Simulation methods, apparatus, computer equipment, and storage media for photoresist spin coating process

Abstract

This application relates to a method, apparatus, computer equipment, and storage medium for simulating photoresist spin coating processes. The method includes: establishing a fan-shaped simulation mesh based on the parameter information of the target wafer, the location information of the photoresist injection port, and the angle of the photoresist injection port; dividing the fan-shaped simulation mesh using a two-dimensional adaptive mesh refinement algorithm to obtain the target simulation mesh; constructing a two-phase fluid mathematical model; the two-phase fluid includes an air phase and a photoresist phase; iteratively solving the two-phase fluid mathematical model based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties to determine the simulated image of the photoresist spin coating process on the target wafer. This method can accurately refine the boundary between the two phases of the two-phase fluid in the photoresist spin coating process, strictly adhering to the geometric constraints of the two-dimensional model, thereby obtaining reliable simulation results for the photoresist spin coating process.

Description

Technical Field

[0001] This application relates to the field of photolithography process simulation technology, and in particular to a method, apparatus, computer equipment, and storage medium for simulating photoresist spin coating process. Background Technology

[0002] In semiconductor manufacturing, photolithography is the core of planar integrated circuit manufacturing, and photoresist coating, as a sub-process, significantly impacts chip yield due to its uniformity. Spin coating is a common method for photoresist application, utilizing the centrifugal force of wafer rotation to uniformly form a photoresist film. Photoresist thickness is affected by parameters such as wafer rotation speed and spin coating time. Traditional experimental optimization is costly and time-consuming, while mature computational fluid dynamics (CFD) simulation technology can optimize process parameters, provide data support, enable rapid design iteration, meet diverse product requirements, improve the predictability and controllability of the manufacturing process, and promote innovation and product advancement. It is a crucial technology in modern micro-nano fabrication. Because photoresist thickness is precisely controlled by various process parameters, such as wafer rotation speed, spin coating time, humidity, and temperature, optimizing photoresist coating performance through traditional experiments requires expensive testing and significant time. However, with the increasing maturity of CFD simulation technology, optimizing these process parameters using simulation has become possible. Simulation of the photoresist spin coating process provides crucial data support for process engineers designing spin coating process parameters. By adjusting different parameters such as spin coating speed, rotation speed, and photoresist concentration in the simulation model, the optimal combination of process parameters can be predicted and optimized to achieve the best pattern resolution and production efficiency. When simulating photolithography processes, the OpenFOAM (Open Source Field Operation and Manipulation) software package is often used to simulate the two-phase fluid in the process. However, currently, OpenFOAM only supports adaptive mesh refinement of hexahedral elements in three-dimensional meshes when simulating two-phase fluids; adaptive refinement of two-dimensional meshes leads to unstable simulation results. Therefore, obtaining reliable simulation results for photoresist spin coating processes is a problem that needs to be solved. Summary of the Invention

[0003] Therefore, it is necessary to provide a method, apparatus, computer equipment, and storage medium for simulating photoresist spin coating processes that can improve the reliability of simulation results for the aforementioned technical problems.

[0004] In a first aspect, this application provides a simulation method for photoresist spin coating process, the method comprising:

[0005] Based on the parameter information of the target wafer, the location information of the photoresist injection port, and the angle of the photoresist injection port, a fan-shaped simulation mesh is established;

[0006] A two-dimensional adaptive mesh refinement algorithm is used to divide the sector-shaped simulation mesh to obtain the target simulation mesh.

[0007] A mathematical model of a two-phase fluid is constructed; the two-phase fluid includes an air phase and a photoresist phase.

[0008] Based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties, the two-phase fluid mathematical model is iteratively solved to determine the simulated image of the photoresist spin coating process of the target wafer.

[0009] In one embodiment, a fan-shaped simulation mesh is established based on the parameter information of the target wafer, the location information of the photoresist injection port, and the angle of the photoresist injection port, including:

[0010] Based on the parameter information of the target wafer, the location information of the photoresist injection port, and the angle of the photoresist injection port, the mesh parameters are determined. The mesh parameters include mesh length, mesh height, and mesh center angle. The mesh length is equal to the radius of the wafer, the mesh height is equal to the height of the photoresist injection port, and the mesh center angle is the angle of the photoresist injection port.

[0011] A sector-shaped simulation mesh is established based on the right-handed Cartesian coordinate system and the aforementioned mesh parameters.

[0012] In one embodiment, a sector-shaped simulation mesh is established based on a right-handed Cartesian coordinate system and the mesh parameters, including:

[0013] The center point of the target wafer is determined, and the center point is used as the origin of a right-handed Cartesian coordinate system. The coordinate axes of the right-handed Cartesian coordinate system are constructed based on the origin of the coordinate system; the coordinate axes include the x-axis, y-axis and z-axis.

[0014] Use the y-axis of the right-handed Cartesian coordinate system as the axis of rotational symmetry;

[0015] Based on the rotational symmetry axis, a sector-shaped simulation mesh is established in the x-axis direction of the right-handed Cartesian coordinate system according to the mesh parameters.

[0016] In one embodiment, the element in the z-axis direction of the right-handed Cartesian coordinate system is kept at 1.

[0017] In one embodiment, a two-dimensional adaptive mesh refinement algorithm is used to divide the sector-shaped simulation mesh to obtain the target simulation mesh, including:

[0018] Based on a two-dimensional adaptive mesh encryption algorithm, the empty boundary or wedge boundary of the sector simulation mesh is determined, and the target interface of the sector simulation mesh is determined based on the empty boundary or the wedge boundary.

[0019] The center position of each edge on the target interface is used as a segmentation node. The fan-shaped simulation mesh is divided based on the segmentation nodes to obtain the target simulation mesh.

[0020] In one embodiment, the two-phase fluid mathematical model is iteratively solved based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties to determine the photoresist spin coating process simulation image of the target wafer, including:

[0021] The target solver in the two-dimensional adaptive mesh refinement algorithm is used to discretize the two-phase fluid mathematical model based on the boundary conditions of the target simulation mesh, the photoresist spin coating process parameters, the air fluid properties and the photoresist fluid properties, and to determine the discretized linear function.

