A three-dimensional fluid simulation method and system for rectangular inductively coupled plasmas

Abstract

This invention discloses a three-dimensional fluid simulation method and system for rectangular inductively coupled plasma, relating to the field of three-dimensional fluid simulation. The method includes: constructing a three-dimensional fluid model of the rectangular inductively coupled plasma using a three-dimensional Cartesian coordinate system; dividing the simulation region in the three-dimensional fluid model into orthogonal grids to obtain multiple grids; setting discharge parameters; performing three-dimensional fluid simulation on the three-dimensional fluid model based on the discharge parameters to obtain uniformity parameters for different grids under the discharge parameters; and determining the uniformity simulation result of the plasma in the three-dimensional fluid model under the discharge parameters based on the uniformity parameters of different grids. The simulation method proposed in this invention can self-consistently simulate various key parameters of a large-area rectangular inductively coupled plasma source, and since this invention is a three-dimensional fluid simulation method, it can consider many three-dimensional effects present in actual processes.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional fluid simulation, and in particular to a three-dimensional fluid simulation method and system for rectangular inductively coupled plasma. Background Technology

[0002] In flat panel display manufacturing, photovoltaic processes, and other surface treatment processes, various plasma technologies are involved, such as etching, deposition, ashing, implantation, and cleaning. These plasma processes often utilize large-area rectangular inductively coupled plasma (ICP) sources, typically ranging from 1 to 3 meters in length and width, and from a few centimeters to tens of centimeters in height. Due to the generally large size of these ICP sources, plasma uniformity is a critical challenge. Plasma uniformity directly affects the uniformity of etching and deposition, ultimately impacting product quality. Therefore, to improve plasma uniformity, it is essential to conduct in-depth and detailed research on the generation and transport processes of the process plasma, and to optimize the coil structure and discharge parameters. Experimental methods are costly, time-consuming, and provide limited information, thus limiting their application in plasma source research. Numerical simulation methods, compared to experiments, are less costly and provide more comprehensive information. Therefore, proposing a comprehensive and computationally efficient simulation method is of great significance for understanding plasma discharge processes, optimizing plasma uniformity, and consequently, optimizing related processes.

[0003] Current plasma fluid simulation methods are mostly designed for simulating plasma sources in semiconductor chip manufacturing processes. These plasma sources are predominantly cylindrical, so the simulations are typically performed in two-dimensional cylindrical coordinates. However, the large-area inductively coupled plasma sources used in flat panel display and photovoltaic processes have rectangular structures, necessitating three-dimensional simulation. Therefore, proposing a three-dimensional fluid simulation method for simulating large-area rectangular inductively coupled plasma sources is crucial.

[0004] Furthermore, simulation efficiency is also a crucial factor; only methods with high simulation efficiency have practical value. This is especially true for simulating large-area three-dimensional plasma sources, where the computational load is enormous, making it paramount to improve computational efficiency. Summary of the Invention

[0005] The purpose of this invention is to provide a three-dimensional fluid simulation method and system for rectangular inductively coupled plasma, which can self-consistently simulate various key parameters of a large-area rectangular inductively coupled plasma source, and can take into account many three-dimensional effects existing in actual processes.

[0006] To achieve the above objectives, the present invention provides the following solution:

[0007] A three-dimensional fluid simulation method for rectangular inductively coupled plasmas, comprising:

[0008] A three-dimensional fluid model of a rectangular inductively coupled plasma was constructed using a three-dimensional rectangular coordinate system.

[0009] The simulation region in the three-dimensional fluid model is divided into orthogonal grids to obtain multiple grids; the simulation region includes a plasma region, a dielectric window, a coil, and a shielding region;

[0010] Set the discharge parameters; the discharge parameters include: air pressure, power, chamber size, and coil shape;

[0011] Based on the discharge parameters, a three-dimensional fluid simulation is performed on the three-dimensional fluid model to obtain the uniformity parameters of different grids under the discharge parameters; the uniformity parameters include: electron density, ion density, neutral particle density, and electron temperature;

[0012] Based on the uniformity parameters of different grids under the discharge parameters, the plasma uniformity simulation results of the three-dimensional fluid model under the discharge parameters are determined.

[0013] Optionally, a three-dimensional fluid simulation is performed on the three-dimensional fluid model based on the discharge parameters to obtain the uniformity parameters of different meshes under the discharge parameters, specifically including:

[0014] Under the discharge parameters, the three-dimensional fluid model is simulated using an iterative calculation method for each grid to obtain the uniformity parameters of each grid under the discharge parameters;

[0015] For any grid, the iterative calculation method is as follows:

[0016] Initialize the uniformity parameters;

[0017] The uniformity parameter for the k-th iteration is calculated based on the uniformity parameter for the (k-1)-th iteration.

