose and depth, as well as the corresponding three-dimensional energy deposition density field, material state field, development rate field, arrival time field, and three-dimensional development profile. Attached Figure Description

[0060] Figure 1 This is the overall flowchart of the electron beam lithography three-dimensional development contour simulation algorithm of the present invention.

[0061] Figure 2 A schematic diagram of fitting a three-dimensional PSF to the three-dimensional energy distribution of Monte Carlo.

[0062] Figure 3 This is a schematic diagram of solving a three-dimensional functional equation based on the block-based fast scanning method.

[0063] Figure 4 This is a schematic diagram of three-dimensional imaging contour extraction; Detailed Implementation

[0064] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0065] This invention relates to a method for simulating the three-dimensional development contours of electron beam lithography photoresist, the overall process of which is as follows: Figure 1 As shown, the process consists of eight steps: classifying photoresist types and establishing a unified mesh; calculating the three-dimensional electron beam energy deposition density field; calculating the initial photoacid concentration distribution (only performed on chemically amplified photoresists); calculating the three-dimensional material state field; calculating the three-dimensional development rate field; solving the three-dimensional equation using a fast scanning method; extracting the three-dimensional development region and development profile; calibrating material parameters and performing independent verification. Through these steps, the electron beam exposure dose is converted into information on the energy deposition, material state, development rate, and development arrival time within the photoresist, ultimately obtaining the three-dimensional development region and development profile at a specified development time. The specific implementation steps are as follows:

[0066] Step S1: Classify photoresist types and establish a unified mesh.

[0067] Read the photoresist type, electron beam parameters, photoresist thickness, substrate type, development time, and grid resolution. If the photoresist is a chemically amplified photoresist, perform photoacid generation and post-exposure baking diffusion branches; if it is a non-chemically amplified photoresist, perform inhibitor attenuation or polymer chain breakage branches.

[0068] A three-dimensional central grid is established, ensuring that the energy deposition density field, material state field, development rate field, and developer arrival time field use the same coordinates. A uniform grid step size is adopted in all three directions.

[0069]

[0070] Where h is the grid step size, and the coordinates of the center of the k-th cell in the depth direction are... The grid step size is set according to the required computational accuracy and computational load.

[0071] Step S2: Calculate the three-dimensional electron beam energy deposition density field.

[0072] A Monte Carlo electron transport model was established based on photoresist, substrate, and electron beam conditions. Accelerating voltage, beam radius, number of primary electrons, material density, photoresist thickness, and substrate structure were set, and the deposition energy of a single primary electron in a three-dimensional voxel was statistically analyzed. Using an example set of conditions—30 kV accelerating voltage, 1 nm beam radius, and 1 million primary electrons—the Monte Carlo calculation window should cover the main energy distribution ranges of forward and backscattering.

[0073] When the Monte Carlo grid does not match the developing target grid, 3D resampling is performed based on the geometric overlap volume of the source and target voxels. Let r be the radial distance from the electron beam central axis, and a double Gaussian PSF is fitted using the Monte Carlo 3D energy distribution, as shown below. Figure 2 As shown.

[0074]

[0075] in, and These are the lateral scales of forward scattering and backscattering, respectively. Let Q(z) be the backscattering weight and Q(z) be the longitudinal energy distribution coefficient. The parameters are fitted using a nonlinear least squares method with upper and lower bounds.

[0076] Read the two-dimensional exposure dose distribution D(x,y) and perform a lateral convolution with the PSF corresponding to that depth at each depth layer:

[0077]

[0078] This yields the energy deposition density field E(x,y,z) co-located with the subsequent three-dimensional grid.

[0079] Step S3: Calculate the initial photoacid concentration distribution (only performed on chemically amplified gels).

[0080] When step S1 determines that the current photoresist is a chemically amplified photoresist, the normalized residual proportion of the photoacid generator after exposure is calculated based on the three-dimensional energy deposition density:

[0081]

[0082] Next, calculate the initial normalized concentration of photoacid at the end of the exposure:

[0083]

[0084] in, This is the photoresist's sensitivity coefficient to electron beam deposition energy for acid generation. If a non-normalized concentration is used, it can be multiplied by the initial photoacid concentration or the initial photoacid generator concentration or acid generation efficiency coefficient.

[0085] If step S1 determines that the current photoresist is a non-chemically amplified photoresist, this step is not executed, and the process proceeds directly to step S4.

[0086] Step S4: Calculate the three-dimensional material state field.

[0087] For chemically amplified adhesives, calculate photoacid diffusion, quencher diffusion, acid-base neutralization, and photoacid-catalyzed deprotection reaction during the post-exposure baking process. The normalized unprotected material state satisfies:

[0088]

[0089] The photoacid and the quencher satisfy the diffusion and acid-base neutralization equations:

[0090]

[0091] The initial conditions are:

[0092]

[0093] in, The coefficient of photoacid-catalyzed deprotection reaction, The coefficient of the acid-base neutralization reaction. and These are the diffusion coefficients of the photoacid and the quencher, respectively. The above equations are discretized using the finite difference method, and the solution is obtained up to the post-exposure baking time. This yields the three-dimensional material state field before development.

