Photoresist model parameter correction method and photoresist model parameter correction system

Abstract

The present application relates to a photoresist model parameter correction method, including selecting initial values of photoresist model parameters, setting initial photoresist model parameter groups x1 as initial points of optimization algorithms according to the selected initial values of photoresist model parameters, each element in the initial photoresist model parameter groups x1 is the initial value of the corresponding photoresist model parameter, generating a plurality of photoresist model parameter groups according to the initial photoresist model parameter x1, and optimizing the plurality of photoresist model parameter groups by Nelder-Mead method according to the plurality of photoresist model parameter groups and experimental values e.

Description

Technical Field

[0001] This invention relates to a method and system for correcting photoresist model parameters. Background Technology

[0002] Photoresist is a crucial material used in photolithography processes during microelectronics manufacturing. In photolithography, photoresist is coated onto the wafer surface and, through mask exposure, baking, and development processes, forms micron- or even nanometer-scale patterns. These patterns are then used in subsequent steps such as etching or ion implantation. Throughout this process, the performance of the photoresist and the precise control of photolithography process parameters are critical to the quality and dimensional accuracy of the final pattern.

[0003] In the photolithography process, the steps related to photoresist include: coating, pre-baking, exposure, baking, development, and hard baking. However, depending on the process node and requirements, not all of these steps will be used in a single photolithography process. Many scientists have done extensive work on photoresist modeling, establishing rigorous physical models of photoresist in exposure, baking, and development. These physical models allow for the quantitative characterization and rigorous calculation of parameters such as temperature, time, exposure dose, and development time in each step, predicting the image profile of the photoresist on the wafer under different exposure and development conditions, calculating the resolution of the mask pattern on the wafer, and analyzing the contrast of the image pattern.

[0004] However, without experimental data to correct the model, the results calculated by the photoresist model cannot fully predict the imaging profile, specifically manifested in discrepancies between the results and those obtained from exposure experiments on the wafer. This discrepancy stems from the parameters input to the photoresist model. Parameters in the photoresist model (such as the light absorption coefficient and development rate constant) need to be corrected using experimental data to ensure the model's accuracy. The precision of these parameter corrections directly affects the reliability of the model's predictions, thus impacting the optimization of the photolithography process. Parameter correction is typically achieved through experimental measurements, data fitting, and optimization algorithms. In other words, without experimental data, the photoresist model's predictions are inaccurate.

[0005] The common process for photoresist model parameter calibration is shown in the attached figure. Figure 1 The process includes: step S01, confirming the experimental layout of the photoresist; step S02, collecting SEM data of the photoresist; step S03, optimizing multiple parameters; and step S04, confirming the model parameters.

[0006] Existing technologies for photoresist model parameter correction mostly utilize experimental data for OPC (Optical Proximity Correction). Specifically, this involves establishing an optical model using experimental data to facilitate subsequent model refinement (this model is an OPC model, specifically a model in model-based OPC). Therefore, photoresist model parameter correction requires a large amount of experimental data. The data comes from the exposure results of the mask pattern on the wafer, which correspond to the pattern on the wafer layout. This part includes experimental layout pattern confirmation and SEM data collection. The layout pattern typically uses a periodically repeating one-dimensional pattern with full through pitch. The periodicity generally includes dense, semi-dense, and iso-patterned patterns. SEM data collection is usually achieved through microscopic observation, scanning electron microscopy (SEM) imaging, and atomic force microscopy (AFM). When obtaining SEM data through experimental layout fabrication experiments, FEM (Focus Exposure Matrix) data is generally acquired.

[0007] Based on the above process, parameters in the photoresist model (such as light absorption coefficient and development rate constant) are determined through experimental data calibration to ensure the model's accuracy. The accuracy of these parameter calibrations directly affects the reliability of the model's predictions, thus impacting the optimization effect of the photolithography process. Parameter calibration is typically achieved through data fitting and optimization algorithms. These algorithms allow for the optimization of parameters in the photoresist model based on experimental data, ensuring that the model's predictions are as consistent as possible with the actual experimental results.

[0008] Photoresist model parameter calibration is a complex and crucial technical task, significantly impacting the accuracy and efficiency of photolithography processes. As photolithography technology continues to evolve, photoresist model parameter calibration techniques also require ongoing innovation and improvement. Summary of the Invention

[0009] Parameters in the photoresist model (such as the light absorption coefficient and development rate constant) need to be calibrated using experimental data to ensure the model's accuracy. The accuracy of these parameter calibrations directly affects the reliability of the model's predictions, thus impacting the optimization of the photolithography process. Parameter calibration is typically achieved through experimental measurements, data fitting, and optimization algorithms. The technical challenges that need to be addressed during calibration involve multiple aspects, including model accuracy, experimental data acquisition, optimization algorithm selection, and computational efficiency. Different optimization algorithms vary in efficiency and accuracy, necessitating the selection and implementation of appropriate algorithms.

