Photolithography simulation method, computer program product, and computer device

Abstract

This invention provides a photolithography simulation method, a computer program product, and a computer device. The photolithography simulation method includes iteratively calculating the particle concentration within the photoresist using a reaction-diffusion equation with an embedded stochastic effects model during the post-exposure baking simulation process. Statistical fluctuations are applied to at least one calculation parameter in the iterative calculation to simulate the randomness in the photolithography process. Based on the results of the post-exposure baking simulation, a simulated photoresist morphology with edge roughness is generated. This photolithography simulation method can directly generate a simulated photoresist morphology with edge roughness, enabling the simulation results to realistically reflect the irregular edge characteristics in the actual photolithography process, thus providing a crucial data foundation for the subsequent quantitative evaluation of line edge roughness and linewidth roughness.

Description

Technical Field

[0001] This invention belongs to the field of photolithography simulation technology, and specifically provides a photolithography simulation method, a computer program product, and a computer device. Background Technology

[0002] Photolithography is a core process in integrated circuit manufacturing. Its principle involves using the photochemical reaction of photoresist coated on a substrate to transfer the pattern from a photomask to the substrate. Rigorous photolithography simulation, as an important tool for layout design, can simulate process steps such as exposure, post-baking (PEB), and development, assisting engineers in optimizing process windows and shortening development cycles. As the feature size of integrated devices continues to shrink, linewidth roughness (LWR) and line edge roughness (LER) have become key defect indicators for evaluating the quality of photolithography processes.

[0003] Currently, mainstream photolithography simulation methods follow strict physical laws, employing deterministic reaction-diffusion equations to numerically solve for the particle concentration within the photoresist based on idealized input conditions such as mask information and optical parameters. Taking a typical "line / spacer" pattern as an example, existing simulation workflows can obtain photoresist profiles with smooth edges and regular morphology. These methods have been widely used in industry, and their calculation results exhibit good repeatability and numerical stability.

[0004] However, existing simulation methods are all based on idealized environmental assumptions and do not consider the non-ideal factors that are common in actual photolithography processes. For example, fluctuations in exposure dose, insufficient smoothness of mask lines, impurities inside the photoresist, differences in environmental cleanliness, and localized mechanical damage can all lead to irregular, jagged edges on the photoresist lines. Due to the lack of modeling capabilities for these stochastic effects, traditional simulations cannot produce simulation results with edge roughness, making it difficult to quantitatively evaluate LER and LWR. Summary of the Invention

[0005] One object of the present invention is to overcome at least one technical defect in the prior art and to provide a photolithography simulation method, a computer program product, and a computer device.

[0006] A further objective of this invention is to introduce a stochastic effect model into the post-exposure baking simulation process so that the simulation results can accurately reflect the irregular edge morphology in the actual photolithography process.

[0007] Another further objective of this invention is to achieve dual stochastic modeling of particle number statistical fluctuations and reaction time uncertainty, thereby avoiding the accuracy loss or computational redundancy caused by traditional fixed time steps.

[0008] Another further objective of this invention is to enable the simulation process to flexibly switch between ideal simulation mode and actual simulation mode, so as to meet the different requirements of simulation speed and accuracy in different application scenarios.

[0009] In particular, according to a first aspect of the present invention, the present invention provides a photolithography simulation method, comprising: During the post-exposure baking simulation, the reaction-diffusion equation with an embedded random effects model is used to iteratively calculate the particle concentration inside the photoresist, so as to apply statistical fluctuations to at least one calculation parameter in the iterative calculation, thereby simulating the randomness in the photolithography process. Based on the results of the post-exposure baking simulation, a photoresist simulation morphology with edge roughness is generated.

[0010] Optionally, the step of iteratively calculating the particle concentration inside the photoresist using the reaction-diffusion equation with an embedded random effects model includes: The photoresist is spatially discretized into multiple grid units; The number of reactant particles, acid particles, and base particles in each grid cell are defined as random variables with a preset probability distribution. The current total reaction rate is determined based on the number of reactant particles, acid particles, and base particles within the grid cell. Generate a random number whose value is uniformly distributed within a preset range; The time step for this iteration is determined based on the total reaction rate and the random number. The simulation time is advanced by the stated time step, and the particle concentration in each of the stated grid cells is updated according to the total reaction rate.