[0022] The discretized linear function is preprocessed using a multi-grid preprocessor to determine the target linear function;

[0023] The target linear function is solved using a conjugate gradient method solver to determine the simulation image of the photoresist spin coating process for the target wafer.

[0024] In one embodiment, the above-mentioned photoresist spin coating process simulation method further includes:

[0025] Convert the simulated image of the photoresist spin coating process into a grayscale simulated image;

[0026] Convert the grayscale simulation image into a binary image;

[0027] The photoresist boundary pixels are determined based on the binary image, and the pixel coordinates of the photoresist boundary pixels are determined.

[0028] The photoresist outline is drawn based on the pixel coordinates.

[0029] Secondly, this application also provides a photoresist spin coating process simulation device, the device comprising:

[0030] The sector simulation mesh determination module is used to establish a sector simulation mesh based on the parameter information of the target wafer, the position information of the photoresist injection port, and the angle of the photoresist injection port.

[0031] The target simulation mesh determination module is used to divide the sector simulation mesh using a two-dimensional adaptive mesh refinement algorithm to obtain the target simulation mesh.

[0032] The fluid model creation module is used to construct a mathematical model of a two-phase fluid; the two-phase fluid includes an air phase and a photoresist phase;

[0033] The simulation image determination module is used to iteratively solve the two-phase fluid mathematical model based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties, and determine the photoresist spin coating process simulation image of the target wafer.

[0034] Thirdly, this application also provides a computer device, the computer device including a memory and a processor, the memory storing a computer program, and the processor executing the computer program to perform the following steps:

[0035] The sector simulation mesh determination module is used to establish a sector simulation mesh based on the parameter information of the target wafer, the position information of the photoresist injection port, and the angle of the photoresist injection port.

[0036] The target simulation mesh determination module is used to divide the sector simulation mesh using a two-dimensional adaptive mesh refinement algorithm to obtain the target simulation mesh.

[0037] The fluid model creation module is used to construct a mathematical model of a two-phase fluid; the two-phase fluid includes an air phase and a photoresist phase;

[0038] The simulation image determination module is used to iteratively solve the two-phase fluid mathematical model based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties, and determine the photoresist spin coating process simulation image of the target wafer.

[0039] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0040] The sector simulation mesh determination module is used to establish a sector simulation mesh based on the parameter information of the target wafer, the position information of the photoresist injection port, and the angle of the photoresist injection port.

[0041] The target simulation mesh determination module is used to divide the sector simulation mesh using a two-dimensional adaptive mesh refinement algorithm to obtain the target simulation mesh.

[0042] The fluid model creation module is used to construct a mathematical model of a two-phase fluid; the two-phase fluid includes an air phase and a photoresist phase;

[0043] The simulation image determination module is used to iteratively solve the two-phase fluid mathematical model based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties, and determine the photoresist spin coating process simulation image of the target wafer.

[0044] The aforementioned simulation method, apparatus, computer equipment, and storage medium for photoresist spin coating process establish a fan-shaped simulation mesh based on the target wafer's parameter information, the location information of the photoresist injection port, and the angle of the photoresist injection port. A two-dimensional adaptive mesh refinement algorithm is used to divide the fan-shaped simulation mesh into a target simulation mesh. A two-phase fluid mathematical model is constructed, comprising an air phase and a photoresist phase. Based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties, the two-phase fluid mathematical model is iteratively solved to determine the simulated image of the photoresist spin coating process on the target wafer. This solves the problem that OpenFOAM currently only supports adaptive mesh refinement for hexahedral elements in three-dimensional meshes when simulating two-phase fluids, while unstable simulation results occur when adaptively refining two-dimensional meshes. The above scheme uses a two-dimensional adaptive mesh refinement algorithm to divide the fan-shaped simulation mesh to determine the target simulation mesh, thereby determining the simulated image of the photoresist spin coating process on the target wafer based on the target simulation mesh and the two-phase fluid mathematical model. It can accurately refine the interface between two phases of the two-phase fluid in the photoresist spin coating process, avoiding droplet breakage and numerical instability, maintaining the integrity of the axisymmetric mesh, and strictly following the geometric constraints of the two-dimensional model, thereby obtaining reliable simulation results of the photoresist spin coating process. Attached Figure Description

[0045] Figure 1 This is an application environment diagram of a photoresist spin coating process simulation method in one embodiment;

[0046] Figure 2 This is a flowchart illustrating a simulation method for photoresist spin coating in one embodiment;

[0047] Figure 3 Here is an example diagram of a fan-shaped simulation mesh in one embodiment;

[0048] Figure 4 This is an example diagram of an octree refinement structure in one embodiment;

[0049] Figure 5 This is an example diagram of a quadtree refinement structure in one embodiment;

[0050] Figure 6 This is an example diagram of a quadtree refinement structure in another embodiment;

[0051] Figure 7 This is an example simulation image of the photoresist spin coating process on a target wafer in one embodiment.

[0052] Figure 8 This is a flowchart illustrating the simulation method for photoresist spin coating in another embodiment;

[0053] Figure 9 This is an example diagram of a two-dimensional dam failure calculation in one embodiment;

[0054] Figure 10 Here is an example image of a grid-segmented image in one embodiment;

[0055] Figure 11 This is a schematic diagram of a photoresist spin coating process simulation device in one embodiment;

[0056] Figure 12 FIG. 1 is a diagram showing the internal structure of a computer device in one embodiment. Detailed Implementation

[0057] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0058] The photoresist spin coating process simulation method provided in this application embodiment can be applied to, for example... Figure 1 In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be integrated onto server 104 or placed on a cloud or other network server. Server 104 establishes a fan-shaped simulation mesh based on the parameter information of the target wafer, the location information of the photoresist injection port, and the angle of the photoresist injection port; it uses a two-dimensional adaptive mesh refinement algorithm to divide the fan-shaped simulation mesh into a target simulation mesh; it constructs a two-phase fluid mathematical model; the two-phase fluid includes an air phase and a photoresist phase; based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties, iteratively solves the two-phase fluid mathematical model to determine the photoresist spin coating process simulation image of the target wafer, and sends the photoresist spin coating process simulation image to terminal 102 via a communication network. Terminal 102 can be, but is not limited to, various personal computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can include smart speakers, smart TVs, smart air conditioners, smart vehicle devices, etc. Portable wearable devices can include smartwatches, smart bracelets, and head-mounted devices. Server 104 can be implemented using a standalone server or a server cluster consisting of multiple servers.