[0018] Based on the uniformity parameter of the (k-1)th iteration and the uniformity parameter of the kth iteration, determine whether the iteration termination condition is met, and obtain the first judgment result;

[0019] If the first judgment result indicates no, then return to the step "Calculate the uniformity parameter of the kth iteration based on the uniformity parameter of the (k-1)th iteration";

[0020] If the first judgment result indicates yes, then the uniformity parameter of the kth iteration is output as the uniformity parameter of the grid under the discharge parameters.

[0021] Optionally, the uniformity parameter for the k-th iteration is calculated based on the uniformity parameter for the (k-1)-th iteration, specifically including:

[0022] Based on the uniformity parameters of the (k-1)th iteration, the wave equations of the electric field are solved by the frequency domain finite difference method to obtain the induced electric field of the kth iteration within the grid, and the deposition power density of the induced electric field of the kth iteration within the grid in the plasma is determined.

[0023] Based on the uniformity parameter of the (k-1)th iteration, a semi-implicit method is used to solve the Poisson equation, obtain the electric potential of the kth iteration within the grid, and determine the electrostatic field of the kth iteration within the grid.

[0024] Based on the uniformity parameter of the (k-1)th iteration and the electrostatic field of the kth iteration, the continuity equation of electrons, the momentum equation of ions and the continuity equation of ions are solved by explicit method to obtain the electron density, ion velocity and ion density in the grid for the kth iteration.

[0025] Based on the uniformity parameter of the (k-1)th iteration, the electrostatic field of the kth iteration, the deposition power density of the induced electric field in the plasma of the kth iteration, and the electron density of the kth iteration, the energy conservation equation of the electron is solved by an explicit method to obtain the electron temperature of the kth iteration within the grid.

[0026] The continuity equation of neutral particles is solved explicitly using the uniformity parameter of the (k-1)th iteration, the electron density of the kth iteration, and the electron temperature of the kth iteration to obtain the neutral particle density in the grid for the kth iteration.

[0027] Optionally, based on the uniformity parameters of the (k-1)th iteration, the wave equations of the electric field are solved using the frequency domain finite difference method to obtain the induced electric field of the kth iteration within the grid, and the deposition power density of the induced electric field of the kth iteration within the grid in the plasma is determined, specifically including:

[0028] Based on the uniformity parameters of the (k-1)th iteration, the wave equations of the electric field are solved using the frequency domain finite difference method to obtain the induced electric field in the k-th iteration within the grid; the wave equations of the electric field are:

[0029]

[0030] Based on the induced electric field of the k-th iteration within the grid, the deposition power density of the induced electric field in the plasma during the k-th iteration within the grid is calculated using the following formula.

[0031]

[0032] Among them, E k Let J represent the induced electric field in the k-th iteration. coilJ represents the coil current density. p,k Let μk represent the plasma current density in the k-th iteration, μ0 represent the permeability in vacuum, and ε0 represent the permittivity in vacuum. r ε represents the relative permeability. r σ represents the relative permittivity. p,k Let ω represent the plasma conductivity in the k-th iteration, ω represent the angular frequency of the discharge, j represent the imaginary unit, e represent the unit charge, and n represent the plasma conductivity in the k-th iteration. e,k-1 Let m represent the electron density in the (k-1)th iteration. e Indicates electron mass, v en Represents the elastic collision frequency between electrons and the background gas; Re() denotes taking the real part; E k * Indicates taking E k The conjugate of ; ▽ denotes the gradient operator; P ind,k This represents the deposition power density of the induced electric field in the plasma during the k-th iteration within the grid.

[0033] Optionally, based on the uniformity parameter of the (k-1)th iteration, a semi-implicit method is used to solve the Poisson equation to obtain the potential within the grid for the kth iteration, and to determine the electrostatic field within the grid for the kth iteration, specifically including:

[0034] Based on the uniformity parameter of the (k-1)th iteration, a semi-implicit method is used to solve the Poisson equation to obtain the potential within the grid for the kth iteration; the Poisson equation is:

[0035]

[0036] Based on the electric potential in the k-th iteration within the grid, the electrostatic field in the k-th iteration within the grid is calculated using the following formula.

[0037]

[0038] in, Let q represent the potential in the k-th iteration. i,l n represents the charge of the l-th ion. i,l,k-1 E represents the density of the l-th ion in the (k-1)-th iteration. s,k Let L represent the electrostatic field in the k-th iteration, and L represent the number of ion types.

[0039] Alternatively, the continuity equation for electrons is:

[0040]

[0041]

[0042]

[0043]

[0044] The continuity equation for ions is:

[0045] Γ i,l,k =n i,l,k-1 u i,l,k-1 ;

[0046]

[0047] The momentum equation for an ion is:

[0048]

[0049] The energy conservation equation for electrons is:

[0050]

[0051] Among them, T e,k Let q represent the electron temperature in the k-th iteration. e W is the electron energy flux density. e μ represents the energy loss caused by electron collisions. e D represents the electron mobility. e,k Let k represent the diffusion coefficient of the electron in the k-th iteration. B T represents the Boltzmann constant. e,k-1 Γ represents the electron temperature in the (k-1)th iteration. e,k Let n represent the electron flux in the k-th iteration. e,k S represents the electron density in the k-th iteration. e The source term represents electrons, t represents time, and u represents the source term. i,l,k Let m represent the velocity of the l-th ion in the k-th iteration. i,l T represents the mass of the l-th ion. i,l M represents the temperature of the l-th ion. i,l Let n represent the collision term of the l-th ion. i,l,k Γ represents the density of the l-th ion in the k-th iteration. i,l,k u represents the flux of the l-th ion in the k-th iteration. i,l,k-1 S represents the velocity of the l-th ion in the (k-1)-th iteration. i,l This represents the source term for the l-th ion.

