Photolithography post-bake simulation method, parameter calibration method, adjustment method, device, medium and product

Abstract

The application provides a photoresist post-baking simulation method, a parameter calibration method, an adjustment method, equipment, a medium and a product. The three-dimensional light intensity distribution in the photoresist is obtained, the initial concentration distribution of the substance in the photoresist after exposure is calculated based on the three-dimensional light intensity distribution, and the initial concentration distribution is processed by using an implicit-explicit hybrid algorithm to obtain the concentration of the developing inhibitor in the photoresist. Therefore, the diffusion term and the reaction term are separated and processed by using the implicit-explicit hybrid algorithm, the overall calculation efficiency is improved while ensuring the diffusion calculation precision, and the photoresist post-baking simulation is more efficient and accurate.

Description

Technical Field

[0001] This application relates to the technical field of photolithography process simulation, and in particular to a post-baking simulation method, parameter calibration method, adjustment method, equipment, medium and product for photoresist. Background Technology

[0002] In semiconductor manufacturing processes, the photolithography process includes key steps: exposure, post-baking, and development. During this process, post-baking not only eliminates the standing wave effect in the photoresist but also drives the deprotection of the development inhibitor through an acid-catalyzed reaction, directly affecting the precision and uniformity of the final photoresist pattern.

[0003] Photolithography simulation can verify whether the designed pattern can be correctly copied into the photoresist. However, since the post-baking process involves complex reaction diffusion physics mechanisms, its simulation calculations need to simultaneously handle the three-dimensional diffusion and chemical reaction kinetics of acid and alkali substances. This significantly increases the computational complexity and time cost, resulting in significant contradictions in efficiency, accuracy, and parameter adaptability of the post-baking simulation methods for photoresist provided by existing technologies. These methods are unable to meet the dual requirements of advanced photolithography processes for efficient three-dimensional simulation and accurate parameter optimization.

[0004] Therefore, how to perform post-baking simulation of photoresist more efficiently and accurately is a technical problem that needs to be solved in this field. Summary of the Invention

[0005] This application provides a method for post-baking simulation of photoresist, a parameter calibration method, an adjustment method, equipment, media, and products. It optimizes the calculation of post-baking simulation through an implicit-explicit hybrid algorithm, thereby performing post-baking simulation of photoresist more efficiently and accurately.

[0006] The first aspect of this application provides a post-baking simulation method for photoresist, comprising: acquiring a three-dimensional light intensity distribution in the photoresist; calculating an initial concentration distribution of the material in the photoresist after exposure based on the three-dimensional light intensity distribution; processing the initial concentration distribution using an implicit-explicit hybrid algorithm to obtain the concentration of the developer inhibitor in the photoresist; wherein the implicit-explicit hybrid algorithm comprises: solving the diffusion term using an implicit method and solving the reaction term using an explicit method.

[0007] A second aspect of this application provides a method for calibrating the parameters of a photoresist, comprising: determining the three-dimensional morphology data of the photoresist according to the method described in the first aspect; performing error analysis on the three-dimensional morphology data and actual experimental results to obtain an error function; and optimizing the parameters of the photoresist in reverse using the error function.

[0008] A third aspect of this application provides a method for adjusting the parameters of a photoresist, comprising: determining the three-dimensional morphology data of the photoresist according to the method described in the first aspect; and adjusting the photolithography simulation parameters until the three-dimensional morphology data of the photoresist after development meets preset conditions.

[0009] A fourth aspect of this application provides an electronic device, comprising: a processor and a memory communicatively connected to the processor; the memory storing computer-executable instructions; and the processor executing the computer-executable instructions stored in the memory to implement the methods described in the first, second, or third aspects.

[0010] The fifth aspect of this application provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the methods described in the first, second, or third aspects.

[0011] The sixth aspect of this application provides a computer program product, including a computer program that, when executed by a processor, implements the methods described in the first, second, or third aspects.

[0012] In summary, the photoresist post-baking simulation method, parameter calibration method, adjustment method, equipment, medium, and product provided in this application obtain the three-dimensional light intensity distribution in the photoresist, calculate the initial concentration distribution of the material in the photoresist after exposure based on the three-dimensional light intensity distribution, and process the initial concentration distribution using an implicit-explicit hybrid algorithm to obtain the concentration of the developer inhibitor in the photoresist. By separating and processing the diffusion and reaction terms through the implicit-explicit hybrid algorithm, it overcomes the technical problems of slow calculation speed due to limitations imposed by CFL conditions and high complexity caused by the need to solve nonlinear equations in implicit methods. It can significantly improve the overall computational efficiency while ensuring the accuracy of diffusion calculations, and is particularly suitable for complex reaction-diffusion processes in chemically amplified photoresists. Furthermore, by separating and processing the diffusion and reaction terms, combining the advantages of implicit and explicit methods, and accelerating diffusion calculations through the Crank-Nicolson implicit algorithm and FFT, it significantly improves the numerical stability and computational efficiency of three-dimensional diffusion. Additionally, the forward Euler explicit algorithm directly solves the reaction term, avoiding the complexity of nonlinear equations, thereby significantly shortening the overall computation time while ensuring the accuracy of diffusion calculations. Achieving efficient and high-precision PEB simulation provides key support for the digital development of advanced node lithography processes. Attached Figure Description

[0013] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. The drawings included herein are incorporated in and constitute a part of this specification, illustrating embodiments consistent with this application, and are used together with the description to explain the principles of this application.

