Method and device for obtaining carbon concentration boundary layer in silicon carbide grown by liquid phase method and product

Abstract

The invention provides a method and device for obtaining a carbon concentration boundary layer in liquid phase method growth silicon carbide and a product, and relates to the technical field of single crystal growth, and the method comprises the steps: building a geometric model according to the structure information of a liquid phase method growth silicon carbide system, and carrying out calculation grid division; obtaining a plurality of groups of simulation results based on the constructed numerical calculation model; according to the carbon concentration value of each calculation grid in each group of simulation results, a first relation function between the carbon concentration boundary layer thickness of each column of calculation grids and the centrifugal distance is determined, and 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 relation function among the electromagnetic induction heating frequency, the carbon concentration boundary layer thickness and the centrifugal distance according to the first relation function; and determining the distribution condition of the target carbon concentration boundary layer from the second relation function, and optimizing the structure of the system for growing the silicon carbide by the liquid phase method according to the distribution condition of the target carbon concentration boundary layer.

Description

Technical Field

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

[0002] When growing silicon carbide using the 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 to improve the subsequent preparation process. Especially for the more complicated solid-liquid interface area, it is difficult to obtain the distribution of the carbon concentration boundary layer in this area through experiments at a high cost. Therefore, it is urgent to propose a method, device and product for obtaining the carbon concentration boundary layer in the liquid phase growth of silicon carbide to obtain the accurate distribution of the carbon concentration boundary layer, so as to guide the optimization of subsequent processes. Summary of the invention

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

[0004] A first aspect of an embodiment of the present application provides a method for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide, the method comprising: 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; The distribution of the target carbon concentration boundary layer is determined from the second relationship function, and the structure of the liquid phase method silicon carbide growth system is optimized according to the distribution of the target carbon concentration boundary layer.

[0005] The second aspect of the embodiment of the present application further provides a device for obtaining a carbon concentration boundary layer in a liquid phase grown silicon carbide, which is used to perform the method for obtaining a carbon concentration boundary layer in a liquid phase grown silicon carbide according to the first aspect of the embodiment of the present application, and the device comprises: 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.

[0006] The third aspect of the embodiments of the present application also provides an electronic device, including a memory, a processor and a computer program stored on the memory, wherein the processor executes the computer program to implement the steps in the method for obtaining the carbon concentration boundary layer in liquid phase grown silicon carbide described in the first aspect of the embodiments of the present application.

[0007] The fourth aspect of the embodiments of the present application further provides a computer-readable storage medium having a computer program / instruction stored thereon. When the computer program / instruction is executed by a processor, the steps in the method for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide described in the first aspect of the embodiments of the present application are implemented.

[0008] The fifth aspect of the embodiments of the present application further provides a computer program product, which, when executed on an electronic device, enables a processor to implement the steps in the method for obtaining a carbon concentration boundary layer in silicon carbide grown by a liquid phase method as described in the first aspect of the embodiments of the present application.

[0009] The embodiment of the present application provides a method for obtaining a carbon concentration boundary layer in a liquid phase grown silicon carbide. The method comprises: establishing a geometric model and performing computational grid division according to structural information of a liquid phase grown silicon carbide system; setting boundary conditions of the corresponding computational grid in the geometric model, setting electromagnetic induction control equations, heat transfer flow control equations and component transport control equations to obtain a numerical calculation model; based on the numerical calculation model, simulating electromagnetic induction heating processes, heat transfer flow processes and component transport processes under multiple different electromagnetic induction heating frequencies to obtain multiple groups of simulation results; and simulating the various components of the silicon melt in each group of the simulation results. Calculate the carbon concentration value at the grid, and determine the first relationship function between the carbon concentration boundary layer thickness and the centrifugal distance of each column of calculation grids on the side of the silicon melt at the solid-liquid interface under 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; determine the second relationship function between the electromagnetic induction heating frequency, the carbon concentration boundary layer thickness and the centrifugal distance based on multiple first relationship functions; 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 system based on the distribution of the target carbon concentration boundary layer.

