Photoresist spin coating process simulation method and computer equipment

Abstract

The present application relates to a method and computer equipment for simulating a photoresist spin-coating process. Based on parameter information of a target wafer and position information of a photoresist injection port, a fan-shaped simulation grid is established; the fan-shaped simulation grid is a fan-shaped space region in a cylindrical space; the cylindrical space is a space region enclosed by spatial extension with the surface of the target wafer as the bottom surface and the plane where the photoresist injection port is located as the top surface; a two-phase flow fluid mathematical model is established; through a target solver, the two-phase flow fluid mathematical model is iteratively solved according to the boundary conditions of the fan-shaped simulation grid, the fluid properties corresponding to the two-phase fluid and the initial conditions of the process simulation, and the simulation results of the photoresist spin-coating process are determined, thereby improving the simulation efficiency of the photoresist spin-coating process, avoiding the high cost and time consumption required by traditional simulation methods, and making the adjustment and optimization of process parameters more efficient and flexible.

Description

Technical Field

[0001] The present application relates to the technical field of process simulation, and in particular to a method for simulating a photoresist spin coating process and a computer device. Background Art

[0002] In semiconductor manufacturing, photolithography is the core of integrated circuit planar processing. As a sub-process of photolithography, the uniformity of the spin-coating process affects key line width uniformity, line width roughness uniformity, and overlay accuracy, further affecting chip yield. Photoresist uniformity is crucial for pattern clarity and accuracy, as uneven photoresist coating can lead to pattern distortion or error. Simulation of the photoresist spin-coating process provides important data support for process engineers when designing spin-coating process parameters, laying the foundation for efficient and accurate optimization of the spin-coating process.

[0003] However, the existing photoresist spin coating process simulation method has the problem of low efficiency, and no effective solution has been proposed so far. Summary of the Invention

[0004] Based on this, it is necessary to provide a photoresist spin coating process simulation method and computer equipment to address the above technical problems.

[0005] In a first aspect, the present application provides a method for simulating a photoresist spin coating process, the method comprising:

[0006] Based on parameter information of the target wafer and position information of the photoresist injection port, a sector-shaped simulation grid is established; the sector-shaped simulation grid is a sector-shaped spatial region in a cylindrical space; the cylindrical space is a spatial region enclosed by spatial extension with the surface of the target wafer as the bottom surface and the plane where the photoresist injection port is located as the top surface; the plane where the photoresist injection port is located is parallel to the surface of the target wafer;

[0007] Obtaining boundary conditions corresponding to the sector-shaped simulation grid, fluid properties corresponding to the two-phase fluid, and initial conditions for process simulation;

[0008] Establish a mathematical model of two-phase flow;

[0009] The target solver is used to iteratively solve the two-phase flow fluid mathematical model according to the boundary conditions, the fluid properties and the process simulation initial conditions to determine the photoresist spin coating process simulation results.

[0010] In one embodiment, the parameter information of the target wafer includes a radius; the position information of the photoresist injection port includes a height of the photoresist injection port; and establishing a sector-shaped simulation grid based on the parameter information of the target wafer and the position information of the photoresist injection port includes:

[0011] Determine grid parameters corresponding to a sector-shaped simulation grid based on parameter information of the target wafer, position information of the photoresist injection port, and a preset angle; the grid parameters include length, height, and center angle; the length of the sector-shaped simulation grid is equal to the radius of the target wafer; the height of the sector-shaped simulation grid is equal to the height of the photoresist injection port; and the center angle of the sector-shaped simulation grid is equal to the preset angle;

[0012] Establishing an initial sector-shaped simulation grid based on a right-handed Cartesian coordinate system and the grid parameters;

[0013] According to a preset division rule, the initial sector-shaped simulation grid is divided into a grid to obtain a sector-shaped simulation grid; the sector-shaped simulation grid includes a plurality of sub-grid units; the number of the sub-grid units gradually decreases along the positive direction of the x-axis of the right-handed Cartesian coordinate system.

[0014] In one embodiment, the parameter information of the target wafer includes center coordinates; and establishing an initial sector-shaped simulation grid based on a right-handed Cartesian coordinate system and the grid parameters includes:

[0015] Determining the origin of a right-handed Cartesian coordinate system according to the center coordinates of the target wafer;

[0016] Determining the rotational symmetry axis corresponding to the initial sector-shaped simulation grid according to the y-axis of the right-handed Cartesian coordinate system;

[0017] According to the grid parameters and the rotational symmetry axis, an initial fan-shaped simulation grid is generated along the positive direction of the x-axis of the right-handed Cartesian coordinate system; the initial fan-shaped simulation grid is symmetrically distributed along the xy plane of the right-handed Cartesian coordinate system; the photoresist injection port is arranged on a side of the initial fan-shaped simulation grid close to the rotational symmetry axis.

[0018] In one embodiment, in a right-handed Cartesian coordinate system, the sector-shaped simulation grid includes a bottom surface, a front surface, a rear surface, an upper surface, and a right side surface; and obtaining boundary conditions corresponding to the sector-shaped simulation grid includes:

[0019] Using the solid wall boundary condition as the boundary condition corresponding to the bottom surface of the sector-shaped simulation grid;

[0020] Using wedge boundary conditions as boundary conditions corresponding to the front surface and the back surface of the fan-shaped simulation grid;

[0021] The atmospheric boundary conditions are used as the boundary conditions corresponding to the upper surface and the right side surface of the sector-shaped simulation grid.

[0022] In one embodiment, obtaining the fluid properties corresponding to the two-phase fluid includes:

[0023] Acquire a physical simulation model; the physical simulation model is a laminar flow model;

[0024] Based on the physical simulation model, the fluid properties corresponding to the two-phase fluid are determined; the two-phase fluid includes an air phase and a photoresist phase; the fluid properties corresponding to the air include a fluid viscosity model, a first dynamic viscosity, and a first density; the fluid properties corresponding to the photoresist include a fluid viscosity model, a second dynamic viscosity, a second density, and gravity.