[0052] Optionally, based on the uniformity parameter of the (k-1)th iteration, the electron density of the kth iteration, and the electron temperature of the kth iteration, an explicit method is used to solve the continuity equation of the neutral particles to obtain the neutral particle density within the grid for the kth iteration, specifically including:

[0053] Based on the electron density and electron temperature of the k-th iteration within the grid, the source term of the neutral particle in the k-th iteration within the grid is obtained.

[0054] Based on the uniformity parameter of the (k-1)th iteration, the source term of the neutral particles in the kth iteration within the grid, the electron density of the kth iteration, and the electron temperature of the kth iteration, the neutral particle density in the kth iteration is obtained by explicitly solving the continuity equation of the neutral particles. The continuity equation of the neutral particles is as follows:

[0055]

[0056]

[0057] Where, n n,k Let Γ represent the neutral particle density in the k-th iteration. n,k S represents the flux of neutral particles. n,k D represents the source term of the neutral particle in the k-th iteration; n n represents the diffusion coefficient of neutral particles; n,k-1 Let represent the neutral particle density in the (k-1)th iteration.

[0058] Optionally, based on the uniformity parameters of different grids under the discharge parameters, the plasma uniformity simulation results of the three-dimensional fluid model under the discharge parameters are determined, specifically including:

[0059] Calculate the percentage density error for the density of different particles in different grids;

[0060] Calculate the percentage temperature error of the electron temperature of different particles in different grids;

[0061] Determine whether the density error percentage is greater than a preset density percentage threshold to obtain a second determination result;

[0062] Determine whether the temperature error percentage is greater than a preset temperature percentage threshold to obtain a third determination result;

[0063] If both the second and third judgment results are negative, then the plasma distribution of the three-dimensional fluid model under the discharge parameters is uniform.

[0064] If either the second judgment result or the third judgment result is true, then the plasma distribution of the three-dimensional fluid model under the discharge parameters is non-uniform.

[0065] A three-dimensional fluid simulation system for rectangular inductively coupled plasmas, wherein the three-dimensional fluid simulation system for rectangular inductively coupled plasmas is applied to the three-dimensional fluid simulation method for rectangular inductively coupled plasmas described above, and the three-dimensional fluid simulation system for rectangular inductively coupled plasmas includes:

[0066] The building module is used to construct a three-dimensional fluid model of a rectangular inductively coupled plasma using a three-dimensional Cartesian coordinate system.

[0067] The partitioning module is used to divide the simulation region in the three-dimensional fluid model into orthogonal meshes, resulting in multiple meshes; the simulation region includes a plasma region, a dielectric window, a coil, and a shielding region;

[0068] A setting module is used to set discharge parameters; the discharge parameters include: air pressure, power, chamber size, and coil shape.

[0069] The simulation module is used to perform a three-dimensional fluid simulation on the three-dimensional fluid model based on the discharge parameters, and to obtain the uniformity parameters of different grids under the discharge parameters; the uniformity parameters include: electron density, ion density, neutral particle density and electron temperature;

[0070] The simulation result determination module is used to determine the plasma uniformity simulation results of the three-dimensional fluid model under the discharge parameters based on the uniformity parameters of different grids under the discharge parameters.

[0071] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0072] A three-dimensional fluid simulation method for rectangular inductively coupled plasma includes: constructing a three-dimensional fluid model of the rectangular inductively coupled plasma using a three-dimensional Cartesian coordinate system; since this is a three-dimensional fluid simulation method, it can consider many three-dimensional effects present in actual processes; dividing the simulation region in the three-dimensional fluid model into orthogonal grids to obtain multiple grids; setting discharge parameters; performing three-dimensional fluid simulation on the three-dimensional fluid model based on the discharge parameters to obtain the uniformity parameters of different grids under the discharge parameters; and determining the uniformity simulation result of the plasma in the three-dimensional fluid model under the discharge parameters based on the uniformity parameters of different grids. The simulation method proposed in this invention can self-consistently simulate various key parameters of a large-area rectangular inductively coupled plasma source. Attached Figure Description

[0073] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0074] Figure 1 This is a flowchart of a three-dimensional fluid simulation method for rectangular inductively coupled plasma in an embodiment of the present invention;

[0075] Figure 2 This is a schematic diagram of a three-dimensional fluid simulation method for rectangular inductively coupled plasma in an embodiment of the present invention. Detailed Implementation

[0076] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0077] The purpose of this invention is to provide a three-dimensional fluid simulation method and system for rectangular inductively coupled plasma. By adopting a three-dimensional fluid simulation method, many three-dimensional effects existing in actual processes can be considered, and various key parameters of a large-area rectangular inductively coupled plasma source can be simulated in a self-consistent manner.