[0014] Figure 1 A schematic flowchart of an embodiment of the photoresist post-baking simulation method provided in this application;

[0015] Figure 2 A cross-sectional schematic diagram of the light field distribution in the photoresist provided in this application;

[0016] Figure 3 This is a schematic diagram of the initial distribution of acid concentration in the photoresist provided in this application;

[0017] Figure 4 A schematic diagram showing the distribution of developer inhibitors in the photoresist provided in this application;

[0018] Figure 5 A schematic diagram of the morphology of the photoresist after development provided in this application;

[0019] Figure 6 A flowchart of an embodiment of the photoresist post-baking simulation method provided in this application;

[0020] Figure 7 An iterative schematic diagram illustrating the post-baking simulation of the implicit-explicit hybrid algorithm provided in this application;

[0021] Figure 8 A schematic flowchart of an embodiment of the calibration method for simulation parameters of the photoresist provided in this application;

[0022] Figure 9 A schematic diagram of the structure of an embodiment of the electronic device provided in this application.

[0023] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0024] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0025] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a particular order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented, for example, in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0026] This application addresses the technical problem of efficient simulation calculation of chemically amplified photoresist post-baking models in existing photolithography processes by providing an implicit-explicit hybrid algorithm that can efficiently and accurately simulate and analyze the chemically amplified photoresist post-baking process.

[0027] In semiconductor manufacturing processes, photolithography is the core step in achieving nanometer-scale feature sizes for chips, while photolithography simulation can verify whether the designed pattern can be correctly copied onto the photoresist. As Moore's Law continues to advance and chip feature sizes continue to shrink, photoresist materials have gradually upgraded from traditional non-chemically amplified (DNQ) photoresists to chemically amplified (CAR) photoresists to meet the demands for higher resolution and process stability.

[0028] CAR photoresist utilizes a photo-acid catalytic reaction to achieve controlled decomposition of the developer inhibitor. Its process flow includes key steps: exposure, post-exposure bake (PEB), and development. The PEB process not only eliminates the standing wave effect in the photoresist but also drives the deprotection of the developer inhibitor through an acid-catalyzed reaction, directly affecting the accuracy and uniformity of the final photoresist pattern. However, the PEB process involves complex reaction-diffusion physics mechanisms, and its simulation calculations must simultaneously handle the three-dimensional diffusion and chemical reaction kinetics of acid and base substances, significantly increasing computational complexity and time costs.

[0029] Specifically, photolithography simulation mainly consists of two parts: optical simulation and photoresist simulation. Optical simulation describes the illumination characteristics of the light source, including its focusing and imaging in the photoresist after passing through the mask, and the formation of a spatial image. The photoresist simulation model simulates subsequent process steps, such as post-baking PEB and development. CAR photoresist is widely used in modern high-resolution lithography, and its core simulation process is as follows: After exposure simulation, the latent image (photoacid distribution, products of photoinduced reactions) in the photoresist can be calculated using the spatial image. Then, PEB activates the photoacid to catalyze the deprotection of the development inhibitor, making it soluble. PEB simulation calculates the concentration of unreacted development inhibitor after PEB. The subsequent development simulation module simulates the development process and then obtains the photoresist pattern. In this entire process, PEB simulation serves as the intermediate bridge between photolithography simulation and development simulation calculations, and its calculation time is significant.

[0030] One existing photoresist simulation technique is a parameter fitting model, which specifically constructs a mapping relationship between light intensity and photoresist morphology based on experimental data, and quickly generates results by simplifying the physical process (such as Gaussian convolution or thresholding models). This method is computationally efficient, but lacks accurate description of the three-dimensional morphology and cannot reflect the dynamic evolution of the acid catalytic reaction in the PEB process, resulting in a large deviation between the simulation results and the actual process.

[0031] Another existing photoresist simulation technique is the full physical model, which rigorously models the physicochemical processes of photoresist during exposure, baking, and development. For example, while the explicit Euler method can guarantee computational accuracy, it is extremely slow due to the constraints of time and space steps in CFL conditions. Some schemes use 2D approximations or convolution operations to replace three-dimensional diffusion calculations, which improves efficiency but sacrifices the accuracy of the topography in the depth direction.

[0032] Furthermore, existing technologies lack the ability to calibrate parameters for chemically amplified photoresists, making it difficult to infer key reaction rate parameters (such as k1-k5) from experimental data, thus limiting the predictive power of the model.

[0033] In summary, existing technologies exhibit significant contradictions in terms of efficiency, accuracy, and parameter adaptability, making it difficult to meet the dual demands of advanced lithography processes for efficient 3D simulation and precise parameter optimization.

