A plasma source simulation method, system, electronic device and storage medium

Abstract

The present invention discloses a plasma source simulation method, system, electronic device and storage medium, and relates to the technical field of capacitive coupling plasma source simulation. The method comprises: dividing a target area into a plurality of mutually connected orthogonal grids; determining the flow state parameters of electrons and the flow state parameters of heavy particles of the capacitive coupling plasma source to be simulated at the current moment and determining the electron fluid equation group, the heavy particle fluid equation group and the discrete form electrostatic field equation at the current moment; thereby determining the electric potential and electric field strength at the current moment and the flow state parameters of electrons and the flow state parameters of heavy particles at the next moment, and when a preset termination condition is met, determining the flow state parameters, electric potential and electric field strength within a second set time period as the simulation result of the capacitive coupling plasma source to be simulated. The present invention improves the simulation efficiency of the capacitive coupling plasma source.

Description

Technical Field

[0001] The present invention relates to the technical field of capacitively coupled plasma source simulation, and in particular to a plasma source simulation method, system, electronic equipment and storage medium. Background Art

[0002] Capacitively coupled plasma source is one of the most important plasma sources in industry. It has the advantages of simple structure, low cost, and the ability to produce large-area uniform plasma. It is widely used in material etching and deposition processes and plays an important role in the production of semiconductor chips. In order to efficiently optimize the chamber structure and discharge conditions of the plasma source, numerical simulation of the discharge process is essential, and people often use fluid models to perform numerical simulations. However, common simulation methods have a series of difficulties, such as the large amount of calculation required to solve the Poisson equation, the poor stability of the electron fluid equation, and the slow convergence speed in some cases, which makes it difficult to simulate capacitively coupled plasma efficiently. Summary of the invention

[0003] The purpose of the present invention is to provide a plasma source simulation method, system, electronic equipment and storage medium, which improve the simulation efficiency of the capacitively coupled plasma source.

[0004] To achieve the above object, the present invention provides the following solutions:

[0005] A method for simulating a plasma source, the method comprising:

[0006] Dividing a target area into a plurality of orthogonal grids connected to each other; the target area includes a discharge chamber and a dielectric area of ​​a capacitively coupled plasma source to be simulated;

[0007] Determine the flow state parameters of electrons and heavy particles of the capacitively coupled plasma source to be simulated at the current moment; the flow state parameters of electrons include density and temperature, the flow state parameters of heavy particles include density, flow velocity and temperature; the heavy particles include: ions and neutral particles;

[0008] Determining the electron fluid equations at the current moment according to the flow state parameters of the electrons at the current moment; the electron fluid equations include: an electron continuity equation and an electron energy equation;

[0009] Determine the heavy particle fluid equations at the current moment according to the flow state parameters of the heavy particles at the current moment; the heavy particle fluid equations include: a heavy particle continuity equation, a heavy particle momentum equation and a heavy particle energy equation;

[0010] Determine the electrostatic field equation at the current moment according to the flow state parameters of the electrons at the current moment and the flow state parameters of the ions at the current moment;

[0011] According to the flow state parameters of electrons at the current moment, the flow state parameters of electrons in the first set time period, the flow state parameters of heavy particles at the current moment and the flow state parameters of heavy particles in the first set time period, the super-relaxation acceleration parameters at the current moment are obtained; the first set time period has a start time of the first moment, an end time of the first set time period is the second moment, the first moment is the moment when the step "dividing the target area into a plurality of orthogonal grids connected to each other" starts, and the second moment is the previous moment;

[0012] Combined with the super-relaxation acceleration method, according to the flow state parameters of the electrons at the current moment, the flow state parameters of the heavy particles at the current moment and the super-relaxation acceleration parameters at the current moment, the source term of the electrons at the current moment, the source term of the heavy particles at the current moment, the transport coefficient of the electrons at the current moment and the transport coefficient of the heavy particles at the current moment are obtained;

[0013] The electrostatic field equation at the current moment is discretized by using the finite volume method and the semi-implicit format to obtain the electrostatic field equation at the current moment in a discrete form on the orthogonal grid; the semi-implicit format is a semi-implicit format that corrects electron migration and diffusion;

[0014] Substituting the flow state parameters of electrons at the current moment, the flow state parameters of ions at the current moment, and the transport coefficient of electrons at the current moment into the discrete form electrostatic field equation at the current moment and solving them to obtain the electric potential on the orthogonal grid at the current moment;

[0015] Calculate the electric field intensity on the orthogonal grid at the current moment according to the electric potential on the orthogonal grid at the current moment;

[0016] Using a finite volume method, an upwind scheme and a multi-step explicit Euler method, the electronic fluid equations at the current moment are discretized to obtain a discrete form of the electronic fluid equations at the current moment on the orthogonal grid;

[0017] Substituting the flow state parameters of the electrons at the current moment, the source term of the electrons at the current moment, the transport coefficient of the electrons at the current moment, the electric potential at the current moment, and the electric field strength at the current moment into the discrete form electron fluid equations at the current moment, to obtain the flow state parameters of the electrons at the next moment;

[0018] Using a finite volume method and a single-step explicit Euler method, the heavy particle fluid equations at the current moment are discretized to obtain a discrete form of the heavy particle fluid equations at the current moment on the orthogonal grid;

[0019] Substituting the flow state parameters of the heavy particles at the current moment, the source term of the heavy particles at the current moment, the transport coefficient of the heavy particles at the current moment, the electric potential at the current moment, and the electric field intensity at the current moment into the discrete form heavy particle fluid equations at the current moment, to obtain the flow state parameters of the heavy particles at the next moment;

[0020] Determine whether the preset termination condition is met at the current moment;

[0021] If satisfied, the flow state parameters of the electrons, the flow state parameters of the heavy particles, the electric potential and the electric field strength within the second set time period are determined as the simulation result of the capacitively coupled plasma source to be simulated; the start time of the second set time period is the first moment, the end time of the second set time period is the third moment, and the third moment is the moment when the preset termination condition is satisfied;

[0022] If not satisfied, replace the flow state parameters of electrons at the current moment with the flow state parameters of electrons at the next moment, replace the flow state parameters of heavy particles at the current moment with the flow state parameters of heavy particles at the next moment, and return to the step "determine the electron fluid equations at the current moment based on the flow state parameters of electrons at the current moment".