[0010] During the calibration process, it is necessary to continuously iterate and compare experimental data (data obtained from real exposure experiments) and simulation data (data obtained from simulations under corresponding conditions based on preset photoresist model parameters). From the perspective of solving equations, it is entirely possible to solve the equations of the photoresist model and calculate the direction of gradient descent of the model function to solve the system of equations. However, the computation of the photoresist model is lengthy, and the differentiation of the function for the imaging process requires a lot of time. This is because imaging is a three-dimensional image, and the post-baking after photolithography exposure includes a point spread function, making it difficult to differentiate the function for the imaging process. In contrast, forward calculation of the PEB latent image takes much less time, so optimization in this case is suitable for derivative-free optimization algorithms. In this case, facing multiple parameters of the photoresist model, the downhill simplex algorithm (referring to the Nelder-Mead downhill simplex method) is an algorithm for finding local minima of multivariate functions, an iterative algorithm for solving nonlinear optimization problems, and is particularly suitable for optimization problems where derivative calculation is difficult. The inventors found through experimental research that this is very useful in the calibration of complex photoresist model parameters, because these models are often nonlinear and it is not easy to obtain analytical derivatives. Applying it to photoresist model parameter calibration can achieve rapid calibration with relatively little computation. The downhill simplex algorithm can achieve rapid convergence by minimizing the error between simulation and experimental results.

[0011] The present invention is proposed in view of the above situation, and its purpose is to provide a photoresist model parameter correction method and a photoresist model parameter correction system, which can achieve fast correction with less computation and improve the accuracy of the photoresist model for predicting non-optimized patterns.

[0012] Technical solutions to solve technical problems

[0013] To address the aforementioned problems, the photoresist model parameter correction method according to the first aspect of the present invention includes the following steps:

[0014] Step (1): Perform a graphical confirmation of the experimental layout of the photoresist to select the photoresist model and photoresist model parameters corresponding to the experimental layout;

[0015] Step (2) Collect SEM data of the photoresist and obtain experimental value e related to the size of the photoresist pattern based on the SEM data;

[0016] Step (3): Select the initial values ​​of the photoresist model parameters. Based on the selected initial values ​​of the photoresist model parameters, set the initial photoresist model parameter group x1 as the initial point of the optimization algorithm. Each element in the initial photoresist model parameter group x1 is the initial value of the corresponding photoresist model parameter. Generate multiple photoresist model parameter groups based on the initial photoresist model parameter x1. Optimize the multiple photoresist model parameter groups using the Nelder-Mead method based on the multiple photoresist model parameter groups and the experimental value e.

[0017] Step (4) Replace the photoresist model parameter group in the photoresist model with the photoresist model parameter group that has the smallest difference between the simulation result value and the experimental value e, and use the photoresist model with the replaced photoresist model parameter group to simulate the photoresist.

[0018] Furthermore, in step (3),

[0019] Set the parameter group of the photoresist model that needs to be optimized to x.

[0020] The simulation results of the photoresist model are set as the simulation function f(x).

[0021] The difference between the simulated value of f(x) and the experimental value e is set as the evaluation function p(f(x),e).

[0022] The evaluation function values ​​of each photoresist model parameter set are obtained by substituting them into the evaluation function p(f(x),e).

[0023] Based on multiple photoresist model parameter sets, experimental value e, and evaluation function values ​​of each photoresist model parameter set, the Nelder-Mead method is used to perform expansion or contraction operations on the multiple photoresist model parameter sets to optimize them.

[0024] Furthermore, the photoresist model parameters include the light absorption coefficient and the development rate.

[0025] Furthermore, the termination condition of the optimization algorithm loop is that the number of iterations reaches the set predetermined number.

[0026] Furthermore, the termination condition of the optimization algorithm loop is that the difference between the photoresist model parameters obtained through optimization in this iteration and the photoresist model parameters obtained through optimization in the previous iteration is less than 0.001.

[0027] Furthermore, the photoresist model parameter group x2, x3...x n+1 It consists of multiple variables generated using a random function based on x1 varying within a 5% range.

[0028] Furthermore, the evaluation function p(f(x),e) is the root mean square error of the simulation function f(x) and the experimental value e.

[0029] Furthermore, the range of the reflection coefficient is α greater than or equal to 1.

[0030] Furthermore, the shrinkage coefficient ranges from ρ to 0 and less than or equal to 0.5.

[0031] Furthermore, the range of the expansion coefficient is γ greater than 1 and less than or equal to 10.

