Method for controlling the solid / liquid interface of a melt in the purification of indium by direct pulling based on numerical simulation

Abstract

The disclosed method for controlling the solid / liquid interface of a melt in indium purification by numerical simulation optimization belongs to the technical field of high-purity metal material preparation, and is based on multi-physical field numerical simulation to obtain a process control scheme for a stable solid / liquid interface of a melt by establishing a mapping relationship between an external magnetic field and process parameters-interface data-impurity concentration. The method comprises the following steps: obtaining original data of a Czochralski furnace and indium physical properties, calculating a geometric model and grid partitioning, and establishing a mathematical model; based on experimental historical data, setting boundary conditions, simulating the seeding, shoulder growth and key processes of constant diameter in the Czochralski process of indium purification; coupling multi-physical fields to analyze the change of the solid / liquid interface of the melt in the Czochralski process; based on the numerical simulation results, constructing a deep reinforcement learning model, establishing a mapping relationship among process parameters, interface data and impurity concentration, realizing a process "prediction-verification-optimization" closed loop iteration, and obtaining process parameters for the stable preparation of 8N high-purity indium.

Description

Technical Field

[0001] This invention belongs to the field of high-purity metal material preparation technology, specifically relating to a method for controlling the solid / liquid interface of the solution in indium Czochralski purification based on numerical simulation optimization. Background Technology

[0002] High-purity indium is a key raw material supporting the development of semiconductors and is widely used in high-tech fields such as electronics, photovoltaics, and new energy. 4N5-5N indium is mainly used for preparing ITO targets, 5N-6N is mainly used for preparing high-purity alloys and compounds, 6N-7N high-purity indium is mainly used for synthesizing compound semiconductors such as indium phosphide, indium antimonide, and indium arsenide, and 7N-8N high-purity indium is mainly used in molecular beam epitaxy sources and binders for detection and analysis. With the development of AI, higher requirements are placed on the purity and stability of high-purity indium. Currently, the main methods for preparing 7N and higher purity indium are vacuum distillation, zone melting, and Czochralski crystal growth. Among these, Czochralski crystal growth is characterized by its pollution-free operation, high efficiency, and ease of industrialization, making it a key process for preparing 7N and higher purity indium.

[0003] Czochralski (Czochralski) is a type of directional solidification purification. It mainly involves controlling parameters such as Czochralski speed and temperature to allow the metal to solidify and be purified at the solid-liquid interface as a seed crystal is introduced. The key technology lies in controlling the stability of the solid / liquid interface of the solution. Methods for preparing high-purity indium by Czochralski crystal pulling are described in relevant patent literature. Patent publication number CN 115522078 A discloses an apparatus and method for preparing ultra-high-purity indium by vacuum distillation coupled with single-crystal pulling. This method involves loading indium material into an embedded crucible, moving a condenser directly above the embedded crucible for vacuum distillation, moving a heat shield directly above the crucible, lowering a seed crystal above the indium material, and then pulling the crystal to obtain ultra-high-purity indium with a purity greater than 7N. Patent publication number CN 116254592 A discloses a method for preparing ultra-high-purity indium with a purity greater than 7N, using high-purity metallic indium with a purity greater than 6N as raw material and ultra-high-purity indium with a purity greater than 7N as a seed crystal, controlling the steps and parameters of the pulling process to prepare ultra-high-purity indium with a purity greater than 7N. Patent publication number CN 111455405... Patent B discloses a method and apparatus for preparing high-purity indium through multi-unit series multi-stage electrolytic refining. Specifically, it discloses a method and apparatus for preparing high-purity indium through multi-unit series multi-stage electrolytic refining, including a pre-electrolysis storage tank, an electrolytic cell, a post-electrolysis storage tank, and a first circulation pump connected by pipes and a U-shaped channel to form an electrolytic refining circulation system. Through this electrolytic cell, four steps are performed: primary electrolysis, vacuum distillation, secondary electrolysis, and single crystal growth, to obtain high-purity indium with good quality consistency and a purity of 8N. The above patent mainly mentions the method of preparing high-purity indium by Czochralski crystal pulling, but it does not delve into the key elements of Czochralski crystal pulling control, making it difficult to produce stable high-purity indium products of 7N and above, and thus offering little practical guidance for actual production. Due to the low melting point of indium, the actual temperature control of the melt during Czochralski pulling is difficult. Parameter adjustments are usually made by empirically observing changes in the solid / liquid interface, lacking quantitative data feedback. Furthermore, the changes in the solid / liquid interface of the melt are closely related to the temperature and flow fields within the furnace. These fields are primarily influenced by a series of factors, including furnace pressure, current, crucible rotation speed, seed crystal rotation speed, Czochralski speed, thermal field structure, Czochralski temperature, and Czochralski speed. The process parameters are complex, interacting and difficult to coordinate. Therefore, providing a stable solid / liquid interface process control scheme is of great significance for stable production. Summary of the Invention

