Method, apparatus and product for obtaining carbon concentration boundary layer in liquid-phase growth of silicon carbide

Abstract

The present application provides a method, apparatus and product for obtaining a carbon concentration boundary layer in the growth of silicon carbide by the liquid phase method, which relates to the technical field of single crystal growth, and includes: establishing a geometric model according to the structural information of the silicon carbide growth system by the liquid phase method, and performing calculation grid division; obtaining multiple groups of simulation results based on the constructed numerical calculation model; according to the carbon concentration values at each calculation grid in each group of simulation results, determining a first relationship function between the carbon concentration boundary layer thickness and the centrifugal distance of each column of calculation grids, where the centrifugal distance refers to the vertical distance between the column of calculation grids and the central axis of the solid-liquid interface; according to the first relationship function, determining a second relationship function between the electromagnetic induction heating frequency, the carbon concentration boundary layer thickness and the centrifugal distance; determining the distribution of the target carbon concentration boundary layer from the second relationship function, and optimizing the structure of the silicon carbide growth system by the liquid phase method according to the distribution of the target carbon concentration boundary layer.

Description

Technical Field

[0001] The present application relates to the technical field of single crystal growth, and particularly to a method, device and product for obtaining a carbon concentration boundary layer in the growth of silicon carbide by a liquid phase method. Background Art

[0002] When growing silicon carbide by a liquid phase method (solution growth method), the growth environment temperature is very high, and it is difficult to accurately measure the relevant environmental information during the growth of silicon carbide for improving subsequent preparation processes. Especially for the solid-liquid interface region with relatively complex conditions, the cost of obtaining the distribution of the carbon concentration boundary layer in this region through experiments is relatively high and difficult to achieve. Therefore, there is an urgent need to propose a method, device and product for obtaining a carbon concentration boundary layer in the growth of silicon carbide by a liquid phase method to obtain the accurate distribution of the carbon concentration boundary layer for guiding the optimization of subsequent processes. Summary of the Invention

[0003] In view of the above problems, the embodiments of the present application provide a method, device and product for obtaining a carbon concentration boundary layer in the growth of silicon carbide by a liquid phase method to overcome or at least partially solve the above problems.

[0004] In the first aspect of the embodiments of the present application, a method for obtaining a carbon concentration boundary layer in the growth of silicon carbide by a liquid phase method is provided. The method includes:

[0005] Establish a geometric model according to the structural information of the silicon carbide growth system by the liquid phase method and perform computational grid division;

[0006] Set the boundary conditions for the corresponding computational grids in the geometric model, set the electromagnetic induction control equation, heat transfer and flow control equation, and component transport control equation to obtain a numerical calculation model;

[0007] Based on the numerical calculation model, simulate the electromagnetic induction heating process, heat transfer and flow process, and component transport process at multiple different electromagnetic induction heating frequencies to obtain multiple sets of simulation results;

[0008] According to the carbon concentration values at each computational grid of the silicon melt in each set of simulation results, determine the first relationship function between the carbon concentration boundary layer thickness and the centrifugal distance of each column of computational grids on the silicon melt side of the solid-liquid interface at the corresponding electromagnetic induction heating frequency. The centrifugal distance refers to the perpendicular distance between the column of computational grids and the central axis of the solid-liquid interface;

[0009] According to multiple first relationship functions, determine the second relationship function between the electromagnetic induction heating frequency, the carbon concentration boundary layer thickness and the centrifugal distance;

[0010] Determine the distribution of the target carbon concentration boundary layer from the second relationship function, and optimize the structure of the liquid-phase method for growing silicon carbide according to the distribution of the target carbon concentration boundary layer.

[0011] In the second aspect of the embodiments of the present application, there is also provided a device for obtaining a carbon concentration boundary layer in the liquid-phase method for growing silicon carbide, which is applied to execute the method for obtaining a carbon concentration boundary layer in the liquid-phase method for growing silicon carbide in the first aspect of the embodiments of the present application. The device includes:

[0012] A geometric model establishment module, configured to establish a geometric model according to the structural information of the liquid-phase method for growing silicon carbide system, and perform computational grid division;

[0013] A numerical calculation model establishment module, configured to set boundary conditions for corresponding computational grids in the geometric model, set an electromagnetic induction control equation, a heat transfer and flow control equation, and a component transport control equation, to obtain a numerical calculation model;

[0014] A simulation module, configured to simulate the electromagnetic induction heating process, the heat transfer and flow process, and the component transport process at multiple different electromagnetic induction heating frequencies based on the numerical calculation model, to obtain multiple sets of simulation results;

[0015] A first relationship function determination module, configured to determine a first relationship function between the carbon concentration boundary layer thickness and the centrifugal distance of each column of computational grids on the silicon melt side of the solid-liquid interface at a corresponding electromagnetic induction heating frequency according to the carbon concentration values of each computational grid of the silicon melt in each set of the simulation results, where the centrifugal distance refers to the perpendicular distance between the column of computational grids and the central axis of the solid-liquid interface;

[0016] A second relationship function determination module, configured to determine a second relationship function between the electromagnetic induction heating frequency, the carbon concentration boundary layer thickness, and the centrifugal distance according to multiple first relationship functions;

[0017] A carbon concentration boundary layer determination module, configured to determine the distribution of the target carbon concentration boundary layer from the second relationship function, and optimize the structure of the liquid-phase method for growing silicon carbide according to the distribution of the target carbon concentration boundary layer.

[0018] In the third aspect of the embodiments of the present application, there is also provided an electronic device, including a memory, a processor, and a computer program stored on the memory, where the processor executes the computer program to implement the steps in the method for obtaining a carbon concentration boundary layer in the liquid-phase method for growing silicon carbide in the first aspect of the embodiments of the present application.

[0019] In a fourth aspect of the embodiments of the present application, there is also provided a computer-readable storage medium, on which a computer program / instructions are stored, and when the computer program / instructions are executed by a processor, the steps in the method for obtaining the carbon concentration boundary layer in the liquid-phase growth of silicon carbide according to the first aspect of the embodiments of the present application are implemented.

[0020] In a fifth aspect of the embodiments of the present application, there is also provided a computer program product, which, when running on an electronic device, causes a processor to implement the steps in the method for obtaining the carbon concentration boundary layer in the liquid-phase growth of silicon carbide according to the first aspect of the embodiments of the present application when executed.

[0021] A method for obtaining a carbon concentration boundary layer in the liquid-phase growth of silicon carbide provided by the embodiments of the present application includes: establishing a geometric model according to the structural information of the liquid-phase growth of silicon carbide system, and performing computational grid division; setting boundary conditions for the computational grids corresponding to the geometric model, setting electromagnetic induction control equations, heat transfer and flow control equations, and component transport control equations to obtain a numerical calculation model; based on the numerical calculation model, simulating the electromagnetic induction heating process, heat transfer and flow process, and component transport process at multiple different electromagnetic induction heating frequencies to obtain multiple sets of simulation results; according to the carbon concentration values at each computational grid of the silicon melt in each set of simulation results, determining a first relationship function between the carbon concentration boundary layer thickness and the centrifugal distance of each column of computational grids on the silicon melt side of the solid-liquid interface at the corresponding electromagnetic induction heating frequency, where the centrifugal distance refers to the perpendicular distance between the column of computational grids and the central axis of the solid-liquid interface; according to multiple first relationship functions, determining a second relationship function between the electromagnetic induction heating frequency, the carbon concentration boundary layer thickness, and the centrifugal distance; determining the distribution of the target carbon concentration boundary layer from the second relationship function, and optimizing the structure of the liquid-phase growth of silicon carbide system according to the distribution of the target carbon concentration boundary layer.