[0034] Therefore, existing simulation methods struggle to balance computational efficiency and 3D topographic accuracy, leading to a reliance on extensive experimental trial and error for process parameter optimization, which significantly prolongs the R&D cycle and increases costs.

[0035] This application proposes an efficient and accurate full physical simulation method for this scenario. It optimizes the PEB process calculation through an implicit-explicit hybrid algorithm (IMES), thereby enabling more efficient and accurate post-baking simulation of photoresist. It also supports the solution of three-dimensional concentration distribution and parameter calibration, providing key support for the digital development of advanced node lithography processes.

[0036] The technical solutions of this application will be described in detail below with specific embodiments. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0037] Figure 1 This is a schematic flowchart of an embodiment of the photoresist post-baking simulation method provided in this application. Specifically, as shown... Figure 1 The post-baking simulation method for the photoresist shown includes:

[0038] S101: Obtain the three-dimensional light intensity distribution in the photoresist.

[0039] Specifically, this embodiment of the application takes positive CAR development as an example to perform simulation analysis and modeling of the chemically amplified photoresist (PEB) process. Firstly, in S101, the 3D light intensity distribution in the photoresist can be obtained using the optical simulation module and denoted as I(x,y,z). Here, the three-dimensional light intensity distribution refers to the light intensity distribution in the photoresist along the X, Y, and Z spatial dimensions. For example, Figure 2 This is a cross-sectional schematic diagram of the light field distribution in the photoresist provided in this application.

[0040] In one embodiment, the algorithm used by the optical simulation module to calculate light intensity can be either the Abbe point source accumulation method or the Hopkins algorithm. The parameters set include the exposure wavelength λ, illumination conditions, mask pattern, etc., to calculate the three-dimensional light intensity distribution.

[0041] S102: Based on the three-dimensional light intensity distribution obtained in S101, calculate the initial concentration distribution of the material in the photoresist after exposure.

[0042] In one embodiment, the initial concentration distribution includes: an initial distribution of acid concentration [A] in the photoresist after exposure, an initial distribution of alkali concentration [B] in the photoresist after exposure, and an initial distribution of developer inhibitor concentration [M] in the photoresist after exposure. For example, Figure 3 This is a schematic diagram of the initial distribution of acid concentration in the photoresist provided in this application.

[0043] In one embodiment, in S102, the initial concentration distribution is calculated based on the three-dimensional light intensity distribution and process parameters. The process parameters of the photoresist refer to the parameters input in the photolithography process, including Dill A / B / C values, refractive index n, and photoresist thickness h, etc. For example, the concentration value can be calculated through the Dill parameter model.

[0044] S103: The initial concentration distribution obtained in S102 is processed using an implicit-explicit hybrid algorithm to obtain the concentration of the developer inhibitor in the photoresist. For example, Figure 4 This is a schematic diagram showing the distribution of the developer inhibitor in the photoresist provided in this application.

[0045] The implicit-explicit hybrid algorithm provided in this application combines implicit and explicit methods in its numerical computation algorithm. Specifically, it includes solving the diffusion term using an implicit method and solving the reaction term using an explicit method. Implicit methods include FFT, Crank-Nicolson, etc., while explicit methods include forward Euler methods, etc.

[0046] More specifically, the method of solving the diffusion term using an implicit method provided in the embodiments of this application includes:

[0047] The Fast Fourier Transform (FFT) is used to accelerate the diffusion calculation of acid and base substances in the XY direction. The FFT is an algorithm that accelerates convolution operations, enabling rapid solutions for diffusion calculations in the XY direction.

[0048] The Crank-Nicolson implicit algorithm is used to solve for the diffusion of acid and base substances in the Z direction. The Crank-Nicolson implicit algorithm is a second-order accurate implicit difference method that improves numerical stability by averaging explicit and implicit discretization equations.

[0049] The solution for the diffusion term is obtained by using the Crank-Nicolson implicit algorithm to ensure numerical stability, which is especially suitable for the implicit solution of diffusion in the Z direction and avoids the limitations of the CFL condition; the diffusion calculation in the XY direction is accelerated by FFT to reduce the computational complexity.

[0050] In one embodiment, an implicit method is used to calculate the 3D diffusion process of acids and bases in the PEB process, including rapid calculations in the XY direction using FFT. If the initial concentration distribution is a periodic pattern, FFT calculation can be performed directly; however, if the initial concentration distribution is an isolated pattern, zero-padding is required before FFT calculation. Subsequently, the Crank-Nicolson implicit algorithm is used to simulate diffusion in the Z direction, with Neumann conditions as the boundary conditions. The parameters of the PEB model include acid diffusion length, base diffusion length, initial normalized base concentration, five reaction rates k1-k5, baking time, and temperature. Because the diffusion is calculated using an implicit algorithm, the diffusion length and baking time are not limited by the CFL conditions, and accurate solutions can still be obtained even if the diffusion coefficient D is much larger than the mesh size.

[0051] More specifically, the method for solving reaction terms using an explicit approach provided in this embodiment includes:

[0052] The reaction concentrations of acid-base substances are calculated using the forward Euler explicit algorithm. The forward Euler explicit algorithm is a first-order precision explicit difference method that directly calculates the next time-step value from the current time-step value.