[0078] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0079] Example 1

[0080] like Figure 1 and Figure 2 As shown, the three-dimensional fluid simulation method for rectangular inductively coupled plasma of the present invention includes:

[0081] Step 101: Construct a three-dimensional fluid model of a rectangular inductively coupled plasma using a three-dimensional Cartesian coordinate system.

[0082] Step 102: Divide the simulation region in the three-dimensional fluid model into orthogonal grids to obtain multiple grids; the simulation region includes the plasma region, dielectric window, coil and shielding region.

[0083] Step 103: Set the discharge parameters; the discharge parameters include: air pressure, power, chamber size and coil shape.

[0084] Step 104: Perform a three-dimensional fluid simulation on the three-dimensional fluid model based on the discharge parameters to obtain the uniformity parameters of different grids under the discharge parameters; the uniformity parameters include: electron density, ion density, neutral particle density and electron temperature.

[0085] Step 105: Based on the uniformity parameters of different grids under the discharge parameters, determine the plasma uniformity simulation results of the three-dimensional fluid model under the discharge parameters.

[0086] Based on the discharge parameters, a three-dimensional fluid simulation is performed on the three-dimensional fluid model to obtain the uniformity parameters of different meshes under the discharge parameters, specifically including:

[0087] Under the discharge parameters, the three-dimensional fluid model is simulated using an iterative calculation method for each grid to obtain the uniformity parameters of each grid under the discharge parameters.

[0088] For any grid, the iterative calculation method is as follows:

[0089] Initialize the uniformity parameters.

[0090] The uniformity parameter for the k-th iteration is calculated based on the uniformity parameter for the (k-1)-th iteration.

[0091] Based on the uniformity parameter of the (k-1)th iteration and the uniformity parameter of the kth iteration, determine whether the iteration termination condition is met, and obtain the first judgment result.

[0092] If the first judgment result indicates no, then return to the step "Calculate the uniformity parameter of the kth iteration based on the uniformity parameter of the (k-1)th iteration".

[0093] If the first judgment result indicates yes, then the uniformity parameter of the kth iteration is output as the uniformity parameter of the grid under the discharge parameters.

[0094] The iteration must meet the following four conditions to terminate:

[0095] (1) The error between the electron density of the kth iteration and the electron density of the (k-1)th iteration is less than the first preset threshold.

[0096] (2) The error between the ion density of the kth iteration and the ion density of the (k-1)th iteration is less than the second preset threshold.

[0097] (3) The error between the electron temperature of the kth iteration and the electron temperature of the (k-1)th iteration is less than the third preset threshold.

[0098] (4) The error between the neutral particle density of the kth iteration and the neutral particle density of the (k-1)th iteration is less than the fourth preset threshold.

[0099] The uniformity parameters for the k-th iteration are calculated based on the uniformity parameters from the (k-1)-th iteration, specifically including:

[0100] Based on the uniformity parameters of the (k-1)th iteration, the wave equations of the electric field are solved using the frequency domain finite difference method to obtain the induced electric field of the kth iteration within the grid, and the deposition power density of the induced electric field of the kth iteration within the grid in the plasma is determined.

[0101] In practical applications, the final output induced electric field deposition power density in the plasma is equal to the power in the discharge parameters.

[0102] Based on the uniformity parameter of the (k-1)th iteration, a semi-implicit method is used to solve the Poisson equation, obtain the electric potential of the kth iteration within the grid, and determine the electrostatic field of the kth iteration within the grid.

[0103] Based on the uniformity parameter of the (k-1)th iteration and the electrostatic field of the kth iteration, the continuity equation of electrons, the momentum equation of ions, and the continuity equation of ions are solved explicitly to obtain the electron density, ion velocity, and ion density in the grid for the kth iteration.

[0104] Based on the uniformity parameter of the (k-1)th iteration, the electrostatic field of the kth iteration, the deposition power density of the induced electric field in the plasma of the kth iteration, and the electron density of the kth iteration, the energy conservation equation of the electron is solved by an explicit method to obtain the electron temperature of the kth iteration within the grid.

[0105] The continuity equation of neutral particles is solved explicitly using the uniformity parameter of the (k-1)th iteration, the electron density of the kth iteration, and the electron temperature of the kth iteration to obtain the neutral particle density in the grid for the kth iteration.

[0106] Inductively coupled plasma sources primarily rely on the induced electric field generated by the current in the radio frequency coil to drive the discharge. Assuming that the electromagnetic field and current density change harmonicly with time, the induced electric field within the grid can be obtained by solving the wave equation of the electric field.