[0010] The specific beneficial effects are: The embodiment of the present application establishes a numerical calculation model to simulate the heat transfer flow process and component transport process under different electromagnetic induction heating frequencies, and obtains multiple sets of simulation results. Then, according to the carbon concentration value of each calculation grid in the silicon melt in the simulation results, the first relationship function between the carbon concentration boundary layer thickness and the centrifugal distance of each column of calculation grids on the side of the silicon melt at the solid-liquid interface is determined. The embodiment of the present application fully takes into account that the carbon concentration boundary layer on the side of the silicon melt at the solid-liquid interface is not a boundary layer of uniform thickness, so through numerical simulation, the carbon concentration boundary layer thickness at different centrifugal distances (the vertical distance between the column of calculation grids and the central axis of the solid-liquid interface) is determined, and the 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the description of the embodiments of the present application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0012] Figure 1 It is a flow chart of the steps of a method for obtaining a carbon concentration boundary layer in liquid phase growth of silicon carbide provided in an embodiment of the present application; Figure 2It is a schematic diagram of the structure of a system for producing silicon carbide by a liquid phase method provided in an embodiment of the present application; Figure 3 It is a schematic diagram of the computational grid division of a solid-liquid interface provided in an embodiment of the present application; Figure 4 is a supersaturation distribution curve from the solid-liquid interface to the carbon dissolution interface provided in an embodiment of the present application; Figure 5 is a carbon concentration distribution curve from the solid-liquid interface to the carbon dissolution interface provided in an embodiment of the present application; Figure 6 is a curve diagram of a first relationship function under different electromagnetic induction heating frequencies provided in an embodiment of the present application; Figure 7 It is a structural schematic diagram of a carbon concentration boundary layer acquisition device provided in an embodiment of the present application; Figure 8 is a schematic diagram of an electronic device provided in an embodiment of the present application; Figure symbols: 1. Silicon melt; 2. Graphite crucible; 3. Side graphite support; 4. Carbon felt; 5. Copper coil. DETAILED DESCRIPTION

[0013] The exemplary embodiments of the present application will be described in more detail below in conjunction with the accompanying drawings in the embodiments of the present application. Although the exemplary embodiments of the present application are shown in the accompanying 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 in order to enable a more thorough understanding of the present application and to enable the scope of the present application to be fully communicated to those skilled in the art.

[0014] As a third-generation semiconductor material, SiC has excellent properties such as large bandgap, high thermal conductivity, and high chemical stability. It is a semiconductor material with great application prospects. At present, there are three mainstream growth methods for SiC, namely physical vapor transport, high-temperature chemical vapor deposition, and liquid phase method. Among them, SiC grown by 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 liquid phase method to grow SiC single crystal system.

[0015] The liquid phase method is also called 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 the carbon dissolves into the Si melt due to the high temperature and local unsaturation. Then, the carbon is transported to the bottom of the seed crystal by convection and diffusion, where the temperature near the seed crystal is relatively low, and the carbon here becomes supersaturated, and finally a SiC crystal grows. Among them, this supersaturation provides a driving force for the growth of SiC.

[0016] Induction heating is the use of electromagnetic induction to generate current inside the heated material (such as crucible, side graphite support, etc.), relying on the energy of these eddy currents to achieve the purpose of heating. Induction heating as a heating method is of great significance in liquid phase growth systems. The temperature field and thermal field of the growth system determine the quality of the crystal. However, the relevant parameters of the induction heating system and the structural layout of the components will affect the distribution of heat 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 geometry and relative position of the coil and crucible in the system should be carefully determined.

[0017] 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 relevant environmental information during the growth of silicon carbide to improve 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 more complex solid-liquid interface area, it is difficult to obtain the distribution of the carbon concentration boundary layer in this area through experiments at a high cost.

[0018] In view of the above problems, the embodiments of the present application propose a method, device and product for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide, so as to obtain an accurate distribution of the carbon concentration boundary layer, so as to guide further optimization of subsequent processes. In conjunction with the accompanying drawings, the following describes in detail a method, device and product for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide provided by the embodiments of the present application through some embodiments and their application scenarios.

[0019] The first aspect of the present application provides a method for obtaining a carbon concentration boundary layer in a liquid phase grown silicon carbide, referring to Figure 1 , Figure 1 A flow chart of the steps of a method for obtaining a carbon concentration boundary layer in a liquid phase grown silicon carbide according to an embodiment of the present application is provided, such as Figure 1 As shown, the method includes: Step S101, establishing a geometric model and performing computational meshing according to structural information of a liquid phase method silicon carbide growth system; In the embodiment of the present application, silicon carbide is prepared by liquid phase method. In the present embodiment, the liquid phase method for growing silicon carbide system refers to any system that can be used to prepare silicon carbide by liquid phase method (such as a 6-inch SiC growth system). The embodiment of the present application does not limit the specific structure and size parameters of the liquid phase method for growing silicon carbide system. Among them, the structural information of the liquid phase method for growing silicon carbide system can be information such as the size and position of each component in the system. For example, refer to Figure 2 , Figure 2 A schematic diagram of the structure of a liquid phase method for producing silicon carbide is shown, Figure 2As shown in FIG. 1 , the liquid phase method for growing silicon carbide system includes at least the following components: 1. silicon melt; 2. graphite crucible; 3. side graphite support; 4. carbon felt; 5. copper coil. Figure 2 As shown, the graphite crucible 1 is located in the center of the system, and the crucible is filled with silicon melt 2. The side graphite support 3 is located on the side of the crucible, which serves as the main heating element in the system and transfers the heat obtained by electromagnetic induction to the crucible and the melt in the crucible through radiation. The carbon felt 4 is located outside the side graphite support 3, which plays a role of support and heat preservation. The copper coil 5 is located outside the carbon felt 4 for electromagnetic induction heating.