[0053] The concentration of the developer inhibitor is solved directly using an explicit method.

[0054] The reaction term can be solved directly using the forward Euler explicit algorithm, without the need for iterative solution of the nonlinear equation system, thus reducing computational resource consumption.

[0055] In one embodiment, the concentrations of acid-base substances and development inhibitors during the PEB process are obtained using the Euler forward explicit method.

[0056] As can be seen, the step-by-step processing of the physicochemical calculations in the photoresist PEB process achieves efficient simulation of the post-baking stage. First, an optical simulation algorithm is used to obtain the three-dimensional light intensity distribution of each grid point in the photoresist, serving as input for subsequent calculations. Second, based on the light intensity distribution and process parameters, the initial concentration distribution of acid and alkali substances, including acid concentration [A], alkali concentration [B], and developer inhibitor concentration [M], is calculated using the Dill parameter model. Finally, an implicit-explicit hybrid algorithm is used to solve the diffusion and reaction processes of acid and alkali substances step-by-step: the diffusion term is calculated in the XY direction using an implicit method, while the Z direction is solved using a tridiagonal matrix algorithm to ensure numerical stability; the reaction term is calculated directly using the forward Euler explicit method, avoiding the solution of nonlinear equations. The entire process achieves efficient and high-precision simulation by separating the diffusion and reaction terms and combining the advantages of implicit and explicit methods.

[0057] In summary, the photoresist post-baking simulation method provided in this application obtains the three-dimensional light intensity distribution in the photoresist, calculates the initial concentration distribution of the material in the photoresist after exposure based on the three-dimensional light intensity distribution, and processes the initial concentration distribution using an implicit-explicit hybrid algorithm to obtain the concentration of the developer inhibitor in the photoresist. By separating the diffusion and reaction terms through the implicit-explicit hybrid algorithm, it overcomes the technical problems of slow calculation speed due to limitations imposed by CFL conditions and high complexity caused by the need to solve nonlinear equations in implicit methods. This method can significantly improve the overall computational efficiency while ensuring the accuracy of diffusion calculations, and is particularly suitable for complex reaction-diffusion processes in chemically amplified photoresists. Furthermore, by separating the diffusion and reaction terms and combining the advantages of implicit and explicit methods, the method accelerates diffusion calculations using the Crank-Nicolson implicit algorithm and FFT, significantly improving the numerical stability and computational efficiency of three-dimensional diffusion. Additionally, the forward Euler explicit algorithm directly solves the reaction terms, avoiding the complexity of nonlinear equations, thereby significantly shortening the overall computation time while ensuring the accuracy of diffusion calculations. Achieving efficient and high-precision PEB simulation provides key support for the digital development of advanced node lithography processes.

[0058] In particular, since the explicit forward Euler calculation method is very slow in calculating the diffusion equation and its accuracy is related to the time discrepancy, and it must also satisfy the CFL condition to ensure stability, this implicit-explicit algorithm solves the diffusion term using FFT and CN implicit methods. It can simultaneously calculate the acid-base concentrations after diffusion at all points in the next time step through matrix operations, and then calculates the reaction term using the forward Euler method, avoiding the solution of nonlinear equations. The algorithm proposed in this patent is faster and has no CFL limitation. Compared with the parameter models used in photolithography, such as the light intensity threshold model, this method is a full physical model and can obtain more accurate 3D results. On the other hand, the PEB model proposed in this invention can be used to further calibrate the chemically amplified photoresist parameters. The calibrated photoresist parameters can accurately predict experimental results and guide the adjustment of the photolithography process.

[0059] Furthermore, the photoresist post-baking simulation method provided in this application embodiment, after obtaining the concentration of the developer inhibitor in the photoresist, further includes: performing a developer simulation process on the concentration distribution of the developer inhibitor to generate three-dimensional morphology data of the photoresist; wherein, the developer simulation process includes: calculating the development rate using an enhanced concave model, and / or, using a level set algorithm to track the development front.

[0060] Specifically, the enhanced notch model is an improved development rate model that considers the nonlinear relationship between developer concentration and developer penetration. The level set algorithm is a numerical method for tracking interface evolution, representing the interface through implicit functions, and is suitable for calculating complex morphologies. Specifically, the development rate can be calculated using the development simulation module based on the developer concentration; the rate model can be an enhanced notch model, a mock model, etc. Finally, the level set algorithm or the fast traversal algorithm is used to obtain the 3D morphology of the photoresist. For example, Figure 5 This is a schematic diagram of the morphology of the photoresist after development, provided in this application.

[0061] As can be seen, this embodiment can generate three-dimensional morphology data of photoresist by using the development simulation module to quantify the development process based on the initial concentration distribution of acid and alkali substances, enhancing the concave model, and tracking the development front using the level set algorithm. This step, through the combination of the development rate model and the interface tracking algorithm, accurately simulates the dynamic removal process of photoresist in the developer, generating a three-dimensional pattern that conforms to the actual process. This significantly improves the accuracy of photoresist morphology prediction, enhances the combination of the concave model and the level set algorithm, and can more realistically reflect the nonlinear dynamics of the development process, providing a reliable basis for process parameter optimization.