[0107] In specific applications, based on the uniformity parameters of the (k-1)th iteration, the wave equations of the electric field are solved using the frequency domain finite difference method to obtain the induced electric field of the kth iteration within the grid, and the deposition power density of the induced electric field of the kth iteration within the grid in the plasma is determined, specifically including:

[0108] Based on the uniformity parameters of the (k-1)th iteration, the wave equations of the electric field are solved using the frequency domain finite difference method to obtain the induced electric field in the k-th iteration within the grid; the wave equations of the electric field are:

[0109]

[0110] Based on the induced electric field of the k-th iteration within the grid, the deposition power density of the induced electric field in the plasma during the k-th iteration within the grid is calculated using the following formula.

[0111]

[0112] Among them, E k Let J represent the induced electric field in the k-th iteration. coil J represents the coil current density. p,k Let μk represent the plasma current density in the k-th iteration, μ0 represent the permeability in vacuum, and ε0 represent the permittivity in vacuum. r ε represents the relative permeability. r σ represents the relative permittivity. p,k Let ω represent the plasma conductivity in the k-th iteration, ω represent the angular frequency of the discharge, j represent the imaginary unit, e represent the unit charge, and n represent the plasma conductivity in the k-th iteration. e,k-1 Let m represent the electron density in the (k-1)th iteration. e Indicates electron mass, v en Represents the elastic collision frequency between electrons and the background gas; Re() denotes taking the real part; E k * Indicates taking E k The conjugate of ; ▽ denotes the gradient operator; P ind,k This represents the deposition power density of the induced electric field in the plasma during the k-th iteration within the grid.

[0113] Based on the uniformity parameters of the (k-1)th iteration, a semi-implicit method is used to solve the Poisson equation, obtain the electric potential within the grid for the kth iteration, and determine the electrostatic field within the grid for the kth iteration, specifically including:

[0114] Based on the uniformity parameter of the (k-1)th iteration, a semi-implicit method is used to solve the Poisson equation to obtain the potential within the grid for the kth iteration; the Poisson equation is:

[0115]

[0116] To overcome the limitation of time step imposed by the relaxation time of the medium, increase the time step, and improve the computation speed, a semi-implicit method is used to numerically solve the Poisson equation.

[0117] Based on the electric potential in the k-th iteration within the grid, the electrostatic field in the k-th iteration within the grid is calculated using the following formula.

[0118]

[0119] in, Let q represent the potential in the k-th iteration. i,l n represents the charge of the l-th ion. i,l,k-1 E represents the density of the l-th ion in the (k-1)-th iteration. s,k Let L represent the electrostatic field in the k-th iteration, and L represent the number of ion types.

[0120] The continuity equation for electrons is:

[0121]

[0122]

[0123]

[0124]

[0125] The continuity equation for electrons is solved using an explicit method. By employing different time steps at different spatial locations, multiple time steps are explicitly advanced, thereby improving the efficiency of the simulation.

[0126] The continuity equation for ions is:

[0127] Γ i,l,k =n i,l,k-1 u i,l,k-1 ;

[0128]

[0129] The momentum equation for an ion is:

[0130]

[0131] The energy conservation equation for electrons is:

[0132]

[0133] Among them, T e,k Let q represent the electron temperature in the k-th iteration. e W is the electron energy flux density. e μ represents the energy loss caused by electron collisions. e D represents the electron mobility. e,k Let k represent the diffusion coefficient of the electron in the k-th iteration. B T represents the Boltzmann constant. e,k-1 Γ represents the electron temperature in the (k-1)th iteration. e,k Let n represent the electron flux in the k-th iteration. e,kS represents the electron density in the k-th iteration. e The source term represents electrons, t represents time, and u represents the source term. i,l,k Let m represent the velocity of the l-th ion in the k-th iteration. i,l T represents the mass of the l-th ion. i,l M represents the temperature of the l-th ion. i,l Let n represent the collision term of the l-th ion. i,l,k Γ represents the density of the l-th ion in the k-th iteration. i,l,k u represents the flux of the l-th ion in the k-th iteration. i,l,k-1 S represents the velocity of the l-th ion in the (k-1)-th iteration. i,l This represents the source term for the l-th ion. Based on the uniformity parameter of the (k-1)-th iteration, the electron density of the k-th iteration, and the electron temperature of the k-th iteration, an explicit method is used to solve the continuity equation for neutral particles, obtaining the neutral particle density within the grid for the k-th iteration. Specifically, this includes:

[0134] Based on the electron density and electron temperature of the k-th iteration within the grid, the source term of the neutral particle in the k-th iteration within the grid is obtained.

[0135] The source term for neutral particles is a function of electron density and electron temperature, i.e., S. n =S n (n e ,T e ).