[0022] Specific beneficial effects are as follows:

[0023] In the embodiments of the present application, by establishing a numerical calculation model, the heat transfer and flow process and the component transport process at different electromagnetic induction heating frequencies are simulated to obtain multiple sets of simulation results. Furthermore, according to the carbon concentration values at each computational grid in the silicon melt in the simulation results, a first relationship function between the carbon concentration boundary layer thickness and the centrifugal distance of each column of computational grids on the silicon melt side of the solid-liquid interface is determined. The embodiments of the present application fully consider that the carbon concentration boundary layer on the silicon melt side of the solid-liquid interface is not a boundary layer with a uniform thickness. Therefore, through numerical simulation, the carbon concentration boundary layer thickness at different centrifugal distances (the perpendicular distance between the column of computational grids and the central axis of the solid-liquid interface) is determined, and a second relationship function between the electromagnetic induction heating frequency, the carbon concentration boundary layer thickness, and the centrifugal distance is generated, so as to obtain the accurate distribution of the carbon concentration boundary layer. Description of the Drawings

[0024] To more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings required for the description of the embodiments of the present application. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0025] Figure 1 is a step flow chart of a method for obtaining a carbon concentration boundary layer in the growth of silicon carbide by the liquid phase method provided by an embodiment of the present application;

[0026] Figure 2 is a schematic structural diagram of a system for producing silicon carbide by the liquid phase method provided by an embodiment of the present application;

[0027] Figure 3 is a schematic diagram of the computational grid division of a solid-liquid interface provided by an embodiment of the present application;

[0028] Figure 4 is a curve diagram of the supersaturation distribution from the solid-liquid interface to the carbon dissolution interface provided by an embodiment of the present application;

[0029] Figure 5 is a curve diagram of the carbon concentration distribution from the solid-liquid interface to the carbon dissolution interface provided by an embodiment of the present application;

[0030] Figure 6 is a schematic curve diagram of a first relationship function at different electromagnetic induction heating frequencies provided by an embodiment of the present application;

[0031] Figure 7 is a schematic structural diagram of a device for obtaining a carbon concentration boundary layer provided by an embodiment of the present application;

[0032] Figure 8 is a schematic diagram of an electronic device provided by an embodiment of the present application;

[0033] Reference numerals: 1, silicon melt; 2, graphite crucible; 3, side graphite support; 4, carbon felt; 5, copper coil. Detailed implementation manners

[0034] The following will more specifically describe the exemplary embodiments of the present application in conjunction with the drawings in the embodiments of the present application. Although the exemplary embodiments of the present application are shown in the drawings, it should be understood that the present application can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present application can be more thoroughly understood and the scope of the present application can be fully communicated to those skilled in the art.

[0035] As a third-generation semiconductor material, SiC has excellent properties such as a large bandgap, high thermal conductivity, and high chemical stability, making it a semiconductor material with great application prospects. Currently, there are three mainstream growth methods for SiC, namely physical vapor transport method, high-temperature chemical vapor deposition method, and liquid-phase method. Among them, SiC grown by the liquid-phase method has been proven to have advantages such as high crystal quality, easy diameter expansion, and easy p-type doping. Induction heating is usually used to provide heat in the SiC single crystal growth system by the liquid-phase method.

[0036] The liquid-phase method, also known as the solution growth method. In the liquid-phase method, the graphite crucible serves not only as a container but also as a carbon source for the Si melt. Specifically, the crucible is heated to a sufficiently high temperature by an induction coil, where carbon dissolves into the Si melt due to high temperature and local unsaturation. Then, carbon is transported under the action of convection and diffusion to below the seed crystal, where the temperature is relatively low near the seed crystal and carbon becomes supersaturated, and finally, SiC crystals grow. Among them, this supersaturation provides the driving force for the growth of SiC.

[0037] Induction heating, that is, using the method of electromagnetic induction to generate current inside the material to be heated (such as crucible, side graphite support, etc.), and relying on the energy of these eddy currents to achieve the heating purpose. Induction heating as a heating method is of great significance in the liquid-phase growth system. The temperature field and thermal field of the growth system determine the crystal quality. However, the relevant parameters of the induction heating system and the structural layout of the components will affect the heat distribution during the induction heating process, and thus affect the growth quality and growth rate of the crystal. Therefore, for a specific induction heating system, the induction heating frequency, the geometric shapes of the coil and crucible, and their relative positions in the system should be carefully determined.

[0038] When growing silicon carbide by the liquid-phase method (solution growth method), the growth environment temperature is very high, making it difficult to conduct experiments and accurately measure the relevant environmental information during the growth process of silicon carbide for improving subsequent preparation processes. Therefore, it is necessary to use numerical simulation to explore the process of growing silicon carbide by the liquid-phase method. Especially for the relatively complex solid-liquid interface region, it is costly and difficult to obtain the distribution of the carbon concentration boundary layer in this region through experiments.

[0039] In view of the above problems, the embodiments of this application propose a method, device, and product for obtaining the carbon concentration boundary layer in the growth of silicon carbide by the liquid-phase method to obtain the accurate distribution of the carbon concentration boundary layer for guiding the further optimization of subsequent processes. The following will, in conjunction with the accompanying drawings, elaborate on a method, device, and product for obtaining the carbon concentration boundary layer in the growth of silicon carbide by the liquid-phase method provided by the embodiments of this application through some embodiments and their application scenarios.

[0040] The first aspect of the embodiments of this application provides a method for obtaining the carbon concentration boundary layer in the growth of silicon carbide by the liquid-phase method, referring toFigure 1 , Figure 1 is a flowchart of the steps for obtaining the carbon concentration boundary layer in the growth of silicon carbide by the liquid phase method provided by the embodiments of the present application. As Figure 1 shown, the method includes:

[0041] Step S101: Establish a geometric model based on the structural information of the silicon carbide growth system by the liquid phase method, and perform computational grid division;

[0042] In the embodiments of the present application, silicon carbide is prepared by the liquid phase method. In this embodiment, the silicon carbide growth system by the liquid phase method represents any system that can be used to prepare silicon carbide by the liquid phase method (such as a 6-inch SiC growth system). The embodiments of the present application do not limit the specific structure and dimensional parameters of the silicon carbide growth system by the liquid phase method. Among them, the structural information of the silicon carbide growth system by the liquid phase method can be information such as the dimensions and positions of various components in the system. Exemplarily, referring to Figure 2 , Figure 2 shows a schematic structural diagram of a silicon carbide production system by the liquid phase method. As Figure 2 shown, the silicon carbide growth system by the liquid phase method at least includes the following components: 1. silicon melt; 2. graphite crucible; 3. side graphite support; 4. carbon felt; 5. copper coil. As Figure 2 shown, the graphite crucible 1 is located at the center of the system, the crucible is filled with the silicon melt 2, and the side graphite support 3 is located on the side of the crucible and serves as the main heating element in the system, transferring the heat obtained by electromagnetic induction to the crucible and the melt in the crucible through radiation heat transfer. The carbon felt 4 is located outside the side graphite support 3 and plays a role in support and heat preservation. The copper coil 5 is located outside the carbon felt 4 and is used for electromagnetic induction heating.

[0043] Based on the structural information of the silicon carbide growth system by the liquid phase method (including the structures and dimensional parameters of various components, etc.), use modeling software to perform geometric modeling on the structure of the silicon carbide growth system by the liquid phase method to obtain the corresponding geometric model. Then perform computational grid division on the geometric model, including the computational grid division of the carbon concentration boundary layer in the geometric model. Specifically, the more the number of computational grids divided, the more accurate the results obtained by numerical calculation. The number of computational grids can be determined according to the actual computational resources.

[0044] Step S102: Set the boundary conditions of the corresponding computational grids in the geometric model, set the electromagnetic induction control equation, heat transfer and flow control equation, and component transport control equation to obtain a numerical calculation model.