[0020] According to the structural information of the liquid phase method for growing silicon carbide system (including the structure and size parameters of each component), the modeling software is used to geometrically model the structure of the liquid phase method for growing silicon carbide system to obtain the corresponding geometric model. Then the geometric model is divided into computational grids, including the computational grid division of the carbon concentration boundary layer in the geometric model. Specifically, the more computational grids are divided, the more accurate the results obtained from the numerical calculation. The number of computational grids can be determined according to the actual amount of computational resources.

[0021] Step S102, setting the boundary conditions of the corresponding calculation grid in the geometric model, setting the electromagnetic induction control equation, the heat transfer flow control equation and the component transport control equation, and obtaining the numerical calculation model.

[0022] Set the boundary conditions of the corresponding computational grid in the geometric model. Specifically, define the boundary conditions and working pressures between the various components in the geometric model during the electromagnetic induction heating process, heat transfer flow process, and component transport process using the liquid phase method (i.e., the boundary conditions of each computational grid). For example: the boundary conditions of the contact surface between the inner wall of the crucible and the silicon melt, the temperature of the outer wall of the furnace in the geometric model, the pressure in the furnace, the boundary conditions of the gas-liquid interface (free surface) in the geometric model, and the boundary conditions of other solid-gas contact surfaces in the geometric model.

[0023] Specifically, the boundary conditions in the embodiments of the present application include: Boundary conditions of electromagnetic induction heating process: The outer boundary of the region adopts a balloon boundary. On the edge of its boundary, the magnetic field is neither perpendicular to the edge nor parallel to the edge. This boundary condition is to simulate infinity and reduce the amount of calculation; the other boundaries adopt natural boundary conditions. The tangential component of the magnetic field intensity and the normal component of the magnetic induction intensity on the contact surface of the two contacting objects remain continuous ( , ). H t represents the tangential component of the magnetic field intensity, B n Represents the normal component of magnetic induction intensity.

[0024] Boundary conditions for heat transfer flow process: The inner wall of the coil is the temperature boundary condition (It is equivalent to giving this wall a fixed temperature C), the other walls are coupled walls (the temperature and heat flux density on both sides of the interface are equal); the surface tension gradient (Malaygo force) is set on the free surface of the silicon melt, and the rest are no-slip boundaries (i.e. )speed.

[0025] Boundary conditions at the interface (gas-liquid boundary): set the surface tension gradient ;in, represents the surface tension coefficient in N / m, and T represents the temperature in °C.

[0026] In a possible implementation manner, 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.

[0027] Specifically, before numerical solution, it is necessary to set corresponding boundary conditions to simulate the real situation. This includes adding dissolution boundary conditions to the interface between the crucible and the silicon melt to simulate the dissolution of the graphite crucible; adding precipitation boundary conditions to the interface between the silicon melt and the crystal to simulate the precipitation of silicon carbide crystals. Both of these boundaries are equilibrium concentration boundaries of carbon. C eq .

[0028] In addition, at the free surface of the melt (interface between the melt and the gas), the normal gradient of the concentration is set to ,in, C c represents the molar concentration of carbon, x Indicates the direction perpendicular to the free surface. In order to simulate the real situation, silicon carbide crystals will not precipitate on the free surface. In actual operation, water cooling is usually passed through the inner area of ​​the coil to keep the inner wall of the coil at room temperature. In order to save computing resources, the water cooling inside the coil is simplified, and the temperature of the inner wall of the coil is given as room temperature during the solution. The remaining contact surfaces are set as temperature continuous walls, and the temperature on the left and right sides of the contact surfaces with different structures is continuous.

[0029] 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 in the heat transfer flow process, and the control equations in the component transport process are set. For example: the electromagnetic induction control equation in the geometric model, the heat transfer flow control equation satisfied by the melt-crystal region in the geometric model, the heat transfer 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 induced heat in the geometric model when electromagnetic induction heating is performed under specific conditions (electromagnetic induction heating frequency), that is, the induced power of each calculation grid in the geometric model. The heat transfer flow control equation is used to solve the thermal 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-induction phenomenon in the copper coil (that is, the above-mentioned electromagnetic induction control equation) is set, so that when simulating the electromagnetic induction heating process, the influence of the self-induction phenomenon in the copper coil on the thermal field is added, and the accuracy of the obtained simulation results is further improved.