[0011] Optionally, the reaction-diffusion equation of the embedded random effects model includes the following covariance correction equation: ; ; ; in, , , These represent the concentrations of reactant particles, acid, and base, respectively. , , These represent the expected number of reactant particles, acid particles, and base particles within a single grid cell, respectively. This represents the volume of a single grid cell. , , The rate constant is for and The covariance is defined as: , for and The covariance is defined as: .

[0012] Optionally, the reaction-diffusion equation of the embedded random effects model further includes the following overall reaction rate equation: ; in, Represents a state with a given number of particles. The overall reaction rate is below. , , These represent the number of reactant particles, acid particles, and base particles within a single grid cell, respectively. This represents the volume of a single grid cell. , , is the rate constant.

[0013] Optionally, the time step is calculated according to the following formula: ; in, The time step is... The random number is a number whose value is uniformly distributed in the interval [0, 1]. .

[0014] Optionally, the edge roughness includes line edge roughness and linewidth roughness, and after the step of generating the photoresist simulation morphology with edge roughness, the method further includes: The quantitative indices of the line edge roughness and the line width roughness are calculated based on the simulated morphology of the photoresist.

[0015] Optionally, the random effects model supports enabling or disabling configuration; When the random effects model is disabled, the post-exposure baking simulation process is calculated using a deterministic reaction-diffusion equation to generate a photoresist simulation morphology with smooth edges. When the stochastic effects model is enabled, the post-exposure baking simulation process is calculated using the reaction-diffusion equation embedded in the stochastic effects model to generate a photoresist simulation morphology with edge roughness.

[0016] Optionally, the exposure simulation process is performed before the post-exposure baking simulation process is executed; After performing the post-exposure baking simulation process, a development simulation process is performed; Both the exposure simulation process and the development simulation process are calculated using deterministic reaction-diffusion equations.

[0017] According to a second aspect of the present invention, a computer program product is provided, comprising a computer program that, when executed by a processor, implements the steps of the photolithography simulation method described above.

[0018] According to a third aspect of the present invention, a computer device is provided, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the photolithography simulation method described in any one of the above descriptions.

[0019] The photolithography simulation method of this invention employs an iterative calculation using a reaction-diffusion equation with an embedded stochastic effect model during the post-exposure baking simulation process, and applies statistical fluctuations to the calculation parameters. This effectively simulates the stochastic effects in actual photolithography processes, overcoming the limitation of traditional deterministic simulations that can only output ideal smooth edge morphologies. This method can directly generate simulated photoresist morphologies with edge roughness, enabling the simulation results to realistically reflect the irregular edge characteristics in actual photolithography processes. This provides a crucial data foundation for the subsequent quantitative evaluation of line edge roughness and linewidth roughness.

[0020] Furthermore, the photolithography simulation method of this invention discretizes the photoresist space into grid cells, defines the number of particles within each cell as a random variable, and dynamically determines the iteration time step based on the total reaction rate and uniformly distributed random numbers. This achieves dual stochastic modeling of the statistical fluctuations in particle numbers and the uncertainty of reaction time during the reaction-diffusion process. This method avoids the accuracy loss or computational redundancy caused by manually presetting a fixed time step in traditional deterministic simulations. It ensures that the time progression strictly follows the probability distribution law of chemical reactions, enabling more accurate characterization of statistical fluctuation behavior within extremely small photoresist regions, and providing a favorable data structure foundation for the large-scale parallel acceleration of subsequent algorithms.