[0045] Set the boundary conditions for the computational grids corresponding to the geometric model. Specifically, define the boundary conditions and working pressures (i.e., the boundary conditions for each computational grid) between various components inside the geometric model during the electromagnetic induction heating process, heat transfer and fluid flow process, and component transport process using the liquid phase method. For example: the boundary conditions at the contact surface between the inner wall of the crucible and the silicon melt, the temperature of the outer wall of the furnace chamber in the geometric model, the pressure inside the furnace, the boundary conditions at the gas-liquid interface (free surface) in the geometric model, the boundary conditions at the contact surfaces between other solids and gases in the geometric model, etc.

[0046] Specifically, the boundary conditions in the embodiments of the present application include:

[0047] Boundary conditions for the electromagnetic induction heating process: The outer boundary of the region adopts a balloon boundary. On the boundary line, the magnetic field is neither perpendicular nor parallel to the boundary line. This boundary condition is used to simulate infinity and reduce the computational amount; the remaining boundaries adopt natural boundary conditions, and the tangential component of the magnetic field strength and the normal component of the magnetic induction intensity are continuous on the contact surfaces of two contacting objects ( , ). H t represents the tangential component of the magnetic field strength, B n represents the normal component of the magnetic induction intensity.

[0048] Boundary conditions for the heat transfer and fluid flow process: The inner wall surface of the coil is a temperature boundary condition (equivalent to giving a fixed temperature C to this wall surface), and the remaining wall surfaces are coupled wall surfaces (the temperatures and heat flux densities on both sides of the interface are equal); a surface tension gradient (Marangoni force) is set on the free surface of the silicon melt, and the rest are no-slip boundaries (i.e., ) velocity.

[0049] Boundary conditions at the interface (gas-liquid boundary): Set a surface tension gradient ; where, represents the surface tension coefficient N / m, and T represents the temperature °C.

[0050] In a possible implementation manner, the setting of the boundary conditions for the computational grids corresponding to the geometric model includes:

[0051] Add a dissolution boundary condition to the interface between the crucible and the silicon melt in the geometric model;

[0052] Add a precipitation boundary condition to the interface between the silicon melt and the crystal in the geometric model; where, the dissolution boundary condition and the precipitation boundary condition are the same, and are both expressed as the following formula:

[0053] ;

[0054] Among them, is the molar mass of silicon; is the density of silicon; e is the mathematical constant Euler's number; T is the temperature at the grid, °C eq is the equilibrium concentration of carbon dissolved in the silicon melt.

[0055] Specifically, before numerical solution, corresponding boundary conditions need to be set to simulate the real situation. Among them, a dissolution boundary condition is added to the interface between the crucible and the silicon melt to simulate the dissolution of the graphite crucible; a precipitation boundary condition is added to the interface between the silicon melt and the crystal to simulate the precipitation of silicon carbide crystals. Both of these two types of boundaries are the equilibrium concentration boundaries of carbon C eq .

[0056] In addition, at the free surface of the melt (the interface between the melt and the gas), the normal gradient of the concentration is set to , where C c represents the molar concentration of carbon, x represents the direction perpendicular to the free surface. In order to simulate that silicon carbide crystals will not precipitate on the free surface under real conditions. During actual operation, water cooling is usually passed through the internal area of the coil to keep the inner wall surface of the coil at room temperature. To save computing resources, the internal water cooling of the coil is simplified, and the temperature of the inner wall surface of the coil is set to room temperature during solution. The remaining contact surfaces are all set as temperature-continuous wall surfaces, and the temperatures on both sides of the contact surfaces with different structures are continuous.

[0057] In this embodiment, the geometric model is initialized, and the control equations corresponding to each component and each region in the geometric model during the electromagnetic induction heating process using the liquid phase method, the control equations during the heat transfer and flow process, and the control equations during the component transport process are set. For example: the electromagnetic induction control equation in the geometric model, the heat transfer and flow control equation satisfied by the melt-crystal region in the geometric model, the heat transfer and flow control equation satisfied by the gas region in the geometric model, etc. Among them, the electromagnetic induction control equation is used to solve the distribution of the induced heat in the geometric model, that is, the induced power of each calculation grid in the geometric model, when electromagnetic induction heating is performed under specific conditions (electromagnetic induction heating frequency). The heat transfer and flow control equation is used to solve the heat field information (such as temperature) and flow field information of each calculation grid in the geometric model under specific conditions (electromagnetic induction heating frequency). In addition, when defining the control equation, the control equation corresponding to the self-inductance phenomenon in the copper coil (that is, the above-mentioned electromagnetic induction control equation) is set, so as to add the influence of the self-inductance phenomenon in the copper coil on the heat field when simulating the electromagnetic induction heating process, and further improve the accuracy of the obtained simulation results.

[0058] Specifically, the control equation for the electromagnetic induction heating process (that is, the above-mentioned electromagnetic induction control equation) includes the following formula:

[0059] ;

[0060] ;

[0061] Among them, represents the electric field strength in V / m, is the induced current in A / m 2 , is the magnetic potential vector (dimensionless quantity, without unit), t is the current time in s, r is the distance in m, μ is the magnetic permeability in H / m; during electromagnetic induction heating, an alternating current is passed through the copper coil ; Among them, J 0 is the amplitude (maximum value) of the current density in A / m 2 ; is the angular frequency in rad / s; t is the current time; , f is the electromagnetic induction frequency in kHz.

[0062] Substitute the physical property parameters of each of the said components into the control equations of the electromagnetic induction heating process and the heat transfer and fluid flow process. The physical property parameters at least include the material conductivity and density of each component. In this embodiment, according to the materials used in the actual production process (i.e., the materials of each component in the liquid-phase method for growing silicon carbide system), substitute the physical property parameters of each component (the conductivity of each material, the density of the material, etc.) into the control equations of the electromagnetic induction heating process and the heat transfer and fluid flow process to establish a numerical calculation model.

[0063] Heat transfer and fluid flow means that through the induction heating process, heat distributions are present on each device in the system (i.e., the crystal growth furnace). Among them, the protective gas and the silicon melt are the fluid parts, and the rest are the solid parts. The silicon melt flows and the inner wall surface of the graphite crucible dissolves through radiation and convection. In one possible implementation manner, the heat transfer and fluid flow control equations include:

[0064] Continuity equation: ;

[0065] Momentum equation: ;

[0066] Energy equation: ;

[0067] Among them, represents finding the gradient (i.e., solving the first-order derivative in the direction perpendicular to the crystal growth interface); represents the velocity in m / s; Denotes density kg / m 3 ; p Denotes pressure Pa; Denotes dynamic viscosity Pa·s; Denotes gravitational acceleration m / s 2 ; Denotes coefficient of thermal expansion; T Denotes temperature at the grid point °C; Denotes reference temperature °C; Is Lorentz force density N / m 3 ; Denotes specific heat capacity; Denotes thermal conductivity of silicon melt; Denotes heat source W / m 3 ; Denotes the transpose of the velocity gradient, t Denotes the current time; Denotes induced current density; Is magnetic induction intensity.

[0068] Substitute the density of the solid material of each component into the control equation of the heat transfer and flow process in the solid material region:

[0069] ;

[0070] Among them, Denotes the density of the solid material kg / m 3 ; Denotes the specific heat capacity of the solid material; Denotes the thermal conductivity of the solid material; Denotes heat source W / m 3 ; The densities of the solid materials are respectively: the density of the crucible, the density of the graphite support component, the density of the carbon felt, and the density of the copper coil. In this embodiment, the control equations in the solid material region include: the control equation of the crucible region, the control equation of the graphite support component on the side of the crucible, the control equation of the copper coil, and the control equation of the carbon felt. Therefore, when substituting the densities of the solid materials of each component into the control equation, the densities of the solid materials are: the density of the crucible, the density of the graphite support component, the density of the carbon felt, and the density of the copper coil.