[0030] Specifically, the control equation of the electromagnetic induction heating process (i.e., the above-mentioned electromagnetic induction control equation) includes the following formula: ; ; in, Indicates the electric field strength v / m, is the induced current A / m 2 , is the magnetic potential vector (dimensionless quantity, no unit), t is the current time s, r is the distance m, μ is the magnetic permeability H / m; during electromagnetic induction heating, an alternating current is passed through the copper coil ;in, J 0 is the current density amplitude (maximum value) A / m 2 ; is the angular frequency rad / s; t is the current time; , f is the electromagnetic induction frequency in kHz.

[0031] Substitute the physical property parameters of each component into the control equations of the electromagnetic induction heating process and the heat transfer flow process, wherein 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 growth silicon carbide system), the physical property parameters of each component (the conductivity of each material, the density of the material, etc.) are substituted into the control equations of the electromagnetic induction heating process and the heat transfer flow process to establish a numerical calculation model.

[0032] Heat transfer flow refers to the process of induction heating, which makes each device in the system (i.e., crystal growth furnace) have heat distribution, where the protective gas and silicon melt are fluid parts and the rest are solid parts. The silicon melt flows and the inner wall of the graphite crucible dissolves through radiation and convection. In a possible implementation, the heat transfer flow control equation includes: Continuity equation: ; Momentum equation: ; Energy equation: ; in, It means to find the gradient (i.e., to solve the first-order derivative perpendicular to the crystal growth interface); Indicates speed m / s; Indicates density kg / m 3 ; p Indicates pressure Pa; Indicates dynamic viscosity Pa·s; Indicates the acceleration due to gravity m / s 2 ; represents the coefficient of thermal expansion; T Indicates the temperature at the grid in °C; Indicates reference temperature °C; is the Lorentz force density N / m 3 ; represents specific heat capacity; represents the thermal conductivity of silicon melt; Indicates heat source W / m 3 ; represents the transpose of the velocity gradient, t Indicates the current time; represents the induced current density; is the magnetic induction intensity.

[0033] Substitute the density of the solid material of each component into the governing equation of the heat transfer flow process in the solid material area: ; in, Indicates the density of solid materials kg / m3 ; It represents the specific heat capacity of solid materials; Represents the thermal conductivity of solid materials; Indicates heat source W / m 3 ; 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. In this embodiment, the control equations of 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 the density of the solid material of each component is substituted into the control equation, the density of the solid material is: 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.

[0034] When the temperature is high, the graphite crucible will dissolve at the interface between the silicon melt and the graphite crucible. In the process of solving the heat transfer flow, the velocity field and temperature field of the silicon melt area will be obtained, and the carbon concentration distribution in the silicon melt will be obtained according to the velocity field and temperature field. Finally, the growth rate of the crystal is solved by the carbon concentration distribution, that is, the solution process of component transport. In a possible implementation, the component transport control equation includes: ; in, It means to find the gradient (i.e., to solve the first-order derivative perpendicular to the crystal growth interface); 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 (that is, to solve the second-order derivative perpendicular to the crystal growth interface).

[0035] Specifically, in the subsequent numerical solution process, the component transport control equation is crucial, and the key factor that ultimately leads to the quality of crystal growth and the amount of crystal precipitation is the carbon concentration distribution in the silicon melt. The initial component transport equation is: ; in , k=1,2……N ; Indicates density kg / m 3 ; t Indicates the current time. Indicates shared k The mass fraction of different components; x Indicates the distance m; u Indicates speed m / s; Indicates shared k Mass diffusion coefficient of different components in silicon melt kg / (m·s); expressk The mass concentration source terms of different components in the silicon melt.

[0036] Combined with the numerical calculation process of the embodiment of the present application, the solution is reasonably simplified. This solution is for steady state, which is independent of time, that is, , this item can be ignored. In numerical calculation, only the transport and calculation of carbon are set, so k =1. In addition, when solving the problem, there will be no carbon atoms in the silicon melt in the initial state, so =0. The source of carbon is the carbon on the crucible wall dissolving into the silicon melt. Then convert the mass fraction into molar concentration, and the final component transport control equation in this numerical calculation process is obtained as follows: .

[0037] Step S103, based on the numerical calculation model, simulating the electromagnetic induction heating process, heat transfer flow process and component transport process under multiple different electromagnetic induction heating frequencies to obtain multiple groups of simulation results.

[0038] In this embodiment, each set of simulation results includes, at the electromagnetic induction heating frequency, the information of the electromagnetic induction heating process (e.g., the induction power of each calculation grid), the information of the heat transfer flow process (e.g., the temperature value, thermal field, flow field information, silicon melt velocity, etc. of each calculation grid), and the information of the component transport process (e.g., the carbon concentration value of each calculation grid). Among them, the commonly used frequency in the liquid phase growth of silicon carbide is 1kHz-5kHz, and multiple different electromagnetic induction heating frequencies can be taken within the frequency range of 1kHz-5kHz, such as 1kHz, 2kHz, 3kHz, 4kHz and 5kHz.