[0023] The present invention also provides a plasma source simulation system, the system comprising:

[0024] A grid division module, used for dividing a target area into a plurality of orthogonal grids connected to each other; the target area includes a discharge chamber and a dielectric area of ​​a capacitively coupled plasma source to be simulated;

[0025] The current moment flow state parameter determination module is used to determine the flow state parameters of the electrons and the flow state parameters of the heavy particles of the capacitive coupled plasma source to be simulated at the current moment; the flow state parameters of the electrons include density and temperature, the flow state parameters of the heavy particles include density, flow velocity and temperature; the heavy particles include: ions and neutral particles;

[0026] An electron fluid equation group determination module is used to determine the electron fluid equation group at the current moment according to the flow state parameters of the electrons at the current moment; the electron fluid equation group includes: an electron continuity equation and an electron energy equation;

[0027] A heavy particle fluid equation group determination module is used to determine the heavy particle fluid equation group at the current moment according to the flow state parameters of the heavy particles at the current moment; the heavy particle fluid equation group includes: a heavy particle continuity equation, a heavy particle momentum equation and a heavy particle energy equation;

[0028] An electrostatic field equation determination module, used to determine the electrostatic field equation at the current moment according to the flow state parameters of the electrons at the current moment and the flow state parameters of the ions at the current moment;

[0029] A super-relaxation acceleration parameter determination module, used for obtaining the super-relaxation acceleration parameter at the current moment according to the flow state parameter of the electrons at the current moment, the flow state parameter of the electrons in the first set time period, the flow state parameter of the heavy particles at the current moment and the flow state parameter of the heavy particles in the first set time period; the first set time period is a start time of the first moment, the end time of the first set time period is a second moment, the first moment is the moment when the step of "dividing the target area into a plurality of orthogonal grids connected to each other" starts, and the second moment is the previous moment;

[0030] A source term and transport coefficient determination module is used to combine the super-relaxation acceleration method to obtain the source term of the electron at the current moment, the source term of the heavy particle at the current moment, the transport coefficient of the electron at the current moment, and the transport coefficient of the heavy particle at the current moment according to the flow state parameter of the electron at the current moment, the flow state parameter of the heavy particle at the current moment, and the super-relaxation acceleration parameter at the current moment;

[0031] The first discrete module is used to discretize the electrostatic field equation at the current moment by using the finite volume method and the semi-implicit format to obtain the electrostatic field equation at the current moment in a discrete form on the orthogonal grid; the semi-implicit format is a semi-implicit format that corrects electron migration and diffusion;

[0032] The potential calculation module is used to substitute the flow state parameters of the electrons at the current moment, the flow state parameters of the ions at the current moment and the transport coefficient of the electrons at the current moment into the discrete form electrostatic field equation at the current moment and solve it to obtain the potential on the orthogonal grid at the current moment;

[0033] An electric field strength calculation module, used to calculate the electric field strength on the orthogonal grid at a current moment according to the electric potential on the orthogonal grid at a current moment;

[0034] A second discretization module is used to discretize the electronic fluid equations at the current moment by using a finite volume method, an upwind scheme and a multi-step explicit Euler method to obtain a discrete form of the electronic fluid equations at the current moment on the orthogonal grid;

[0035] An electron flow state parameter calculation module is used to substitute the electron flow state parameter at the current moment, the electron source term at the current moment, the electron transport coefficient at the current moment, the electric potential at the current moment, and the electric field strength at the current moment into the discrete form electron fluid equation group at the current moment to obtain the electron flow state parameter at the next moment;

[0036] A third discretization module is used to discretize the heavy particle fluid equations at the current moment by using a finite volume method and a single-step explicit Euler method to obtain a discrete form of the heavy particle fluid equations at the current moment on the orthogonal grid;

[0037] A heavy particle flow state parameter calculation module is used to substitute the flow state parameters of the heavy particles at the current moment, the source term of the heavy particles at the current moment, the transport coefficient of the heavy particles at the current moment, the electric potential at the current moment, and the electric field intensity at the current moment into the discrete form heavy particle fluid equation group at the current moment to obtain the flow state parameters of the heavy particles at the next moment;

[0038] A judgment module is used to judge whether the preset termination condition is met at the current moment;

[0039] A first execution module is used to determine the flow state parameters of the electrons, the flow state parameters of the heavy particles, the electric potential and the electric field strength within a second set time period as the simulation result of the capacitively coupled plasma source to be simulated if the preset termination condition is met at the current moment; the start time of the second set time period is the first moment, the end time of the second set time period is a third moment, and the third moment is the moment when the preset termination condition is met;

[0040] The second execution module is used to replace the flow state parameters of electrons at the current moment with the flow state parameters of electrons at the next moment, and replace the flow state parameters of heavy particles at the current moment with the flow state parameters of heavy particles at the next moment if the preset termination condition is not met at the current moment, and return to the electronic fluid equation group determination module.

[0041] The present invention also provides an electronic device, comprising:

[0042] one or more processors;

[0043] a storage device having one or more programs stored thereon;

[0044] When the one or more programs are executed by the one or more processors, the one or more processors are enabled to implement the above-described methods.

[0045] The present invention also provides a storage medium on which a computer program is stored, wherein the computer program implements the above-mentioned method when executed by a processor.

[0046] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0047] The present invention discloses a plasma source simulation method, system, electronic device and storage medium, the method comprising: dividing a target area into a plurality of mutually connected orthogonal grids; determining the flow state parameters of electrons and the flow state parameters of heavy particles of a capacitively coupled plasma source to be simulated at the current moment and determining the electron fluid equation group, the heavy particle fluid equation group and the discrete form electrostatic field equation at the current moment; thereby determining the electric potential and electric field strength at the current moment and the flow state parameters of electrons and the flow state parameters of heavy particles at the next moment, and when a preset termination condition is met, determining the flow state parameters, electric potential and electric field strength within a second set time period as the simulation result of the capacitively coupled plasma source to be simulated. The present invention improves the simulation efficiency of the capacitively coupled plasma source. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0049] Figure 1 A flow chart of a method for simulating a plasma source provided by an embodiment of the present invention;

[0050] Figure 2 A block diagram of a simulation system of a plasma source provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0051] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0052] The purpose of the present invention is to provide a plasma source simulation method, system, electronic equipment and storage medium, aiming to improve the simulation efficiency of a capacitively coupled plasma source, and can be applied to the field of capacitively coupled plasma source simulation technology.

[0053] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0054] A fast simulation method is proposed for the capacitively coupled plasma source commonly found in industry.

[0055] The simulation method is based on the fluid mechanics model of capacitively coupled plasma. By solving the Poisson equation of the electrostatic field and the continuity equation, momentum conservation equation and energy conservation equation of each particle (including electrons, various ions and neutral particles, ions and neutral particles are collectively referred to as heavy particles), the spatiotemporal distribution of the macroscopic state (density, flow rate and temperature) of each particle is obtained. The spatiotemporal distribution of these states can be used to predict the performance of the capacitively coupled plasma source when used in processing technologies such as etching and deposition (for example, the density and spatial distribution of specific particle components can reflect the efficiency and uniformity of the processing). By performing multiple simulations under different chamber structures, gas compositions and process conditions, the influence of various factors on the performance of the capacitively coupled plasma source can also be analyzed, thereby optimizing the design of the capacitively coupled plasma source.