[0071] At higher temperatures, there will be dissolution of the graphite crucible at the interface between the silicon melt and the graphite crucible. During the solution of the heat transfer and flow process, the velocity field and temperature field in the silicon melt region will be obtained, and the carbon concentration distribution in the silicon melt will be obtained based on the velocity field and temperature field. Finally, the crystal growth rate is solved through the carbon concentration distribution, that is, the solution process of component transport. In one possible implementation, the component transport control equation includes:

[0072] ;

[0073] Among them, represents the calculation of the gradient (i.e., the first derivative in the direction perpendicular to the crystal growth interface); represents density; represents velocity; represents the molar concentration of carbon; represents the mass diffusion coefficient of carbon in the silicon melt; represents the calculation of the second derivative (i.e., the second derivative in the direction perpendicular to the crystal growth interface).

[0074] Specifically, in the subsequent numerical solution process, the component transport control equation is crucial. The key factor leading to the crystal growth quality and the crystal precipitation amount is the carbon concentration distribution in the silicon melt. The initial component transport equation is:

[0075] ;

[0076] Among them , k = 1, 2……N ; represents density kg / m 3 ; t represents the current time, represents there are k mass fractions of different components; x represents distance m; u represents velocity m / s; represents there are k mass diffusion coefficients of different components in the silicon melt kg / (m·s); represents k mass concentration source terms of different components in the silicon melt.

[0077] Combined with the numerical calculation process of the embodiments of the present application for reasonable simplification, this solution is for solving the steady state, which is independent of time, that is , and this term can be ignored. During the numerical calculation, only the transport and calculation of carbon are set, so k = 1. In addition, during the solution, there are no carbon atoms in the silicon melt in the initial state, so = 0. The source of carbon is the dissolution of carbon at the crucible wall into the silicon melt. Then, converting the mass fraction into the molar concentration, the final component transport control equation in this numerical calculation process is: .

[0078] Step S103, based on the numerical calculation model, simulate the electromagnetic induction heating process, heat transfer and flow process, and component transport process at multiple different electromagnetic induction heating frequencies to obtain multiple sets of simulation results.

[0079] In this embodiment, each set of simulation results includes information on the electromagnetic induction heating process (such as the induced power of each computational grid), heat transfer and fluid flow process (such as the temperature values of each computational grid, thermal field, fluid flow field information, silicon melt velocity, etc.), and component transport process (such as the carbon concentration values of each computational grid) obtained by solving the electromagnetic induction control equation, heat transfer and fluid flow control equation, and component transport control equation at the electromagnetic induction heating frequency. Among them, the commonly used frequency in the liquid-phase growth of silicon carbide is 1 kHz - 5 kHz, and multiple different electromagnetic induction heating frequencies can be selected within this frequency range of 1 kHz - 5 kHz, such as 1 kHz, 2 kHz, 3 kHz, 4 kHz, and 5 kHz.

[0080] Specifically, for each electromagnetic induction heating frequency, simulate the electromagnetic induction heating process at this frequency. Specifically, by solving the electromagnetic induction control equation in the electromagnetic induction heating numerical model, the electromagnetic induction heating process at this frequency (i.e., part of the simulation results) is obtained, including the current values on each component in the geometric model during electromagnetic induction heating at this frequency, and the magnitude of the induced power value of each computational grid, that is, the induced heat density (i.e., induced power density) on each component. By solving the heat transfer and fluid flow control equation, the heat transfer and fluid flow process is simulated, that is, the process of stable growth of silicon carbide single crystal (i.e., part of the simulation results), including: during the process of stable growth of silicon carbide single crystal, the temperature values of each computational grid in the geometric model, thermal field, fluid flow field information, silicon melt velocity, etc. By solving the heat transfer and fluid flow control equation at the current time, the velocity information of the silicon melt region at the current time is obtained, and then this velocity is substituted into the component transport control equation. By solving the component transport control equation, information such as the carbon concentration corresponding to each computational grid at the current time can be obtained (i.e., part of the simulation results).

[0081] Step S104: According to the carbon concentration values at each computational grid of the silicon melt in each set of the simulation results, determine the first relationship function between the carbon concentration boundary layer thickness and the centrifugal distance of each column of computational grids on the silicon melt side of the solid-liquid interface at the corresponding electromagnetic induction heating frequency, where the centrifugal distance refers to the perpendicular distance between this column of computational grids and the central axis of the solid-liquid interface.

[0082] In the embodiments of the present application, the thickness of the concentration boundary layer refers to the thickness of the carbon concentration boundary layer on the silicon melt side of the solid-liquid interface. When growing silicon carbide by the liquid phase method, the temperature is very high and it is difficult to conduct experiments. Therefore, it is impossible to accurately obtain the carbon concentration distribution at the growth interface and the thickness of the carbon concentration boundary layer at each position of the growth interface. At a relatively high temperature, the graphite crucible will dissolve at the interface between the silicon melt and the graphite crucible. During the solution of the heat transfer and flow process, the velocity field and temperature field of the silicon melt region will be obtained. Based on the velocity field and temperature field, the carbon concentration distribution in the silicon melt can be obtained, and thus the growth rate of the crystal can be solved through the carbon concentration distribution (i.e., the component transport process is simulated). In addition, when solving the component transport control equation, the crucible dissolution process will be simulated near the interface between the graphite crucible and the silicon melt. There is also a concentration boundary layer in this region (the interface between the graphite crucible and the silicon melt). However, in the numerical simulation of growing silicon carbide by the liquid phase method, only the carbon concentration distribution at the solid-liquid interface is ultimately concerned. Therefore, in the embodiments of the present application, no special restrictions are imposed on the carbon concentration distribution near the interface between the graphite crucible and the silicon melt.

[0083] Referring to Figure 3 , Figure 3 FIG. shows a schematic diagram of the computational grid division of a solid-liquid interface. As Figure 3 shown, for the silicon melt side of the solid-liquid interface, computational grid division is performed to obtain the carbon concentration boundary layer. For the carbon concentration boundary layer here (in this case, the thickness of the obtained carbon concentration boundary layer is the same at each position), taking the vertically arranged computational grids as a column, the grids of the growth interface are numbered starting from the central axis. The column of grids perpendicular to the growth interface at the central axis is taken as the first column of grids, and so on, so as to obtain the computational grid columns corresponding to each position of the solid-liquid interface. The perpendicular distance from the central axis of each column of computational grids is the centrifugal distance. Different centrifugal distances may correspond to different boundary layer thicknesses at the corresponding positions.

[0084] In addition, considering that the model is rotationally symmetric, when performing simulation calculations based on the numerical calculation model, only half of the model needs to be calculated to reduce the computational amount of the simulation calculations. Exemplarily, the SiC seed crystal is 6 inches, that is, 75 mm. Carbon concentration boundary layer grids are added to the melt side of the growth interface. Among them, the thickness of the first layer of carbon concentration boundary layer grids is 0.05 mm and the width is 0.5 mm. Therefore, in this example, there are (75 / 0.5 = 150) 150 columns of grids in the silicon melt region, which together form the computational grids of the carbon concentration boundary layer.

[0085] In a possible implementation manner, step S104, according to the carbon concentration values at each computational grid of the silicon melt in each group of the simulation results, determining a first relationship function between the carbon concentration boundary layer thickness and the centrifugal distance of each column of computational grids on the silicon melt side of the solid-liquid interface under the corresponding electromagnetic induction heating frequency, includes:

[0086] Step S1041: Determine the carbon concentration values at each computational grid of the silicon melt according to each set of the simulation results.