[0039] Specifically, for each electromagnetic induction heating frequency, the electromagnetic induction heating process under the electromagnetic induction heating frequency is simulated. Specifically, by solving the electromagnetic induction control equation in the electromagnetic induction heating numerical model, the electromagnetic induction heating process under the electromagnetic induction heating frequency (i.e., part of the simulation results) is obtained, including the current value on each component in the geometric model when electromagnetic induction heating is performed at the electromagnetic induction heating frequency, and the numerical value of the induced power of each calculation grid, i.e., the induced heat density (i.e., the induced power density) on each component. By solving the heat transfer flow control equation, the heat transfer flow process, i.e., the process of stable growth of silicon carbide single crystal (i.e., part of the simulation results) is simulated, including: the temperature value, thermal field, flow field information, silicon melt velocity, etc. of each calculation grid in the geometric model during the stable growth of silicon carbide single crystal. By solving the heat transfer flow control equation at the current time, the silicon melt area at the current time is obtained. Speed ​​information, and then the speed Substituting the component transport control equation into the equation and solving it, we can obtain information such as the carbon concentration corresponding to each computational grid at the current time (i.e., part of the simulation results).

[0040] Step S104, determining a first relationship function between the carbon concentration boundary layer thickness and the centrifugal distance of each column of calculation grids on one side of the silicon melt at the solid-liquid interface under the corresponding electromagnetic induction heating frequency according to the carbon concentration values ​​at each calculation grid of the silicon melt in each group of the simulation results, wherein the centrifugal distance refers to the vertical distance between the column of calculation grids and the central axis of the solid-liquid interface.

[0041] In the embodiment of the present application, the thickness of the concentration boundary layer refers to the thickness of the carbon concentration boundary layer on one side of the silicon melt at the solid-liquid interface. When silicon carbide is grown by liquid phase method, the temperature is very high and it is difficult to conduct experiments, so it is impossible to accurately obtain the carbon concentration distribution of the growth interface and the thickness of the carbon concentration boundary layer at each position of the growth interface. When the temperature is high, the graphite crucible will be dissolved at the interface between the silicon melt and the graphite crucible. In the process of solving the heat transfer flow, the velocity field and temperature field of the silicon melt area will be obtained, and the carbon concentration distribution in the silicon melt will be obtained according to the velocity field and the temperature field, so as to solve the growth rate of the crystal by the carbon concentration distribution (i.e., simulate the component transport process). 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, and there is also a concentration boundary layer in this area (the interface between the graphite crucible and the silicon melt), but in the numerical simulation of the growth of silicon carbide by liquid phase method, only the carbon concentration distribution at the solid-liquid interface is concerned, so the embodiment of the present application does not make special restrictions on the carbon concentration distribution near the interface between the graphite crucible and the silicon melt.

[0042] Reference Figure 3 , Figure 3 A schematic diagram of the computational grid division of a solid-liquid interface is shown in FIG. Figure 3 As shown, for the silicon melt side of the solid-liquid interface, the computational grid is divided 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 at each position is the same), the vertically arranged computational grids are taken as one column, and 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 vertical distance of each column of computational grids from the central axis is the centrifugal distance. Different centrifugal distances may result in different boundary layer thicknesses at corresponding positions.

[0043] In addition, considering that the model is circularly symmetrical, when performing simulation calculations based on the numerical calculation model, only half of the model can be calculated to reduce the amount of calculations for the simulation calculations. For example, the SiC seed crystal is 6 inches, i.e. 75 mm, and a carbon concentration boundary layer grid is added to the melt side of the growth interface, where the first layer of carbon concentration boundary layer grid has a thickness of 0.05 mm and a width of 0.5 mm. Therefore, in this example, there are a total of (75 / 0.5=150) 150 columns of grids in the silicon melt area, which together constitute the calculation grid of the carbon concentration boundary layer.

[0044] In a possible implementation, step S104, according to the carbon concentration value at each calculation grid of the silicon melt in each group of the simulation results, determines 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, including: Step S1041, determining the carbon concentration value at each calculation grid of the silicon melt according to each group of simulation results.

[0045] Specifically, the simulation results are obtained by solving the control equation. Then, according to the component transport control equation in the simulation results, The solution result can be used to obtain the carbon concentration at each grid in the silicon melt area, that is, the proportion of carbon atoms and silicon atoms at the silicon carbide crystal growth interface can be known, that is, the carbon content and silicon content at the silicon carbide crystal growth interface.

[0046] Step S1042: Calculate the supersaturation of each calculation grid according to the carbon concentration value.