[0025] In one embodiment, the iteratively solving the two-phase flow mathematical model according to the boundary conditions, the fluid properties, and the process simulation initial conditions by a target solver to determine the photoresist spin coating process simulation results includes:

[0026] Get the target solver;

[0027] By means of the target solver, the two-phase flow fluid mathematical model is spatially discretized according to the boundary conditions, the fluid properties and the process simulation initial conditions to obtain a linear system;

[0028] Preprocessing the linear system through a preprocessor to obtain a target linear system;

[0029] The target linear system is iteratively solved by an iterative solver until the solution meets a preset convergence condition, thereby obtaining a simulation result of the photoresist spin coating process; the simulation result of the photoresist spin coating process includes a velocity field, a pressure field and a volume fraction.

[0030] In one embodiment, the method further comprises:

[0031] Determining a photoresist distribution image according to the photoresist spin coating process simulation result;

[0032] Performing contour extraction processing on the photoresist distribution image to obtain photoresist contour data;

[0033] A photoresist profile image is generated based on the photoresist profile data.

[0034] In a second aspect, the present application further provides a device for simulating a photoresist spin coating process, the device comprising:

[0035] A grid establishment module is used to establish a sector-shaped simulation grid based on parameter information of the target wafer and position information of the photoresist injection port; the sector-shaped simulation grid is a sector-shaped spatial region in a cylindrical space; the cylindrical space is a spatial region enclosed by spatial extension with the surface of the target wafer as the bottom surface and the plane where the photoresist injection port is located as the top surface; the plane where the photoresist injection port is located is parallel to the surface of the target wafer;

[0036] An acquisition module, configured to acquire boundary conditions corresponding to the sector-shaped simulation grid, fluid properties corresponding to the two-phase fluid, and initial conditions for process simulation;

[0037] Model building module, used to build a two-phase flow mathematical model;

[0038] The simulation result determination module is used to iteratively solve the two-phase flow fluid mathematical model according to the boundary conditions, the fluid properties and the process simulation initial conditions through a target solver to determine the simulation result of the photoresist spin coating process.

[0039] In a third aspect, the present application further provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the method described in any one of the embodiments of the first aspect are implemented.

[0040] In a fourth aspect, the present application further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in any one of the embodiments of the first aspect above.

[0041] In a fifth aspect, the present application further provides a computer program product, comprising a computer program, which, when executed by a processor, implements the steps of the method described in any one of the embodiments of the first aspect above.

[0042] The above-mentioned photoresist spin-coating process simulation method and computer equipment establish a sector-shaped simulation grid based on the parameter information of the target wafer and the location information of the photoresist injection port. This avoids the high computational complexity caused by using a complete cylindrical space as the simulation grid, effectively saving computing resources. At the same time, based on the sector-shaped simulation grid, it helps to quickly and accurately understand the photoresist flow phenomena and trends, laying the foundation for improving the efficiency and accuracy of photoresist spin-coating process simulation. Furthermore, through the target solver, the mathematical model of the two-phase flow fluid is iteratively solved according to the boundary conditions, fluid properties, and initial conditions of the process simulation corresponding to the sector-shaped simulation grid. It can accurately and efficiently derive the simulation results of the photoresist spin-coating process, improve the efficiency of the photoresist spin-coating process simulation, avoid the high cost and time consumption required by traditional simulation methods, and make the adjustment and optimization of process parameters more efficient and flexible. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the technical solutions in the embodiments of the present application or related technologies, the following briefly introduces the drawings required for use in the embodiments of the present application or related technical descriptions. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying any creative work.

[0044] Figure 1 1 is a schematic flow chart of a method for simulating a photoresist spin coating process in one embodiment;

[0045] Figure 2 A schematic flow chart of steps for establishing a sector-shaped simulation grid in one embodiment;

[0046] Figure 3 is a schematic diagram of a photoresist spin coating process in one embodiment;

[0047] Figure 4 is a schematic diagram of a sector-shaped simulation grid in one embodiment;

[0048] Figure 5 A top view of a fan-shaped simulation grid in one embodiment;

[0049] Figure 6 A partial schematic diagram of a sector-shaped simulation grid in one embodiment;

[0050] Figure 7 A schematic flow chart of the steps for determining simulation results of a photoresist spin coating process in one embodiment;

[0051] Figure 8 A schematic diagram of a process for generating a photoresist profile image in one embodiment;

[0052] Figure 9 is a schematic diagram of a photoresist distribution image in one embodiment;

[0053] Figure 10 is a schematic diagram of a photoresist profile image in one embodiment;

[0054] Figure 11 is a structural block diagram of a photoresist spin coating process simulation device in one embodiment;

[0055] Figure 12 FIG. 1 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0056] 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.

[0057] In an exemplary embodiment, Figure 1 As shown, Figure 1 FIG. 1 is a flow chart of a method for simulating a photoresist spin coating process in one embodiment; the method for simulating a photoresist spin coating process includes the following steps:

[0058] Step S101 : establishing a sector-shaped simulation grid based on parameter information of a target wafer and position information of a photoresist injection port.

[0059] Among them, the fan-shaped simulation grid is a fan-shaped space area in the cylindrical space; the cylindrical space is a space area enclosed by spatial extension with the surface of the target wafer as the bottom surface and the plane where the photoresist injection port is located as the top surface; the plane where the photoresist injection port is located is parallel to the surface of the target wafer.

[0060] Among them, the parameter information of the target wafer may include, but is not limited to, the surface parameters and radius of the target wafer; wherein, the surface parameters may include, but are not limited to, the surface flatness. The photoresist injection port refers to a dedicated port for introducing photoresist into the surface of the target wafer; the photoresist injection port can be a nozzle, a needle or other type of delivery device, and it is only necessary to ensure that the photoresist can be coated on the surface of the target wafer with a uniform thickness, and no specific limitation is made here. The position information of the photoresist injection port includes the height of the photoresist injection port; the height of the photoresist injection port refers to the vertical distance of the photoresist injection port relative to the surface of the target wafer. It should be noted that the parameter information of the target wafer and the position information of the photoresist injection port need to be selected according to the actual simulation requirements, and no specific limitation is made here.

[0061] It should be noted that, since the photoresist has axial symmetry during the spin coating process, this embodiment uses the surface of the target wafer as the bottom surface and the plane where the photoresist injection port is located as the top surface, and uses a fan-shaped space area in the columnar space enclosed by spatial extension as the simulation grid, which makes full use of the axial symmetry. It can not only more effectively capture the flow characteristics of the rotating area, but also effectively reduce the calculation complexity, thereby improving the calculation efficiency.