[0056] Example 1

[0057] Figure 1 Flow chart of the simulation method of the plasma source provided by the embodiment of the present invention. Figure 1 As shown, the simulation method of the plasma source in this embodiment includes:

[0058] Step 101: Divide a target area into a plurality of orthogonal grids connected to each other; the target area includes a discharge chamber and a dielectric area of ​​a capacitively coupled plasma source to be simulated.

[0059] Step 102: Determine the flow state parameters of the capacitively coupled plasma source to be simulated at the current moment.

[0060] Specifically, step 102 includes:

[0061] Step 1021: Determine the flow state parameters of electrons and heavy particles of the capacitively coupled plasma source to be simulated at the current moment; the flow state parameters of electrons include density and temperature, and the flow state parameters of heavy particles include density, flow velocity and temperature; heavy particles include: ions and neutral particles.

[0062] Step 103: Determine the current equation group and the discrete electrostatic field equation according to the current flow state parameters.

[0063] Specifically, step 103 includes:

[0064] Step 1031: Determine the electron fluid equations at the current moment according to the flow state parameters of the electrons at the current moment; the electron fluid equations include: an electron continuity equation and an electron energy equation.

[0065] Step 1032: Determine the heavy particle fluid equations at the current moment according to the flow state parameters of the heavy particles at the current moment; the heavy particle fluid equations include: heavy particle continuity equation, heavy particle momentum equation and heavy particle energy equation.

[0066] Step 1033: Determine the electrostatic field equation at the current moment according to the flow state parameters of the electrons at the current moment and the flow state parameters of the ions at the current moment.

[0067] Step 1034: Obtain the super-relaxation acceleration parameters at the current moment according to the flow state parameters of electrons at the current moment, the flow state parameters of electrons in the first set time period, the flow state parameters of heavy particles at the current moment and the flow state parameters of heavy particles in the first set time period; the first set time period has a start time of the first moment, an end time of the first set time period is the second moment, the first moment is the moment when the step "dividing the target area into multiple orthogonal grids connected to each other" starts, and the second moment is the previous moment.

[0068] Step 1035: In combination with the super-relaxation acceleration method, according to the flow state parameters of the electrons at the current moment, the flow state parameters of the heavy particles at the current moment and the super-relaxation acceleration parameters at the current moment, the source term of the electrons at the current moment, the source term of the heavy particles at the current moment, the transport coefficient of the electrons at the current moment and the transport coefficient of the heavy particles at the current moment are obtained.

[0069] Step 1036: Discretize the electrostatic field equation at the current moment by using the finite volume method and the semi-implicit format to obtain the discrete form of the electrostatic field equation at the current moment on an orthogonal grid; the semi-implicit format is a semi-implicit format that corrects electron migration and diffusion.

[0070] Step 104: Determine the electric potential and electric field strength on the orthogonal grid at the current moment.

[0071] Specifically, step 104 includes:

[0072] Step 1041: Substitute the flow state parameters of electrons at the current moment, the flow state parameters of ions at the current moment, and the transport coefficient of electrons at the current moment into the discrete form electrostatic field equation at the current moment and solve them to obtain the electric potential on the orthogonal grid at the current moment.

[0073] Step 1042: Calculate the electric field strength on the orthogonal grid at the current moment according to the electric potential on the orthogonal grid at the current moment.

[0074] Step 105: Determine the flow state parameters at the next moment according to the equation group at the current moment.

[0075] Specifically, step 105 includes:

[0076] Step 1051: using the finite volume method, the upwind scheme and the multi-step explicit Euler method, the electron fluid equations at the current moment are discretized to obtain the discrete form of the electron fluid equations at the current moment on the orthogonal grid.

[0077] Step 1052: Substitute the electron flow state parameters at the current moment, the electron source term at the current moment, the electron transport coefficient at the current moment, the electric potential at the current moment, and the electric field strength at the current moment into the discrete form electron fluid equation group at the current moment to obtain the electron flow state parameters at the next moment.

[0078] Step 1053: Discretize the heavy particle fluid equations at the current moment by using the finite volume method and the single-step explicit Euler method to obtain the heavy particle fluid equations at the current moment in a discrete form on an orthogonal grid.

[0079] Step 1054: Substitute the flow state parameters of the heavy particles at the current moment, the source terms of the heavy particles at the current moment, the transport coefficients of the heavy particles at the current moment, the electric potential at the current moment, and the electric field strength at the current moment into the discrete form of the heavy particle fluid equations at the current moment to obtain the flow state parameters of the heavy particles at the next moment.

[0080] Step 106: Determine whether the current moment satisfies a preset termination condition.

[0081] If so, step 107 is executed: the flow state parameters, electric potential and electric field strength of the second set time period are determined as simulation results.

[0082] Specifically, step 107 is as follows: determining the flow state parameters of electrons, the flow state parameters of heavy particles, the electric potential and the electric field strength within the second set time period as the simulation results of the capacitively coupled plasma source to be simulated; the start time of the second set time period is the first moment, the end time of the second set time period is the third moment, and the third moment is the moment when the preset termination condition is met.

[0083] If not, execute step 108 : replace the flow state parameters at the current moment with the flow state parameters at the next moment, and return to step 103 .

[0084] Specifically, step 108 includes:

[0085] Step 1081: Replace the flow state parameters of electrons at the current moment with the flow state parameters of electrons at the next moment.

[0086] Step 1082: Replace the flow state parameters of the heavy particles at the current moment with the flow state parameters of the heavy particles at the next moment.

[0087] As an optional implementation, step 1031 specifically includes:

[0088] The electron continuity equation at the current moment is determined according to the electron density at the current moment.

[0089] The electron energy equation at the current moment is determined according to the electron temperature at the current moment.

[0090] The electron continuity equation at the current moment and the electron energy equation at the current moment are determined as the electron fluid equation group at the current moment.

[0091] As an optional implementation, step 1032 specifically includes:

[0092] The heavy particle continuity equation at the current moment is determined according to the density of the heavy particles at the current moment.

[0093] The momentum equation of the heavy particles at the current moment is determined according to the flow velocity of the heavy particles at the current moment.

[0094] The heavy particle energy equation at the current moment is determined according to the temperature of the heavy particles at the current moment.

[0095] The heavy particle continuity equation at the current moment, the heavy particle momentum equation at the current moment and the heavy particle energy equation at the current moment are determined as the heavy particle fluid equation group at the current moment.

[0096] Specifically, the simulation method is based on the finite volume method for solving partial differential equations. The specific steps for performing a simulation are:

[0097] Step 1: Mesh division.

[0098] (1) The capacitively coupled plasma source to be simulated, which includes a discharge chamber region (the plasma in the capacitively coupled plasma source will be generated and evolved in the discharge chamber region) and an adjacent dielectric region, is divided into mutually connected orthogonal grids, thereby obtaining grid topology information and geometric information required for subsequent calculations.