[0047] Wherein, supersaturation refers to the supersaturated state of a solution. At a certain temperature, a certain solvent can dissolve a certain solute, and the one-to-one correspondence is a saturated state. In a possible implementation, the step S1042, according to the carbon concentration value, calculates the supersaturation of each calculation grid, including: The supersaturation of each computational grid is calculated according to the following formula: ; in, S is the supersaturation, c Calculate the carbon concentration value mol / m at the grid for this layer 3 , c eq Calculate the carbon equilibrium concentration mol / m at the grid for this layer 3 Specifically, due to the carbon balance concentration c eq It will be affected by temperature. Therefore, when calculating the supersaturation at each computational grid, it is also necessary to first determine the carbon equilibrium concentration value at the computational grid based on the thermal field temperature information in the simulation results.c eq .

[0048] Step S1043: for each column of calculation grids, determine the distance between the calculation grid at the maximum supersaturation value and the solid-liquid interface as the carbon concentration boundary layer thickness corresponding to the centrifugal distance of the column of calculation grids.

[0049] 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.

[0050] Step S1044: obtaining the first relationship function according to the corresponding relationship between the carbon concentration boundary layer thickness and the centrifugal distance.

[0051] 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.

[0052] Reference Figure 5 , Figure 5 A carbon concentration distribution curve from the solid-liquid interface to the carbon dissolution interface is shown, for example, the carbon concentration distribution from the growth interface to the carbon dissolution interface 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 concentration value. It can be seen that the carbon concentration changes particularly drastically near the silicon melt side of the crystal growth interface, and it can also be seen that the carbon concentration changes particularly drastically near the interface between the graphite crucible and the silicon melt. Corresponding Figure 4 The supersaturation of the first column of grids is the largest at 0.434mm from the growth interface. By finding the carbon concentration at 0.434mm, it can be found that the carbon concentration in the first column of grids increases rapidly from the growth interface to 0.434mm (that is, the thickness of the carbon concentration boundary layer at the growth interface), changes slowly from 0.434mm to 105.566mm (defined as the carbon concentration stable area), and rises rapidly from 105.566mm to 106mm (defined as the carbon dissolution boundary layer).

[0053] It should be noted that the thickness of the entire carbon concentration boundary layer is not exactly the same, the carbon concentration boundary layer thickness at the actual solid-liquid interface position is not uniform, and the carbon concentration boundary layer thickness at different positions of the solid-liquid interface is inconsistent. For each set of simulation results, the carbon concentration boundary layer thickness corresponding to different centrifugal distances can be obtained, thereby generating a first relationship function for a specific electromagnetic induction heating frequency.

[0054] Step S105: 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.

[0055] Specifically, for each set of simulation results, a set of electromagnetic induction heating frequencies and corresponding first relationship functions can be obtained, and then according to multiple sets of simulation results, multiple sets of corresponding relationships between electromagnetic induction heating frequencies, carbon concentration boundary layer thickness and centrifugal distance are obtained, and fitting is performed to obtain the second relationship function. Figure 6 , Figure 6 A schematic diagram of a curve of a first relationship function under different electromagnetic induction heating frequencies is shown, such as Figure 6As shown, the abscissa is the centrifugal distance, and the ordinate is the most suitable carbon concentration boundary layer grid thickness. Exemplarily, in the liquid phase method of growing silicon carbide, the commonly used frequency is 1kHz-5kHz, and the value is taken at intervals of 0.5kHz, and 0.5kHz, 1kHz, 1.5kHz, 2kHz, 2.5kHz, 3kHz, 3.5kHz, 4kHz, 4.5kHz and 5kHz are obtained, a total of 10 groups of simulation results, and 10 first relationship functions corresponding to the 10 groups of simulation results. Then, by fitting these 10 first relationship functions, the 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 is to represent the relationship between the centrifugal distance and the carbon concentration boundary layer thickness under a specific electromagnetic induction heating frequency, and the second relationship function is to represent the relationship between the electromagnetic induction heating frequency, the centrifugal distance and the carbon concentration boundary layer thickness. For different liquid phase method growth silicon carbide systems, the structures are different, and the corresponding first relationship function and the second relationship function are different. In the embodiment of the present application, the specific function types of the first relationship function and the second relationship function are not limited.

[0056] Step S106, 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.

[0057] Specifically, in practical applications, the thickness of the carbon concentration boundary layer required for each current position (centrifugal distance) is determined from the second relationship function according to one or more electromagnetic induction heating frequencies (i.e., the current electromagnetic induction heating frequency) required for the actual growth of silicon carbide by the liquid phase method. Thus, based on the distribution of the determined 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) (i.e., the thickness of the carbon concentration boundary layer at each position), the structure of the liquid phase method silicon carbide growth system is optimized to guide the improvement and optimization of the structure of related components and the growth operation process of the liquid phase method silicon carbide growth. The specific improvement method is not limited in the embodiments of the present application. Exemplarily, according to the thickness balance 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 final system at each position reaches an ideal balance to improve production quality.

[0058] In a possible implementation, the step S106, 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: Step S1061, according to the second relationship function, calculate the first judgment index and the second judgment index of the thickness distribution of the target carbon concentration boundary layer; 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.