[0059] In one embodiment, such as Figure 2As shown, a simulation method for photoresist spin coating process is provided. This embodiment illustrates the application of this method to a terminal. It is understood that this method can also be applied to a server, and to a system including both a terminal and a server, and can be implemented through interaction between the terminal and the server. In this embodiment, the method includes the following steps:

[0060] S210. Based on the parameter information of the target wafer, the position information of the photoresist injection port, and the angle of the photoresist injection port, a fan-shaped simulation mesh is established.

[0061] The target wafer's parameter information includes its surface parameters and radius; surface parameters include surface flatness. The photoresist injection port is a dedicated port for introducing photoresist onto the target wafer surface; the photoresist injection port can be a nozzle, needle, or other type of delivery device, as long as it ensures that the photoresist is coated on the target wafer surface with a uniform thickness; no specific limitations are made here. The photoresist injection port's location information includes its height; the photoresist injection port height refers to the vertical distance of the photoresist injection port relative to the target wafer surface. The target wafer's parameter information and the angle of the photoresist injection port can be set according to actual needs.

[0062] It should be noted that, to simulate the two-dimensional axisymmetric flow of photoresist spin coating, a fan-shaped mesh region needs to be established. The bottom surface of the fan-shaped simulation mesh is the base of the target wafer, the top surface is the plane where the photoresist injection port is located, and the length is the radius of the target wafer. The fan-shaped simulation mesh can be a fan-shaped spatial region within a cylindrical space enclosed by extending the target wafer's base as the bottom surface and the plane where the photoresist injection port is located as the top surface.

[0063] S220. A two-dimensional adaptive mesh refinement algorithm is used to divide the sector simulation mesh to obtain the target simulation mesh.

[0064] Among them, the two-dimensional adaptive mesh refinement algorithm is a method for adaptively refining the mesh of a two-dimensional model during simulation. Adaptive mesh refinement is a technique that dynamically adjusts the mesh density, aiming to automatically optimize the mesh distribution based on changes in physical quantities during computation, thereby improving computational accuracy and efficiency. The core idea of ​​adaptive mesh refinement technology is to dynamically adjust the mesh density based on changes in physical quantities within the computational domain, such as velocity gradients and pressure gradients. In regions with drastic flow field changes, such as turbulence and boundary layers, the mesh is automatically refined to capture details; while in regions with smaller changes, the mesh is automatically coarsened to save computational resources.

[0065] It should be noted that when simulating a 2D model, OpenFOAM can still divide the model into a hexahedral mesh, but it needs to constrain the unit of one coordinate dimension of the mesh to 1. That is, the constrained coordinate dimension will not participate in the mesh refinement calculation. For example, a sector-shaped simulation mesh is shown below. Figure 3 As shown, only one grid thickness is set in the z-axis direction, with the leftmost axis as the rotational symmetry axis. During photoresist spin coating of the target wafer, the photoresist flows from the photoresist injection port to the target wafer, and the substrate corresponding to the target wafer rotates around the rotational symmetry axis at a certain rotational speed to spin coat the photoresist onto the entire surface of the target wafer.

[0066] The existing OpenFOAM adaptive mesh refinement algorithm, when performing mesh refinement, uses an octree thinning scheme for mesh division and refinement of the 3D model. The octree thinning structure is as follows: Figure 4As shown. In three-dimensional space, hexahedral elements are subdivided using an octree structure. Each hexahedral element is associated with a so-called refinement level, which determines whether the element needs to be further subdivided to improve local mesh accuracy. When refinement is required, a hexahedral element is uniformly cut into eight smaller sub-elements, each maintaining its hexahedral shape. These sub-elements share 36 faces, with 12 faces located inside the original parent element and the remaining 24 faces connected to adjacent elements. During element refinement, to maintain the continuity and accuracy of the numerical simulation, sub-elements inherit some key properties from the parent element. Specifically, the element center value of the sub-elements is initialized to the element center value of the parent element, where the element center value can be the volume average of physical quantities such as pressure or temperature. This is because most solvers in OpenFOAM are based on flux, which is typically represented in simulations as a surface field, i.e., a value associated with the mesh surface. Flux is the physical quantity passing through a unit area per unit time. Since most OpenFOAM solvers are flux-based, and flux is related to mesh surfaces, the center values ​​of sub-elements are initialized to the center values ​​of the parent element during element refinement to ensure the continuity and accuracy of the numerical simulation. For flux-related surface fields, the values ​​on the refined surfaces require special handling. These refined surfaces are called "sub-surfaces," and they are four new faces created by dividing a face of the parent element. During refinement, the initial values ​​of these sub-surfaces are set to the values ​​of the corresponding parent faces. This approach ensures the consistency and conservation of flux during mesh refinement, while avoiding numerical discontinuities or errors caused by mesh changes. Through this meticulous value transfer and initialization mechanism, the adaptive mesh refinement algorithm based on the 3D model can improve the accuracy and reliability of complex flow simulations while maintaining computational efficiency. However, in the process of mesh generation using the octree refinement scheme, the mesh along the z-axis is divided. If the octree refinement scheme is used to mesh the aforementioned sector simulation mesh, it can lead to large errors and difficulty in convergence when iteratively solving the two-phase fluid mathematical model based on the divided mesh.