[0087] Specifically, the simulation results are obtained by solving the governing equations. Furthermore, according to the solution results of the component transport governing equations in the simulation results, the carbon concentrations at each grid in the silicon melt region can be obtained, that is, it can be known what proportions of carbon atoms and silicon atoms are at the silicon carbide crystal growth interface, namely the carbon content and silicon content at the silicon carbide crystal growth interface.

[0088] Step S1042: Calculate the supersaturation of each computational grid according to the carbon concentration values.

[0089] Among them, the supersaturation refers to the supersaturated state of the solution. At a certain temperature, a certain solvent can dissolve a certain solute, and it is in a saturated state when they correspond one by one. In a possible implementation manner, in step S1042, calculating the supersaturation of each computational grid according to the carbon concentration values includes:

[0090] Calculate the supersaturation of each computational grid according to the following formula:

[0091] ;

[0092] Among them, S is the supersaturation, c is the carbon concentration value mol / m at this layer of computational grid 3 , c eq is the carbon equilibrium concentration mol / m at this layer of computational grid 3 . Specifically, since the carbon equilibrium concentration c eq is affected by temperature, therefore, when calculating the supersaturation at each computational grid, it is also necessary to first determine the carbon equilibrium concentration value c eq at this computational grid according to the thermal field temperature information in the simulation results.

[0093] Step S1043: For each column of computational grids, determine the distance between the computational grid at the maximum supersaturation and the solid-liquid interface as the carbon concentration boundary layer thickness corresponding to the centrifugal distance of this column of computational grids.

[0094] Specifically, the supersaturation of the solid-liquid interface is 0. This is because one side of the solid-liquid interface is solid, so the supersaturation S here is 0. When one side of the silicon melt is slightly away from the solid-liquid interface, and the temperature here is low, the carbon equilibrium concentration is low, and the carbon here will be supersaturated, which will cause silicon carbide crystals to precipitate; but when the distance from the solid-liquid interface is very far, when it is close to the crucible, the temperature here is high, the equilibrium concentration is high, and the carbon here is unsaturated. Therefore, for one side of the silicon melt, the supersaturation increases first and then decreases as it moves away from the solid-liquid interface. There must be a maximum supersaturation Smax on one side of the silicon melt below the seed crystal in the silicon melt region. The distance between the maximum supersaturation and the solid-liquid interface is the thickness of the carbon concentration boundary layer at the corresponding position (the position where the column of calculation grids is located, that is, the position corresponding to the centrifugal distance). For example, for the calculation grid column 5mm away from the central axis (that is, the 10th column of calculation grids), the distance between the calculation grid at the maximum supersaturation and the solid-liquid interface is calculated to be 7mm, then the thickness of the carbon concentration boundary layer at 5mm from the central axis can be obtained as 7mm.

[0095] Step S1044: obtaining the first relationship function according to the corresponding relationship between the carbon concentration boundary layer thickness and the centrifugal distance.

[0096] Reference Figure 4 , Figure 4 A supersaturation distribution curve from the solid-liquid interface to the carbon dissolution interface is shown, for example, the supersaturation distribution from the growth interface to the carbon dissolution interface (the interface between the crucible and the silicon melt) at the central axis (the first column of grids), the horizontal axis represents the distance to the solid-liquid interface, and the vertical axis represents the carbon supersaturation. It can be seen that the carbon supersaturation changes particularly dramatically near the silicon melt side of the crystal growth interface, and it can also be seen that the carbon supersaturation changes particularly dramatically near the interface between the graphite crucible and the silicon melt, but in the actual liquid phase method of silicon carbide, the growth interface (solid-liquid interface) is the most concerned. Figure 4 The positions of the supersaturated area and the unsaturated area at the first column of grids can be basically obtained. It can be obtained that the supersaturation is maximum at 0.434 mm from the growth interface of the first column of grids, and the supersaturation is 0 on the growth interface. In this embodiment, the supersaturated area of ​​carbon concentration is used as the thickness of the carbon concentration boundary layer, which means that the thickness of the carbon concentration boundary layer for the first column of calculation grids is 0.434 mm.

[0097] Reference Figure 5 , Figure 5Shows a carbon concentration distribution curve from the solid-liquid interface to the carbon dissolution interface. For example, the carbon concentration distribution from the growth interface to the carbon dissolution interface at the central axis (the first column grid). The abscissa represents the distance from the solid-liquid interface, and the ordinate represents the carbon concentration value. It can be seen that the carbon concentration changes particularly sharply near the silicon melt side of the crystal growth interface, and it can also be seen that the carbon concentration changes particularly sharply near the interface between the graphite crucible and the silicon melt. Corresponding Figure 4 At the position 0.434 mm away from the growth interface in the first column grid, the supersaturation is the largest. By finding the carbon concentration at 0.434 mm, it can be obtained that the carbon concentration increases rapidly from the growth interface to 0.434 mm in the first column grid (that is, the thickness of the carbon concentration boundary layer at the growth interface). From 0.434 mm to 105.566 mm, the carbon concentration changes slowly (defined as the carbon concentration stable region). From 105.566 mm to 106 mm, the carbon concentration rises rapidly (defined as the carbon dissolution boundary layer).

[0098] It should be noted that the thickness of the entire carbon concentration boundary layer is not exactly the same. The thickness of the carbon concentration boundary layer at the actual solid-liquid interface position is not uniform, and the thickness of the carbon concentration boundary layer at different positions of the solid-liquid interface is inconsistent. For each set of simulation results, the thickness of the carbon concentration boundary layer corresponding to different centrifugal distances can be obtained, thereby generating a first relationship function for a specific electromagnetic induction heating frequency.

[0099] Step S105, according to multiple said first relationship functions, determine a second relationship function between the electromagnetic induction heating frequency, the carbon concentration boundary layer thickness, and the centrifugal distance.

[0100] Specifically, for each set of simulation results, a set of electromagnetic induction heating frequencies and the corresponding first relationship functions can be obtained. Thus, based on multiple sets of simulation results, multiple corresponding relationships between the electromagnetic induction heating frequency, the carbon concentration boundary layer thickness, and the centrifugal distance are obtained, and fitting is performed to obtain the second relationship function. Refer to Figure 6 , Figure 6 Shows a schematic curve diagram of the first relationship function under different electromagnetic induction heating frequencies, such as Figure 6As shown, the abscissa is the centrifugal distance, and the ordinate is the thickness of the most suitable carbon concentration boundary layer grid. Exemplarily, in the liquid-phase growth of silicon carbide, the common frequencies are 1 kHz - 5 kHz, and values are taken at intervals of 0.5 kHz, obtaining 0.5 kHz, 1 kHz, 1.5 kHz, 2 kHz, 2.5 kHz, 3 kHz, 3.5 kHz, 4 kHz, 4.5 kHz, and 5 kHz, a total of 10 sets of simulation results, as well as 10 first relationship functions corresponding to these 10 sets of simulation results. Then, by fitting these 10 first relationship functions, a second relationship function between the electromagnetic induction heating frequency, the carbon concentration boundary layer thickness, and the centrifugal distance is determined. The first relationship function represents the relationship between the centrifugal distance and the carbon concentration boundary layer thickness at a specific electromagnetic induction heating frequency, and the second relationship function represents the relationship among the electromagnetic induction heating frequency, the centrifugal distance, and the carbon concentration boundary layer thickness. For different liquid-phase growth silicon carbide systems with different structures, correspondingly, the obtained first relationship function and second relationship function are different. In the embodiments of the present application, the specific function types of the first relationship function and the second relationship function are not limited.

[0101] Step S106: Determine the distribution of the target carbon concentration boundary layer from the second relationship function, and optimize the structure of the liquid-phase growth silicon carbide system according to the distribution of the target carbon concentration boundary layer.