[0059] 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 embodiment of the present application, the distribution of the target carbon concentration boundary layer (i.e., the thickness of the carbon concentration boundary layer at each position) is first determined according to the second relationship function, and then the corresponding first judgment index and second judgment index are calculated according to the distribution.

[0060] 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 (S>0) of the thickness of the carbon concentration boundary layer, as shown in the following formula: Among them, L max Refers to the maximum thickness of the carbon concentration boundary layer in each centrifugal distance, mm; L min Refers to the minimum thickness of the carbon concentration boundary layer in each centrifugal distance, mm.

[0061] The second judgment index represents the thickness distribution uniformity M (1>M>0) of the target carbon concentration boundary layer as a whole, as shown in the following formula: Among them, L max It refers to the maximum value of the thickness of the carbon concentration boundary layer in each centrifugal distance, mm; Lmin refers to the minimum value of the thickness of the carbon concentration boundary layer in each centrifugal distance, mm.

[0062] It should be noted that, for a liquid phase method for growing silicon carbide systems, the more uniform the thickness of the carbon concentration boundary layer, the better the silicon carbide growth effect. Therefore, the embodiment of the present application first calculates the second relationship function to obtain the distribution of the carbon concentration boundary layer, and then determines the degree of distribution uniformity of the carbon concentration boundary layer by calculating the first judgment index and the second judgment index.

[0063] Step S1062: modify the structural parameters of the liquid phase method silicon carbide growth system according to the first judgment index and the second judgment index to obtain an optimized liquid phase method silicon carbide growth system.

[0064] Specifically, first determine whether the first preset condition is met (whether it is less than the first preset threshold) based on the first judgment index S. Because the smaller S is, the more favorable the carbon concentration boundary layer thickness distribution is. When the first judgment index S does not meet the first preset condition, directly modify the structural parameters of the liquid phase growth silicon carbide system. For example, adjust the thickness of the carbon felt, or adjust the size of the crucible, for example, increase or decrease the inner wall diameter of the crucible by 1 unit length.

[0065] If the first judgment index S meets the preset condition, continue to judge according to the second judgment index M, M is uniformity, and the smaller M is, the more favorable the carbon concentration boundary layer thickness distribution is. Determine whether the second judgment index M meets the second preset condition (whether it is less than the second preset threshold). In the case where the second judgment index M does not meet the second preset condition, directly modify the structural parameters of the liquid phase growth silicon carbide system (for example, increase or decrease according to a fixed unit length (thickness)) to obtain an optimized liquid phase growth silicon carbide system. In the embodiment of the present application, the specific structural parameter modification method is not limited.

[0066] After modifying the structural parameters, the method further comprises: Re-execute the step of calculating the modified second relational function of the liquid phase method growth silicon carbide system; According to S101-S105, the second relationship function of the modified liquid phase method silicon carbide growth 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 (first preset conditions and second preset conditions) are not met, the structural parameters of the liquid phase method silicon carbide growth system are modified, and the above steps are repeated until the first judgment index and the second judgment index meet the preset conditions, thereby obtaining the optimal liquid phase method silicon carbide growth system.

[0067] In addition, in actual applications, there may be a variety of different structures of liquid phase grown silicon carbide systems. For different structures, the second relationship function of the corresponding structure is calculated 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 grown silicon carbide system with the smallest first judgment index is selected. If there are multiple liquid phase grown silicon carbide systems with basically the same first judgment index (the difference in S is between ±0.01Smax, and Smax is the maximum value of S), then judgment is made according to the second judgment index M, where M is uniformity. The smaller M is, the more favorable the distribution of carbon concentration boundary layer thickness is. The structure of the liquid phase grown silicon carbide system with the smallest value of the second judgment index is selected and determined as the optimal structure.

[0068] In a possible implementation, the method further includes: 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 have a carbon concentration value difference between two adjacent calculation grids within a first preset threshold.

[0069] The third relationship function is obtained according to the corresponding relationship between the carbon concentration stable area and the centrifugal distance.

[0070] 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.