[0067] For example, a two-dimensional adaptive mesh refinement algorithm is used to divide the sector-shaped simulation mesh to obtain the target simulation mesh, including:

[0068] Based on the two-dimensional adaptive mesh densification algorithm, the empty boundary or wedge boundary of the fan-shaped simulation mesh is determined, and the target interface of the fan-shaped simulation mesh is determined based on the empty boundary or wedge boundary. The center position of each edge on the target interface is used as the segmentation node, and the fan-shaped simulation mesh is divided into meshes based on the segmentation nodes to obtain the target simulation mesh.

[0069] It should be noted that in the OpenFOAM-based 2D adaptive mesh refinement algorithm, a quadtree mesh subdivision method is used instead of the original octree mesh subdivision method. The core of quadtree subdivision lies in dividing the cells to introduce new cells, while ensuring that unnecessary subdivisions are not performed in the z-axis direction of a single-layer mesh, so as to maintain the structure and computational efficiency of the 2D mesh.

[0070] Specifically, the boundary conditions of the sector simulation mesh are determined. Based on these boundary conditions, the empty or wedge-shaped boundaries of the sector simulation mesh are determined. Empty boundaries belong to the "Empty" boundary, and wedge-shaped boundaries belong to the "Wedge" boundary. Specifically, solid wall boundary conditions can be used as the boundary conditions corresponding to the bottom surface of the sector simulation mesh, wedge-shaped boundary conditions as the boundary conditions corresponding to the front and back surfaces of the sector simulation mesh, and atmospheric boundary conditions as the boundary conditions corresponding to the top and right surfaces of the sector simulation mesh. Solid wall boundary conditions describe the behavior of the photoresist fluid in contact with the solid wall surface, i.e., the target wafer surface. Wedge-shaped boundary conditions are suitable for axisymmetric problems and are used to simulate axisymmetric geometries. Atmospheric boundary conditions are used to simulate fluid inflow or outflow from the computational domain. The interface containing the empty or wedge-shaped boundary is used as the target interface of the sector simulation mesh. The center position of each edge on the target interface is used as a partitioning node. The sector simulation mesh is then divided based on these partitioning nodes to obtain the target simulation mesh.

[0071] For example, Figure 5 As shown, after determining the empty boundary of the sector simulation mesh, the center position of each edge of the target interface on the empty boundary is used as a splitting node. Based on the splitting nodes, the target interface is divided into four new sub-faces, and each new sub-face is assigned a new owner cell and neighboring cells. Other interfaces in the sector simulation mesh besides the target interface can be divided into two new faces based on the splitting nodes. Based on the above splitting method, four new internal faces can be created within the sector simulation mesh. The addition of these internal faces ensures the integrity and connectivity of the mesh cells and provides the necessary structural support for subsequent numerical calculations.

[0072] For example, Figure 6As shown, the wedge-shaped boundary of the fan-shaped simulation mesh is determined. The fan-shaped simulation mesh is not a standard hexahedral shape; the target interface at the wedge boundary contains three vertices. During the refinement process of the fan-shaped simulation mesh, the target interface is divided into two new faces, one containing four vertices and the other containing three vertices. Additionally, an internal face containing three vertices should be added, one of which is the midpoint of the centerline edge. In axisymmetric photoresist spin coating simulations, the cells on the centerline need to be meshed in the above manner to ensure the geometric correctness of the mesh and the accuracy of the calculation. Through a precise quadtree subdivision method, the overall mesh count is optimized while ensuring the mesh accuracy in key areas, reducing computational resource consumption.

[0073] The aforementioned fan-shaped simulation mesh generation method effectively divides the simulation mesh during the photoresist spin coating process, generating a highly adaptable and accurate mesh to meet simulation requirements. This scheme not only improves the local resolution of the target simulation mesh but also maintains the connectivity between them, providing a foundation for efficient numerical simulation.

[0074] S230. Construct a mathematical model for two-phase fluid.

[0075] The two-phase fluid includes an air phase and a photoresist phase.

[0076] It should be noted that a two-phase fluid mathematical model can be built using OpenFOAM. The `constant` folder in OpenFOAM contains the physical property files required by the program. The photoresist spin coating process can be viewed as a process of layering and motion; therefore, a laminar flow model can be used as the mathematical model for the two-phase fluid. Laminar flow is a type of fluid flow characterized by smooth, regular flow paths, with fluid particles moving in straight lines parallel to the pipe axis, and each layer not interfering with the others. The two-phase fluid mathematical model includes the continuity equation, momentum equation, and interface tracking equation. The continuity equation describes the principle of mass conservation in fluids; the momentum equation includes the Navier-Stokes equations, used to describe the continuity and momentum conservation of the fluid; and the interface tracking equation includes the volume fraction equation, used to describe the position and shape of the interface between the two phases.

[0077] S240. Based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties, the two-phase fluid mathematical model is iteratively solved to determine the simulation image of the photoresist spin coating process of the target wafer.

[0078] In the right-handed Cartesian coordinate system, the sector-shaped simulation mesh includes a bottom surface, a front surface, a back surface, a top surface, and a right surface. Solid wall boundary conditions are used as the boundary conditions corresponding to the bottom surface of the sector-shaped simulation mesh; wedge-shaped boundary conditions are used as the boundary conditions corresponding to the front and back surfaces; and atmospheric boundary conditions are used as the boundary conditions corresponding to the top and right surfaces. Photoresist spin-coating process parameters include the initial photoresist injection speed, the initial rotational speed of the target wafer, and the process atmosphere. The initial photoresist injection speed and the initial rotational speed of the target wafer can be set according to actual needs, and the process atmosphere is standard atmospheric pressure. The corresponding fluid properties for air include fluid viscosity model, aerodynamic viscosity, and air fluid density. The corresponding fluid properties for photoresist include fluid viscosity model, photoresist dynamic viscosity, photoresist fluid density, and environmental gravity. Aerodynamic viscosity, air fluid density, photoresist dynamic viscosity, and photoresist fluid density can be set according to actual needs. Fluid viscosity models can be constant viscosity models. A constant viscosity model means that in the simulation of photoresist spin coating process, the dynamic viscosity of the fluid is regarded as a constant and does not change with the temperature or pressure.