[0021] Furthermore, the photolithography simulation method of this invention designs the random effects model as a configurable option that can be enabled or disabled. When the random effects model is disabled, the simulation process uses a traditional deterministic reaction-diffusion equation, outputting a smooth-edged photoresist morphology, suitable for rapid verification and ideal condition analysis. When the random effects model is enabled, the simulation process uses a reaction-diffusion equation with embedded random effects, outputting a photoresist morphology with edge roughness, suitable for defect analysis and process window evaluation. Users can flexibly select the simulation mode according to specific needs, balancing different requirements for simulation speed and accuracy.

[0022] The above and other objects, advantages and features of the present invention will become more apparent to those skilled in the art from the following detailed description of specific embodiments of the invention in conjunction with the accompanying drawings. Attached Figure Description

[0023] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 This is a flowchart of a photolithography simulation method according to an embodiment of the present invention; Figure 2 This is a flowchart of iterative calculation using a random effects model according to an embodiment of the present invention; Figure 3 This is a schematic diagram of a computer program product according to an embodiment of the present invention; Figure 4 This is a schematic diagram of a computer-readable storage medium according to an embodiment of the present invention; Figure 5 This is a schematic block diagram of a computer device according to an embodiment of the present invention. Detailed Implementation

[0024] Reference will now be made in detail to embodiments of the invention, one or more of which are illustrated in the accompanying drawings. The various embodiments provided are intended to explain the invention and not to limit it. In fact, various modifications and variations to the invention will be apparent to those skilled in the art without departing from the scope or spirit of the invention. For example, a feature illustrated or described as part of one embodiment may be used with another embodiment to produce yet another embodiment. Therefore, the invention is intended to cover such modifications and variations within the scope of the appended claims and their equivalents.

[0025] In the description of this embodiment, it should be understood that the term "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified. When a feature "includes or contains" one or more of the features it covers, unless otherwise specifically described, this indicates that other features are not excluded and may be further included.

[0026] In the description of this embodiment, the terms "one embodiment," "some embodiments," "some examples," "one example," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0027] This invention provides a photolithography simulation method. Figure 1 This is a flowchart of a photolithography simulation method according to an embodiment of the present invention, such as... Figure 1 As shown, the photolithography simulation method includes at least the following steps: Step S101: During the post-exposure baking simulation, the reaction-diffusion equation with an embedded random effects model is used to iteratively calculate the particle concentration inside the photoresist, so as to apply statistical fluctuations to at least one calculation parameter in the iterative calculation, thereby simulating the randomness in the photolithography process.

[0028] Specifically, Post Exposure Bake (PEB) is a crucial step in the photolithography process. In this step, the exposed photoresist is heated to a certain temperature, causing acid molecules generated by the decomposition of the photoacid-generating agent to diffuse within the photoresist and catalyze a chemical reaction (i.e., deprotection reaction) in the reactant particles, thereby altering the solubility properties of the photoresist. PEB simulation uses computer simulation to model this physicochemical process and calculate the spatiotemporal distribution of the concentrations of various substances within the photoresist.

[0029] Reaction-diffusion equations are a class of partial differential equations that describe the simultaneous diffusion of substances in space and the occurrence of chemical reactions. In this invention, these equations are used to describe the diffusion behavior of acid and base molecules, as well as the chemical reaction kinetics between reactant particles, acid molecules, and base molecules. Traditional reaction-diffusion equations are deterministic, meaning that given initial and boundary conditions, the calculation result is uniquely determined.

[0030] The reaction-diffusion equation with embedded random effects model proposed in this embodiment refers to the modification of the traditional deterministic reaction-diffusion equation by introducing a random effects model, so that the solution of the equation is no longer a deterministic value, but a random process with statistical distribution.

[0031] Particle concentration refers to the number of a certain type of particle per unit volume. In this invention, the particles involved mainly include: reactant particles (unreacted active groups in the photoresist), acid particles (acid molecules produced by the decomposition of photoacid-generating agents), and base particles (alkaline substances in the diffusion process). Particle concentration is the core variable in the reaction-diffusion equation, and its spatiotemporal distribution determines the final morphology of the photoresist.