[0102] Specifically, in practical applications, according to one or more electromagnetic induction heating frequencies (i.e., the current electromagnetic induction heating frequency) required for the actual liquid-phase growth of silicon carbide, the thickness of the carbon concentration boundary layer required at each current position (centrifugal distance) is determined from the second relationship function. Thus, based on the determined distribution of the target carbon concentration boundary layer (i.e., the carbon concentration boundary layer corresponding to the current electromagnetic induction heating frequency in the second relationship function), that is, the thickness of the carbon concentration boundary layer at each position, the structure of the liquid-phase growth silicon carbide system is optimized to guide the improvement and optimization of the relevant component structures and growth operation processes of the liquid-phase growth of silicon carbide. In the embodiments of the present application, the specific improvement methods are not limited. Exemplarily, according to the thickness balance degree of the target boundary layer at each position, the size of the crucible is adjusted, so that the thickness of the carbon concentration boundary layer of the finally obtained system at each position reaches an ideal balance degree, thereby improving the production quality.

[0103] In a possible implementation manner, the step S106: Determine the distribution of the target carbon concentration boundary layer from the second relationship function, and optimize the structure of the liquid-phase growth silicon carbide system according to the distribution of the target carbon concentration boundary layer, includes:

[0104] Step S1061: Calculate a first judgment index and a second judgment index of the thickness distribution of the target carbon concentration boundary layer according to the second relationship function. The first judgment index represents the maximum difference in the thickness distribution of the target carbon concentration boundary layer. The second judgment index represents the thickness distribution uniformity of the target carbon concentration boundary layer.

[0105] The target carbon concentration boundary layer refers to the carbon concentration boundary layer at each position determined from the second relationship function according to the electromagnetic induction heating frequency required by the actual production process (i.e., the current electromagnetic induction heating frequency). In the embodiments of the present application, first, according to the second relationship function, the distribution of the target carbon concentration boundary layer (i.e., the thickness of the carbon concentration boundary layer at each position) is determined, and then, according to the distribution, the corresponding first judgment index and second judgment index are calculated.

[0106] Specifically, the first judgment index represents the maximum difference in the thickness distribution of the target carbon concentration boundary layer, that is, the difference between the maximum thickness value and the minimum thickness value in the thickness distribution of the entire target carbon concentration boundary layer, that is, the range S of the carbon concentration boundary layer thickness (S > 0), as shown in the following formula:

[0107] ; where L max refers to the maximum thickness value of the carbon concentration boundary layer at each centrifugal distance, in mm; L min refers to the minimum thickness value of the carbon concentration boundary layer at each centrifugal distance, in mm.

[0108] The second judgment index represents the thickness distribution uniformity M (1 > M > 0) of the entire target carbon concentration boundary layer, as shown in the following formula:

[0109] ; where L max refers to the maximum thickness value of the carbon concentration boundary layer at each centrifugal distance, in mm; Lmin refers to the minimum thickness value of the carbon concentration boundary layer at each centrifugal distance, in mm.

[0110] It should be noted that for the liquid-phase method for growing silicon carbide system, the more uniform the thickness of the carbon concentration boundary layer, the better the growth effect of silicon carbide. Therefore, in the embodiments of the present application, first, the distribution of the carbon concentration boundary layer is obtained by calculating the second relationship function, and then, the first judgment index and the second judgment index are calculated to judge the distribution uniformity of the carbon concentration boundary layer.

[0111] Step S1062: Modify the structural parameters of the liquid-phase method for growing silicon carbide system according to the first judgment index and the second judgment index to obtain an optimized liquid-phase method for growing silicon carbide system.

[0112] Specifically, first, it is determined whether the first preset condition (whether it is less than the first preset threshold) is satisfied according to the first judgment index S. Since the smaller the S, the more favorable the thickness distribution of the carbon concentration boundary layer. When the first judgment index S does not satisfy the first preset condition, the structural parameters of the liquid-phase growth silicon carbide system are directly modified. Exemplarily, the thickness of the carbon felt is adjusted, or the size of the crucible is adjusted. For example, the inner wall diameter of the crucible is increased or decreased by 1 unit length.

[0113] If the first judgment index S satisfies the preset condition, continue to judge according to the second judgment index M. M is the uniformity. The smaller the M, the more favorable the thickness distribution of the carbon concentration boundary layer. It is judged whether the second judgment index M satisfies the second preset condition (whether it is less than the second preset threshold). When the second judgment index M does not satisfy the second preset condition, the structural parameters of the liquid-phase growth silicon carbide system are directly modified (for example, increased or decreased according to a fixed unit length (thickness)) to obtain an optimized liquid-phase growth silicon carbide system. In the embodiments of the present application, the specific modification method of the structural parameters is not limited.

[0114] After modifying the structural parameters, the method further includes:

[0115] Re-execute the step of calculating the second relationship function of the modified liquid-phase growth silicon carbide system;

[0116] According to S101 - S105, the second relationship function of the modified liquid-phase growth silicon carbide system is calculated, and then step S106 is executed to calculate the corresponding first judgment index and second judgment index. When the corresponding preset conditions (the first preset condition and the second preset condition) are not satisfied, the structural parameters of the liquid-phase growth silicon carbide system are modified, and the above steps are repeated until the first judgment index and the second judgment index satisfy the preset conditions to obtain the optimal liquid-phase growth silicon carbide system.

[0117] In addition, in actual application, there may be multiple different structures of the liquid-phase growth silicon carbide system. For different structures, the second relationship function corresponding to each structure is calculated respectively according to steps S101 - S105, and then step S1061 is executed to calculate the corresponding first judgment index and second judgment index. First, according to the first judgment index, the liquid-phase growth silicon carbide system with the smallest first judgment index is selected. If there are multiple liquid-phase growth silicon carbide systems with basically the same first judgment index (the difference in S is between ±0.01Smax, where Smax is the maximum value of S), then the second judgment index M is further judged. M is the uniformity. The smaller the M, the more favorable the thickness distribution of the carbon concentration boundary layer. The structure of the liquid-phase growth silicon carbide system with the smallest value of the second judgment index is selected and determined as the best structure.

[0118] In a possible implementation manner, the method further includes:

[0119] According to the carbon concentration value, calculate the carbon concentration stable region of each column of calculation grids, where the carbon concentration stable region is the region where the difference between the carbon concentration values of two adjacent calculation grids in the column of calculation grids is within a first preset threshold.

[0120] According to the corresponding relationship between the carbon concentration stable region and the centrifugal distance, obtain the third relationship function.

[0121] According to multiple third relationship functions, determine the fourth relationship function between the electromagnetic induction heating frequency, the carbon concentration stable region and the centrifugal distance.

[0122] In the embodiments of the present application, in the silicon melt, in addition to being able to determine the thickness distribution of the carbon concentration boundary layer on the silicon melt side of the solid-liquid interface, the distribution of the carbon concentration stable region in the silicon melt can also be determined. Among them, the carbon concentration stable region refers to the region where the carbon concentration is relatively stable and continuous and the change amount is small, that is, the region where the difference between the carbon concentration values of two adjacent calculation grids in the column of calculation grids is within a first preset threshold. As Figure 5 shown, the carbon concentration changes particularly violently near the silicon melt side of the crystal growth interface, and the carbon concentration changes particularly violently near the interface between the graphite crucible and the silicon melt. The carbon concentration increases rapidly in the carbon concentration boundary layer (when reaching 0.434 mm from the growth interface), the carbon concentration changes slowly in the carbon concentration stable region (when from 0.434 mm to 105.566 mm), and the carbon concentration rises rapidly in the carbon dissolution boundary layer (when from 105.566 mm to 106 mm). In the embodiments of the present application, according to the carbon concentration values of each calculation grid in each set of simulation results, the carbon concentration stable region of each column of calculation grids is calculated, so as to determine the functional relationship (the third relationship function) between the carbon concentration stable region and the centrifugal distance, and then, according to multiple third relationship functions obtained from multiple sets of simulation results, fitting is performed to determine the fourth relationship function between the electromagnetic induction heating frequency, the carbon concentration stable region and the centrifugal distance. So as to determine the distribution of the carbon stable region in the current model according to the electromagnetic induction heating frequency actually required for growing silicon carbide by the liquid phase method, so as to construct a more accurate numerical model and further improve the accuracy of the numerical calculation results.