[0099] The mesh topology information usually includes: the number of mesh cells, cell surfaces and vertices; the surfaces and vertices that make up each cell; the vertices that make up each surface; the cells on both sides of each surface, etc. The mesh geometry information usually includes: the position of each cell, cell surface and vertex; the volume of each cell; the area of ​​each surface; the distance from each surface to the centroid of the cells on both sides, etc. The mesh topology information and geometry information will be used in steps 4, 5 and 6 to construct the spatial discretization format of the differential equation under the finite volume method.

[0100] The partitioning method can adopt the conventional partitioning method of orthogonal grid under the finite volume method.

[0101] Compared with non-orthogonal grids, using orthogonal grids can greatly simplify the numerical format and improve the efficiency and accuracy of the simulation.

[0102] Step 2: Initialization.

[0103] (1) Determine the type of physical quantity for which initial values ​​need to be set based on the discharge gas composition of the capacitively coupled plasma source to be simulated and the simulation requirements.

[0104] The physical quantities that need to set initial values ​​usually need to include at least: electron density n e , electron temperature T e , the density n of the heavy particles. It may also include, as appropriate, the flow rate u of the heavy particles (if the momentum equation of the corresponding component is to be considered in the simulation), the temperature T of the heavy particles (if the energy equation of the corresponding component is to be considered in the simulation), etc.

[0105] Simulation requirements usually include simulation efficiency, accuracy, correctness, and the degree of concern for a certain physical process. These requirements determine whether it is necessary to solve the momentum equation or energy equation for a certain heavy particle component.

[0106] (2) Based on the grid division results of step 1, for each physical quantity, use its discrete value on each grid to describe its spatial distribution in the simulation area. On this basis, assign initial values ​​to the physical quantities (discrete values ​​on the grid) that need to be set.

[0107] Each physical quantity has a spatial distribution only in its definition domain. The definition domain of the physical quantities n, u, T of the flow state of each component is inside the discharge chamber.

[0108] Step 3: Calculate the collision reaction source term and transport coefficient.

[0109] (1) According to the discharge gas composition of the capacitively coupled plasma source to be simulated, the simulation requirements, and the macroscopic flow state of the particles at the current moment (n, u, T), the source term and transport coefficient in the fluid equations for each particle are calculated.

[0110] Among them, the source terms that need to be calculated usually need to include at least: the electron particle number source term Energy source term Particle number source term for each heavy particle Optionally, it can also include: Momentum source term for each heavy particle (if you want to consider the momentum equation of the corresponding component in the simulation) and the energy source term ( or )(If you want to consider the energy equation of the corresponding component in the simulation). Where t is time, K e is the average total kinetic energy of the electron, m is the mass of the heavy particle, K is the average total kinetic energy of the heavy particle, C v is the isochoric heat capacity of heavy particles.

[0111] The transport coefficients that need to be calculated include the mobility μ of each particle (if the migration-diffusion approximation is used in the simulation to replace the momentum equation of the corresponding component), the diffusion coefficient D (if the (migration) diffusion approximation is used in the simulation to replace the momentum equation of the corresponding component), the viscosity coefficient η (if the simulation wishes to use a complete momentum equation including a viscosity term), the thermal conductivity κ (if the simulation wishes to consider the energy equation of the corresponding component), etc.

[0112] The composition of the discharge gas determines what kinds of collision reactions occur in the system, and thus determines the calculation formulas for the source term and transport coefficient to a certain extent.

[0113] Simulation requirements usually include simulation efficiency, accuracy, correctness, and the degree of concern for a certain physical process. These requirements determine whether it is necessary to solve the viscosity term, momentum equation, or energy equation of a certain heavy particle component, thereby determining which source terms and transport coefficients need to be calculated. These requirements also determine whether it is necessary to consider the impact of a certain collision reaction in the system on the number of particles, momentum, and energy, thereby determining the calculation formula for calculating source terms and transport coefficients to a certain extent.

[0114] The types of heavy particle source terms and heavy particle transport coefficients that need to be calculated depend on the specific heavy particle fluid equation model used. The specific calculation formulas for the source terms and transport coefficients depend on the user.

[0115] Common methods for calculating transport coefficients are: mobility Diffusion coefficient Shear viscosity coefficient Thermal conductivity Where e is the unit charge, T' is the temperature of the particle (including the electron temperature T e and the temperature T of heavy particles), n' is the particle density (including the electron density n e and heavy particle density n), m is the particle mass (including the mass of the electron and the mass of the heavy particles), m r is the reduced mass of the particle and the background gas particles, v is the elastic collision frequency between the particle and the background gas particles (n′, T′ are known quantities, m, m r , v is the input parameter).

[0116] If you want to get converged simulation results faster in periodic steady-state problems, you can also use the idea of ​​super-relaxation acceleration on the basis of conventional methods to appropriately scale the reaction coefficients or source terms of important collision reactions. For example, if a certain ionization reaction plays an important role in the convergence of the simulation, you can first record the relative change of plasma density within a cycle. (n p1 , n p2Represent the plasma density before and after a cycle respectively), and then select an appropriate function f (for example, f(x) = min(a, max(b, cx+1)), where abc are constants determined empirically) to convert the contribution of the collision reaction to the particle number source term Corrected to

[0117] Among them, the measurement method of the relative change of plasma density, the form of the correction function and the type of source terms that need to be corrected are all determined by experience.

[0118] Step 4: Solve for the electrostatic field.

[0119] (1) A semi-implicit correction is made to the charge density term in the Poisson equation for the electrostatic field.

[0120] Poisson's equation is a differential equation describing the electrostatic field. Its form in the discharge chamber region is In the dielectric region it takes the form Where D is the electric displacement vector, E is the electric field intensity, represents the electric potential, Z i represents the charge of particle component i, ε0 and ε represent the dielectric constants in vacuum and medium respectively, is the differential operator symbol; e is the unit charge, n i is the density of the ith particle.

[0121] The idea of ​​semi-implicit correction is to correct the electron density at the current moment in the charge density term to the electron density at the future moment. The specific operation method is as follows: 1) First, the vacuum dielectric constant ε0 of the Poisson equation in the fluid region is corrected to the vacuum dielectric constant that predicts electron migration. in, To predict the vacuum dielectric constant for electron migration, Δt is the calculation interval of Poisson's equation, μ e is the electron mobility. 2) Then, the electron density n is replaced by e Corrected to account for electron diffusion: in, To predict the electron density of electron diffusion, D e is the electron diffusion coefficient, T e is the temperature of the electron. 3) Finally, the modified Poisson's equation in the fluid region is obtained as follows:

[0122] The purpose of the semi-implicit correction of the Poisson's equation is to eliminate the strong coupling between the electric field and the electrons, so that the Poisson's equation can use a longer calculation interval than the electron fluid equations, thereby greatly reducing the number of solutions to the Poisson's equation and significantly improving the computational efficiency of the simulation.