[0032] Statistical fluctuation refers to the differences in simulation results across multiple runs due to the discreteness of the number of molecules and the randomness of reaction timing. At the microscopic scale, the number of molecules is finite, and the movement and collisions of individual particles are random; therefore, the occurrence time and rate of chemical reactions are not entirely deterministic. This invention introduces this statistical fluctuation through a stochastic effects model, enabling the simulation results to reflect the random characteristics of actual photolithography processes.

[0033] Step S102: Based on the results of the post-exposure baking simulation, a photoresist simulation morphology with edge roughness is generated.

[0034] The results of the post-exposure baking simulation reflect the spatial distribution of reactant particles, acid particles, and alkali particles within the photoresist after the PEB process. Since the concentration distribution of reactant particles determines the dissolution rate of the photoresist during development, these data are fundamental to generating the final photoresist morphology.

[0035] Edge roughness refers to the degree of deviation between the edge of a photoresist line and an ideal smooth edge. In this invention, edge roughness can include line edge roughness (LER) and line width roughness (LWR). LER describes the degree of undulation of the line edge in the horizontal direction, while LWR describes the degree of variation of the line width along the length direction. These two indicators are key parameters for evaluating the quality of photolithography processes and directly affect the accuracy of subsequent etching processes.

[0036] The photolithography simulation method of this invention employs an iterative calculation using a reaction-diffusion equation with an embedded stochastic effect model during the post-exposure baking simulation process, and applies statistical fluctuations to the calculation parameters. This effectively simulates the stochastic effects in actual photolithography processes, overcoming the limitation of traditional deterministic simulations that can only output ideal smooth edge morphologies. This method can directly generate simulated photoresist morphologies with edge roughness, enabling the simulation results to realistically reflect the irregular edge characteristics in actual photolithography processes. This provides a crucial data foundation for the subsequent quantitative evaluation of line edge roughness and linewidth roughness.

[0037] Figure 2 This is a flowchart of iterative calculation using a random effects model according to an embodiment of the present invention, such as... Figure 2As shown, iteratively calculating the particle concentration inside the photoresist using the reaction-diffusion equation with an embedded random effects model may include the following steps: Step S201: Discretize the photoresist in space into multiple grid units.

[0038] This step divides the continuous photoresist region into a finite number of tiny volumetric units (mesh units), each with the same volume. Discretization allows the originally continuous partial differential equations to be solved in discrete form on a computer.

[0039] Step S202: Define the number of reactant particles, acid particles, and base particles in each grid cell as random variables with a preset probability distribution.

[0040] This step changes the traditional approach of treating the number of particles as a fixed value in deterministic simulations, and instead treats it as a random variable that follows a specific probability distribution (such as the Poisson distribution), thus laying the foundation for subsequent modeling of random fluctuations.

[0041] Step S203: Determine the current total reaction rate based on the number of reactant particles, acid particles, and base particles within the grid cell.

[0042] This step calculates the total reaction rate at the current moment based on the actual number of the three types of particles within the current grid cell. The total reaction rate reflects how quickly the chemical reaction occurs under the current conditions.

[0043] Step S204: Generate a random number whose value is uniformly distributed within a preset interval.

[0044] This step generates a uniformly distributed random number using a pseudo-random number generator. This random number is used for subsequent time step calculations, reflecting the random nature of the timing of chemical reactions.

[0045] Step S205: Determine the time step for this iteration based on the total reaction rate and the random number.

[0046] The time step in this step is not a fixed value, but is dynamically determined based on the current total reaction rate: the larger the total reaction rate, the shorter the time step; the smaller the total reaction rate, the longer the time step.

[0047] Step S206: Advance the simulation time with a time step and update the particle concentration in each grid cell according to the total reaction rate.

[0048] This step advances the simulation time by one time step and updates the reactant particle concentration, acid particle concentration, and base particle concentration in each grid cell based on the currently calculated total reaction rate. After the update is complete, return to step S203 and repeat the above process until the preset simulation end time is reached.