[0062] Step S102 , obtaining boundary conditions corresponding to the sector-shaped simulation grid, fluid properties corresponding to the two-phase fluid, and initial conditions for process simulation.

[0063] The boundary conditions corresponding to the sector simulation grid refer to the boundary conditions corresponding to each surface of the sector simulation grid. They are used to constrain the form of the solution during the simulation process. For example, during the simulation process, boundary conditions specify the value or variation pattern of a physical quantity at the boundary, thereby restricting the solution space. It can be understood that boundary conditions can reduce the size of the computational domain and improve computational efficiency.

[0064] The two-phase fluid includes an air phase and a photoresist phase; the fluid properties corresponding to the two-phase fluid are used to characterize the behavior of the two-phase fluid; the fluid properties may include but are not limited to density, viscosity, and surface tension.

[0065] Among them, the initial conditions of the process simulation may include but are not limited to the initial speed of photoresist injection, the initial rotation speed of the target wafer and the process atmosphere; for example, the initial speed of photoresist injection is v1, the initial rotation speed of the target wafer is w1, and the process atmosphere is standard atmospheric pressure.

[0066] It should be noted that the boundary conditions corresponding to the sector-shaped simulation grid, the fluid properties corresponding to the two-phase fluid, and the initial conditions of the process simulation all need to be set according to actual simulation requirements and are not specifically limited here.

[0067] Step S103: establishing a two-phase flow mathematical model.

[0068] The mathematical model of two-phase flow is used to describe the physical properties and behavior of two-phase fluids. It includes the continuity equation, the momentum equation, and the interface tracking equation. The continuity equation describes the principle of conservation of mass in the fluid; the momentum equation includes the Navier-Stokes (NS) equation, which describes the continuity and momentum conservation of the fluid; and the interface tracking equation includes the volume fraction (VOF) equation, which describes the position and shape of the interface between the two phases.

[0069] Exemplarily, the continuity equation is shown in formula (1).

[0070]

[0071] Where, ρ represents the density of the fluid; t represents time; u represents the velocity field of the fluid; The continuity equation states that the rate of change of the fluid's density over time plus the divergence of the product of the fluid's density and velocity equals zero. This means that the mass of the fluid can neither be created nor destroyed within any volume. In the simulation of the photoresist spin coating process, for incompressible fluids, the density ρ is a constant that does not vary with time or space. Therefore, the continuity equation simplifies to Equation (2).

[0072]

[0073] Formula (2) shows that the divergence of the fluid velocity field must be zero to ensure that there is no accumulation or loss of mass.

[0074] Exemplarily, the momentum equation, i.e., the NS equation, is shown in formula (3).

[0075]

[0076] Among them, ρ represents the density of the fluid; u represents the velocity field of the fluid, which is a vector function; t represents time; p represents the pressure field of the fluid, which is a scalar function; u represents the dynamic viscosity of the fluid; represents the gradient operator, which is used to calculate the derivative of the velocity field; represents the Laplace operator, which is used to calculate the second-order derivative of the velocity field; f represents the external force, such as gravity or electromagnetic force.

[0077] It should be noted that the momentum equation, also known as the NS equation, comprehensively describes the velocity field, pressure field of the fluid and their changes in time and space. It can be used to analyze and predict the behavior of photoresist fluid, including the velocity field, pressure field of the fluid and the interaction between the fluid and the solid boundary.

[0078] For example, the interface tracking equation, i.e., the VOF equation, is shown in formula (4).

[0079]

[0080] Among them, α i , represents the volume fraction of the i-th item; t, represents time; u i , represents the velocity vector of the i-th term. The interface tracking equation, also known as the VOF equation, can track and simulate the volume fractions of different fluid phases, thereby indirectly determining the position and shape of the photoresist interface. Solving the VOF equation can predict the distribution of photoresist, the dynamic behavior of the photoresist interface, and complex flow phenomena caused by interfacial tension.

[0081] Step S104 , using a target solver, the two-phase flow mathematical model is iteratively solved according to boundary conditions, fluid properties, and initial conditions of the process simulation to determine the simulation result of the photoresist spin coating process.

[0082] Among them, the target solver can be but is not limited to an interFoam solver; it should be noted that the target solver can accurately simulate and track the interfaces between different fluid phases in multiphase flow. This simulation capability is crucial for understanding and predicting the flow behavior of photoresist.

[0083] Alternatively, in an exemplary embodiment, in terms of the algorithm selection corresponding to the target solver, the pressure-implicit with Splitting of Operators (PIMPLE) method is selected to solve the two-phase flow fluid mathematical model. In incompressible flow, the density of the fluid is constant, which results in a strong coupling relationship between the continuity equation and the momentum equation. The PIMPLE algorithm allows the velocity field and the pressure field to be updated simultaneously in each time step by implicitly solving the pressure field. When processing multiphase flow, the PIMPLE algorithm can be combined with the interface tracking technology to effectively capture and update the interface between different fluid phases, which is crucial for accurately simulating the fluid interface dynamics in the photoresist spin coating process.

[0084] Exemplarily, the target solver is used to iteratively solve the two-phase flow fluid mathematical model according to the boundary conditions, fluid properties and initial conditions of the process simulation, and gradually approximate the solution until the convergence criteria are met to determine the simulation results of the photoresist spin coating process.

[0085] In this embodiment, a fan-shaped simulation grid is established based on the parameter information of the target wafer and the position information of the photoresist injection port. This avoids the problem of high computational complexity caused by using a complete cylindrical space as the simulation grid, effectively saving computing resources. At the same time, based on the fan-shaped simulation grid, it helps to quickly and accurately understand the photoresist flow phenomena and trends, laying the foundation for improving the efficiency and accuracy of the photoresist spin-coating process simulation. Furthermore, through the target solver, the two-phase flow fluid mathematical model is iteratively solved according to the boundary conditions, fluid properties, and process simulation initial conditions corresponding to the fan-shaped simulation grid. It can accurately and efficiently derive the simulation results of the photoresist spin-coating process, improve the efficiency of the photoresist spin-coating process simulation, avoid the high cost and time consumption required by traditional simulation methods, and make the adjustment and optimization of process parameters more efficient and flexible.