[0032] The photoresist model parameter correction system according to the second aspect of the present invention includes the following modules:

[0033] Experimental layout confirmation module, which performs graphic confirmation of the experimental layout of photoresist;

[0034] The SEM data collection module collects SEM data of the photoresist and obtains experimental values ​​related to the size of the photoresist pattern based on the SEM data.

[0035] The photoresist model parameter optimization module selects initial values ​​for the photoresist model parameters. Based on these initial values, it sets an initial photoresist model parameter set x1 as the initial point for the optimization algorithm. This initial photoresist model parameter set x1 is a multi-dimensional vector, where each element represents the initial value of the corresponding photoresist model parameter. Multiple photoresist model parameter sets are generated based on the initial photoresist model parameter x1. Using these multiple photoresist model parameter sets and the experimental value e, the Nelder-Mead method is used to optimize the multiple photoresist model parameter sets, thereby reducing the difference between the simulation result value and the experimental value e of the optimized photoresist model parameter sets.

[0036] The photoresist model parameter verification module replaces the photoresist model parameter set in the photoresist model with the photoresist model parameter set whose difference between the simulation result value and the experimental value e is the smallest.

[0037] The photoresist was simulated by correcting the photoresist model parameter set.

[0038] Invention Effects

[0039] The photoresist model parameter correction method and system of the present invention have the advantages of achieving rapid correction with less computation in photoresist model parameter correction, and improving the accuracy of the prediction results of the photoresist model for non-optimized patterns. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating an example of a photoresist model parameter correction method according to an embodiment of the present invention.

[0041] Figure 2a This is a flowchart illustrating the optimization of photoresist model parameters according to an embodiment of the present invention.

[0042] Figure 2b This is a flowchart illustrating the optimization of photoresist model parameters according to an embodiment of the present invention.

[0043] Figure 3a This is a graph showing the error between the simulation results and experimental results before parameter correction of the photoresist model when the linewidth / spacing ratio is 1:1.

[0044] Figure 3b This is a graph showing the error between the simulation results and experimental results before parameter correction of the photoresist model when the linewidth / spacing ratio is 1:2.

[0045] Figure 3c This is a graph showing the error between the simulation results and experimental results before parameter correction of the photoresist model when the linewidth / spacing ratio is 1:3.

[0046] Figure 3d This is a graph showing the error between the simulation results and experimental results before parameter correction of the photoresist model when the linewidth / spacing ratio is 1:5.

[0047] Figure 3e This is a graph showing the error between the simulation results and experimental results before parameter correction of the photoresist model when the linewidth / spacing ratio is 1:10.

[0048] Figure 4a This is a graph showing the error between the simulation results and experimental results after parameter correction of the photoresist model when the linewidth / spacing ratio is 1:1.

[0049] Figure 4b This is a graph showing the error between the simulation results and experimental results after parameter correction of the photoresist model when the linewidth / spacing ratio is 1:2.

[0050] Figure 4c This is a graph showing the error between the simulation results and experimental results after parameter correction of the photoresist model when the linewidth / spacing ratio is 1:3.

[0051] Figure 4d This is a graph showing the error between the simulation results and experimental results after parameter correction of the photoresist model when the linewidth / spacing ratio is 1:5.

[0052] Figure 4eThis is a graph showing the error between the simulation results and experimental results after parameter correction of the photoresist model when the linewidth / spacing ratio is 1:10.

[0053] Figure 5 This is a structural block diagram illustrating the photoresist model parameter correction system according to an embodiment of the present invention.

[0054] Label Explanation

[0055] 100 Photoresist Model Parameter Correction System

[0056] 1001 Experimental Layout Confirmation Module

[0057] 1002SEM Data Collection Module

[0058] 1003 Photoresist Model Parameter Optimization Module

[0059] 1004 photoresist model parameter confirmation module Detailed Implementation

[0060] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are implemented based on the technical solution of the present invention, providing detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0061] For ease of description, spatial relative terms such as “below,” “under,” “down,” “above,” “up,” etc., may be used herein to describe the relationship of one element or feature relative to another element or feature as shown in the figure. It should be understood that spatial relative terms are intended to include different orientations of the device used or operated in addition to those shown in the figure. For example, if the device in the figure were flipped, an element described as “below” or “under” other elements or features would be oriented as “above” other elements or features.

[0062] Unless otherwise specified, the terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. Terms should be understood to have the meaning consistent with their meaning in the context of the relevant art and should not be interpreted in an idealized or overly formalized manner, unless explicitly stated otherwise herein.