[0123] (2) Using the finite volume method, the modified Poisson equation is discretized into the electric potential A system of linear equations satisfied by discrete values.

[0124] The discretization method is the same as the conventional finite volume method. The specific discretization method is: integrate the electrostatic field Poisson equation on each unit (the grid information obtained in step 1 is required), and the integration result on each unit constitutes an equation in the linear equation system.

[0125] Note 2: The input to this step includes the input obtained in step 4(1) and The density of each ionic component n i distribution, and a series of input parameters (Z i , ε, etc.) The output of this step is a system of linear equations (the solution of the linear equations is the potential discrete values ​​of ).

[0126] (3) Solve the discretized linear equations to obtain the potential The discrete spatial distribution of .

[0127] The linear equations can be solved using conventional methods such as the Krylov subspace series method.

[0128] (4) Using numerical differentiation under the finite volume method, calculate the potential The electric field strength E distribution corresponding to the distribution. The calculation formula is The numerical differentiation calculation method adopts the conventional method of calculating spatial derivatives under the finite volume method.

[0129] Step 5: Solve the electron fluid equations.

[0130] (1) Electric field E and electron temperature T in the reference simulation area e The spatial distribution of physical quantities such as electron fluid equations is analyzed, and the stability of the electron fluid equations at different spatial positions is analyzed, so as to set different time steps Δt (for the electron fluid equations) for different grids.

[0131] You need to set a longer time step for a grid with high stability and a shorter time step for a grid with low stability. The time steps should be integer multiples, and the time step on the surface should be the maximum of the time steps of the cells on both sides.

[0132] The specific method of dividing the grid into different time steps depends on experience. Experience shows that a specific judgment method with better effect is: if the electric field E on a grid is greater than the threshold, or the electron temperature T eIf it is greater than the threshold (optional, belongs to input information, can be spatially varying), or the grid is statically judged to have low stability (belongs to input information), then this grid is set to a short time step, otherwise this grid is set to a long time step.

[0133] (2) Under the finite volume method, the electron fluid equations are spatially discretized using the upwind scheme.

[0134] The electron fluid equations are in the form of Among them J e is the electron particle number flux, Q e is the energy flux, p e =n e T e Represents electron pressure.

[0135] The discretization method is as follows: 1) First, the equations are integrated in each unit according to the conventional finite volume method to obtain:

[0136]

[0137] Where V and A represent the volume of the grid cell and the area of ​​the cell surface, respectively, and the subscripts c and s represent the grid cell c and the surface s of the grid cell c, respectively. 2) Then the migration term in the flux on the cell surface is processed using the upwind scheme, that is:

[0138] The subscripts c1 and c2 represent the two units on both sides of the surface s respectively.

[0139] Compared with other spatial discrete formats, the advantages of using the upwind format are simple implementation, small calculation amount and high stability.

[0140] (3) Using the multi-step explicit Euler method, the electron density n is calculated based on the grid time step obtained in step 5(1) and the spatial discretization of the electron fluid equation derived in step 5(2). e and the electron temperature T e By advancing time, we can obtain the electron density and electron temperature at the next moment.

[0141] The explicit Euler method advances the physical quantity g from time t to t+Δt as follows:

[0142]

[0143] In this step, g is the electron density n e and electron energy density 1.5n e T e .

[0144] In the multi-step explicit Euler method, for every time a long-step unit is advanced, a short-step unit needs to be advanced several times (the number is the ratio of the long to the short time step). The specific implementation method is: 1) First, calculate the flux on all surfaces to advance all units by one (long or short) time step; 2) Then, refresh the flux on the short-step surface to advance the short-step unit by a short time step; 3) Repeat the previous step until the sum of the accumulated short steps is equal to the long step.

[0145] Due to the low stability of the electron fluid equations, this step often requires continuous (cyclic) advancement of multiple long time steps. The total number of time steps required depends on the specific problem, and a typical value is one-two-hundredth of the power cycle.

[0146] Compared with the implicit method, the explicit Euler method can effectively reduce the amount of single-step calculation while maintaining high stability, thereby effectively improving the computational efficiency of the simulation method. Compared with the single-step method, the multi-step method can effectively overcome the influence of the poor stability of the electron fluid equations in the sheath layer and near the electrode tip, and can also effectively improve the computational efficiency of the simulation method.

[0147] Step 6: Solve the heavy particle fluid equations. (Step 6 has no dependency on step 5 and can be interchanged).

[0148] (1) Establish an appropriate set of heavy particle fluid equations based on the discharge gas composition and simulation requirements.

[0149] Specifically, 1) first, the types of heavy particles present in the discharge process are determined based on the discharge gas composition; 2) then, based on the trade-off between simulation efficiency and the correctness of the simulation results, the complete fluid mechanics equations for all heavy particles are simplified to remove some unimportant particles and equations that do not need to be solved.

[0150] A complete system of fluid equations consists of the continuity equation, momentum equation, and energy equation:

[0151]

[0152] Among them, p, q represents the pressure, viscosity tensor and heat conduction flux of heavy particles, m, Z, C v They represent the mass, charge (0 for neutral particles) and isochoric heat capacity of heavy particles, respectively; η, η′, κ represent the shear viscosity, volume viscosity and thermal conductivity of heavy particle transport coefficients, respectively. Represents the unit tensor.

[0153] There are many ways to simplify the complete fluid equations, for example, 1) ignore the viscosity term: Simplified to ) Ignore the energy equation: Simplified to T = T0; where T0 in the above formula is the temperature of the background gas. 3) Use the migration diffusion approximation to replace the momentum equation: Simplified to In addition, it is also possible to combine simplified methods or use a modified migration-diffusion approximation, etc. Note 4: This step only establishes the equation and does not involve actual calculations.

[0154] (2) Using the finite volume method, the fluid dynamics equations for heavy particles are spatially discretized.

[0155] The spatial discretization method of the finite volume method is to integrate the equations over each element (and use an appropriate format to handle the flux on the element surface).

[0156] (3) In the discrete form of the heavy particle fluid dynamics equations, the single-step explicit Euler method is used to time-advance the density n of the heavy particles, the flow velocity u of the heavy particles, and the temperature T of the heavy particles.

[0157] Just use the regular single-step explicit Euler method (single-step here means that the step size does not vary with space). The formula for the explicit Euler method to advance the physical quantity g from time t to t+Δt is:

[0158]

[0159] In this step, g is the heavy particle density n, momentum density mnu and thermal energy density nC v T.

[0160] Since the heavy particle fluid equations are relatively stable, in this step, you can choose whether to split the total time step required for advancement into multiple small time steps for cyclic advancement (the fewer the splits, the better, but the maximum length of each small time step is limited by stability). The total time step required for advancement is determined according to the specific problem. The number of time step splits for different particles does not have to be the same.