[0094] For non-chemically amplified photoresists containing inhibitors, post-exposure baking-diffusion is not performed; the normalized inhibitor state is directly calculated based on the three-dimensional energy deposition density.

[0095]

[0096] in, The response coefficient is for non-chemically amplified adhesive materials.

[0097] For PMMA positive photoresist, the actual number-average molecular weight field is calculated based on the electron beam-induced molecular chain breakage relationship:

[0098]

[0099] in, The initial number-average molecular weight of PMMA before exposure. This represents the chain breakage yield per unit deposition energy. For PMMA density, is Avogadro's constant.

[0100] Step S5: Calculate the three-dimensional development rate field.

[0101] For chemically amplified or non-chemically amplified photoresists characterized by the normalized inhibitory material state m, the development rate is calculated using the MACK model:

[0102]

[0103] in, Based on the development rate, The development rate is the standard. is the material state threshold, and n is the development contrast index.

[0104] For PMMA, it can make Alternatively, the MACK model can be used, or the Greeneich molecular weight development rate model can be used directly:

[0105]

[0106] in, Based on the development rate, For reference development rate coefficient, For reference molecular weight, This is an exponential parameter relating molecular weight to development rate. From this, the three-dimensional development rate field R(x,y,z) is obtained.

[0107] Step S6: Solve the three-dimensional equations using the fast scan method.

[0108] Substitute the three-dimensional development rate field obtained in step S5 into the process function equation:

[0109]

[0110] Where T(x,y,z) represents the time it takes for the developer to travel from the initial contact boundary to the center of the grid cell. The top surface of the photoresist is used as the initial boundary, and the remaining grid points are initialized to infinity.

[0111] like Figure 3 The FSM (Free Surface Scanning) method sequentially scans the 3D mesh along eight directions: (+x,+y,+z), (-x,+y,+z), (+x,-y,+z), (-x,+y,+z), (+x,+y,-z), (-x,+y,-z), (+x,-y,-z), and (-x,-y,-z). The mesh is divided into spatial blocks, and each block is rescanned after receiving an updated boundary arrival time. The scan stops when the maximum change in the complete eight-direction scan is less than a preset tolerance or when the maximum number of scan cycles is reached.

[0112] Step S7: Extract the three-dimensional development area and development contour.

[0113] like Figure 4 Given a specified development time The development state of each three-dimensional unit is determined based on the arrival time field:

[0114]

[0115] in, This indicates that the unit has been reached by the developer within the specified time. This indicates that the cell still contains residual photoresist; The isosurface is used as the continuous three-dimensional development boundary to output the three-dimensional development profile.

[0116] Step S8: Calibrate material parameters and perform independent verification.

[0117] The experimental development profiles or linewidth data at different depths are divided into training and validation sets. The residual between the i-th experimental linewidth and the simulated linewidth under the same dose, depth, and development conditions is:

[0118]

[0119] The nonlinear least squares method with upper and lower bound constraints is used to solve for the calibration parameters in the corresponding material branch:

[0120]

[0121] After training, the parameters are frozen, and the root mean square error is calculated using only the validation set.

[0122]

[0123] The final output includes PSF fitting parameters, material model parameters, training error, validation error, as well as three-dimensional energy deposition density field, material state field, development rate field, arrival time field, and three-dimensional development profile.

[0124] The above embodiments are used to illustrate the technical solution of the present invention. The electron beam accelerating voltage, beam spot size, photoresist and substrate materials, photoresist thickness, exposure dose, developer, development time, grid step size, and material model parameters can all be adjusted according to the actual process.

Claims

1. A method for simulating and calculating three-dimensional development using electron beam lithography, characterized in that, Includes the following steps: Step S1: Classification of photoresist types and establishment of a unified mesh; Step S2: Calculate the three-dimensional electron beam energy deposition density field; Step S3: Calculate the initial photoacid concentration distribution; Step S4: Calculate the three-dimensional material state field; Step S5: Calculate the three-dimensional development rate field; Step S6: Solve the three-dimensional equations using the fast scan method; Step S7: Extract the three-dimensional developing area and developing contour; Step S8: Calibrate the material parameters and perform independent verification.