[0136] Based on the uniformity parameter of the (k-1)th iteration, the source term of the neutral particles in the kth iteration within the grid, the electron density of the kth iteration, and the electron temperature of the kth iteration, the neutral particle density in the kth iteration is obtained by explicitly solving the continuity equation of the neutral particles. The continuity equation of the neutral particles is as follows:

[0137]

[0138]

[0139] Where, n n,k Let Γ represent the neutral particle density in the k-th iteration. n,k S represents the flux of neutral particles. n,k D represents the source term of the neutral particle in the k-th iteration; n n represents the diffusion coefficient of neutral particles; n,k-1 This represents the neutral particle density in the (k-1)th iteration.

[0140] Based on the uniformity parameters of different grids under the discharge parameters, the plasma uniformity simulation results of the three-dimensional fluid model under the discharge parameters are determined, specifically including:

[0141] Calculate the percentage density error for the density of different particles in different grids.

[0142] Calculate the percentage temperature error of the electron temperature of different particles in different grids.

[0143] Determine whether the density error percentage is greater than a preset density percentage threshold to obtain a second determination result.

[0144] Determine whether the temperature error percentage is greater than a preset temperature percentage threshold to obtain a third determination result.

[0145] If both the second and third judgment results are negative, then the plasma distribution of the three-dimensional fluid model under the discharge parameters is uniform.

[0146] If either the second judgment result or the third judgment result is true, then the plasma distribution of the three-dimensional fluid model under the discharge parameters is non-uniform.

[0147] Example 2

[0148] A three-dimensional fluid simulation system for rectangular inductively coupled plasmas is provided. This system is applied to the three-dimensional fluid simulation method for rectangular inductively coupled plasmas described in Example 1. The three-dimensional fluid simulation system for rectangular inductively coupled plasmas includes:

[0149] The building module is used to construct a three-dimensional fluid model of a rectangular inductively coupled plasma using a three-dimensional Cartesian coordinate system.

[0150] The partitioning module is used to divide the simulation region in the three-dimensional fluid model into orthogonal meshes, resulting in multiple meshes; the simulation region includes the plasma region, the dielectric window, the coil, and the shielding region.

[0151] The setting module is used to set the discharge parameters, which include: air pressure, power, chamber size, and coil shape.

[0152] The simulation module is used to perform three-dimensional fluid simulation on the three-dimensional fluid model based on the discharge parameters, and obtain the uniformity parameters of different grids under the discharge parameters; the uniformity parameters include: electron density, ion density, neutral particle density and electron temperature.

[0153] The simulation result determination module is used to determine the plasma uniformity simulation results of the three-dimensional fluid model under the discharge parameters based on the uniformity parameters of different grids under the discharge parameters.

[0154] This invention establishes a comprehensive, computationally fast, and efficient three-dimensional fluid simulation method for the discharge chamber of large-area rectangular inductively coupled plasma sources commonly used in flat panel display, photovoltaic, and other surface material processing technologies. This method can simulate the characteristics of rectangular inductively coupled plasmas, study the influence of different discharge parameters and coil shapes on plasma uniformity, and provide a basis for predicting plasma discharge processes, optimizing plasma uniformity, and promoting the development of plasma sources for related processes. Furthermore, to address the issue of high computational complexity, this invention proposes using a frequency domain method to solve the induced electromagnetic field, a semi-implicit method to solve the Poisson equation, and an explicit method to solve the electron continuity equation and energy conservation equation, significantly improving simulation efficiency.

[0155] The technical effects that this invention can achieve are:

[0156] Advantage 1: Comprehensive functionality.

[0157] Currently, few programs can simulate large-area three-dimensional rectangular inductively coupled plasma sources. The simulation method proposed in this patent can consistently simulate various key parameters of a large-area rectangular inductively coupled plasma source, such as electron density, electron temperature, ion density, ion velocity, neutral particle density, power deposition density, and the three-dimensional spatial distribution of the induced electric field. Furthermore, this simulation method can investigate the influence of different coil shapes on plasma homogeneity. It can also study the effect of the lower plate bias voltage on the plasma.

[0158] Advantage 2: High efficiency.

[0159] Simulation efficiency is crucial for optimizing plasma processing chambers and processes. This is especially true for large-area rectangular inductively coupled plasma sources used in flat panel display and photovoltaic processes, which require 3D modeling for simulation. The large chamber size further increases the computational burden. The method proposed in this patent uses a frequency domain approach to solve for the electromagnetic field, avoiding the need to solve for the electromagnetic field at every time step, thus accelerating the simulation. Simultaneously, a semi-implicit method is used to solve the Poisson equation, overcoming the limitation of dielectric relaxation time and increasing the time step size for solving the Poisson equation, thereby improving simulation efficiency. Furthermore, unlike most implicit methods used in inductively coupled plasma simulations, this patent employs an explicit method to solve the electron continuity equation and electron energy conservation equation. By using different time steps at different spatial locations, explicit multi-time-step progression is achieved, avoiding the solution of linear equation systems and significantly improving simulation efficiency.

[0160] Advantage 3: High simulation dimension.