[0123] In the second aspect of the embodiments of the present application, a device for obtaining the carbon concentration boundary layer in the liquid phase method for growing silicon carbide is further provided, which is applied to execute the method for obtaining the carbon concentration boundary layer in the liquid phase method for growing silicon carbide described in the first aspect. Refer to Figure 7 , Figure 7 shows a schematic structural diagram of a device for obtaining the carbon concentration boundary layer. As Figure 7 shown, the device includes:

[0124] A geometric model establishment module, which is used to establish a geometric model based on the structural information of the silicon carbide growth system by the liquid phase method and perform computational grid division;

[0125] A numerical calculation model establishment module, which is used to set the boundary conditions of the corresponding computational grids in the geometric model, set the electromagnetic induction control equation, heat transfer and flow control equation, and component transport control equation to obtain a numerical calculation model;

[0126] A simulation module, which is used to simulate the electromagnetic induction heating process, heat transfer and flow process, and component transport process at multiple different electromagnetic induction heating frequencies based on the numerical calculation model to obtain multiple sets of simulation results;

[0127] A first relationship function determination module, which is used to determine a first relationship function between the carbon concentration boundary layer thickness and the centrifugal distance of each column of computational grids on the silicon melt side of the solid-liquid interface at the corresponding electromagnetic induction heating frequency according to the carbon concentration values at each computational grid of the silicon melt in each set of simulation results, where the centrifugal distance refers to the perpendicular distance between the column of computational grids and the central axis of the solid-liquid interface;

[0128] A second relationship function determination module, which is used to determine a second relationship function between the electromagnetic induction heating frequency, the carbon concentration boundary layer thickness, and the centrifugal distance according to multiple first relationship functions;

[0129] A carbon concentration boundary layer determination module, which is used to determine the distribution of the target carbon concentration boundary layer from the second relationship function and optimize the structure of the silicon carbide growth system by the liquid phase method according to the distribution of the target carbon concentration boundary layer.

[0130] In a possible implementation manner, the first relationship function determination module includes:

[0131] A carbon concentration value determination sub-module, which is used to determine the carbon concentration values at each computational grid of the silicon melt according to each set of simulation results;

[0132] An oversaturation calculation sub-module, which is used to calculate the oversaturation of each computational grid according to the carbon concentration values;

[0133] A boundary layer thickness calculation sub-module, which is used to determine, for each column of computational grids, the distance between the computational grid at the maximum oversaturation and the solid-liquid interface as the carbon concentration boundary layer thickness corresponding to the centrifugal distance of the column of computational grids;

[0134] A first relationship function generation sub-module, which is used to obtain the first relationship function according to the corresponding relationship between the carbon concentration boundary layer thickness and the centrifugal distance.

[0135] In a possible implementation manner, the oversaturation calculation sub-module is used to:

[0136] Calculate the supersaturation of each computational grid according to the following formula:

[0137] ;

[0138] wherein, S is the supersaturation, c is the carbon concentration value at the computational grid of this layer, c eq is the carbon equilibrium concentration at the computational grid of this layer.

[0139] In a possible implementation manner, the device further includes a carbon concentration stable region determination module, configured to:

[0140] Calculate the carbon concentration stable region of each column of computational grids according to the carbon concentration value, where the carbon concentration stable region is the region where the computational grids are located, and the difference between the carbon concentration values of two adjacent computational grids in this column of computational grids is within a first preset threshold;

[0141] Obtain the third relationship function according to the corresponding relationship between the carbon concentration stable region and the centrifugal distance;

[0142] Determine the fourth relationship function among the electromagnetic induction heating frequency, the carbon concentration stable region and the centrifugal distance according to multiple third relationship functions.

[0143] In a possible implementation manner, the heat transfer and flow control equation includes:

[0144] Continuity equation: ;

[0145] Momentum equation: ;

[0146] Energy equation: ;

[0147] wherein, represents taking the gradient; represents the velocity; represents the density; p represents the pressure; represents the dynamic viscosity; represents the gravitational acceleration; represents the thermal expansion coefficient; T represents the temperature at the grid; represents the reference temperature; represents the specific heat capacity; represents the thermal conductivity; represents the heat source; represents the transpose of the velocity gradient; represents the induced current density; is the magnetic induction intensity.

[0148] In a possible implementation, the component transport control equation is as follows:

[0149] ;

[0150] where, denotes taking the gradient; denotes density; denotes velocity; denotes the molar concentration of carbon; denotes the mass diffusion coefficient of carbon in the silicon melt; denotes taking the second derivative.

[0151] In a possible implementation, the numerical calculation model establishment module includes a boundary condition setting sub-module for:

[0152] Adding a dissolution boundary condition to the interface between the crucible and the silicon melt in the geometric model;

[0153] Adding a precipitation boundary condition to the interface between the silicon melt and the crystal in the geometric model; where, the dissolution boundary condition and the precipitation boundary condition are the same, and are both expressed as the following formula:

[0154] ;

[0155] where, is the molar mass of silicon; is the density of silicon; e is the mathematical constant Euler's number; T is the temperature at the grid, C eq is the equilibrium concentration of carbon dissolved in the silicon melt.

[0156] In a possible implementation, determining the distribution of the target carbon concentration boundary layer from the second relationship function, and optimizing the structure of the liquid-phase method for growing silicon carbide according to the distribution of the target carbon concentration boundary layer, includes:

[0157] Calculating a first judgment index and a second judgment index for the thickness distribution of the target carbon concentration boundary layer according to the second relationship function; the first judgment index represents the maximum difference in the thickness distribution of the target carbon concentration boundary layer; the second judgment index represents the thickness distribution uniformity of the target carbon concentration boundary layer;

[0158] Modifying the structural parameters of the liquid-phase method for growing silicon carbide according to the first judgment index and the second judgment index to obtain an optimized liquid-phase method for growing silicon carbide system.

[0159] The embodiments of the present application also provide an electronic device, referring to Figure 8 , Figure 8It is a schematic diagram of an electronic device proposed in an embodiment of the present application. As Figure 8 shown, the electronic device 100 includes: a memory 110 and a processor 120. The memory 110 is communicatively connected to the processor 120 via a bus. A computer program is stored in the memory 110, and this computer program can run on the processor 120, thereby implementing the steps in the method for obtaining the carbon concentration boundary layer in the liquid-phase growth of silicon carbide disclosed in the embodiments of the present application.

[0160] The embodiments of the present application also provide a computer-readable storage medium, on which a computer program / instructions are stored. When the computer program / instructions are executed by a processor, the steps in the method for obtaining the carbon concentration boundary layer in the liquid-phase growth of silicon carbide disclosed in the embodiments of the present application are implemented.

[0161] The embodiments of the present application also provide a computer program product. When the computer program product runs on an electronic device, it causes the processor to implement the steps in the method for obtaining the carbon concentration boundary layer in the liquid-phase growth of silicon carbide disclosed in the embodiments of the present application when executed.

[0162] Each embodiment in this specification is described in a progressive manner. The key point of each embodiment is the difference from other embodiments. For the same or similar parts among the embodiments, reference can be made to each other.

[0163] The embodiments of the present application are described with reference to the flowcharts and / or block diagrams of the methods, devices, electronic devices, and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing terminal devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing terminal devices generate a device for implementing the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0164] These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing terminal device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured product including an instruction device, and the instruction device implements the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0165] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal device, so that a series of operation steps are executed on the computer or other programmable terminal device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable terminal device provide for implementing the process Figure 1 in one process or multiple processes and / or blocks Figure 1 steps for the functions specified in one block or multiple blocks.