2. The electron beam lithography three-dimensional development simulation calculation method as described in claim 1, characterized in that: Read the photoresist type, photoresist thickness, electron beam parameters, development time, and spatial resolution; Photoresists are classified into chemically amplified resists and non-chemically amplified resists. A three-dimensional unit center grid is established according to a preset grid step size, so that the energy deposition density field, material state field, development rate field, and developer arrival time field use the same spatial coordinates, wherein the grid step size in the three spatial directions satisfies: Depth direction The center coordinates of each grid cell are: 。 3. The electron beam lithography three-dimensional development simulation calculation method as described in claim 1, characterized in that: A Monte Carlo electron transport model was established based on electron beam acceleration voltage, beam spot radius, number of primary electrons, photoresist material, photoresist thickness, and substrate material to obtain the energy deposition distribution of a single primary electron in the three-dimensional space of the photoresist. The Monte Carlo energy deposition distribution is resampled to the unified grid established in step S1 according to the voxel geometric overlap relationship, and a double Gaussian point diffusion function varying with depth is fitted based on the resampled energy deposition distribution: In the formula, The radial distance between the grid position and the central axis of the electron beam. The longitudinal energy deposition attenuation coefficient, and These are the lateral scales of forward scattering and backscattering, respectively. The weight of the backscattered component in the total radial energy deposition; the dose distribution of the two-dimensional electron beam exposure. Convolving with the point spread function yields the three-dimensional electron beam energy deposition density field: 。 4. The electron beam lithography three-dimensional development simulation calculation method as described in claim 1, characterized in that: When step S1 determines that the photoresist is a chemically amplified photoresist, the normalized residual proportion of photoacid generator after exposure is calculated based on the three-dimensional electron beam energy deposition density field obtained in step S2: Since photoacid is generated by PAG, it is equivalent to the reduction of PAG, so the normalized initial photoacid concentration at the end of the exposure can be calculated: In the formula, This is the acid-generating sensitivity coefficient of the photoresist to electron beam deposition energy; when the photoresist is a non-chemically amplified photoresist, skip this step and proceed to step S4.

5. The electron beam lithography three-dimensional development simulation calculation method as described in claim 1, characterized in that: For chemically amplified adhesives, calculate photoacid diffusion, quencher diffusion, acid-base neutralization, and photoacid-catalyzed deprotection reactions during the post-exposure baking process; let... As a normalized inhibitory material, This represents the normalized concentration of photoacid. Given the normalized concentration of the quencher, the reaction-diffusion equation is: In the formula, The coefficient of photoacid-catalyzed deprotection reaction. The coefficient of the acid-base neutralization reaction. and The diffusion coefficients of the photoacid and the quencher are respectively; the reaction-diffusion equation is solved using the finite element method or the finite difference method up to the post-exposure baking time. The three-dimensional material state field before chemical magnification and development was obtained. , For non-chemically amplified resists containing inhibitors, the post-exposure drying reaction diffusion process is not performed. The normalized inhibitor state field is directly calculated based on the three-dimensional electron beam energy deposition density field obtained in step S2. In the formula, The normalized inhibitor state of the non-chemically amplified gel. The response coefficient of the non-chemically amplified adhesive material. For non-chemically amplified gels that do not involve inhibitors, such as PMMA, the three-dimensional number-average molecular weight field is calculated based on the electron beam-induced polymer chain breakage relationship; the number-average molecular weight field is: In the formula, This is the three-dimensional number-average molecular weight field after exposure. The initial number-average molecular weight of PMMA before exposure. This represents the yield of molecular chain breakage per unit deposition energy. For PMMA density, is Avogadro's constant.

6. The electron beam lithography three-dimensional development simulation calculation method as described in claim 1, characterized in that: Based on the three-dimensional material state field obtained in step S4, the development rate of each mesh element is calculated using the MACK development rate model: In the formula, To normalize the material state, Based on the development rate, The development rate is the standard. This refers to the development contrast parameter. These are parameters related to the material state threshold; for PMMA adhesives, the three-dimensional development rate field is obtained by using either the MACK development rate model based on the normalized number-average molecular weight or the Greeneich development rate model based on the number-average molecular weight. , In the formula, Based on the development rate, For reference development rate coefficient, For reference molecular weight, The exponential parameter between molecular weight and development rate is used to obtain the three-dimensional development rate field co-located with the energy deposition density field. .

7. The electron beam lithography three-dimensional development simulation calculation method as described in claim 1, characterized in that: Substitute the three-dimensional development rate field obtained in step S5 into the three-dimensional equation: In the formula, This is the time required for the developer to reach the corresponding grid cell; The top surface of the photoresist is set as the initial contact boundary of the developer, and a rapid scanning method is used along the three-dimensional space. , and The arrival time of each grid cell is iteratively updated in eight scanning directions. The minimum time value that meets the conditions is taken as the solution to the equation until the maximum change in the arrival time field is less than the preset convergence tolerance or the preset maximum number of scanning rounds is reached, thus obtaining the three-dimensional developer arrival time field.

8. The electron beam lithography three-dimensional development simulation calculation method as described in claim 1, characterized in that: The arrival time field of the three-dimensional developer obtained in step S6 is compared with the specified development time. The development state of each grid cell is determined by comparison using the following formula: In the formula, This indicates that the corresponding grid cell has been reached by the developer. This indicates that the corresponding mesh cell still contains residual photoresist; extraction The isosurfaces are used to obtain the three-dimensional development profile.

9. The electron beam lithography three-dimensional development simulation calculation method as described in claim 1, characterized in that: The experimental development profile data is divided into training data and independent validation data. The nonlinear least squares method with parameter upper and lower bound constraints is used to calibrate the point spread function parameters in step S2 and the material model parameters in steps S3 to S5. After the parameter calibration is completed, the parameters are fixed, and the error between the simulated development profile and the experimental development profile is calculated using the independent validation data to obtain the final three-dimensional development profile prediction result.

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