[0161] If you want to get convergent simulation results faster in periodic steady-state problems, you can appropriately amplify the time step for some neutral particle components that cannot respond to periodic electric fields. For example, when the charged particles are advanced by Δt, the neutral particles can be advanced by tens to hundreds of Δt. At this time, the total time step for different particles does not have to be the same.

[0162] Step 7: Repeat the above calculations in a loop

[0163] (1) Repeat the calculation work from step 3 to step 6 until the judgment condition of simulation completion is met.

[0164] Commonly used judgment conditions are: the calculation reaches a specified time (that is, the cumulative advancement time is greater than a threshold) or reaches a specified convergence accuracy (the relative change of certain physical quantities within a certain advancement time is less than a threshold).

[0165] The specific cycle is similar to: calculate source terms and transport coefficients → solve electrostatic fields → promote the electron flow state (i.e. solve the electron fluid equations) → promote the flow state of all heavy particles (i.e. solve the heavy particle fluid equations) → determine whether the simulation is completed → (if the simulation is not completed) calculate source terms and transport coefficients → ... Or: step 3 → step 4 → step 5 → step 6 → determine whether the simulation is completed → (if the simulation is not completed) step 3 → ....

[0166] (2) Output the calculation results of each physical quantity.

[0167] Each output physical quantity can be its discrete time and space distribution. Discrete time distribution means that the physical quantity can be output in multiple calculation cycles. Discrete space distribution means that the physical quantity can be output in multiple grids.

[0168] Example 2

[0169] Figure 2 The block diagram of the simulation system of the plasma source provided by the embodiment of the present invention is shown in FIG. Figure 2 As shown, the simulation system of the plasma source in this embodiment includes:

[0170] The grid division module 201 is used to divide the target area into a plurality of orthogonal grids connected to each other; the target area includes the discharge chamber and the dielectric area of ​​the capacitively coupled plasma source to be simulated.

[0171] The current moment flow state parameter determination module 202 is used to determine the flow state parameters of the capacitively coupled plasma source to be simulated at the current moment.

[0172] Specifically, the current flow state parameter determination module 202 specifically includes:

[0173] The submodule 2021 for determining the flow state parameters at the current moment is used to determine the flow state parameters of electrons and the flow state parameters of heavy particles of the capacitively coupled plasma source to be simulated at the current moment; the flow state parameters of electrons include density and temperature, and the flow state parameters of heavy particles include density, flow velocity and temperature; heavy particles include: ions and neutral particles.

[0174] The module 203 for determining the set of equations and the electrostatic field equations in discrete form is used to determine the set of equations and the electrostatic field equations in discrete form at the current moment according to the flow state parameters at the current moment.

[0175] Specifically, the equation group and discrete form electrostatic field equation determination module 203 specifically includes:

[0176] The electron fluid equation group determination submodule 2031 is used to determine the electron fluid equation group at the current moment according to the flow state parameters of the electrons at the current moment; the electron fluid equation group includes: an electron continuity equation and an electron energy equation.

[0177] The heavy particle fluid equation group determination submodule 2032 is used to determine the heavy particle fluid equation group at the current moment according to the flow state parameters of the heavy particles at the current moment; the heavy particle fluid equation group includes: heavy particle continuity equation, heavy particle momentum equation and heavy particle energy equation.

[0178] The electrostatic field equation determination module 2033 is used to determine the electrostatic field equation at the current moment according to the flow state parameters of the electrons and the flow state parameters of the ions at the current moment.

[0179] The super-relaxation acceleration parameter determination module 2034 is used to obtain the super-relaxation acceleration parameters at the current moment according to the flow state parameters of electrons at the current moment, the flow state parameters of electrons in the first set time period, the flow state parameters of heavy particles at the current moment and the flow state parameters of heavy particles in the first set time period; the first set time period has a start time of the first moment, an end time of the first set time period is the second moment, the first moment is the moment when the step "dividing the target area into multiple orthogonal grids connected to each other" starts, and the second moment is the previous moment.

[0180] The source term and transport coefficient determination module 2035 is used to combine the super-relaxation acceleration method to obtain the source term of the electron at the current moment, the source term of the heavy particles at the current moment, the transport coefficient of the electron at the current moment and the transport coefficient of the heavy particles at the current moment according to the flow state parameters of the electrons at the current moment, the flow state parameters of the heavy particles at the current moment and the super-relaxation acceleration parameters at the current moment.

[0181] The first discrete module 2036 is used to discretize the electrostatic field equation at the current moment by using the finite volume method and the semi-implicit format to obtain the discrete form of the electrostatic field equation at the current moment on an orthogonal grid; the semi-implicit format is a semi-implicit format that corrects electron migration and diffusion.

[0182] The electric potential and electric field strength determination module 204 is used to determine the electric potential and electric field strength on the orthogonal grid at the current moment.

[0183] Specifically, the electric potential and electric field strength determination module 204 specifically includes:

[0184] The electric potential calculation module 2041 is used to substitute the flow state parameters of electrons, the flow state parameters of ions and the transport coefficient of electrons at the current moment into the discrete form electrostatic field equation at the current moment and solve them to obtain the electric potential on the orthogonal grid at the current moment.

[0185] The electric field strength calculation submodule 2042 is used to calculate the electric field strength on the orthogonal grid at the current moment according to the electric potential on the orthogonal grid at the current moment.

[0186] The next moment flow state parameter determination module 205 is used to determine the next moment flow state parameters according to the current moment equation group.

[0187] Specifically, the next moment flow state parameter determination module 205 specifically includes:

[0188] The second discretization module 2051 is used to discretize the electronic fluid equations at the current moment by using the finite volume method, the upwind scheme and the multi-step explicit Euler method to obtain the electronic fluid equations at the current moment in a discrete form on an orthogonal grid.

[0189] The electron flow state parameter calculation module 2052 is used to substitute the electron flow state parameters at the current moment, the electron source term at the current moment, the electron transport coefficient at the current moment, the electric potential at the current moment and the electric field strength at the current moment into the discrete form electron fluid equation group at the current moment to obtain the electron flow state parameters at the next moment.

[0190] The third discretization module 2053 is used to discretize the heavy particle fluid equations at the current moment by using the finite volume method and the single-step explicit Euler method to obtain the heavy particle fluid equations at the current moment in a discrete form on an orthogonal grid.

[0191] The heavy particle flow state parameter calculation module 2054 is used to substitute the flow state parameters of the heavy particles at the current moment, the source term of the heavy particles at the current moment, the transport coefficient of the heavy particles at the current moment, the electric potential at the current moment, and the electric field strength at the current moment into the discrete form of the heavy particle fluid equation group at the current moment to obtain the flow state parameters of the heavy particles at the next moment.

[0192] The judgment module 206 is used to judge whether the current moment satisfies the preset termination condition.

[0193] If the preset termination condition is met at the current moment, the first execution module 207 is executed, and the first execution module 207 is used to determine the flow state parameters, electric potential and electric field strength of the second set time period as the simulation result.