[0086] In one embodiment, the parameter information of the target wafer includes the radius; the position information of the photoresist injection port includes the height of the photoresist injection port; wherein the height of the photoresist injection port refers to the vertical distance of the photoresist injection port relative to the surface of the target wafer. Figure 2 As shown, Figure 2 The flowchart of the steps for establishing a sector-shaped simulation grid in one embodiment is shown. The sector-shaped simulation grid is established based on parameter information of the target wafer and position information of the photoresist injection port, including the following steps:

[0087] Step S201 : determining grid parameters corresponding to a sector-shaped simulation grid based on parameter information of a target wafer, position information of a photoresist injection port, and a preset angle.

[0088] Among them, the grid parameters include length, height and center angle; the length of the fan-shaped simulation grid is equal to the radius of the target wafer; the height of the fan-shaped simulation grid is equal to the height of the photoresist injection port; and the center angle of the fan-shaped simulation grid is equal to the preset angle.

[0089] The preset angle needs to be set according to actual needs and is not specifically limited here. It is understandable that the preset angle will affect the thickness of the sector-shaped simulation grid. That is, the larger the preset angle, the thicker the sector-shaped simulation grid. Therefore, it is necessary to select an appropriate preset angle to ensure that the sector-shaped simulation grid can minimize the amount of calculation while ensuring the accuracy of the simulation results.

[0090] It should be noted that, see Figure 3 , Figure 3 This is a schematic diagram of the photoresist spin-coating process. The photoresist injection port is located directly above the center of the target wafer. After spin coating begins, photoresist will be ejected from the photoresist injection port at a certain speed and fall onto the target wafer. The substrate corresponding to the target wafer will rotate around the central axis at a certain rotation speed and spin-coat the photoresist onto the entire target wafer surface. Based on this, setting the length of the fan-shaped simulation grid to the radius of the target wafer and the height of the fan-shaped simulation grid to the height of the photoresist injection port can lay the foundation for accurately capturing the flow characteristics of the photoresist.

[0091] Step S202 : establishing an initial sector-shaped simulation grid based on a right-handed Cartesian coordinate system and grid parameters.

[0092] The parameter information of the target wafer includes the center coordinates; the center coordinates are the exact center coordinates of the target wafer.

[0093] Preferably, step S202, establishing an initial sector-shaped simulation grid based on a right-handed Cartesian coordinate system and grid parameters, includes the following steps:

[0094] Step 1: Determine the origin of the right-handed Cartesian coordinate system based on the center coordinates of the target wafer.

[0095] Exemplarily, the center of the target wafer is determined according to the center coordinates of the target wafer, and the center of the target wafer is determined as the origin of a right-handed Cartesian coordinate system.

[0096] Step 2: Determine the rotational symmetry axis corresponding to the initial sector-shaped simulation grid based on the y-axis of the right-handed Cartesian coordinate system.

[0097] For example, see Figure 4 , based on the right-handed Cartesian coordinate system, the y-axis of the right-handed Cartesian coordinate system is used as the rotational symmetry axis corresponding to the initial fan-shaped simulation grid.

[0098] Step 3: Generate an initial fan-shaped simulation grid along the positive direction of the x-axis of the right-handed Cartesian coordinate system according to the grid parameters and the rotational symmetry axis.

[0099] The initial sector-shaped simulation grid is symmetrically distributed along the xy plane of the right-handed Cartesian coordinate system; and the photoresist injection port is arranged on a side of the initial sector-shaped simulation grid close to the rotational symmetry axis.

[0100] For example, see Figures 4 to 6 , the length of the grid parameters corresponding to the fan-shaped simulation grid is recorded as x1, the height is recorded as h, and the center angle is recorded as θ, and the initial fan-shaped simulation grid is generated along the positive direction of the x-axis of the right-handed Cartesian coordinate system; Figure 4 It can be seen that the rotational symmetry axis is on the positive half of the y-axis of the right-handed Cartesian coordinate system; it can be seen from Figure 5 It can be seen that the initial fan-shaped simulation grid is symmetrically distributed along the xy plane of the right-handed Cartesian coordinate system; Figure 6 It can be seen that the photoresist injection port is set on the side of the initial sector-shaped simulation grid close to the rotational symmetry axis, and the target wafer is on the xz plane of the right-handed Cartesian coordinate system; based on the grid parameters corresponding to the sector-shaped simulation grid, namely the length x1, height h and center angle θ, it can be determined that the coordinates of point P1 are (x1, 0, -x1*tan(θ / 2)), the coordinates of point P2 are (x2, 0, -x2*tan(θ / 2)), and the coordinates of P3 are (0, h, 0).

[0101] Step S203 : dividing the initial sector-shaped simulation grid according to a preset division rule to obtain a sector-shaped simulation grid.

[0102] The fan-shaped simulation grid includes a plurality of subgrid units; the number of the subgrid units gradually decreases along the positive direction of the x-axis of the right-handed Cartesian coordinate system.

[0103] The preset division rule needs to be set according to actual needs and is not specifically limited here. The preset division rule can be: the closer to the rotational symmetry axis, the finer the sub-grid unit division. It should be noted that the finer the division of sub-grid units near the rotational symmetry axis can effectively save computing resources while ensuring the accuracy of the simulation results.

[0104] For example, see Figures 4 to 6 Based on the initial sector simulation grid, the initial sector simulation grid is divided according to the preset division rules to obtain the sector simulation grid. Figures 4 to 6 It can be seen that the number of sub-grid units in the fan-shaped simulation grid gradually decreases along the positive direction of the x-axis of the right-handed Cartesian coordinate system.

[0105] In this embodiment, based on the parameter information of the target wafer, the position information of the photoresist injection port and the preset angle, the grid parameters corresponding to the fan-shaped simulation grid can be accurately determined; then, based on the grid parameters and the right-handed Cartesian coordinate system, the initial fan-shaped simulation grid can be accurately established; further, according to the preset division rules, the initial fan-shaped simulation grid is grid-divided to obtain the fan-shaped simulation grid, thereby avoiding the problem of high computational complexity caused by using a complete cylindrical space as a simulation grid, effectively saving computing resources, and at the same time, based on the fan-shaped simulation grid, it is helpful to quickly and accurately understand the photoresist flow phenomenon and trend, laying the foundation for improving the efficiency and accuracy of the photoresist spin coating process simulation.