[0049] The photolithography simulation method of this invention discretizes the photoresist space into grid cells, defines the number of particles in each cell as a random variable, and dynamically determines the iteration time step based on the total reaction rate and uniformly distributed random numbers. This achieves dual stochastic modeling of the statistical fluctuations in particle numbers and the uncertainty of reaction time during the reaction-diffusion process. This method avoids the accuracy loss or computational redundancy caused by manually preset fixed time steps in traditional deterministic simulations. It ensures that the time progression strictly follows the probability distribution law of chemical reactions, enabling more accurate characterization of statistical fluctuation behavior in extremely small photoresist regions, and providing a favorable data structure foundation for the large-scale parallel acceleration of subsequent algorithms.

[0050] In traditional photolithography simulation, the original post-exposure baking (PEB) process can be described by the following deterministic reaction-diffusion equations: ; ; ; in, , , These represent the concentrations of reactant particles, acid, and base, respectively. The rate constant is Let be the diffusion coefficient of the acid and base. This represents the reaction order.

[0051] The above system of equations has the following deterministic characteristics: Given the initial and boundary conditions, the solution to the above system of equations is uniquely determined. That is, for the same set of input parameters (such as initial concentration distribution, temperature, diffusion coefficient, etc.), each simulation will yield exactly the same results. The above equations treat particle concentration as a continuous variable and assume that molecules are uniformly distributed in space. Under this assumption, concentration changes follow a deterministic differential equation, and there are no random or probabilistic factors. When using the above set of equations for numerical solution, iterative calculations are usually performed using a pre-set fixed time step, and the size of the time step is not dynamically adjusted with changes in the reaction state.

[0052] Therefore, the above traditional equations can only output the simulated morphology of photoresist with ideal smooth edges, and cannot simulate the irregular edge features caused by non-ideal factors in actual photolithography processes.

[0053] In this embodiment, to introduce random effects, the present invention modifies the above-mentioned traditional equation and proposes a covariance correction equation. In other words, the reaction-diffusion equation of the embedded random effects model of the present invention may include the following covariance correction equation: ; ; ; in, , , These represent the concentrations of reactant particles, acid, and base, respectively. , , These represent the expected number of reactant particles, acid particles, and base particles within a single grid cell, respectively. This represents the volume of a single grid cell. , , The rate constant is for and The covariance is defined as: , for and The covariance is defined as: .

[0054] It is understandable that the essential difference between the above covariance correction equation and the traditional equation lies in the addition of a covariance term. and These covariance terms reflect the correlation between the number of different types of particles and are used to correct the effect of microscopic distribution inhomogeneities caused by the finite number of particles on the reaction rate. When the number of particles approaches infinity, the covariance terms approach zero, and the covariance correction equation degenerates into the traditional equation.

[0055] Based on the aforementioned covariance correction equation, this invention further defines the total reaction rate equation. The total reaction rate describes the total probability of a chemical reaction occurring per unit time under a given number of particles. In other words, the reaction-diffusion equation of the embedded stochastic effects model of this invention may also include the following total reaction rate equation: ; in, Represents a state with a given number of particles. The overall reaction rate is below. , , These represent the number of reactant particles, acid particles, and base particles within a single grid cell, respectively. This represents the volume of a single grid cell. , , is the rate constant.

[0056] The three terms in the above overall reaction rate equation correspond to three different reaction pathways: the first term Corresponding to the bimolecular reaction between reactant particles and acid particles; the second term Corresponding to the unimolecular decomposition or deactivation reaction of acid particles; the third item This corresponds to the neutralization reaction between acid particles and base particles.

[0057] Overall reaction rate This reflects the rate at which a chemical reaction occurs under the current particle number condition. It is calculated... This allows for the dynamic determination of the time interval between the next reaction: The larger the value, the faster the response and the shorter the time step; The smaller the step size, the slower the response, and the longer the time step. This dynamic adjustment mechanism avoids the loss of computational accuracy or waste of computational resources caused by improper step size selection in traditional fixed-step methods.

[0058] Based on the aforementioned covariance correction equation and overall reaction rate equation, this invention employs a stochastic simulation method to determine the time step for each iteration. The derivation process is as follows: First, let the initial equation be: ; in, Indicates the initial conditions At that time The probability that no reaction has occurred.