[0194] Specifically, the first execution module 207 is specifically used to: determine the flow state parameters of electrons, the flow state parameters of heavy particles, the electric potential and the electric field strength within the second set time period as the simulation results of the capacitively coupled plasma source to be simulated; the start time of the second set time period is the first moment, the end time of the second set time period is the third moment, and the third moment is the moment when the preset termination condition is met.

[0195] If the preset termination condition is not met at the current moment, the second execution module 208 is executed, and the equation group and the discrete form electrostatic field equation determination module (electronic fluid equation group determination module 2031) are returned. The second execution module 208 is used to replace the flow state parameters at the current moment with the flow state parameters at the next moment.

[0196] Specifically, the second execution module 208 includes:

[0197] The first execution submodule 2081 is used to replace the flow state parameters of the electrons at the current moment with the flow state parameters of the electrons at the next moment.

[0198] The second execution submodule 2082 is used to replace the flow state parameters of the heavy particles at the current moment with the flow state parameters of the heavy particles at the next moment.

[0199] As an optional implementation, the electronic fluid equation group determination module 2031 specifically includes:

[0200] The electron continuity equation determination unit is used to determine the electron continuity equation at the current moment according to the electron density at the current moment.

[0201] The electron energy equation determination unit is used to determine the electron energy equation at the current moment according to the temperature of the electrons at the current moment.

[0202] The electron fluid equation group determination unit is used to determine the electron continuity equation at the current moment and the electron energy equation at the current moment as the electron fluid equation group at the current moment.

[0203] As an optional implementation, according to the heavy particle fluid equations, the module 2032 is determined, specifically including:

[0204] The heavy particle continuity equation determination unit is used to determine the heavy particle continuity equation at the current moment according to the density of the heavy particles at the current moment.

[0205] The heavy particle momentum equation determination unit is used to determine the heavy particle momentum equation at the current moment according to the flow velocity of the heavy particles at the current moment.

[0206] The heavy particle energy equation determination unit is used to determine the heavy particle energy equation at the current moment according to the temperature of the heavy particles at the current moment.

[0207] The heavy particle fluid equation group determination unit is used to determine the heavy particle continuity equation at the current moment, the heavy particle momentum equation at the current moment and the heavy particle energy equation at the current moment as the heavy particle fluid equation group at the current moment.

[0208] As an optional implementation, the discrete algebraic equation determination module 2033 specifically includes:

[0209] The electrostatic field equation determination unit is used to determine the electrostatic field equation of the orthogonal grid at the current moment.

[0210] The correction unit is used to correct the charge density term in the electrostatic field equation to obtain the corrected electrostatic field equation of the orthogonal grid at the current moment.

[0211] The discrete algebraic equation determination unit is used to transform the corrected electrostatic field equation at the current moment into a discrete algebraic equation on an orthogonal grid by using a finite volume method.

[0212] Example 3

[0213] The present invention also provides an electronic device, comprising:

[0214] one or more processors;

[0215] a storage device having one or more programs stored thereon;

[0216] When one or more programs are executed by one or more processors, the one or more processors implement the method in Embodiment 1.

[0217] Example 4

[0218] The present invention also provides a storage medium on which a computer program is stored, wherein the computer program implements the method in embodiment 1 when executed by a processor.

[0219] Advantages of the above method:

[0220] (1) The simulation speed of this method is extremely fast, even more than 100 times that of some common simulation methods. This is because it specifically solves many common performance limiting factors in capacitive coupled plasma simulation: for example, the semi-implicit correction of the Poisson equation solves the problem of excessive computational complexity of the Poisson equation caused by the coupling of the electric field and electrons; the explicit upwind format of the electron fluid equations solves the problem of poor stability of the electron fluid equations and excessive single-step computational complexity of the implicit format; the multi-time step method of the electron fluid equations solves the problem of excessive total computational complexity of the electron fluid equations caused by poor stability of a few grids when high voltage or electrode tips are present; by scaling the time step of the neutral particle fluid equations and the coefficients or source terms of some important collision reactions, the problem of excessive total computational complexity caused by slow convergence in some cases is solved. The combined use of the above multiple targeted solutions makes the entire simulation method have extremely high simulation efficiency.

[0221] (2) The high computational efficiency of the simulation method comes entirely from the design of the numerical method. It does not rely on specific examples or hardware and software platforms, nor does it rely on large-scale parallel algorithms or high-performance linear (nonlinear) solvers. This makes the high performance of the simulation method simple to achieve, easy to reproduce, and stable and controllable.

[0222] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0223] This article uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only used to help understand the device and its core ideas of the present invention. At the same time, for those skilled in the art, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for simulating a plasma source, characterized in that: The method comprises: Dividing a target area into a plurality of orthogonal grids connected to each other; the target area includes a discharge chamber and a dielectric area of ​​a capacitively coupled plasma source to be simulated; Determine the flow state parameters of electrons and heavy particles of the capacitively coupled plasma source to be simulated at the current moment; the flow state parameters of electrons include density and temperature, the flow state parameters of heavy particles include density, flow velocity and temperature; the heavy particles include: ions and neutral particles; Determining the electron fluid equations at the current moment according to the flow state parameters of the electrons at the current moment; the electron fluid equations include: an electron continuity equation and an electron energy equation; Determine the heavy particle fluid equations at the current moment according to the flow state parameters of the heavy particles at the current moment; the heavy particle fluid equations include: a heavy particle continuity equation, a heavy particle momentum equation and a heavy particle energy equation; Determine the electrostatic field equation at the current moment according to the flow state parameters of the electrons at the current moment and the flow state parameters of the ions at the current moment; According to the flow state parameters of electrons at the current moment, the flow state parameters of electrons in the first set time period, the flow state parameters of heavy particles at the current moment and the flow state parameters of heavy particles in the first set time period, the super relaxation acceleration parameters at the current moment are obtained; the first set time period has a start time of the first moment, an end time of the first set time period is the second moment, the first moment is the moment when the step "dividing the target area into a plurality of orthogonal grids connected to each other" starts, and the second moment is the previous moment; Combined with the super-relaxation acceleration method, according to the flow state parameters of the electrons at the current moment, the flow state parameters of the heavy particles at the current moment and the super-relaxation acceleration parameters at the current moment, the source term of the electrons at the current moment, the source term of the heavy particles at the current moment, the transport coefficient of the electrons at the current moment and the transport coefficient of the heavy particles at the current moment are obtained; The electrostatic field equation at the current moment is discretized by using the finite volume method and the semi-implicit format to obtain the electrostatic field equation at the current moment in a discrete form on the orthogonal grid; the semi-implicit format is a semi-implicit format that corrects electron migration and diffusion; Substituting the flow state parameters of electrons at the current moment, the flow state parameters of ions at the current moment, and the transport coefficient of electrons at the current moment into the discrete form electrostatic field equation at the current moment and solving them to obtain the electric potential on the orthogonal grid at the current moment; Calculate the electric field intensity on the orthogonal grid at the current moment according to the electric potential on the orthogonal grid at the current moment; Using a finite volume method, an upwind scheme and a multi-step explicit Euler method, the electronic fluid equations at the current moment are discretized to obtain a discrete form of the electronic fluid equations at the current moment on the orthogonal grid; Substituting the flow state parameters of the electrons at the current moment, the source term of the electrons at the current moment, the transport coefficient of the electrons at the current moment, the electric potential at the current moment, and the electric field strength at the current moment into the discrete form electron fluid equations at the current moment, to obtain the flow state parameters of the electrons at the next moment; Using a finite volume method and a single-step explicit Euler method, the heavy particle fluid equations at the current moment are discretized to obtain a discrete form of the heavy particle fluid equations at the current moment on the orthogonal grid; Substituting the flow state parameters of the heavy particles at the current moment, the source term of the heavy particles at the current moment, the transport coefficient of the heavy particles at the current moment, the electric potential at the current moment, and the electric field intensity at the current moment into the discrete form heavy particle fluid equations at the current moment, to obtain the flow state parameters of the heavy particles at the next moment; Determine whether the preset termination condition is met at the current moment; If satisfied, the flow state parameters of the electrons, the flow state parameters of the heavy particles, the electric potential and the electric field strength within the second set time period are determined as the simulation result of the capacitively coupled plasma source to be simulated; the start time of the second set time period is the first moment, the end time of the second set time period is the third moment, and the third moment is the moment when the preset termination condition is satisfied; If not satisfied, replace the flow state parameters of electrons at the current moment with the flow state parameters of electrons at the next moment, replace the flow state parameters of heavy particles at the current moment with the flow state parameters of heavy particles at the next moment, and return to step "determine the electron fluid equations at the current moment based on the flow state parameters of electrons at the current moment".