[0063] <Photoresist Model Parameter Correction Method>

[0064] An example of the photoresist model parameter correction method according to the embodiments of the present invention includes the following steps:

[0065] Step (1): Perform a graphical confirmation of the experimental layout of the photoresist to select the photoresist model and photoresist model parameters corresponding to the experimental layout;

[0066] Step (2) Collect SEM data of the photoresist and obtain experimental value e related to the size of the photoresist pattern based on the SEM data;

[0067] Step (3): Select the initial values ​​of the photoresist model parameters. Based on the selected initial values ​​of the photoresist model parameters, set the initial photoresist model parameter group x1 as the initial point of the optimization algorithm. Each element in the initial photoresist model parameter group x1 is the initial value of the corresponding photoresist model parameter. Generate multiple photoresist model parameter groups based on the initial photoresist model parameter x1. Optimize the multiple photoresist model parameter groups using the Nelder-Mead method based on the multiple photoresist model parameter groups and the experimental value e.

[0068] Step (4) Replace the photoresist model parameter group in the photoresist model with the photoresist model parameter group that has the smallest difference between the simulation result value and the experimental value e, and use the photoresist model with the replaced photoresist model parameter group to simulate the photoresist.

[0069] Figure 1 Figure 1 is a flowchart illustrating an example of a photoresist model parameter correction method according to an embodiment of the present invention. Figure 2 is a flowchart illustrating photoresist model parameter optimization according to an embodiment of the present invention.

[0070] Below, refer to Figure 1 The flowchart of an example of a photoresist model parameter correction method according to an embodiment of the present invention will be described in detail.

[0071] like Figure 1 As shown, firstly, in step S01, the experimental layout of the photoresist is graphically verified to select the photoresist model and photoresist model parameters corresponding to the experimental layout. Graphical verification of the experimental layout of the photoresist during photolithography is a crucial step to ensure the correctness of the design. This typically includes the following graphical verification contents: Design Rule Check (DRC): ensuring the layout conforms to the design rules of the manufacturing process. This includes checking whether linewidth, spacing, and layers meet the requirements; Layout vs. Schematic Comparison (LVS): verifying the consistency between the layout and the circuit schematic, ensuring that the physical design matches the logic design; Electrical Rule Check (ERC): checking electrical characteristics, such as current density and power distribution, to ensure that the circuit can function normally in physical implementation; Optical Proximity Correction (OPC): adjusting the layout to compensate for optical proximity effects that may occur during photolithography, ensuring that the actual manufactured pattern is consistent with the design, etc.

[0072] The layout graphics involved in this invention generally adopt a periodically repeating one-dimensional graphic with full pitch. The period generally includes dense, semi-dense, and iso graphics.

[0073] Next, in step S02, SEM data of the photoresist is collected using methods such as microscopic observation, scanning electron microscopy (SEM) imaging, and atomic force microscopy (AFM) to obtain experimental values ​​e related to the photoresist. When obtaining SEM data through experimental pattern fabrication experiments, FEM (Focus Exposure Matrix) data is generally acquired. During the photolithography process, the collection of scanning electron microscopy (SEM) data is a crucial step for analyzing and optimizing the photolithography process. SEM data collection can include the following steps: 1. Sample preparation: Photolithography is performed before SEM analysis; 2. SEM setup: SEM parameters, such as accelerating voltage, working distance, and detector type, are set according to the characteristics of the photolithography and the analysis requirements; 3. Image acquisition: The photoresist is scanned using the SEM to acquire high-resolution images; 4. Data analysis: Dimensional measurement: Key dimensions (CD), such as linewidth and spacing, are measured using image analysis software; 5. Defect detection: Defects in the pattern are identified and classified, such as broken lines, short circuits, and particulate contamination. 6. Morphology analysis: Observe the three-dimensional morphology of the pattern and evaluate the quality of the photolithography process.

[0074] Next, in step S03, initial values ​​for the photoresist model parameters are selected. Based on the selected initial values ​​for the photoresist model parameters, an initial photoresist model parameter group x1 is set as the initial point for the optimization algorithm. This initial photoresist model parameter group x1 is a multi-dimensional vector, where each element is the initial value of the corresponding photoresist model parameter. Multiple photoresist model parameter groups are generated based on the initial photoresist model parameter x1. Based on the multiple photoresist model parameter groups and the experimental value e, the multiple photoresist model parameter groups are optimized using the Nelder-Mead method to reduce the difference between the simulation result value of the optimized photoresist model parameter group and the experimental value e.

[0075] In step S04, the photoresist model parameter set in the photoresist model is replaced with the photoresist model parameter set whose difference between the simulation result value and the experimental value e is the smallest.

[0076] The photoresist was simulated by correcting the photoresist model parameter set.

[0077] Next, step S03 will be described in detail. The following description is merely an example to illustrate the technical solution of the present invention more clearly, and the scope of protection of the present invention is not limited thereto.