[0062] Figure 6 A flowchart of an embodiment of the photoresist post-baking simulation method provided in this application is shown below. Figure 6 This paper illustrates a specific implementation of the post-baking simulation method for photoresist provided in this application. Specifically, as follows: Figure 6 As shown, firstly, the 3D light intensity distribution in the photoresist is obtained using the optical simulation module. Then, based on the 3D light front distribution and process parameters such as exposure dose in the photoresist, the concentration distribution of the material after exposure is calculated and recorded as the initial concentration distribution. Subsequently, the diffusion process of acid and alkali substances during PEB is calculated using an implicit method, and the reaction process of acid and alkali substances during PEB is calculated using an explicit method. The concentration of the developer inhibitor is then calculated using the explicit method. Finally, based on the calculated developer inhibitor concentration, the morphology of the target photoresist after development is predicted.

[0063] Figure 7 This is a schematic diagram illustrating the iterative process of post-baking simulation using the implicit-explicit hybrid algorithm provided in this application. The following diagram is in conjunction with the attached... Figure 7 The implicit-explicit hybrid algorithm provided in this application will be described.

[0064] First, the reaction-diffusion equation corresponding to chemical photoresist PEB can be expressed by the following formulas, with Formula 1 and Formula 2 being used after exposure and before PEB:

[0065] Formula 1

[0066] Formula 2

[0067] In the PEB process, Equations 3, 4, and 5 are used:

[0068] Formula 3

[0069] Formula 4

[0070] Formula 5

[0071] Where [PAG] is the concentration of PAG, [A] and [B] are the molecular concentrations of acids and bases, respectively, and [M] is the concentration of the developer inhibitor. C is the sensitivity parameter Dill-C, and I(r) is the light intensity distribution during exposure. is the rate constant. and These are the diffusion coefficients of the acid and the base, respectively.

[0072] The reaction-diffusion equation described above can be solved by considering the initial distributions of acid concentration [A], alkali concentration [B], and developer inhibitor concentration [M], along with the boundary conditions set for A and B. For example, the alkali concentration in the initial conditions of a typical PEB simulation is set to... The concentration of the developer inhibitor was set to And there are .

[0073] Furthermore, the above reaction-diffusion equations can be solved using forward Euler methods, which calculate the concentration distribution and concentration increment at the current time and solve for the concentration at the next time. However, when it comes to diffusion problems, forward Euler methods are very complex and slow, and the simulation time interval has a very strict constraint relationship with the diffusion rate. However, since the reaction term is included, it is not feasible to use Crank-Nicolson fully implicit solutions like DNQ.

[0074] Therefore, the implicit-explicit mixing method provided in this application uses the Crank-Nicolson implicit method to solve for the diffusion term and then uses forward Euler to solve for the reaction term, specifically including the following steps:

[0075] First, regarding the diffusion terms in Formulas 4 and 5 and The implicit method is used to obtain good stability, while the remaining reaction terms are solved explicitly to avoid solving nonlinear equations.

[0076] Diffusion can be expressed by the following formulas six and seven:

[0077] Formula Six

[0078] Formula 7

[0079] The reaction term can be expressed by the following formulas eight and nine:

[0080] Formula 8

[0081] Formula Nine

[0082] Subsequently, considering the initial concentration distribution of substance A as follows: Under periodic boundary conditions, the solution to the diffusion equation in Formula 6 above can be expressed by Formula 10:

[0083] Formula 10

[0084] in, and This represents the distance to the point (x, y). Furthermore, Equation 10 can also be expressed as the convolution of the initial concentration distribution with a Gaussian function, thus represented by Equation 11:

[0085] Formula Eleven

[0086] Among them are:

[0087]

[0088] The convolution operation can be accelerated using the FFT algorithm, which can be represented by the following formula:

[0089] Formula 12

[0090] Subsequently, after obtaining the two-dimensional concentration distribution of each layer in the z-direction, the final three-dimensional concentration distribution can be obtained by using the one-dimensional Crank-Nicolson algorithm in the z-direction. Among them, the one-dimensional diffusion equation shown in Equation Thirteen can be discretized by the Crank-Nicolson algorithm and expressed as Equation Fourteen:

[0091] Formula Thirteen

[0092] Formula Fourteen

[0093] Subsequently, the order was given:

[0094]

[0095] Formula 14 above can then be rewritten as Formula 15 as follows:

[0096] Formula Fifteen

[0097] Here, the superscript of 'c' indicates the nth or n+1th time, and the subscript indicates the position in the z-direction. Considering that the terms on the right-hand side of the equation are known, this is a tridiagonal problem; therefore, the tridiagonal matrix algorithm can efficiently solve for the concentration distribution at time n+1. The implicit method no longer solves point-by-point along the z-direction sequentially, but instead solves for all points at once within a specific time step, i.e., solving a system of equations all at once.