[0166] Although the preferred embodiments of the embodiments of the present application have been described, those skilled in the art can make additional changes and modifications once they learn the basic creative concept. Therefore, the appended claims are intended to be construed to include the preferred embodiments and all changes and modifications falling within the scope of the embodiments of the present application.

[0167] Finally, it should also be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or terminal device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or elements inherent to such process, method, article or terminal device. Without further limitation, an element defined by the statement "comprising an..." does not exclude the presence of additional identical elements in the process, method, article or terminal device comprising the element.

[0168] The above has introduced in detail a method, apparatus and product for obtaining a carbon concentration boundary layer in liquid-phase growth of silicon carbide provided by the present application. Specific examples are used in this article to elaborate on the principle and implementation manner of the present application. The description of the above embodiments is only used to help understand the method and its core idea of the present application; at the same time, for those of ordinary skill in the art, according to the idea of the present application, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present application.

Claims

1. A method for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide, characterized in that: The method comprises: According to the structural information of the liquid phase growth silicon carbide system, a geometric model is established and computational meshing is performed; Setting boundary conditions of the corresponding calculation grid in the geometric model, setting electromagnetic induction control equations, heat transfer flow control equations and component transport control equations, and obtaining a numerical calculation model; Based on the numerical calculation model, the electromagnetic induction heating process, heat transfer flow process and component transport process under multiple different electromagnetic induction heating frequencies are simulated to obtain multiple groups of simulation results; According to the carbon concentration values ​​at each calculation grid of the silicon melt in each group of the simulation results, determining a first relationship function between the carbon concentration boundary layer thickness and the centrifugal distance of each column of the calculation grid on one side of the silicon melt at the solid-liquid interface at the corresponding electromagnetic induction heating frequency, wherein the centrifugal distance refers to the vertical distance between the column of calculation grids and the central axis of the solid-liquid interface; Determining a second relationship function among the electromagnetic induction heating frequency, the carbon concentration boundary layer thickness and the centrifugal distance according to the plurality of the first relationship functions; Determining the distribution of the target carbon concentration boundary layer from the second relationship function, and optimizing the structure of the liquid phase method silicon carbide growth system according to the distribution of the target carbon concentration boundary layer; Among them, according to the carbon concentration value at each calculation grid of the silicon melt in each group of the simulation results, a first relationship function between the carbon concentration boundary layer thickness and the centrifugal distance of each column of the calculation grid on one side of the silicon melt at the solid-liquid interface under the corresponding electromagnetic induction heating frequency is determined, including: According to each group of simulation results, determining the carbon concentration value at each calculation grid of the silicon melt; Calculating the supersaturation of each calculation grid according to the carbon concentration value; For each column of calculation grids, the distance between the calculation grid at the maximum value of supersaturation and the solid-liquid interface is determined as the carbon concentration boundary layer thickness corresponding to the centrifugal distance of the calculation grid in this column; The first relationship function is obtained according to the corresponding relationship between the carbon concentration boundary layer thickness and the centrifugal distance.

2. The method for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide according to claim 1, characterized in that: Calculating the supersaturation of each calculation grid according to the carbon concentration value includes: The supersaturation of each computational grid is calculated according to the following formula: ； in, S is the supersaturation, c Calculate the carbon concentration value at the grid for this layer, c eq Calculate the carbon equilibrium concentration at the grid for this layer.

3. The method for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide according to claim 2, characterized in that: The method further comprises: According to the carbon concentration value, a carbon concentration stable region of each column of calculation grids is calculated, wherein the carbon concentration stable region is a region where calculation grids in the column of calculation grids are located and the difference between the carbon concentration values ​​of two adjacent calculation grids is within a first preset threshold; According to the corresponding relationship between the carbon concentration stable area and the centrifugal distance, a third relationship function is obtained; According to the plurality of third relationship functions, a fourth relationship function among the electromagnetic induction heating frequency, the carbon concentration stable region and the centrifugal distance is determined.

4. The method for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide according to claim 1, characterized in that: The heat transfer flow governing equations include: Continuity equation: ; Momentum equation: ; Energy equation: ; in, It means to find the gradient; Indicates speed; represents density; p represents pressure; represents dynamic viscosity; represents the acceleration due to gravity; represents the thermal expansion coefficient; T represents the temperature at the grid; Indicates the reference temperature; represents specific heat capacity; represents thermal conductivity; Indicates heat source; represents the transpose of the velocity gradient; represents the induced current density; is the magnetic induction intensity.

5. The method for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide according to claim 1, characterized in that: The component transport control equation is: ； in, It means to find the gradient; Indicates density; Indicates speed; represents the molar concentration of carbon; represents the mass diffusion coefficient of carbon in silicon melt; It means to find the second-order derivative.

6. The method for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide according to claim 1, characterized in that: The step of setting the boundary conditions of the corresponding computational grid in the geometric model includes: adding a dissolution boundary condition to the interface between the crucible and the silicon melt in the geometric model; Add a precipitation boundary condition to the interface between the silicon melt and the crystal in the geometric model; wherein the dissolution boundary condition and the precipitation boundary condition are the same, and are both expressed as the following formula: ； in, is the molar mass of silicon; is the density of silicon; e is the mathematical constant Euler number; T is the temperature at the grid, C eq is the equilibrium concentration of carbon dissolved in silicon melt.

7. The method for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide according to claim 1, characterized in that: Determining the distribution of the target carbon concentration boundary layer from the second relationship function, and optimizing the structure of the liquid phase method silicon carbide growth system according to the distribution of the target carbon concentration boundary layer, includes: According to the second relationship function, a first judgment index and a second judgment index of the thickness distribution of the target carbon concentration boundary layer are calculated; the first judgment index represents the maximum difference in the thickness distribution of the target carbon concentration boundary layer; the second judgment index represents the uniformity of the thickness distribution of the target carbon concentration boundary layer; According to the first judgment index and the second judgment index, the structural parameters of the liquid phase method silicon carbide growth system are modified to obtain an optimized liquid phase method silicon carbide growth system.

8. A device for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide, characterized in that: A method for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide according to any one of claims 1 to 7, the device comprising: The geometric model building module is used to build the geometric model and perform computational meshing based on the structural information of the liquid phase method silicon carbide growth system; A numerical calculation model building module is used to set the boundary conditions of the corresponding calculation grid in the geometric model, set the electromagnetic induction control equation, the heat transfer flow control equation and the component transport control equation, and obtain the numerical calculation model; A simulation module, for simulating the electromagnetic induction heating process, heat transfer flow process and component transport process under multiple different electromagnetic induction heating frequencies based on the numerical calculation model, and obtaining multiple groups of simulation results; A first relationship function determination module is used to determine, according to the carbon concentration value at each calculation grid of the silicon melt in each group of the simulation results, a first relationship function between the carbon concentration boundary layer thickness of each column of the calculation grid on one side of the silicon melt at the solid-liquid interface and the centrifugal distance at the corresponding electromagnetic induction heating frequency, wherein the centrifugal distance refers to the vertical distance between the column of calculation grids and the central axis of the solid-liquid interface; A second relationship function determination module, used to determine a second relationship function between the electromagnetic induction heating frequency, the carbon concentration boundary layer thickness and the centrifugal distance according to a plurality of the first relationship functions; The carbon concentration boundary layer determination module is used to determine the distribution of the target carbon concentration boundary layer from the second relationship function, and optimize the structure of the liquid phase method silicon carbide growth system according to the distribution of the target carbon concentration boundary layer.

9. An electronic device, characterized in that: The method comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the method for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide according to any one of claims 1 to 7.

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