[0106] In one embodiment, Figure 4 As shown, in the right-handed Cartesian coordinate system, the sector simulation grid includes the bottom surface, front surface, back surface, top surface, and right surface; the boundary conditions corresponding to the sector simulation grid are obtained, including:

[0107] The solid wall boundary condition is used as the boundary condition corresponding to the bottom surface of the sector-shaped simulation grid;

[0108] Use wedge boundary conditions as the boundary conditions corresponding to the front and back surfaces of the fan-shaped simulation grid;

[0109] The atmospheric boundary conditions are used as the boundary conditions corresponding to the upper and right surfaces of the sector-shaped simulation grid.

[0110] Among them, the solid wall boundary condition is used to describe the behavior of the photoresist fluid when it contacts the solid wall, that is, the target wafer surface; the wedge boundary condition is applicable to axisymmetric problems and is used to simulate geometric structures with axisymmetry; the atmospheric boundary condition is used to simulate the situation where the fluid flows into or out of the computational domain.

[0111] In this embodiment, by setting corresponding boundary conditions for each surface of the sector-shaped simulation grid, a data foundation is laid for realizing the photoresist spin coating process simulation.

[0112] In one embodiment, obtaining fluid properties corresponding to a two-phase fluid includes the following steps:

[0113] Step 1: Obtain a physical simulation model.

[0114] The physical simulation model is a laminar flow model. Laminar flow refers to the flow state of a fluid under low Reynolds number conditions, in which the fluid flow is orderly and smooth, and each fluid particle flows in a direction parallel to the boundary without significant mixing or vortexing.

[0115] Step 2: Determine the fluid properties corresponding to the two-phase fluid based on the physical simulation model.

[0116] The two-phase fluid includes an air phase and a photoresist phase; the fluid properties corresponding to the air include a fluid viscosity model, a first dynamic viscosity, and a first density; and the fluid properties corresponding to the photoresist include a fluid viscosity model, a second dynamic viscosity, a second density, and gravity. It is understood that the first dynamic viscosity, first density, second dynamic viscosity, second density, and gravity are all related to the fluid involved in the actual simulation. The specific data needs to be determined based on the actual results and are not specifically limited here.

[0117] The fluid viscosity model includes a constant viscosity model; the constant viscosity model means that in the simulation of the photoresist spin coating process, the dynamic viscosity of the fluid is regarded as a constant and does not change with changes in temperature or pressure.

[0118] It should be noted that the photoresist spin coating process simulation method can be, but is not limited to, implemented based on OpenFOAM software.

[0119] For example, when implementing a photoresist spin-coating process simulation based on OpenFOAM software, the constant folder in OpenFOAM contains the physical property files required by the program. In the momentumTransport file in OpenFOAM, the physical simulation model can be set to a laminar flow model; and through the physical simulation model, the fluid properties corresponding to the two-phase fluid can be determined. For example, for the air phase: the fluid viscosity model is a constant viscosity model, that is, viscosityModel is constant, the first dynamic viscosity is α1, and the second density is β1; for the photoresist phase, the fluid viscosity model is a constant viscosity model, the second dynamic viscosity is α2, and the second density is set to β2. At the same time, since the rotational symmetry axis is the y-axis of the right-handed Cartesian coordinate system, the gravity can be determined to be (0g 0); further, the surface tension coefficient between the two-phase fluid can be determined to be γ.

[0120] In this embodiment, based on the physical simulation model, the fluid properties corresponding to the two-phase fluid are determined, which lays a data foundation for realizing the simulation of the photoresist spin coating process.

[0121] In one embodiment, Figure 7 As shown, Figure 7 The flowchart of the steps for determining the simulation results of a photoresist spin coating process in one embodiment is shown. The target solver is used to iteratively solve the two-phase flow mathematical model based on boundary conditions, fluid properties, and initial conditions of the process simulation to determine the simulation results of the photoresist spin coating process, including the following steps:

[0122] Step S701: Obtain a target solver.

[0123] The target solver may be, but is not limited to, an interFoam solver.

[0124] Step S702 : Using a target solver, the two-phase flow mathematical model is spatially discretized according to boundary conditions, fluid properties, and initial conditions of process simulation to obtain a linear system.

[0125] Step S703: preprocessing the linear system through a preprocessor to obtain a target linear system.

[0126] The preconditioner may be, but is not limited to, a geometric algebraic multigrid (GAMG) solver. GAMG is an efficient algorithm for accelerating the solution of linear systems, combining geometric multigrid and algebraic multigrid methods. This algorithm is particularly effective in solving large-scale linear systems because it can gradually reduce residual errors at different levels of grids, thereby achieving faster convergence.

[0127] Step S704 , performing iterative solving on the target linear system through an iterative solver until the solution satisfies a preset convergence condition, thereby obtaining a simulation result of the photoresist spin coating process.

[0128] The iterative solver may be, but is not limited to, a preconditioned conjugate gradient solver (PCG). An iterative solver is a numerical method for solving linear or nonlinear equations, and finds a solution by successive approximation.

[0129] Among them, the preset convergence conditions need to be set according to the actual solution requirements and are not specifically limited here.

[0130] It should be noted that GAMG, as a preconditioner, can improve the condition number of linear systems, thereby reducing the number of iterations of the iterative solver and speeding up the solution. The PCG solver, combined with the preconditioner, can handle linear systems more stably and is suitable for large-scale problem processing.

[0131] The simulation results for the photoresist spin coating process include velocity field, pressure field, and volume fraction. The velocity field describes the velocity distribution of the photoresist at each point in space; the pressure field describes the pressure distribution of the photoresist at each point in space; and the volume fraction describes the proportion of one phase in a two-phase fluid at a given point in space.