[0059] Assuming the initial probability is 1 (i.e., no reaction has occurred at the initial time), solving the above differential equation yields: ; make Combining the probability density, we can obtain... arrive The state changes over time, and from this, we can obtain: ; in, For time step, A random number whose value is uniformly distributed in the interval [0, 1]. The total reaction rate is denoted as .

[0060] Therefore, the time step for each iteration can be determined according to the above formula. Based on this time step, the particle concentration in each grid cell can be iteratively updated by combining it with the overall reaction rate.

[0061] After generating a simulated photoresist morphology with edge roughness, quantitative indices for line edge roughness and linewidth roughness can be calculated based on the simulated morphology. These quantitative indices can objectively reflect the degree of deviation between the photoresist line edges and ideal smooth edges, providing data for parameter optimization and defect analysis in the photolithography process.

[0062] In practical applications, different simulation scenarios often have different requirements for computational efficiency and simulation accuracy. For example, in the rapid process verification stage, users may be more concerned with simulation speed; while in the defect analysis and process window evaluation stage, users are more concerned with the realism of the simulation results. Therefore, this embodiment supports enabling or disabling the random effects model. Specifically, when the random effects model is disabled, the post-exposure baking simulation process uses deterministic reaction-diffusion equations for calculation, generating a photoresist simulation morphology with smooth edges. In this case, the computational load is relatively small, suitable for rapid verification and ideal condition analysis. When the random effects model is enabled, the post-exposure baking simulation process uses reaction-diffusion equations embedded with the random effects model for calculation, generating a photoresist simulation morphology with edge roughness. Thus, users can flexibly choose the simulation mode according to specific needs, balancing different requirements for simulation speed and simulation accuracy.

[0063] In one optional embodiment, the exposure simulation process is performed before the post-exposure baking simulation process; and the development simulation process is performed after the post-exposure baking simulation process. That is, the photolithography simulation method of this embodiment sequentially executes the exposure simulation process, the post-exposure baking simulation process, and the development simulation process. Both the exposure simulation process and the development simulation process are calculated using deterministic reaction-diffusion equations, while only the post-exposure baking simulation process introduces a stochastic effects model.

[0064] The photolithography simulation methods described in the above embodiments can be implemented using computer program instructions. Therefore, this embodiment also provides a computer program product 41, a computer-readable storage medium 42, and a computer device 43. Figure 3 This is a schematic diagram of a computer program product according to an embodiment of the present invention. Figure 4 This is a schematic diagram of a computer-readable storage medium according to an embodiment of the present invention. Figure 5 This is a schematic block diagram of a computer device according to an embodiment of the present invention.

[0065] Computer program product 41 includes computer program 411, which, when executed by processor 431, implements any of the aforementioned photolithography simulation methods. Computer-readable storage medium 42 stores the aforementioned computer program 411, which, when executed by processor 431, implements any of the aforementioned photolithography simulation methods. Computer device 43 may include memory 432, processor 431, and computer program 411 stored in memory 432 and running on processor 431.

[0066] The computer program 411 used to perform the operations of this invention may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-related instructions, microcode, firmware instructions, status setting data, integrated circuit configuration data, or source code or object code written in any combination of one or more programming languages ​​and procedural programming languages.

[0067] Computer program 411 may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the latter case, the remote computer may be connected to the user's computer via any type of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, to perform aspects of the invention, electronic circuits including, for example, programmable logic circuits, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs) may execute computer-readable program instructions to personalize the electronic circuits by utilizing state information of computer-readable program instructions.

[0068] For the purposes of this embodiment, computer program product 41 refers to a related product containing computer program 411. Computer-readable storage medium 42 is a tangible device capable of holding and storing computer program 411, and can be any device capable of containing, storing, communicating, propagating, or transmitting computer program 411 for use by or in conjunction with an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable storage medium 42 include: portable computer disks, hard disks, random access memory 432 (RAM), read-only memory 432 (ROM), erasable programmable read-only memory 432 (EPROM or flash memory), static random access memory 432 (SRAM), portable optical disc read-only memory 432 (CD-ROM), digital multifunction disc (DVD), memory stick, floppy disk, mechanical encoding device, and any suitable combination thereof.