[0079] Specifically, the two-phase fluid mathematical model is iteratively solved using the target solver in OpenFOAM based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties until the convergence criterion is met, thereby determining the simulation image of the photoresist spin coating process of the target wafer.

[0080] For example, the simulated image of the photoresist spin coating process of the target wafer obtained by the above method is as follows: Figure 7 As shown. It is understandable that... Figure 7 The simulation image of the photoresist spin coating process did not show droplet breakage or numerical instability. The mesh was correctly refined, and the mesh at the axisymmetric location did not need to be changed. Therefore, the two-dimensional adaptive mesh refinement algorithm can correctly refine the wedge-shaped mesh at the axis of symmetry.

[0081] In the aforementioned simulation method for photoresist spin coating, a fan-shaped simulation mesh is established based on the parameter information of the target wafer, the position information of the photoresist injection port, and the angle of the photoresist injection port. A two-dimensional adaptive mesh refinement algorithm is used to divide the fan-shaped simulation mesh to obtain the target simulation mesh. A two-phase fluid mathematical model is constructed, comprising an air phase and a photoresist phase. Based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties, the two-phase fluid mathematical model is iteratively solved to determine the simulation image of the photoresist spin coating process for the target wafer. This solves the problem that OpenFOAM currently only supports adaptive mesh refinement for hexahedral elements in three-dimensional meshes when simulating two-phase fluids, while the simulation results become unstable when adaptively refining two-dimensional meshes. The above scheme uses a two-dimensional adaptive mesh refinement algorithm to divide the fan-shaped simulation mesh to determine the target simulation mesh, thereby determining the simulation image of the photoresist spin coating process for the target wafer based on the target simulation mesh and the two-phase fluid mathematical model. It can accurately refine the interface between two phases of the two-phase fluid in the photoresist spin coating process, avoiding droplet breakage and numerical instability, maintaining the integrity of the axisymmetric mesh, and strictly following the geometric constraints of the two-dimensional model, thereby obtaining reliable simulation results of the photoresist spin coating process.

[0082] In one embodiment, such as Figure 8 As shown, based on the parameter information of the target wafer, the location information of the photoresist injection port, and the angle of the photoresist injection port, a fan-shaped simulation mesh is established, including:

[0083] S310. Based on the parameter information of the target wafer, the position information of the photoresist injection port, and the angle of the photoresist injection port, determine the mesh parameters.

[0084] The mesh parameters include mesh length, mesh height, and mesh center angle; the mesh length is equal to the radius of the wafer, the mesh height is equal to the height of the photoresist injection port, and the mesh center angle is the angle of the photoresist injection port.

[0085] The target wafer parameters include its center coordinates, surface parameters, and radius; surface parameters include surface flatness. The photoresist injection port refers to the dedicated port used to introduce photoresist onto the target wafer surface. The angle of the photoresist injection port can be set according to actual needs. Mesh parameters refer to the parameter information of the constructed fan-shaped simulation mesh, including its length, height, and central angle; the length of the fan-shaped simulation mesh is equal to the radius of the target wafer, the height of the fan-shaped simulation mesh is equal to the height of the photoresist injection port, and the central angle of the fan-shaped simulation mesh is equal to a preset angle.

[0086] S320. Based on the right-handed Cartesian coordinate system and mesh parameters, a sector-shaped simulation mesh is established.

[0087] In this system, the element along the z-axis of the right-handed Cartesian coordinate system is kept at 1.

[0088] For example, the method for establishing a sector-shaped simulation mesh can be as follows: determine the center point of the target wafer, take the center point as the origin of the right-handed Cartesian coordinate system, and construct the coordinate axes of the right-handed Cartesian coordinate system based on the origin; the coordinate axes include the x-axis, y-axis and z-axis; take the y-axis of the right-handed Cartesian coordinate system as the rotational symmetry axis; based on the rotational symmetry axis, establish a sector-shaped simulation mesh in the x-axis direction of the right-handed Cartesian coordinate system according to the mesh parameters.

[0089] Specifically, a right-handed Cartesian coordinate system is constructed using the center coordinates of the target wafer as the origin. Based on this system, the y-axis is used as the axis of rotational symmetry. The initial sector-shaped simulation mesh is symmetrically distributed along the xy-plane of the right-handed Cartesian coordinate system, and the photoresist injection port is located on the side of the initial sector-shaped simulation mesh closest to the axis of rotational symmetry. Based on the mesh parameters of the sector-shaped simulation mesh, a sector-shaped simulation mesh is generated along the positive x-axis of the right-handed Cartesian coordinate system.

[0090] In the above scheme, the elements in the z-axis direction of the right-handed Cartesian coordinate system are kept at 1, which enables the subsequent meshing of the sector simulation mesh through a two-dimensional adaptive mesh refinement algorithm, ensuring the accuracy of the sector simulation mesh division and thus improving the reliability of the obtained photoresist spin coating process simulation image.

[0091] In one embodiment, the two-phase fluid mathematical model is iteratively solved based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties to determine the simulated image of the photoresist spin coating process on the target wafer, including:

[0092] The target solver in the two-dimensional adaptive mesh refinement algorithm is used to discretize the two-phase fluid mathematical model based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties, and to determine the discretized linear function. The discretized linear function is preprocessed by a multi-mesh preprocessor to determine the target linear function. The target linear function is solved by the conjugate gradient method solver to determine the simulation image of the photoresist spin coating process of the target wafer.

[0093] The objective solver can be the interFoam solver in OpenFOAM, and the multigrid preprocessor can be GAMG (Geometric Algebraic Multigrid), which can accelerate convergence through the synergistic effect of different grid levels. It requires explicitly creating a grid hierarchy from fine to coarse. The conjugate gradient method, or PCG (Preconditioned Conjugate Gradient), is an iterative algorithm that accelerates convergence by introducing a preprocessing matrix and is mainly used to solve large-scale linear equation systems.