[0098] Subsequently, considering that the boundary condition in the z-direction is a Neumann condition, two virtual layers need to be set. ,as well as The top and bottom layers have the following formulas sixteen and seventeen:

[0099] Formula Sixteen

[0100] Formula 17

[0101] Combining formulas thirteen through seventeen above, the problem becomes solving the linear system shown in formula eighteen below:

[0102] Formula 18

[0103] That is, it can be expressed by the following formula nineteen:

[0104] Formula 19

[0105] The concentration at time n+1 is the diffusion term plus the reaction term in Formula 19. The concentration at time n+1 can be expressed by the following formula:

[0106] Formula 20

[0107] The concentration of acidic substance A obtained from the solution can be expressed by the following formula 21, and the concentration of basic substance B can be expressed by the following formula 22:

[0108] Formula 21

[0109] Formula 22

[0110] in, Assuming the time step is N, and the final result of PEB calculation requires N time iterations, since the result of each iteration is the initial value for the next iteration, the concentration distribution at time n needs to be calculated first, and then the concentration at time n+1 needs to be calculated.

[0111] Finally, based on Formula 3 and the concentration of acidic substance A in Formula 21, the concentration of the imaging inhibitor M can be obtained during the iteration process using the forward Euler method.

[0112] Combination Figure 7 The process shown calculates the normalized 3D light intensity distribution within the photoresist at time t=0 based on parameters such as illumination conditions, mask pattern, thickness of each film layer, initial extinction coefficient, and exposure dose. Subsequently, based on the normalized 3D light intensity distribution obtained in the previous step, the normalized concentration [PAG] and acid concentration [A] of the photoacid-producing agent (PAG) are calculated, thereby converting the light intensity distribution into the concentration distribution of the chemical substance. The specific formulas can be expressed by the following formulas 23 and 24:

[0113] Formula 23

[0114] Formula 24

[0115] Subsequently, the post-baking time was discretized, and the time interval was set as follows: Thus, under quasi-static conditions, the calculation is performed at... The acid-base reaction process at a certain moment leads to... The change in concentration over time is used to calculate the change in acid-base concentration within each time interval, which can be expressed by the following formulas 25 and 26:

[0116] Formula 25

[0117] Formula 26

[0118] Subsequently, the diffusion concentrations of acid and base in the XY directions at each spatial point were quickly calculated using FFT (Fast Fourier Transform), and the diffusion concentration in the Z direction was obtained by using the Crank-Nicholson implicit method to obtain the difference matrix M, which could be obtained through a single matrix operation. The acid-base concentration at any given time can be specifically expressed using the following formulas 27 and 28:

[0119] Formula 27

[0120] Formula 28

[0121] To demonstrate and verify the feasibility of the embodiments of this application, simulation experiments were conducted, in which the exposure and development parameters were set as shown in Table 1 below.

[0122] Table 1

[0123]

[0124] The visualization results obtained through simulation are as follows: Figures 2-5 As shown, it can be seen that Figure 2 This is a schematic diagram of the cross-sectional light intensity distribution in the photoresist during exposure. Figure 3 for Figure 2 The acid concentration distribution in the PEB photoresist immediately after exposure shows a very obvious standing wave effect. Figure 4 for Figure 3 The results of the corresponding photoresist development inhibitor concentrations after baking show that the standing wave effect is significantly improved. Figure 5 for Figure 4 The diagram shows the morphology of the photoresist after development. The development model algorithm used here is the fast-moving algorithm. The dark cylindrical areas contain photoresist, and the gaps between the pillars are formed by the removal of unexposed photoresist. The bottom CD is 100nm. This model can accurately simulate and predict the lithography of actual advanced nodes. Through preliminary simulation debugging, the dependence on on-site experimental parameter adjustments is reduced, thereby saving costs and time in real experiments.

[0125] This application also provides a method for calibrating the parameters of a photoresist, including: according to... Figure 1 The method shown determines the three-dimensional morphology data of the photoresist; error analysis is performed between the three-dimensional morphology data and the actual experimental results to obtain the error function, and the parameters of the photoresist are optimized in reverse through the error function.

[0126] Specifically, this application provides a parameter calibration method for chemically amplified photoresist based on the three-dimensional morphology data obtained by the photoresist post-baking simulation method and the actual experimental results. The method performs error analysis based on the 3D morphology obtained by the above photolithography simulation method and the actual experimental results, and optimizes the photoresist parameters in reverse through the error function, thereby obtaining accurate photoresist model parameters.

[0127] For example, Figure 8 A schematic flowchart of an embodiment of the calibration method for simulation parameters of the photoresist provided in this application is shown below. Figure 8A model for calibrating chemically amplified photoresist parameters is presented. Parameter calibration is achieved through a feedback optimization mechanism between experimental data and the simulation model: First, based on actual experimental data such as measured exposure, baking, and developing process parameters, these parameters are input into the photoresist simulation model for simulation calculation. Then, by comparing the simulation results of the photoresist morphology after development with the experimentally measured data, an error function characterizing the difference between the two is constructed. Subsequently, a numerical optimization algorithm is used to perform inverse calibration of key photoresist physical properties, including Dill C parameters, refractive index characteristics, and k1-k5 reaction rate constants, etc., and the error function is minimized through continuous iterative optimization. This calibration method effectively improves the prediction accuracy of the photoresist model. Based on the calibrated model, key dimensional changes during the exposure and development process can be accurately simulated, providing a reliable simulation basis for optimizing photolithography process parameters and significantly reducing experimental trial-and-error costs.