[0069] Therefore, those skilled in the art should recognize that although numerous exemplary embodiments of the present invention have been shown and described in detail herein, many other variations or modifications conforming to the principles of the present invention can be directly determined or derived from the disclosure of the present invention without departing from the spirit and scope of the invention. Thus, the scope of the present invention should be understood and construed as covering all such other variations or modifications.

Claims

1. A photolithography simulation method, characterized in that, include: During the post-exposure baking simulation, the reaction-diffusion equation with an embedded random effects model is used to iteratively calculate the particle concentration inside the photoresist, so as to apply statistical fluctuations to at least one calculation parameter in the iterative calculation, thereby simulating the randomness in the photolithography process. Based on the results of the post-exposure baking simulation, a photoresist simulation morphology with edge roughness is generated.

2. The photolithography simulation method according to claim 1, characterized in that, The steps for iteratively calculating the particle concentration inside the photoresist using the reaction-diffusion equation with an embedded random effects model include: The photoresist is spatially discretized into multiple grid units; The number of reactant particles, acid particles, and base particles in each grid cell are defined as random variables with a preset probability distribution. The current total reaction rate is determined based on the number of reactant particles, acid particles, and base particles within the grid cell. Generate a random number whose value is uniformly distributed within a preset range; The time step for this iteration is determined based on the total reaction rate and the random number. The simulation time is advanced by the stated time step, and the particle concentration in each of the stated grid cells is updated according to the total reaction rate.

3. The photolithography simulation method according to claim 2, characterized in that, The reaction-diffusion equation of the embedded random effects model includes the following covariance correction equation: ； ； ； in, , , These represent the concentrations of reactant particles, acid, and base, respectively. , , These represent the expected number of reactant particles, acid particles, and base particles within a single grid cell, respectively. This represents the volume of a single grid cell. , , The rate constant is for and The covariance is defined as: , for and The covariance is defined as: .

4. The photolithography simulation method according to claim 3, characterized in that, The reaction-diffusion equation embedded in the random effects model also includes the following overall reaction rate equation: ； in, Represents a state with a given number of particles. The overall reaction rate is below. , , These represent the number of reactant particles, acid particles, and base particles within a single grid cell, respectively. This represents the volume of a single grid cell. , , is the rate constant.

5. The photolithography simulation method according to claim 4, characterized in that, The time step is calculated according to the following formula: ； in, The time step is... The random number is a number whose value is uniformly distributed in the interval [0, 1]. .

6. The photolithography simulation method according to claim 1, characterized in that, The edge roughness includes line edge roughness and linewidth roughness. After the step of generating the photoresist simulation morphology with edge roughness, the method further includes: The quantitative indices of the line edge roughness and the line width roughness are calculated based on the simulated morphology of the photoresist.

7. The photolithography simulation method according to claim 1, characterized in that, The random effects model supports enabling or disabling configuration; When the random effects model is disabled, the post-exposure baking simulation process is calculated using a deterministic reaction-diffusion equation to generate a photoresist simulation morphology with smooth edges. When the stochastic effects model is enabled, the post-exposure baking simulation process is calculated using the reaction-diffusion equation embedded in the stochastic effects model to generate a photoresist simulation morphology with edge roughness.

8. The photolithography simulation method according to claim 7, characterized in that, Before performing the post-exposure baking simulation process, an exposure simulation process is performed; After performing the post-exposure baking simulation process, a development simulation process is performed; Both the exposure simulation process and the development simulation process are calculated using deterministic reaction-diffusion equations.

9. A computer program product, characterized in that, It includes a computer program that, when executed by a processor, implements the steps of the photolithography simulation method according to any one of claims 1 to 8.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the photolithography simulation method according to any one of claims 1 to 8.

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