[0132] For example, when the target solver is the interFoam solver, the finite volume method is used based on the interFoam solver to spatially discretize the two-phase flow mathematical model according to boundary conditions, fluid properties, and initial conditions for process simulation, resulting in a linear system. The PIMPLE algorithm is then used to couple the pressure and velocity fields to ensure that momentum conservation and incompressibility conditions are met. Furthermore, the GAMG preprocessor is used to preprocess the linear system to obtain the target linear system, thereby improving the solution characteristics of the linear system and reducing the system's condition number. Furthermore, the PCG iterative solver is used to solve the target linear system until the solution meets the preset convergence conditions, resulting in the simulation results of the photoresist spin-coating process.

[0133] Optionally, in another exemplary embodiment, a parallel computing method is adopted to iteratively solve the two-phase flow fluid mathematical model through the target solver according to the boundary conditions, fluid properties and initial conditions of the process simulation to determine the simulation results of the photoresist spin coating process, so as to further improve the efficiency of the photoresist spin coating process simulation.

[0134] In another exemplary embodiment, before obtaining the target solver, it is necessary to complete the parameter configuration of the target solver; the parameters may include, but are not limited to, the solver type, the solution time step, the output interval, the time precision, and the maximum Courant number; wherein, the solution time step needs to be small enough to ensure numerical stability and accuracy; the output interval is used to determine the saving frequency of the simulation results; the time precision is used to control the convergence standard of the solver within the time step; the maximum Courant number is used to control the relative size of the time step and the space step to ensure numerical stability.

[0135] In this embodiment, based on the target solver, preprocessor and iterative solver, the two-phase flow fluid mathematical model is iteratively solved until the solution meets the preset convergence conditions, and the simulation results of the photoresist spin-coating process are obtained. This not only improves the calculation efficiency and shortens the calculation time, but also based on the preset convergence conditions, it can ensure the reliability and stability of the solution process, thereby obtaining accurate simulation results of the photoresist spin-coating process.

[0136] In one embodiment, Figure 8 As shown, Figure 8 FIG. 1 is a flow chart of generating a photoresist profile image in one embodiment; the photoresist spin coating process simulation method further includes the following steps:

[0137] Step S801 : determining a photoresist distribution image according to a photoresist spin coating process simulation result.

[0138] In an exemplary embodiment, assuming that the initial rotation speeds of the target wafer are ω1, ω2, ω3, and ω4, four photoresist spin coating process simulations are performed to obtain four sets of photoresist spin coating process simulation results, respectively, to compare the performance of photoresist spin coating at different initial rotation speeds; further, according to the photoresist spin coating process simulation results, the corresponding photoresist distribution image can be determined, such as Figure 9 shown.

[0139] It should be noted that the photoresist distribution image can be, but is not limited to, displayed after processing using ParaView software. ParaView software primarily displays the photoresist distribution image using automated scripts. These scripts not only possess powerful visualization capabilities but also include computational capabilities, effectively streamlining the data processing process.

[0140] Step S802 , performing contour extraction processing on the photoresist distribution image to obtain photoresist contour data.

[0141] The method for performing contour extraction on a photoresist distribution image may include: converting the photoresist distribution image into a grayscale image; performing image segmentation on the grayscale image according to a preset threshold to obtain a binary image; wherein the binary image includes a photoresist region and a background region; wherein the grayscale values ​​corresponding to pixels in the photoresist region are higher than the preset threshold; and wherein the grayscale values ​​corresponding to pixels in the background region are lower than or equal to the preset threshold; performing boundary pixel scanning on the binary image to determine boundary data between the photoresist and the background; wherein the boundary data includes the coordinate values ​​of each boundary pixel; and finally, using the boundary data as the photoresist contour data. The preset threshold needs to be set according to actual needs and is not specifically limited here.

[0142] Step S803: generating a photoresist profile image based on the photoresist profile data.

[0143] Among them, the photoresist contour image can clearly show the distribution range and morphology of the photoresist on the wafer.

[0144] For example, for Figure 9 The photoresist distribution images shown are converted into four corresponding grayscale images respectively; the four grayscale images are segmented according to a preset threshold value to obtain binary images corresponding to each group; further, the four binary images are scanned for boundary pixels to determine the boundary data between the photoresist and the background corresponding to each group; the boundary data is used as the photoresist contour data of the corresponding group; finally, based on the four corresponding photoresist contour data, that is, the coordinate values ​​of each boundary pixel, a photoresist contour image is generated, as shown in FIG. Figure 10 shown.

[0145] It should be noted that the photoresist profile data can also be used for further analysis, such as calculating key parameters such as photoresist coverage area, thickness distribution, and uniformity. These parameters are crucial for evaluating the quality of the spin coating process.

[0146] In this embodiment, by visualizing the corresponding photoresist spin-coating process simulation results, the corresponding photoresist distribution image can be obtained, so as to more intuitively understand the performance of photoresist spin-coating; then, by performing contour extraction processing on the photoresist distribution image, photoresist contour data is obtained; and based on the photoresist contour data, a photoresist contour image is generated, which intuitively presents the morphological transformation and distribution of the photoresist during the spin-coating process.

[0147] The above-mentioned photoresist spin-coating process simulation method establishes a sector-shaped simulation grid based on the parameter information of the target wafer and the location information of the photoresist injection port. This avoids the high computational complexity caused by using a complete cylindrical space as the simulation grid, effectively conserving computing resources. Furthermore, the sector-shaped simulation grid facilitates a rapid and accurate understanding of photoresist flow phenomena and trends, laying the foundation for improving the efficiency and accuracy of photoresist spin-coating process simulation. Furthermore, through a target solver, the mathematical model of the two-phase flow fluid is iteratively solved according to the boundary conditions, fluid properties, and initial conditions of the process simulation corresponding to the sector-shaped simulation grid. This allows for accurate and efficient simulation results of the photoresist spin-coating process, significantly reducing the high cost and time consumption required by traditional simulation methods and making the adjustment and optimization of process parameters more efficient and flexible.

[0148] It should be understood that, although the various steps in the flowcharts involved in the various embodiments described above are displayed in sequence according to the instructions of the arrows, these steps are not necessarily executed in sequence in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and these steps can be executed in other orders. Moreover, at least a portion of the steps in the flowcharts involved in the various embodiments described above can include multiple steps or multiple stages, and these steps or stages are not necessarily executed and completed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a portion of steps or stages in other steps.