[0128] This application also provides a method for adjusting the parameters of a photoresist, including: according to... Figure 1 The method shown determines the three-dimensional morphology data of the photoresist and adjusts the photolithography simulation parameters until the three-dimensional morphology data of the photoresist after development meets the preset conditions. The photolithography simulation parameters include photoresist thickness, anti-reflection layer parameters, exposure system parameters, baking process parameters, and development kinetic parameters.

[0129] Specifically, based on the three-dimensional morphology data obtained by the photoresist post-baking simulation method, this application can also provide a photolithography adjustment method for chemically amplified photoresist. According to the photolithography simulation method described above, the morphology and size data of the developed photoresist are obtained, and the photolithography simulation parameters are adjusted until the morphology and size data of the developed photoresist meet the expectations. The expectations can be that the value of the three-dimensional morphology data of the photoresist meets a preset threshold.

[0130] In one embodiment, the photoresist parameter adjustment method provided in this application constructs a full-process simulation model of the photoresist. Key variables such as photoresist thickness, anti-reflection layer parameters, exposure system parameters (including objective lens numerical aperture, exposure dose, and light source characteristics), baking process parameters (temperature field distribution and time control), and development kinetics parameters are input into the model for multi-physics coupled simulation to obtain the three-dimensional morphological feature data of the photoresist after development. By establishing a parameter sensitivity analysis mechanism, the simulation results and target critical dimension (CD) are iteratively optimized until the predetermined process indicators are achieved. Compared with the traditional segmented process debugging based on trial and error, this method realizes full-process digital pre-simulation from substrate processing to development process, enabling synergistic optimization of multiple core process parameters, effectively reducing wafer experiment consumption during the R&D stage, and significantly shortening the process development cycle.

[0131] In the foregoing embodiments of this application, the post-baking simulation method, parameter calibration method, and parameter adjustment method for photoresist provided in the embodiments of this application have been described. To implement the functions of the methods provided in the embodiments of this application, the device serving as the execution entity can implement these functions through hardware structures and / or software modules. Whether a particular function is implemented using hardware structures, software modules, or a combination of hardware structures and software modules depends on the specific application and design constraints of the technical solution.

[0132] For example, this application provides a post-baking simulation apparatus for photoresist, comprising: an acquisition module for acquiring a three-dimensional light intensity distribution in the photoresist; a calculation module for calculating the initial concentration distribution of the material in the photoresist after exposure based on the three-dimensional light intensity distribution; and a processing module for processing the initial concentration distribution using an implicit-explicit hybrid algorithm to obtain the concentration of the developer inhibitor in the photoresist; wherein the implicit-explicit hybrid algorithm includes: solving the diffusion term using an implicit method and solving the reaction term using an explicit method.

[0133] For example, this application provides a method for calibrating the parameters of a photoresist, including: a determining module, used to determine parameters according to, for example... Figure 1 The method shown determines the three-dimensional morphology data of the photoresist; the analysis module is used to perform error analysis between the three-dimensional morphology data and the actual experimental results to obtain the error function; the optimization module is used to optimize the parameters of the photoresist in reverse through the error function.

[0134] For example, this application provides a method for adjusting the parameters of a photoresist, including: a determining module, used to adjust parameters according to, for example... Figure 1 The method shown determines the three-dimensional morphology data of the photoresist; the adjustment module is used to adjust the photolithography simulation parameters until the three-dimensional morphology data of the photoresist after development meets the preset conditions.

[0135] It should be understood that the division of the various modules in the above device is merely a logical functional division. In actual implementation, they can be fully or partially integrated into a single physical entity, or they can be physically separated. Furthermore, these modules can be implemented entirely in software via processing element calls; they can be fully implemented in hardware; or some modules can be implemented by processing element calls to software, while others are implemented in hardware. For example, a module can be a separately established processing element, or it can be integrated into a chip within the above device. Alternatively, it can be stored as program code in the memory of the above device, and its functions can be called and executed by a processing element of the device. The implementation of other modules is similar. Moreover, these modules can be fully or partially integrated together, or they can be implemented independently. The processing element here can be an integrated circuit with signal processing capabilities. In the implementation process, each step of the above method or each of the above modules can be completed through integrated logic circuits in the hardware of the processor element or through software instructions.

[0136] For example, these modules can be one or more integrated circuits configured to implement the above methods, such as one or more application-specific integrated circuits (ASICs), one or more digital signal processors (DSPs), or one or more field-programmable gate arrays (FPGAs). As another example, when a module is implemented using processing element scheduler code, the processing element can be a general-purpose processor, such as a central processing unit (CPU) or other processor capable of calling program code. Furthermore, these modules can be integrated together to implement a system-on-a-chip (SOC).