[0078] like Figure 2a As shown, the optimization algorithm iteratively includes the following steps:

[0079] In step S10, firstly, the parameter group of the photoresist model to be optimized is set to x.

[0080] The simulation results of the photoresist model are set as the simulation function f(x).

[0081] After substituting the photoresist model parameter set x into the simulation function f(x), the calculated photoresist simulation result is denoted as s.

[0082] Let the evaluation function for each iteration in the optimization algorithm loop be p(f(x),e), i.e. p(s,e). The evaluation function p(f(x),e), i.e. p(s,e) is the difference between the value of the simulation function f(x) and the experimental value e obtained from the SEM data. Here, the evaluation function p(s,e) can be the root mean square error (RMSE) of the simulation result s and the experimental value e.

[0083] Based on the initial values ​​of the selected N photoresist model parameters, an initial photoresist model parameter set x1 is set as the initial point for the optimization algorithm. This initial photoresist model parameter set x1 is an N-dimensional vector, where each element is the initial value of the corresponding photoresist model parameter, for example, x1 = [parameter 1, parameter 2, parameter 3, ..., parameter N]. Multiple variables are generated based on the photoresist model parameter set x1. Specifically, n photoresist model parameter sets are generated using a random function, varying within, for example, a 5% range: x2, x3, x4...x n+1 .

[0084] In step S11, the photoresist model parameter sets x1, x2, x3...x1 are used as initial points in the (n+1)th set. n+1 Initialization is performed. Specifically, the n+1 photoresist model parameters x1, x2, x3...x n+1 Substitute each value into the evaluation function p(f(x),e) to find x1, x2, x3, ..., x. n+1 Each has its own evaluation function value, and then based on the photoresist model parameter set x1, x2, x3...x n+1 The evaluation function values ​​for each of the n+1 photoresist model parameter sets x1, x2, x3...x n+1 Sort the parameters of the photoresist model from smallest to largest to obtain the sorted parameter sets x1′, x2′, x3′, ..., x n+1 ′.

[0085] In step S12, the first n photoresist model parameter sets x1′, x2′, x3′...x are calculated. n The "centroid" of ′ is the average value of the first n photoresist model parameter sets.

[0086] In step S13, the photoresist model parameter set x is calculated using the following formula. n+1 The reflection point x' r ,

[0087] x r =x0+α(x0-x n+1 ′), where α is the reflection coefficient and α=1.

[0088] In step S14, determine p(f(x) r Are p(f(x1') and e) less than p(f(x1') and e)? If p(f(x1') and e) are less than p(f(x1') and e), then p(f(x1') and e) are less than p(f(x1') and e). r If p(f(x1′), e) is less than p(f(x1′), e), then proceed to step S15; otherwise proceed to step S19.

[0089] In step S15, the expansion operation is performed as follows:

[0090] x e =x0+γ(x r -x0), γ=2 is the expansion coefficient, calculate p(f(x) e ), e), and proceed to step S16.

[0091] In step S16, determine p(f(x) e Is e) less than p(f(x)? r If p(f(x)), e), e e) is less than p(f(x) r If the condition is met, proceed to step S17; otherwise, proceed to step S18.

[0092] In step S17, x e Replace x n+1 ′, and proceed to step S30.

[0093] In step S18, x r Replace x n+1 ′, and proceed to step S30.

[0094] In step S19, determine whether p(f(x1′),e) < p(f(x1′),e) r ),e)<p(f(x n If p(f(x1'),e) < p(f(x'),e), r ),e)<p(f(x n If the condition is true, proceed to step S18; otherwise, proceed to step S20.

[0095] In step S20, it is determined whether p(f(x) is satisfied. n ′),e)<p(f(x r),e)<p(f(x n+1 If p(f(x)),e), then p(f(x)) n ′),e)<p(f(x r ),e)<p(f(x n+1 If the condition is true, proceed to step S21; otherwise, proceed to step S22.

[0096] In step S21, the contraction operation is performed as follows: x c =x0+ρ(x r -x0), ρ=0.5, where ρ is the contraction coefficient, proceed to step S23.

[0097] In step S23, determine whether p(f(x) is satisfied. c ), e) <p(f(x r If p(f(x)) = e), then p(f(x) = e ... c ), e) <p(f(x r If p(f(x) is not satisfied, proceed to step S25. c ), e) <p(f(x r If ), then proceed to step 18.

[0098] In step S25, x c Replace x n+1 ′, and proceed to step S30.

[0099] Step S22, determine whether p(f(x) is satisfied. r ), e)>p(f(x) n+1 If p(f(x)) and e) satisfy p(f(x) r ), e)>p(f(x) n+1 If p(f(x) = '), then proceed to step S24. If p(f(x) is not satisfied... r ), e)>p(f(x) n+1 If ′), e), then proceed to step 30.