2. A plasma source simulation system, characterized in that: The system comprises: A grid division module, used for dividing a target area into a plurality of orthogonal grids connected to each other; the target area includes a discharge chamber and a dielectric area of ​​a capacitively coupled plasma source to be simulated; The current moment flow state parameter determination module is used to determine the flow state parameters of the electrons and the flow state parameters of the heavy particles of the capacitive coupled plasma source to be simulated at the current moment; the flow state parameters of the electrons include density and temperature, the flow state parameters of the heavy particles include density, flow velocity and temperature; the heavy particles include: ions and neutral particles; An electron fluid equation group determination module is used to determine the electron fluid equation group at the current moment according to the flow state parameters of the electrons at the current moment; the electron fluid equation group includes: an electron continuity equation and an electron energy equation; A heavy particle fluid equation group determination module is used to determine the heavy particle fluid equation group at the current moment according to the flow state parameters of the heavy particles at the current moment; the heavy particle fluid equation group includes: a heavy particle continuity equation, a heavy particle momentum equation and a heavy particle energy equation; An electrostatic field equation determination module, used to determine the electrostatic field equation at the current moment according to the flow state parameters of the electrons at the current moment and the flow state parameters of the ions at the current moment; A super-relaxation acceleration parameter determination module, for obtaining the super-relaxation acceleration parameter at the current moment according to the flow state parameter of the electrons at the current moment, the flow state parameter of the electrons in the first set time period, the flow state parameter of the heavy particles at the current moment and the flow state parameter of the heavy particles in the first set time period; the first set time period is a start time of the first moment, the end time of the first set time period is a second moment, the first moment is the moment when the step "dividing the target area into a plurality of orthogonal grids connected to each other" starts, and the second moment is the previous moment; A source term and transport coefficient determination module is used to combine the super-relaxation acceleration method to obtain the source term of the electron at the current moment, the source term of the heavy particle at the current moment, the transport coefficient of the electron at the current moment, and the transport coefficient of the heavy particle at the current moment according to the flow state parameter of the electron at the current moment, the flow state parameter of the heavy particle at the current moment, and the super-relaxation acceleration parameter at the current moment; The first discrete module is used to discretize the electrostatic field equation at the current moment by using the finite volume method and the semi-implicit format to obtain the electrostatic field equation at the current moment in a discrete form on the orthogonal grid; the semi-implicit format is a semi-implicit format that corrects electron migration and diffusion; The potential calculation module is used to substitute the flow state parameters of the electrons at the current moment, the flow state parameters of the ions at the current moment and the transport coefficient of the electrons at the current moment into the discrete form electrostatic field equation at the current moment and solve it to obtain the potential on the orthogonal grid at the current moment; An electric field strength calculation module, used to calculate the electric field strength on the orthogonal grid at a current moment according to the electric potential on the orthogonal grid at a current moment; A second discretization module is used to discretize the electronic fluid equations at the current moment by using a finite volume method, an upwind scheme and a multi-step explicit Euler method to obtain a discrete form of the electronic fluid equations at the current moment on the orthogonal grid; An electron flow state parameter calculation module is used to substitute the electron flow state parameter at the current moment, the electron source term at the current moment, the electron transport coefficient at the current moment, the electric potential at the current moment, and the electric field strength at the current moment into the discrete form electron fluid equation group at the current moment to obtain the electron flow state parameter at the next moment; A third discretization module is used to discretize the heavy particle fluid equations at the current moment by using a finite volume method and a single-step explicit Euler method to obtain a discrete form of the heavy particle fluid equations at the current moment on the orthogonal grid; A heavy particle flow state parameter calculation module is used to substitute the flow state parameters of the heavy particles at the current moment, the source term of the heavy particles at the current moment, the transport coefficient of the heavy particles at the current moment, the electric potential at the current moment, and the electric field intensity at the current moment into the discrete form heavy particle fluid equation group at the current moment to obtain the flow state parameters of the heavy particles at the next moment; A judgment module is used to judge whether the preset termination condition is met at the current moment; A first execution module is used to determine the flow state parameters of the electrons, the flow state parameters of the heavy particles, the electric potential and the electric field strength within a second set time period as the simulation result of the capacitively coupled plasma source to be simulated if the preset termination condition is met at the current moment; the start time of the second set time period is the first moment, the end time of the second set time period is a third moment, and the third moment is the moment when the preset termination condition is met; The second execution module is used to replace the flow state parameters of electrons at the current moment with the flow state parameters of electrons at the next moment, and replace the flow state parameters of heavy particles at the current moment with the flow state parameters of heavy particles at the next moment if the preset termination condition is not met at the current moment, and return to the electronic fluid equation group determination module.

3. An electronic device, characterized in that: include: one or more processors; a storage device having one or more programs stored thereon; When the one or more programs are executed by the one or more processors, the one or more processors are caused to implement the method as claimed in claim 1 .

4. A storage medium, characterized in that: A computer program is stored thereon, wherein when the computer program is executed by a processor, the method according to claim 1 is implemented.

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