[0161] Most current plasma fluid simulation methods simulate two-dimensional axisymmetric structures and cannot simulate three-dimensional chamber structures. The method proposed in this patent is a three-dimensional fluid simulation method, which can therefore take into account many three-dimensional effects existing in actual processes, such as the influence of chamber structure on plasma parameters, the influence of coil shape on plasma uniformity, etc. Therefore, the method proposed in this patent is more in line with the simulation requirements of actual processes.

[0162] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0163] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A three-dimensional fluid simulation method for rectangular inductively coupled plasma, characterized in that, The three-dimensional fluid simulation method for rectangular inductively coupled plasma includes: A three-dimensional fluid model of a rectangular inductively coupled plasma was constructed using a three-dimensional rectangular coordinate system. The simulation region in the three-dimensional fluid model is divided into orthogonal grids to obtain multiple grids; the simulation region includes a plasma region, a dielectric window, a coil, and a shielding region; Set the discharge parameters; the discharge parameters include: air pressure, power, chamber size, and coil shape; Based on the discharge parameters, a three-dimensional fluid simulation is performed on the three-dimensional fluid model to obtain the uniformity parameters of different meshes under the discharge parameters, specifically including: Under the discharge parameters, the three-dimensional fluid model is simulated using an iterative calculation method for each grid to obtain the uniformity parameters of each grid under the discharge parameters; For any grid, the iterative calculation method is as follows: Initialize the uniformity parameters; The uniformity parameters for the k-th iteration are calculated based on the uniformity parameters from the (k-1)-th iteration, specifically including: Based on the uniformity parameters of the (k-1)th iteration, the wave equations of the electric field are solved by the frequency domain finite difference method to obtain the induced electric field of the kth iteration within the grid, and the deposition power density of the induced electric field of the kth iteration within the grid in the plasma is determined. Based on the uniformity parameter of the (k-1)th iteration, a semi-implicit method is used to solve the Poisson equation, obtain the electric potential of the kth iteration within the grid, and determine the electrostatic field of the kth iteration within the grid. Based on the uniformity parameter of the (k-1)th iteration and the electrostatic field of the kth iteration, the continuity equation of electrons, the momentum equation of ions and the continuity equation of ions are solved by explicit method to obtain the electron density, ion velocity and ion density in the grid for the kth iteration. Based on the uniformity parameter of the (k-1)th iteration, the electrostatic field of the kth iteration, the deposition power density of the induced electric field in the plasma of the kth iteration, and the electron density of the kth iteration, the energy conservation equation of the electron is solved by an explicit method to obtain the electron temperature of the kth iteration within the grid. The continuity equation of neutral particles is solved explicitly using the uniformity parameter of the (k-1)th iteration, the electron density of the kth iteration, and the electron temperature of the kth iteration to obtain the neutral particle density in the grid for the kth iteration. Based on the uniformity parameter of the (k-1)th iteration and the uniformity parameter of the kth iteration, determine whether the iteration termination condition is met, and obtain the first judgment result; If the first judgment result indicates no, then return to the step "Calculate the uniformity parameter of the kth iteration based on the uniformity parameter of the (k-1)th iteration"; If the first judgment result indicates yes, then the uniformity parameter of the kth iteration is output as the uniformity parameter of the grid under the discharge parameters; The uniformity parameters include: electron density, ion density, neutral particle density, and electron temperature; Based on the uniformity parameters of different grids under the discharge parameters, the plasma uniformity simulation results of the three-dimensional fluid model under the discharge parameters are determined.

2. The three-dimensional fluid simulation method for rectangular inductively coupled plasma according to claim 1, characterized in that, Based on the uniformity parameters of the (k-1)th iteration, the wave equations of the electric field are solved using the frequency domain finite difference method to obtain the induced electric field of the kth iteration within the grid, and the deposition power density of the induced electric field of the kth iteration within the grid in the plasma is determined, specifically including: Based on the uniformity parameters of the (k-1)th iteration, the wave equations of the electric field are solved using the frequency domain finite difference method to obtain the induced electric field in the k-th iteration within the grid; the wave equations of the electric field are: ； Based on the induced electric field of the k-th iteration within the grid, the deposition power density of the induced electric field in the plasma during the k-th iteration within the grid is calculated using the following formula. ； in, This represents the induced electric field in the k-th iteration. Indicates the coil current density. This represents the plasma current density in the k-th iteration. Represents the magnetic permeability in a vacuum. Represents the dielectric constant in a vacuum. Represents relative permeability. Represents the relative permittivity. This represents the plasma conductivity in the k-th iteration. Indicates the angular frequency of the discharge. Represents the imaginary unit. Represents a unit charge. This represents the electron density in the (k-1)th iteration. Indicates electron mass, This represents the elastic collision frequency between electrons and the background gas. Indicates taking the real part; Indicates taking The conjugate; This indicates the gradient operator; This represents the deposition power density of the induced electric field in the plasma during the k-th iteration within the grid.