[0100] Step S24, perform the contraction operation as follows: x c =x0+ρ(x n+1 Let f(x'-x0), ρ be the contraction coefficient and ρ = 0.5, and calculate p(f(x'-x0). c ), e), proceed to step S26.

[0101] Step S26, determine whether p(f(x) is satisfied. c ), e) <p(f(x n+1 If p(f(x)) and e) satisfy p(f(x) c ), e) <p(f(x n+1If p(f(x) = '), then proceed to step S25. If p(f(x) is not satisfied... c ), e) <p(f(x n+1 If ′), e), then proceed to step 30.

[0102] like Figure 2b As shown, in step S30, the x obtained in this iteration is determined. n+1 'x obtained from the previous loop' n+1 Is the difference less than 0.001? If x in this loop... n+1 'x from the previous loop' n+1 If the difference is less than 0.001, the optimization algorithm loop ends; otherwise, proceed to step S31.

[0103] For example, suppose:

[0104] The variable x from the previous optimization a = {light absorption coefficient 1a, light absorption coefficient 2a, light absorption coefficient 3a, development rate constant 4a, development rate constant 5a, development rate constant 6a, development rate constant 7a,}

[0105] The variable x to be optimized b = {light absorption coefficient 1b, light absorption coefficient 2b, light absorption coefficient 3b, development rate constant 4b, development rate constant 5b, development rate constant 6b, development rate constant 7b,}

[0106]

[0107] In step S31, it is determined whether the number of iterations has reached a specified value, such as 200. If the number of iterations has reached the specified value, the optimization algorithm loop ends; otherwise, proceed to step S11.

[0108] Finally, replace the photoresist model parameters in the photoresist model with the photoresist model parameters obtained after optimization through the above steps.

[0109] In the aforementioned optimization algorithm loop, the reflection coefficient α does not need to be 1; any value greater than 0 is acceptable. Preferably, the reflection coefficient α is greater than or equal to 1. This allows for rapid correction with less computation and improves the accuracy of the photoresist model's predictions for non-optimized patterns.

[0110] In the above optimization algorithm loop, the expansion coefficient γ does not have to be 2; any value greater than 1 is acceptable. The preferred range for the expansion coefficient γ is 1 < γ ≤ 10. This allows for rapid correction with less computation and improves the accuracy of the photoresist model's predictions for non-optimized patterns.

[0111] In the aforementioned optimization algorithm loop, the shrinkage coefficient ρ does not have to be 0.5; ρ only needs to be a value greater than 0 and less than 1. The preferred range for the shrinkage coefficient is 0 < ρ ≤ 0.5. This allows for rapid correction with less computation and improves the accuracy of the photoresist model's prediction results for non-optimized patterns.

[0112] In the above optimization algorithm loop, the photoresist model parameters may include the light absorption coefficient and the development rate.

[0113] In the above optimization algorithm loop, the termination condition of the algorithm loop can be either the number of iterations reaching the set specified number or the difference between the photoresist model parameters obtained by optimization this time and the photoresist model parameters obtained by optimization in the previous time being less than 0.001.

[0114] In the above optimization algorithm loop, the photoresist model parameter set x2, x3...x n+1 It is a set of multiple variables generated by using a random function based on the variation of x1 within a 5% range, but it is not limited to this. Multiple variables can also be generated by using a random function based on the variation of x1 within other ranges (e.g., 1%, 2%, 3%, 4%, 6%, ..., 10%).

[0115] In the above optimization algorithm loop, the evaluation function p(s,e) is the root mean square error of the simulation result s and the experimental value e. However, it is not limited to this. The evaluation function p(s,e) can also be the root mean square error of the simulation result s and the experimental value e.

[0116] After obtaining the optimized photoresist model parameters, the photoresist model will have a more accurate prediction effect on non-optimized patterns. The above optimization algorithm is easy to implement, applicable to various optimization problems, and can enable the photoresist model parameters to converge quickly with appropriate initial values.

[0117] Figure 3a This is a graph showing the error between the simulation results and experimental results before parameter correction of the photoresist model when the linewidth / spacing ratio is 1:1. Figure 3b This is a graph showing the error between the simulation results and experimental results before parameter correction of the photoresist model when the linewidth / spacing ratio is 1:2. Figure 3c This is a graph showing the error between the simulation results and experimental results before parameter correction of the photoresist model when the linewidth / spacing ratio is 1:3. Figure 3d This is a graph showing the error between the simulation results and experimental results before parameter correction of the photoresist model when the linewidth / spacing ratio is 1:5. Figure 3e This is a graph showing the error between the simulation results and experimental results before parameter correction of the photoresist model when the linewidth / spacing ratio is 1:10. Figure 4aThis is a graph showing the error between the simulation results and experimental results after parameter correction of the photoresist model when the linewidth / spacing ratio is 1:1. Figure 4b This is a graph showing the error between the simulation results and experimental results after parameter correction of the photoresist model when the linewidth / spacing ratio is 1:2. Figure 4c This is a graph showing the error between the simulation results and experimental results after parameter correction of the photoresist model when the linewidth / spacing ratio is 1:3. Figure 4d This is a graph showing the error between the simulation results and experimental results after parameter correction of the photoresist model when the linewidth / spacing ratio is 1:5. Figure 4e This is a graph showing the error between the simulation results and experimental results after parameter correction of the photoresist model when the linewidth / spacing ratio is 1:10.