[0094] Specifically, the interFoam solver in OpenFOAM discretizes the two-phase fluid mathematical model based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties to determine the discretized linear function. A multi-grid preprocessor preprocesses the discretized linear function to determine the target linear function. The conjugate gradient method solver then solves the target linear function until the solution converges, thus determining the simulation image of the photoresist spin coating process on the target wafer.

[0095] The above scheme uses the target solver, multi-grid preprocessor and conjugate gradient method in the two-dimensional adaptive grid encryption algorithm to iteratively solve the two-phase fluid mathematical model to obtain the simulation image of the photoresist spin coating process of the target wafer, which can improve the efficiency of obtaining the simulation image of the photoresist spin coating process.

[0096] In one embodiment, the above-mentioned photoresist spin coating process simulation method further includes:

[0097] The simulation image of the photoresist spin coating process is converted into a grayscale simulation image; the grayscale simulation image is converted into a binary image; the boundary pixels of the photoresist are determined based on the binary image, and the pixel coordinates of the boundary pixels of the photoresist are determined; the photoresist outline is drawn based on the pixel coordinates.

[0098] Specifically, the photoresist spin coating process simulation image details the distribution of photoresist on the target wafer surface under different process parameters. The simulation image is read and converted into a grayscale image. Converting a color image to grayscale simplifies subsequent processing, reduces computation, and improves processing speed. Based on the grayscale image, pixels are divided into foreground and background regions according to a pre-set grayscale threshold. The foreground region represents the photoresist area, and the background region represents the non-photoresist area. Foreground pixels have grayscale values ​​greater than the grayscale threshold, while background pixels have grayscale values ​​less than or equal to the grayscale threshold. Converting the image to a binary image makes the extracted photoresist outline clearer. In a binary image, the photoresist outline is defined by pixel edges. By scanning the pixels of the image, the boundary between the photoresist and the background is identified. The boundary pixels of the photoresist and background are tracked, and their coordinates are recorded. The collected boundary pixel coordinates are used to draw the photoresist outline image on a new image.

[0099] Understandably, the photoresist outline image clearly shows the distribution range and morphology of the photoresist on the wafer. The extracted outline can be used for further analysis, and key parameters such as the coverage area, thickness distribution, and uniformity of the photoresist can be calculated.

[0100] Understandably, the aforementioned two-dimensional adaptive mesh refinement algorithm can be widely applied to two-dimensional simulation problems in various fields, including but not limited to fluid mechanics, heat transfer, and chemical reactive flow. For example, it can also be used to capture phase interfaces in multiphase flows. Besides photoresist spin coating simulations, accurate capture of phase interfaces is crucial for understanding fluid interactions and mass and heat transfer processes in multiphase flow simulations such as gas-liquid two-phase flow and liquid-liquid extraction. The two-dimensional adaptive mesh refinement algorithm effectively captures subtle changes at the phase interface, making the simulation results closer to actual physical phenomena. It can also be used for combustion problems. Physical quantities such as temperature and component concentration exhibit huge gradients near the flame front. The algorithm automatically refines the mesh locally near the flame front, better resolving flame front details while maintaining a relatively small computational load. Furthermore, it can be used for flow problems. Under certain conditions, the velocity field may have huge gradients, especially under supersonic conditions, where the gradients of physical quantities before and after the shock wave are extremely large. The algorithm can capture the shock wave well and efficiently reconstruct the distribution of physical quantities in complex flow fields.

[0101] For example, the two-dimensional model simulation method based on the two-dimensional adaptive mesh refinement algorithm described above can also be used to simulate two-dimensional dam-break problems. Dam-break problems, as classic two-dimensional or three-dimensional multiphase and dynamic problems, are often used as test cases to verify and evaluate the accuracy and reliability of multiphase flow numerical methods and models. Many researchers use two-phase flow solvers in OpenFOAM, such as interFoam, to simulate dam-break problems to test the performance of the adopted numerical methods in capturing free surfaces and calculating interphase interactions. Figure 9 As shown, a simplified two-dimensional dam-break simulation example is used. The scenario depicts a dam collapse, with water flowing downstream and impacting downstream structures. The physical process of the two-dimensional dam-break simulation is as follows: Initially, a static water body is used to simulate the water storage of a reservoir, positioned on the left side of the model. At the bottom of the tank, there is a small obstacle, the protrusion at the bottom of the mesh, simulating a structure. During the simulation, at t=0s, the water column is allowed to collapse and flow freely under the influence of gravity. During the collapse, the water flow impacts an obstacle at the bottom of the tank, forming a complex flow field structure, including several water-encased air bubbles. The mesh segmentation image obtained by simulating the two-dimensional dam-break simulation using the above two-dimensional model simulation method based on the two-dimensional adaptive mesh refinement algorithm is shown below. Figure 10As shown, when simulating a two-dimensional dam-break example using a two-dimensional model simulation method based on a two-dimensional adaptive mesh refinement algorithm, the algorithm dynamically refines and adjusts the mesh according to the motion and changes of the fluid. For example, in key areas such as the formation of complex flow field structures by water impacting obstacles and the generation of bubbles, the algorithm automatically increases the mesh density, making the capture of fluid boundaries more accurate and clearly presenting the true flow pattern of the fluid. After applying the two-dimensional adaptive mesh refinement algorithm, the mesh is significantly refined in key areas and continuously adjusted with the movement of the fluid, better adapting to the dynamic characteristics of the fluid. By increasing the mesh density in key areas, numerical calculations can capture the microscopic changes of the fluid more meticulously, such as subtle fluctuations at the phase interface, the formation and evolution of bubbles, etc., thereby improving the calculation accuracy and making the simulation results closer to the actual physical process, achieving an accurate description of complex flow fields. Compared with mesh generation methods that directly increase the overall mesh density, the two-dimensional adaptive mesh refinement algorithm only refines the mesh in key areas of interest, while maintaining a sparser mesh in areas where fluid changes are relatively gentle, avoiding unnecessary waste of computational resources. In this way, while ensuring computational accuracy, computational efficiency is improved and computation time is shortened, enabling more accurate solutions to two-dimensional simulation problems within limited computational resources and time. The aforementioned two-dimensional adaptive mesh refinement algorithm, by dynamically refining the mesh in key regions, accurately captures phase interface changes and effectively balances computational accuracy and cost. It provides a solution that combines accuracy and efficiency for two-dimensional simulation problems on the OpenFOAM platform, expanding the platform's application scope and offering a new method for simulating complex two-dimensional flow fields.