3. The three-dimensional fluid simulation method for rectangular inductively coupled plasma according to claim 2, characterized in that, Based on the uniformity parameters of the (k-1)th iteration, a semi-implicit method is used to solve the Poisson equation, obtain the electric potential within the grid for the kth iteration, and determine the electrostatic field within the grid for the kth iteration, specifically including: Based on the uniformity parameter of the (k-1)th iteration, a semi-implicit method is used to solve the Poisson equation to obtain the potential within the grid for the kth iteration; the Poisson equation is: ； Based on the electric potential in the k-th iteration within the grid, the electrostatic field in the k-th iteration within the grid is calculated using the following formula. ； in, This represents the potential at the k-th iteration. Indicates the first l ion charge quantity Describes the (k-1)th iteration. l Seed ion density, Let the electrostatic field be the value of the k-th iteration. L Indicates the number of different types of ions.

4. The three-dimensional fluid simulation method for rectangular inductively coupled plasma according to claim 3, characterized in that, The continuity equation for electrons is: ； ； ； ； The continuity equation for ions is: ； ； The momentum equation for an ion is: ； The energy conservation equation for electrons is: ； in, This represents the electron temperature in the k-th iteration. For electron energy flux density, This indicates the energy loss caused by electron collisions. Indicates electron mobility. This represents the diffusion coefficient of the electron in the k-th iteration. Represents Boltzmann's constant. This represents the electron temperature in the (k-1)th iteration. This represents the electron flux in the k-th iteration. This represents the electron density in the k-th iteration. The source term represents electrons, and t represents time. Describes the k-th iteration. l Seed ion velocity, Indicates the first l The mass of the seed ions. Indicates the first l Seed ion temperature, Indicates the first l Collision terms of ions, Describes the k-th iteration. l Seed ion density, Describes the k-th iteration. l Flux of seed ions. Describes the (k-1)th iteration. l Seed ion velocity, Indicates the first l The source term of the ion.

5. The three-dimensional fluid simulation method for rectangular inductively coupled plasma according to claim 4, characterized in that, Based on the uniformity parameter of the (k-1)th iteration, the electron density of the kth iteration, and the electron temperature of the kth iteration, an explicit method is used to solve the continuity equation of neutral particles to obtain the neutral particle density within the grid for the kth iteration, specifically including: Based on the electron density and electron temperature of the k-th iteration within the grid, the source term of the neutral particle in the k-th iteration within the grid is obtained. Based on the uniformity parameter of the (k-1)th iteration, the source term of the neutral particles in the kth iteration within the grid, the electron density of the kth iteration, and the electron temperature of the kth iteration, the neutral particle density in the kth iteration is obtained by explicitly solving the continuity equation of the neutral particles. The continuity equation of the neutral particles is as follows: ； ； in, This represents the neutral particle density in the k-th iteration. This represents the flux of neutral particles. The source term represents the neutral particle in the k-th iteration; This represents the diffusion coefficient of neutral particles; This represents the neutral particle density in the (k-1)th iteration.

6. The three-dimensional fluid simulation method for rectangular inductively coupled plasma according to claim 1, characterized in that, Based on the uniformity parameters of different grids under the discharge parameters, the plasma uniformity simulation results of the three-dimensional fluid model under the discharge parameters are determined, specifically including: Calculate the percentage density error for the density of different particles in different grids; Calculate the percentage temperature error of the electron temperature of different particles in different grids; Determine whether the density error percentage is greater than a preset density percentage threshold to obtain a second determination result; Determine whether the temperature error percentage is greater than a preset temperature percentage threshold to obtain a third determination result; If both the second and third judgment results are negative, then the plasma distribution of the three-dimensional fluid model under the discharge parameters is uniform. If either the second judgment result or the third judgment result is true, then the plasma distribution of the three-dimensional fluid model under the discharge parameters is non-uniform.

7. A three-dimensional fluid simulation system for rectangular inductively coupled plasma, characterized in that, The three-dimensional fluid simulation system for rectangular inductively coupled plasma is applied to the three-dimensional fluid simulation method for rectangular inductively coupled plasma according to any one of claims 1-6, wherein the three-dimensional fluid simulation system for rectangular inductively coupled plasma comprises: The building module is used to construct a three-dimensional fluid model of a rectangular inductively coupled plasma using a three-dimensional Cartesian coordinate system. The partitioning module is used to divide the simulation region in the three-dimensional fluid model into orthogonal meshes, resulting in multiple meshes; the simulation region includes a plasma region, a dielectric window, a coil, and a shielding region; A setting module is used to set discharge parameters; the discharge parameters include: air pressure, power, chamber size, and coil shape. The simulation module is used to perform a three-dimensional fluid simulation on the three-dimensional fluid model based on the discharge parameters, and to obtain the uniformity parameters of different grids under the discharge parameters; the uniformity parameters include: electron density, ion density, neutral particle density and electron temperature; The simulation result determination module is used to determine the plasma uniformity simulation results of the three-dimensional fluid model under the discharge parameters based on the uniformity parameters of different grids under the discharge parameters.

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