[0118] Figure 3a , 3b In the diagrams 3c, 3d, 3e, 4a, 4b, 4c, 4d, and 4e, the horizontal axis represents the focusing distance (in μm), and the vertical axis represents the photoresist linewidth (in nm). Figure 3a , 3b The solid colored lines in 3c, 3d, 3e, 4a, 4b, 4c, 4d, and 4e represent different exposure doses (e.g., exposure doses of 28 mJ / cm²). 2 29mJ / cm 2 30mJ / cm 2 31mJ / cm 2 32mJ / cm 2 33mJ / cm 2 34mJ / cm 2 35mJ / cm 2 36mJ / cm 2 The photoresist linewidth values ​​obtained by simulation using a photoresist model when the focusing distances are combined with the focusing distances of -0.2μm, -0.15μm, -0.1μm, -0.05μm, 0μm, 0.05μm, 0.1μm, and 0.15μm respectively.

[0119] The different colored graphic markers represent the FEM (Focus Exposure Matrix) data obtained in the experimental layout tape-out experiment by scanning electron microscopy (SEM) imaging under different combinations of exposure dose and focusing distance, which are the actual measured values ​​of photoresist linewidth.

[0120] The specific error details are shown in the table below. It can be seen that by correcting the photoresist model parameters in this embodiment, the root mean square error, average error, and maximum error of the simulated and experimental values ​​can be significantly reduced compared to before the photoresist model parameters were corrected.

[0121]

[0122] In the table above, pattern 1 represents a photoresist pattern with a line width / spacing ratio of 1:1, pattern 2 represents a photoresist pattern with a line width / spacing ratio of 1:2, pattern 3 represents a photoresist pattern with a line width / spacing ratio of 1:3, pattern 4 represents a photoresist pattern with a line width / spacing ratio of 1:5, and pattern 5 represents a photoresist pattern with a line width / spacing ratio of 1:10.

[0123] As shown in the table above, by correcting and optimizing the photoresist model parameters, compared with the photoresist model before correction, the corrected photoresist model can significantly reduce the error between the size of the simulated photoresist pattern and the size of the actually measured photoresist pattern, greatly improving the accuracy of the simulation results. Furthermore, the photoresist model parameter correction can achieve rapid correction with less computation.

[0124] <System for Photoresist Model Parameter Correction>

[0125] Figure 5 This is a structural block diagram illustrating a photoresist model parameter correction system according to an embodiment of the present invention. Figure 5 As shown, the photoresist model parameter correction system 100 according to the embodiments of the present invention includes the following modules:

[0126] Experimental layout verification module 1001 for graphically verifying the experimental layout of photoresist;

[0127] SEM data collection module 1002 for collecting SEM data of photoresist;

[0128] The photoresist model parameter optimization module 1003 selects initial values ​​for the photoresist model parameters. Based on the selected initial values, it sets an initial photoresist model parameter group x1 as the initial point for the optimization algorithm. This initial photoresist model parameter group x1 is a multi-dimensional vector, where each element is the initial value of the corresponding photoresist model parameter. Multiple photoresist model parameter groups are generated based on the initial photoresist model parameter x1. Based on the multiple photoresist model parameter groups and the experimental value e, the Nelder-Mead method is used to optimize the multiple photoresist model parameter groups so that the difference between the simulation result value of the optimized photoresist model parameter group and the experimental value e is reduced.

[0129] The photoresist model parameter confirmation module 1004 replaces the photoresist model parameter set in the photoresist model with the photoresist model parameter set whose difference between the simulation result value and the experimental value e is the smallest.

[0130] The photoresist model involved in this invention can be used as an algorithm model for all photoresist models, such as positive photoresist and negative photoresist.

[0131] The photoresist models involved in this invention may include light absorption models, development models, chemical reaction models, diffusion models, etc.