[0137] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. A computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the flow or function according to the embodiments of this application is generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0138] For example, Figure 9 A schematic diagram of the structure of an embodiment of the electronic device provided in this application is shown below. Figure 9 The electronic device 2000 shown can be used to perform the photoresist post-baking simulation method, photoresist parameter calibration method, or photoresist parameter adjustment method provided in any embodiment of this application.

[0139] In one embodiment, such as Figure 9 The control device 2000 shown includes one or more processors 2001 and a memory 2002. The memory 2002 stores computer-executable instructions, and the processors 2001 can execute the computer-executable instructions stored in the memory 2002. When the computer-executable instructions are executed by the processor 2001, the processor 2001 implements the photoresist post-baking simulation method, photoresist parameter calibration method, or photoresist parameter adjustment method provided in any of the foregoing embodiments of this application.

[0140] In one embodiment, such as Figure 9 The control device 2000 shown also includes a communication interface 2003, through which the processor 2001 can communicate with other devices, such as sending and receiving data through the communication interface 2003.

[0141] In the above embodiments, it should be understood that the processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor.

[0142] The memory may include random access memory (RAM) and may also include non-volatile memory (NVM), such as at least one disk storage device.

[0143] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, the buses shown in the accompanying drawings are not limited to a single bus or a single type of bus.

[0144] This application also provides a chip for executing instructions, which is used to execute the photoresist post-baking simulation method, photoresist parameter calibration method, or photoresist parameter adjustment method provided in any of the foregoing embodiments of this application.

[0145] This application also provides a computer program product, including a computer program that, when executed, implements the photoresist post-baking simulation method, photoresist parameter calibration method, or photoresist parameter adjustment method provided in any of the foregoing embodiments of this application.

[0146] This application also provides a computer-readable storage medium storing computer-executable instructions. When executed, the computer-executable instructions can be used to implement the photoresist post-baking simulation method, photoresist parameter calibration method, or photoresist parameter adjustment method provided in any of the foregoing embodiments of this application.

[0147] The aforementioned readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The readable storage medium can be any available medium accessible to a general-purpose or special-purpose computer.

[0148] An exemplary readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the readable storage medium. Of course, the readable storage medium can also be a component of the processor. The processor and the readable storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and the readable storage medium can exist as discrete components in the device.

[0149] The division of units is merely a logical functional division; in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or units, and may be electrical, mechanical, or other forms.

[0150] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0151] In addition, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0152] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0153] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0154] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A method for simulating post-baking of photoresist, characterized in that, include: Obtain the three-dimensional light intensity distribution in the photoresist; Based on the three-dimensional light intensity distribution, the initial concentration distribution of the material in the photoresist after exposure is calculated; An implicit-explicit hybrid algorithm is used to process the initial concentration distribution to obtain the concentration of the developer inhibitor in the photoresist; wherein the implicit-explicit hybrid algorithm includes: solving the diffusion term using an implicit method and solving the reaction term using an explicit method.

2. The method according to claim 1, characterized in that, The process of solving the diffusion term using an implicit method includes: Fast Fourier Transform (FFT) is used to accelerate the calculation of diffusion of acid and base substances in the XY direction; And / or, the Crank-Nicolson implicit algorithm is used to solve for the diffusion of acid and base substances in the Z direction.

3. The method according to claim 1, characterized in that, The method of solving for the reaction terms explicitly includes: The reaction concentrations of acid and base substances are calculated using the forward Euler explicit algorithm; And / or, use explicit methods to directly solve for the concentration of the developer inhibitor.

4. The method according to any one of claims 1-3, characterized in that, After obtaining the concentration of the development inhibitor in the photoresist, the method further includes: The concentration distribution of the developer inhibitor is subjected to a development simulation process to generate three-dimensional morphology data of the photoresist; The development simulation process includes: calculating the development rate using an enhanced concave model, and / or tracing the development front using a level set algorithm.

5. The method according to any one of claims 1-3, characterized in that, The calculation of the initial concentration distribution of the material in the photoresist after exposure, based on the three-dimensional light intensity distribution, includes: Based on the three-dimensional light intensity distribution and process parameters, the initial distribution of acid concentration, alkali concentration, and developer inhibitor concentration in the photoresist after exposure were calculated.

6. A method for calibrating the parameters of a photoresist, characterized in that, include: According to the method of claim 4, the three-dimensional morphology data of the photoresist are determined; Error analysis was performed between the three-dimensional topography data and the actual experimental results to obtain the error function; The parameters of the photoresist are optimized in reverse by using an error function.

7. A method for adjusting the parameters of a photoresist, characterized in that, include: According to the method of claim 4, the three-dimensional morphology data of the photoresist are determined; Adjust the photolithography simulation parameters until the three-dimensional morphology data of the photoresist after development meets the preset conditions.

8. An electronic device, characterized in that, include: A processor, and a memory communicatively connected to the processor; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory to implement the method as described in any one of claims 1-7.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the method as described in any one of claims 1-7.

10. A computer program product, characterized in that, Includes a computer program that, when executed by a processor, implements the method as described in any one of claims 1-7.

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