[0149] Based on the same inventive concept, the present application also provides a photoresist spin-coating process simulation device for implementing the aforementioned photoresist spin-coating process simulation method. The solution provided by this device is similar to the solution described in the aforementioned method. Therefore, the specific limitations in one or more of the following photoresist spin-coating process simulation device embodiments can be found in the above-mentioned limitations on the photoresist spin-coating process simulation method, and will not be repeated here.

[0150] In an exemplary embodiment, Figure 11 As shown, a photoresist spin coating process simulation device is provided, including: a grid establishment module 1101, an acquisition module 1102, a model establishment module 1103 and a simulation result determination module 1104;

[0151] The grid establishment module 1101 is used to establish a sector-shaped simulation grid based on parameter information of the target wafer and position information of the photoresist injection port. The sector-shaped simulation grid is a sector-shaped spatial region in a cylindrical space. The cylindrical space is a spatial region enclosed by spatial extension with the surface of the target wafer as the bottom surface and the plane where the photoresist injection port is located as the top surface. The plane where the photoresist injection port is located is parallel to the surface of the target wafer.

[0152] An acquisition module 1102 is used to acquire boundary conditions corresponding to the sector simulation grid, fluid properties corresponding to the two-phase fluid, and initial conditions for process simulation;

[0153] Model building module 1103, used to build a two-phase flow mathematical model;

[0154] The simulation result determination module 1104 is used to iteratively solve the two-phase flow mathematical model according to the boundary conditions, fluid properties and process simulation initial conditions through the target solver to determine the simulation results of the photoresist spin coating process.

[0155] The above-mentioned photoresist spin-coating process simulation device establishes a sector-shaped simulation grid based on the parameter information of the target wafer and the location information of the photoresist injection port. This avoids the high computational complexity caused by using a complete cylindrical space as the simulation grid, effectively saving computing resources. At the same time, the sector-shaped simulation grid facilitates a rapid and accurate understanding of photoresist flow phenomena and trends, laying the foundation for improving the efficiency and accuracy of photoresist spin-coating process simulation. Furthermore, through a target solver, the mathematical model of the two-phase flow fluid is iteratively solved according to the boundary conditions, fluid properties, and initial conditions of the process simulation corresponding to the sector-shaped simulation grid. This can accurately and efficiently derive the simulation results of the photoresist spin-coating process, significantly reducing the high cost and time consumption required by traditional simulation methods, making the adjustment and optimization of process parameters more efficient and flexible.

[0156] In one embodiment, the parameter information of the target wafer includes the radius; the position information of the photoresist injection port includes the height of the photoresist injection port; the grid establishment module 1101 is also used to

[0157] Determine the grid parameters corresponding to the fan-shaped simulation grid based on the parameter information of the target wafer, the position information of the photoresist injection port, and the preset angle; the grid parameters include length, height, and center angle; the length of the fan-shaped simulation grid is equal to the radius of the target wafer; the height of the fan-shaped simulation grid is equal to the height of the photoresist injection port; and the center angle of the fan-shaped simulation grid is equal to the preset angle;

[0158] Based on the right-handed Cartesian coordinate system and grid parameters, an initial sector-shaped simulation grid is established;

[0159] According to a preset division rule, the initial sector-shaped simulation grid is divided into grids to obtain a sector-shaped simulation grid; the sector-shaped simulation grid includes a plurality of sub-grid units; the number of the sub-grid units gradually decreases along the positive direction of the x-axis of the right-handed Cartesian coordinate system.

[0160] In one embodiment, the parameter information of the target wafer includes the center coordinates; the grid establishment module 1101 is also used to

[0161] Determine the origin of the right-handed Cartesian coordinate system based on the center coordinates of the target wafer;

[0162] According to the y-axis of the right-handed Cartesian coordinate system, the rotational symmetry axis corresponding to the initial sector simulation grid is determined;

[0163] According to the grid parameters and the rotational symmetry axis, an initial sector-shaped simulation grid is generated along the positive direction of the x-axis of the right-handed Cartesian coordinate system; the initial sector-shaped simulation grid is symmetrically distributed along the xy plane of the right-handed Cartesian coordinate system; and the photoresist injection port is set on a side of the initial sector-shaped simulation grid close to the rotational symmetry axis.

[0164] In one embodiment, in a right-handed Cartesian coordinate system, the fan-shaped simulation grid includes a bottom surface, a front surface, a back surface, an upper surface, and a right side surface; the acquisition module 1102 is further used to

[0165] The solid wall boundary condition is used as the boundary condition corresponding to the bottom surface of the sector-shaped simulation grid;

[0166] Use wedge boundary conditions as the boundary conditions corresponding to the front and back surfaces of the fan-shaped simulation grid;

[0167] The atmospheric boundary conditions are used as the boundary conditions corresponding to the upper and right surfaces of the sector-shaped simulation grid.

[0168] In one embodiment, the acquisition module 1102 is further configured to

[0169] Obtain a physical simulation model; the physical simulation model is a laminar flow model;

[0170] Based on the physical simulation model, the fluid properties corresponding to the two-phase fluid are determined; the two-phase fluid includes an air phase and a photoresist phase; the fluid properties corresponding to the air include a fluid viscosity model, a first dynamic viscosity, and a first density; the fluid properties corresponding to the photoresist include a fluid viscosity model, a second dynamic viscosity, a second density, and gravity.

[0171] In one embodiment, the simulation result determination module 1104 is further configured to:

[0172] Get the target solver;

[0173] Through the target solver, the mathematical model of two-phase flow is spatially discretized according to the boundary conditions, fluid properties and initial conditions of process simulation to obtain a linear system;

[0174] The linear system is preprocessed through the preprocessor to obtain the target linear system;

[0175] The target linear system is iteratively solved through an iterative solver until the solution meets the preset convergence conditions, and the simulation results of the photoresist spin-coating process are obtained; the simulation results of the photoresist spin-coating process include velocity field, pressure field and volume fraction.

[0176] In one embodiment, the simulation result determination module 1104 is further configured to:

[0177] Determine the photoresist distribution image according to the photoresist spin coating process simulation results;

[0178] Performing contour extraction processing on the photoresist distribution image to obtain photoresist contour data;

[0179] A photoresist profile image is generated based on the photoresist profile data.