[0132] It should be understood that the above description is illustrative and not restrictive. For example, the above embodiments (and / or aspects thereof) can be used in combination with each other. Furthermore, many modifications can be made to adapt particular conditions or materials to the teachings of the various embodiments of the invention without departing from the scope of the invention. While the dimensions and types of materials described herein are used to define parameters of the various embodiments of the invention, the embodiments are not intended to be restrictive but are exemplary. Many other embodiments will become apparent to those skilled in the art upon reading the above description. Therefore, the scope of the various embodiments of the invention should be determined by reference to the appended claims and the full scope of their equivalents.

[0133] Industrial practicality

[0134] The photoresist model parameter correction method and system of the present invention can be applied to photoresist models in the field of photolithography.

Claims

1. A photoresist model parameter correction method, characterized by, Includes the following steps: Step (1): Perform a graphical confirmation of the experimental layout of the photoresist to select the photoresist model and photoresist model parameters corresponding to the experimental layout; Step (2) Collect SEM data of the photoresist and obtain experimental value e related to the size of the photoresist pattern based on the SEM data; Step (3): Select the initial values ​​of the photoresist model parameters. Based on the selected initial values ​​of the photoresist model parameters, set the initial photoresist model parameter group x1 as the initial point of the optimization algorithm. Each element in the initial photoresist model parameter group x1 is the initial value of the corresponding photoresist model parameter. Generate multiple photoresist model parameter groups based on the initial photoresist model parameter x1. Optimize the multiple photoresist model parameter groups using the Nelder-Mead method based on the multiple photoresist model parameter groups and the experimental value e. Step (4) Replace the photoresist model parameter group in the photoresist model with the photoresist model parameter group that has the smallest difference between the simulation result value and the experimental value e, and use the photoresist model with the replaced photoresist model parameter group to simulate the photoresist.

2. The photoresist model parameter correction method according to claim 1, characterized in that, In step (3), Set the parameter group of the photoresist model that needs to be optimized to x. The simulation results of the photoresist model are set as the simulation function f(x). The difference between the simulated value of f(x) and the experimental value e is set as the evaluation function p(f(x),e). The evaluation function values ​​of each photoresist model parameter set are obtained by substituting them into the evaluation function p(f(x),e). Based on multiple photoresist model parameter sets, experimental value e, and evaluation function values ​​of each photoresist model parameter set, the Nelder-Mead method is used to perform expansion or contraction operations on the multiple photoresist model parameter sets to optimize them.

3. The photoresist model parameter correction method according to claim 2, characterized in that, The parameters of the photoresist model include the light absorption coefficient and the development rate.

4. The photoresist model parameter correction method according to claim 2, characterized in that, The termination condition for the optimization algorithm loop is that the number of iterations reaches the set predetermined number.

5. The photoresist model parameter correction method according to claim 2, characterized in that, The termination condition of the optimization algorithm loop is that the difference between the photoresist model parameters obtained through optimization in this iteration and the photoresist model parameters obtained through optimization in the previous iteration is less than 0.

001.

6. The photoresist model parameter correction method according to claim 2, characterized in that, Photoresist model parameter set x2, x3...x n+1 are a plurality of variables generated using a random function to vary within a 5% range from x1.

7. The photoresist model parameter correction method according to claim 2, characterized in that, The evaluation function p(f(x),e) is the root mean square error of the simulation function f(x) and the experimental value e.

8. The photoresist model parameter correction method according to claim 2, characterized in that, The range of values ​​for the reflection coefficient is α greater than or equal to 1.

9. The photoresist model parameter correction method according to claim 2, characterized in that, The shrinkage coefficient ranges from ρ to 0.

5.

10. The photoresist model parameter correction method according to claim 2, characterized in that, The range of the expansion coefficient is γ greater than 1 and less than or equal to 10.

11. A photoresist model parameter correction system, characterized by, Includes the following modules: Experimental layout confirmation module, which performs graphic confirmation of the experimental layout of photoresist; The SEM data collection module collects SEM data of the photoresist and obtains experimental values ​​related to the size of the photoresist pattern based on the SEM data. The photoresist model parameter optimization module selects initial values ​​for the photoresist model parameters. Based on these initial values, it sets an initial photoresist model parameter set x1 as the initial point for the optimization algorithm. This initial photoresist model parameter set x1 is a multi-dimensional vector, where each element represents the initial value of the corresponding photoresist model parameter. Multiple photoresist model parameter sets are generated based on the initial photoresist model parameter x1. Using these multiple photoresist model parameter sets and the experimental value e, the Nelder-Mead method is used to optimize the multiple photoresist model parameter sets, thereby reducing the difference between the simulation result value and the experimental value e of the optimized photoresist model parameter sets. The photoresist model parameter verification module replaces the photoresist model parameter set in the photoresist model with the photoresist model parameter set whose difference between the simulation result value and the experimental value e is the smallest. The photoresist was simulated by correcting the photoresist model parameter set.

Images