[0102] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0103] Based on the same inventive concept, this application also provides a photoresist spin coating process simulation apparatus for implementing the above-described photoresist spin coating process simulation method. The solution provided by this apparatus is similar to the implementation scheme described in the above method. Therefore, the specific limitations of one or more photoresist spin coating process simulation apparatus embodiments provided below can be found in the limitations of the photoresist spin coating process simulation method described above, and will not be repeated here.

[0104] In one embodiment, such as Figure 11 As shown, a simulation device for photoresist spin coating process is provided, including: a fan-shaped simulation mesh determination module 1101, a target simulation mesh determination module 1102, a fluid model creation module 1103, and a simulation image determination module 1104, wherein:

[0105] The sector simulation mesh determination module 1101 is used to establish a sector simulation mesh based on the parameter information of the target wafer, the position information of the photoresist injection port, and the angle of the photoresist injection port.

[0106] The target simulation mesh determination module 1102 is used to divide the sector simulation mesh using a two-dimensional adaptive mesh refinement algorithm to obtain the target simulation mesh.

[0107] Fluid model creation module 1103 is used to construct a mathematical model of a two-phase fluid; the two-phase fluid includes an air phase and a photoresist phase.

[0108] The simulation image determination module 1104 is used to iteratively solve the two-phase fluid mathematical model based on the boundary conditions of the target simulation mesh, the photoresist spin coating process parameters, the air fluid properties and the photoresist fluid properties, and to determine the simulation image of the photoresist spin coating process of the target wafer.

[0109] For example, the sector simulation mesh determination module 1101 is specifically used for:

[0110] Based on the parameter information of the target wafer, the location information of the photoresist injection port, and the angle of the photoresist injection port, the mesh parameters are determined. The mesh parameters include mesh length, mesh height, and mesh center angle. The mesh length is equal to the radius of the wafer, the mesh height is equal to the height of the photoresist injection port, and the mesh center angle is the angle of the photoresist injection port.

[0111] A sector-shaped simulation mesh is established based on a right-handed Cartesian coordinate system and mesh parameters.

[0112] Furthermore, the sector simulation mesh determination module 1101 is also specifically used for:

[0113] Determine the center point of the target wafer and use it as the origin of a right-handed Cartesian coordinate system. Construct the coordinate axes of the right-handed Cartesian coordinate system based on the origin; the coordinate axes include the x-axis, y-axis, and z-axis.

[0114] Use the y-axis of the right-handed Cartesian coordinate system as the axis of rotational symmetry;

[0115] Based on the rotational symmetry axis, a sector-shaped simulation mesh is established in the x-axis direction of the right-handed Cartesian coordinate system according to the mesh parameters.

[0116] Furthermore, the element in the z-axis direction of the right-handed Cartesian coordinate system remains 1.

[0117] For example, the target simulation mesh determination module 1102 is specifically used for:

[0118] Based on the two-dimensional adaptive mesh densification algorithm, the empty boundary or wedge boundary of the sector simulation mesh is determined, and the target interface of the sector simulation mesh is determined based on the empty boundary or wedge boundary.

[0119] The center position of each edge on the target interface is used as a segmentation node. The fan-shaped simulation mesh is divided based on the segmentation nodes to obtain the target simulation mesh.

[0120] For example, the simulation image determination module 1104 is specifically used for:

[0121] The objective solver in the two-dimensional adaptive mesh refinement algorithm is used to discretize the two-phase fluid mathematical model based on the boundary conditions of the objective simulation mesh, the photoresist spin coating process parameters, the air fluid properties and the photoresist fluid properties, and to determine the discretized linear function.

[0122] The discretized linear function is preprocessed using a multi-grid preprocessor to determine the target linear function;

[0123] The target linear function is solved using a conjugate gradient method solver to determine the simulation image of the photoresist spin coating process on the target wafer.

[0124] For example, the above-mentioned photoresist spin coating process simulation device further includes a photoresist contour drawing module, which is used to: convert the photoresist spin coating process simulation image into a grayscale simulation image; convert the grayscale simulation image into a binary image; determine the photoresist boundary pixels based on the binary image, and determine the pixel coordinates of the photoresist boundary pixels; and draw the photoresist contour based on the pixel coordinates.

[0125] Each module in the aforementioned photoresist spin coating process simulation device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in the processor of a computer device in hardware form or independent of it, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each module.

[0126] In one embodiment, a computer device is provided. The computer device may be a terminal, and its internal structure diagram may be as follows: Figure 12 As shown, the computer device includes a processor, memory, input / output interfaces, a communication interface, a display unit, and an input device. The processor, memory, and input / output interfaces are connected via a system bus, and the communication interface, display unit, and input device are also connected to the system bus via the input / output interfaces. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The input / output interfaces are used for exchanging information between the processor and external devices. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, mobile cellular networks, NFC (Near Field Communication), or other technologies. When the computer program is executed by the processor, it implements a photoresist spin coating process simulation method. The display unit is used to form a visually visible image and can be a display screen, a projection device, or a virtual reality imaging device. The display screen can be an LCD screen or an e-ink screen. The input device of the computer device can be a touch layer covering the display screen, or buttons, trackballs, or touchpads set on the casing of the computer device, or external keyboards, touchpads, or mice, etc.

[0127] Those skilled in the art will understand that Figure 12 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0128] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:

[0129] Step 1: Based on the parameter information of the target wafer, the location information of the photoresist injection port, and the angle of the photoresist injection port, establish a fan-shaped simulation mesh;

[0130] Step 2: Use a two-dimensional adaptive mesh refinement algorithm to divide the sector simulation mesh to obtain the target simulation mesh;

[0131] Step 3: Construct a mathematical model for the two-phase fluid; the two-phase fluid includes an air phase and a photoresist phase;

[0132] Step 4: Based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties, iteratively solve the two-phase fluid mathematical model to determine the simulation image of the photoresist spin coating process of the target wafer.