[0071] In the embodiment of the present application, in addition to determining 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 area in the silicon melt can also be determined. The carbon concentration stable area refers to an area where the carbon concentration is relatively stable and continuous with less variation, that is, the area where the difference in carbon concentration values ​​of two adjacent calculation grids in the column of calculation grids is within the first preset threshold. Figure 5 As shown, the carbon concentration changes particularly sharply near the side of the silicon melt near the crystal growth interface, and the carbon concentration changes particularly sharply near the interface between the graphite crucible and the silicon melt. The carbon concentration increases rapidly in the carbon concentration boundary layer (from the growth interface to 0.434 mm), changes slowly in the carbon concentration stable region (0.434 mm to 105.566 mm), and rises rapidly in the carbon dissolution boundary layer (105.566 mm to 106 mm). The embodiment of the present application calculates the carbon concentration stable region of each column of the calculation grid according to the carbon concentration value of each calculation grid in each group of simulation results, thereby determining the functional relationship (third relationship function) between the carbon concentration stable region and the centrifugal distance, and then fitting according to the multiple third relationship functions obtained from the multiple groups of simulation results to determine the fourth relationship function between the electromagnetic induction heating frequency, the carbon concentration stable region and the centrifugal distance. According to the electromagnetic induction heating frequency required for the actual growth of silicon carbide by the liquid phase method, the distribution of the carbon stable region in the current model is determined to construct a more accurate numerical model and further improve the accuracy of the results of the numerical calculation.

[0072] The second aspect of the embodiment of the present application further provides a device for obtaining a carbon concentration boundary layer in a liquid phase grown silicon carbide, which is used to execute the method for obtaining a carbon concentration boundary layer in a liquid phase grown silicon carbide according to the first aspect, referring to Figure 7 , Figure 7 A schematic diagram of the structure of a carbon concentration boundary layer acquisition device is shown, such as Figure 7 As shown, the device comprises: 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.

[0073] In a possible implementation, the first relationship function determination module includes: A carbon concentration value determination submodule, used to determine the carbon concentration value at each calculation grid of the silicon melt according to each group of simulation results; A supersaturation calculation submodule, used to calculate the supersaturation of each calculation grid according to the carbon concentration value; The boundary layer thickness calculation submodule is used to determine, for each column of calculation grids, the carbon concentration boundary layer thickness corresponding to the centrifugal distance of the column of calculation grids, that the distance between the calculation grid at the maximum supersaturation value and the solid-liquid interface is the distance; The first relationship function generating submodule is used to obtain the first relationship function according to the corresponding relationship between the carbon concentration boundary layer thickness and the centrifugal distance.

[0074] In a possible implementation manner, the supersaturation calculation submodule is used to: 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.

[0075] In a possible implementation manner, the device further includes a carbon concentration stable region determination module, which is used to: 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, the 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.

[0076] In a possible implementation, the heat transfer flow control equation includes: 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.

[0077] In a possible implementation, 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.

[0078] In a possible implementation, the numerical calculation model establishment module includes a boundary condition establishment submodule for: 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.

[0079] 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 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.

[0080] The present application also provides an electronic device, referring to Figure 8 , Figure 8 Schematic diagram of an electronic device proposed in an embodiment of the present application. Figure 8 As shown, the electronic device 100 includes: a memory 110 and a processor 120. The memory 110 and the processor 120 are connected via a bus communication. A computer program is stored in the memory 110. The computer program can be run on the processor 120 to implement the steps in the method for obtaining the carbon concentration boundary layer in liquid phase grown silicon carbide disclosed in the embodiment of the present application.

[0081] The embodiment of the present application also provides a computer-readable storage medium having a computer program / instruction stored thereon. When the computer program / instruction is executed by a processor, the steps in the method for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide as disclosed in the embodiment of the present application are implemented.

[0082] The embodiment of the present application also provides a computer program product. When the computer program product is run on an electronic device, the processor is enabled to implement the steps of the method for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide as disclosed in the embodiment of the present application.

[0083] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0084] 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 box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing terminal device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing terminal device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0085] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing terminal device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured product including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0086] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal device so that a series of operating steps are executed on the computer or other programmable terminal device to produce a computer-implemented process, thereby providing instructions for executing on the computer or other programmable terminal device to implement the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0087] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the embodiments of the present application.

[0088] Finally, it should be noted that, in this article, relational terms such as first and second, etc. 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 terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or terminal device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or terminal device. In the absence of further restrictions, the elements defined by the sentence "including one..." do not exclude the existence of other identical elements in the process, method, article or terminal device including the elements.

[0089] The above is a detailed introduction to the method, device and product for obtaining the carbon concentration boundary layer in liquid phase grown silicon carbide provided by the present application. Specific examples are used in this article to illustrate the principles and implementation methods of the present application. The description of the above embodiments is only used to help understand the method of the present application and its core idea; at the same time, for general technicians in this field, according to the ideas of the present application, there will be changes in the specific implementation methods and application scopes. In summary, the content of this specification should not be understood as a limitation on 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; The distribution of the target carbon concentration boundary layer is determined from the second relationship function, and the structure of the liquid phase method silicon carbide growth system is optimized according to the distribution of the target carbon concentration boundary layer.

2. The method for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide according to claim 1, characterized in that: According to the carbon concentration values ​​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.

3. The method for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide according to claim 2, 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.

4. The method for obtaining a carbon concentration boundary layer in liquid phase grown silicon carbide according to claim 3, 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, the 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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 8, 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.

10. 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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