[0180] Each module in the above-mentioned photoresist spin-coating process simulation device can be implemented in whole or in part through software, hardware, or a combination thereof. Each module can be embedded in or independent of a processor in a computer device in the form of hardware, or can be stored in a memory in the computer device in the form of software, so that the processor can call and execute the corresponding operations of each module.

[0181] In an exemplary embodiment, a computer device is provided. The computer device may be a server, and its internal structure diagram may be as shown in FIG. Figure 12As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O) and a communication interface. The processor, the memory and the input / output interface are connected via a system bus, and the communication interface is connected to the system bus via the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store data related to the simulation of the photoresist spin coating process. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal via a network connection. When the computer program is executed by the processor, a method for simulating the photoresist spin coating process is implemented.

[0182] Those skilled in the art will understand that Figure 12 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0183] In one embodiment, a computer device is further provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps in the above method embodiments when executing the computer program.

[0184] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0185] In one embodiment, a computer program product is provided, including a computer program, which implements the steps in the above method embodiments when executed by a processor.

[0186] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, database or other media used in the embodiments provided in this application may include at least one of non-volatile memory and volatile memory. Non-volatile memory may 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 may include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processor involved in the various embodiments provided herein may be, but are not limited to, a general-purpose processor, a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), a programmable logic unit (PLC), a data processing logic unit based on quantum computing, an artificial intelligence (AI) processor, and the like.

[0187] The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, 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 application.

[0188] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.

Claims

1. A photoresist spin coating process simulation method, characterized in that: The method comprises: Based on parameter information of the target wafer and position information of the photoresist injection port, a sector-shaped simulation grid is established; the sector-shaped simulation grid is a sector-shaped spatial region in a cylindrical space; the cylindrical space is a spatial region enclosed by spatial extension with the surface of the target wafer as the bottom surface and the plane where the photoresist injection port is located as the top surface; the plane where the photoresist injection port is located is parallel to the surface of the target wafer; Obtaining boundary conditions corresponding to the sector-shaped simulation grid, fluid properties corresponding to the two-phase fluid, and initial conditions for process simulation; Establish a mathematical model of two-phase flow; The target solver is used to iteratively solve the two-phase flow fluid mathematical model according to the boundary conditions, the fluid properties and the process simulation initial conditions to determine the photoresist spin coating process simulation results.

2. The method according to claim 1, characterized in that The parameter information of the target wafer includes a radius; the position information of the photoresist injection port includes a height of the photoresist injection port; and establishing a sector-shaped simulation grid based on the parameter information of the target wafer and the position information of the photoresist injection port, including: Determine grid parameters corresponding to a sector-shaped simulation grid based on parameter information of the target wafer, position information of the photoresist injection port, and a preset angle; the grid parameters include length, height, and center angle; the length of the sector-shaped simulation grid is equal to the radius of the target wafer; the height of the sector-shaped simulation grid is equal to the height of the photoresist injection port; and the center angle of the sector-shaped simulation grid is equal to the preset angle; Establishing an initial sector-shaped simulation grid based on a right-handed Cartesian coordinate system and the grid parameters; According to a preset division rule, the initial sector-shaped simulation grid is divided into a grid to obtain a sector-shaped simulation grid; the sector-shaped simulation grid includes a plurality of sub-grid units; the number of the sub-grid units gradually decreases along the positive direction of the x-axis of the right-handed Cartesian coordinate system.

3. The method according to claim 2, characterized in that The parameter information of the target wafer includes the center coordinates; the initial sector simulation grid is established based on the right-handed Cartesian coordinate system and the grid parameters, including: Determining the origin of a right-handed Cartesian coordinate system according to the center coordinates of the target wafer; Determining the rotational symmetry axis corresponding to the initial sector-shaped simulation grid according to the y-axis of the right-handed Cartesian coordinate system; According to the grid parameters and the rotational symmetry axis, an initial fan-shaped simulation grid is generated along the positive direction of the x-axis of the right-handed Cartesian coordinate system; the initial fan-shaped simulation grid is symmetrically distributed along the xy plane of the right-handed Cartesian coordinate system; the photoresist injection port is arranged on a side of the initial fan-shaped simulation grid close to the rotational symmetry axis.

4. The method according to claim 1, wherein In a right-handed Cartesian coordinate system, the sector-shaped simulation grid includes a bottom surface, a front surface, a rear surface, an upper surface, and a right surface; and obtaining boundary conditions corresponding to the sector-shaped simulation grid includes: Using the solid wall boundary condition as the boundary condition corresponding to the bottom surface of the sector-shaped simulation grid; Using wedge boundary conditions as boundary conditions corresponding to the front surface and the back surface of the fan-shaped simulation grid; The atmospheric boundary conditions are used as the boundary conditions corresponding to the upper surface and the right side surface of the sector-shaped simulation grid.

5. The method according to claim 1, wherein The obtaining of fluid properties corresponding to the two-phase fluid includes: Acquire a physical simulation model; the physical simulation model is a laminar flow model; Based on the physical simulation model, the fluid properties corresponding to the two-phase fluid are determined; the two-phase fluid includes an air phase and a photoresist phase; the fluid properties corresponding to the air include a fluid viscosity model, a first dynamic viscosity, and a first density; the fluid properties corresponding to the photoresist include a fluid viscosity model, a second dynamic viscosity, a second density, and gravity.

6. The method according to claim 1, characterized in that The method of iteratively solving the two-phase flow mathematical model according to the boundary conditions, the fluid properties, and the process simulation initial conditions by a target solver to determine the photoresist spin coating process simulation result includes: Get the target solver; By means of the target solver, the two-phase flow fluid mathematical model is spatially discretized according to the boundary conditions, the fluid properties and the process simulation initial conditions to obtain a linear system; Preprocessing the linear system through a preprocessor to obtain a target linear system; The target linear system is iteratively solved by an iterative solver until the solution meets a preset convergence condition, thereby obtaining a simulation result of the photoresist spin coating process; the simulation result of the photoresist spin coating process includes a velocity field, a pressure field and a volume fraction.

7. The method according to claim 1, characterized in that The method further comprises: Determining a photoresist distribution image according to the photoresist spin coating process simulation result; Performing contour extraction processing on the photoresist distribution image to obtain photoresist contour data; A photoresist profile image is generated based on the photoresist profile data.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

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

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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