[0133] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0134] Step 1: Based on the parameter information of the target wafer, the position information of the photoresist injection port, and the angle of the photoresist injection port, establish a fan-shaped simulation mesh;

[0135] Step 2: Use a two-dimensional adaptive mesh refinement algorithm to divide the sector simulation mesh to obtain the target simulation mesh;

[0136] Step 3: Construct a mathematical model for the two-phase fluid; the two-phase fluid includes an air phase and a photoresist phase;

[0137] Step 4: Based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties, iteratively solve the two-phase fluid mathematical model to determine the simulation image of the photoresist spin coating process of the target wafer.

[0138] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, performs the following steps:

[0139] Step 1: Based on the parameter information of the target wafer, the position information of the photoresist injection port, and the angle of the photoresist injection port, establish a fan-shaped simulation mesh;

[0140] Step 2: Use a two-dimensional adaptive mesh refinement algorithm to divide the sector simulation mesh to obtain the target simulation mesh;

[0141] Step 3: Construct a mathematical model for the two-phase fluid; the two-phase fluid includes an air phase and a photoresist phase;

[0142] Step 4: Based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties, iteratively solve the two-phase fluid mathematical model to determine the simulation image of the photoresist spin coating process of the target wafer.

[0143] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of related data must comply with the relevant laws, regulations and standards of the relevant countries and regions.

[0144] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0145] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0146] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A simulation method for photoresist spin coating process, characterized in that, include: Based on the parameter information of the target wafer, the location information of the photoresist injection port, and the angle of the photoresist injection port, a fan-shaped simulation mesh is established; A two-dimensional adaptive mesh refinement algorithm is used to divide the sector-shaped simulation mesh to obtain the target simulation mesh. A mathematical model of a two-phase fluid is constructed; the two-phase fluid includes an air phase and a photoresist phase. Based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties, the two-phase fluid mathematical model is iteratively solved to determine the simulated image of the photoresist spin coating process of the target wafer.

2. The method according to claim 1, characterized in that, Based on the parameter information of the target wafer, the location information of the photoresist injection port, and the angle of the photoresist injection port, a fan-shaped simulation mesh is established, including: Based on the parameter information of the target wafer, the location information of the photoresist injection port, and the angle of the photoresist injection port, the mesh parameters are determined. The mesh parameters include mesh length, mesh height, and mesh center angle. The mesh length is equal to the radius of the wafer, the mesh height is equal to the height of the photoresist injection port, and the mesh center angle is the angle of the photoresist injection port. A sector-shaped simulation mesh is established based on the right-handed Cartesian coordinate system and the aforementioned mesh parameters.

3. The method according to claim 2, characterized in that, Based on the right-handed Cartesian coordinate system and the aforementioned mesh parameters, a sector-shaped simulation mesh is established, including: The center point of the target wafer is determined, and the center point is used as the origin of a right-handed Cartesian coordinate system. The coordinate axes of the right-handed Cartesian coordinate system are constructed based on the origin of the coordinate system; the coordinate axes include the x-axis, y-axis and z-axis. Use the y-axis of the right-handed Cartesian coordinate system as the axis of rotational symmetry; Based on the rotational symmetry axis, a sector-shaped simulation mesh is established in the x-axis direction of the right-handed Cartesian coordinate system according to the mesh parameters.

4. The method according to claim 3, characterized in that, In a right-handed Cartesian coordinate system, the element along the z-axis is kept at 1.

5. The method according to claim 1, characterized in that, A two-dimensional adaptive mesh refinement algorithm is used to divide the sector-shaped simulation mesh to obtain the target simulation mesh, including: Based on a two-dimensional adaptive mesh encryption algorithm, the empty boundary or wedge boundary of the sector simulation mesh is determined, and the target interface of the sector simulation mesh is determined based on the empty boundary or the wedge boundary. The center position of each edge on the target interface is used as a segmentation node. The fan-shaped simulation mesh is divided based on the segmentation nodes to obtain the target simulation mesh.

6. The method according to claim 1, characterized in that, Based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties, the two-phase fluid mathematical model is iteratively solved to determine the simulated image of the photoresist spin coating process of the target wafer, including: The target solver in the two-dimensional adaptive mesh refinement algorithm is used to discretize the two-phase fluid mathematical model based on the boundary conditions of the target simulation mesh, the photoresist spin coating process parameters, the air fluid properties and the photoresist fluid properties, and to determine the discretized linear function. The discretized linear function is preprocessed using a multi-grid preprocessor to determine the target linear function; The target linear function is solved using a conjugate gradient method solver to determine the simulation image of the photoresist spin coating process for the target wafer.

7. The method according to claim 1, characterized in that, Also includes: Convert the simulated image of the photoresist spin coating process into a grayscale simulated image; Convert the grayscale simulation image into a binary image; The photoresist boundary pixels are determined based on the binary image, and the pixel coordinates of the photoresist boundary pixels are determined. The photoresist outline is drawn based on the pixel coordinates.

8. A simulation device for photoresist spin coating process, characterized in that, The photoresist spin coating process simulation device includes: The sector simulation mesh determination module is used to establish a sector simulation mesh based on the parameter information of the target wafer, the position information of the photoresist injection port, and the angle of the photoresist injection port. The target simulation mesh determination module is used to divide the sector simulation mesh using a two-dimensional adaptive mesh refinement algorithm to obtain the target simulation mesh. The fluid model creation module is used to construct a mathematical model of a two-phase fluid; the two-phase fluid includes an air phase and a photoresist phase; The simulation image determination module is used to iteratively solve the two-phase fluid mathematical model based on the boundary conditions of the target simulation mesh, photoresist spin coating process parameters, air fluid properties, and photoresist fluid properties, and determine the photoresist spin coating process simulation image of the target wafer.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 7.

Images