[0004] The purpose of this invention is to provide a numerical simulation-based optimization method for controlling the solid / liquid interface in indium Czochralski purification, thereby addressing the shortcomings of existing technologies. By simulating the indium Czochralski purification process using coupled multiphysics fields, the effect of an external magnetic field on suppressing melt flow and stabilizing the solid / liquid interface is obtained. A mapping relationship between "process parameters, interface data, and impurity concentration" is established. Through process optimization using a learning model, a process control scheme for stabilizing the solid / liquid interface is obtained, providing a basis for guiding the stable production of 8N high-purity indium through crystal Czochralski purification.

[0005] To achieve the above objectives, this invention provides a method for controlling the solid / liquid interface of the solution in indium Czochralski purification based on numerical simulation optimization. This method, based on multiphysics numerical simulation, obtains a process control scheme for a stable solid / liquid interface by establishing a mapping relationship between an external magnetic field and process parameters, interface data, and impurity concentration. The method includes the following steps:

[0006] S1. Obtain raw data on the properties of the Czochralski furnace and indium, calculate the geometric model and mesh, and establish a multi-physics, multi-phase mathematical model.

[0007] S2. Based on historical experimental data, set boundary conditions to simulate the key processes of indium Czochralski purification, including crystal pulling, shoulder formation, and equal diameter formation.

[0008] S3. Coupled multiphysics field analysis to analyze the changes in the solid / liquid interface of the solution during the Czochralski process;

[0009] S4. Construct a deep reinforcement learning model to establish the mapping relationship between process parameters, interface data, and impurity concentration;

[0010] S5. The process adopts a closed-loop iteration of "prediction-verification-optimization" to obtain synergistically controllable process parameters.

[0011] Furthermore, in step S1, the data obtained for the Czochralski furnace include the heater, crucible, seed crystal, furnace body geometry and dimensions; the indium physical properties obtained include melting point, latent heat, density, thermal conductivity, specific heat capacity, and viscosity; and the mathematical models include fluid transport model, electromagnetic field control equations, and heat transfer model.

[0012] The fluid transport model includes mass conservation, momentum conservation, and the large eddy simulation governing equations; the heat transfer model includes the change in total energy during the fluid heat transfer process, the enthalpy change rate equation, and the heat transfer equation within the solid. Based on the original data, basic models, and equations, a mathematical model is constructed to facilitate comprehensive calculation and analysis of the simulation process.

[0013] Furthermore, in step S2, the experimental historical data is the data obtained from the Czochralski process for purifying indium, which includes the indium raw material composition, Czochralski speed, Czochralski temperature, Czochralski time, crucible rotation speed, seed crystal rotation speed, furnace pressure, and the indium composition of the experimental results.

[0014] Furthermore, in step S2, the boundary conditions for each stage of the Czochralski process are set as follows: the outer wall of the furnace is an adiabatic boundary condition; the pressure inside the furnace cavity is set to 0.1-0.5 Pa; the graphite and quartz crucibles and the heating element are in face-to-face radiation; the heat at the interface between the crucible and the molten pool is conserved; the molten pool surface and the gas are in convection; the input power of the heating element is used as the heat source; the molten pool wall and surface are insulated boundary conditions; the initial temperature of the seed crystal is 300-600 K; the thermal boundary condition is HeatFlux calculated using full-size thermal field; the molten pool surface is a free-slip boundary condition; the horizontal rotation speed of the sidewalls and bottom is set to be consistent with the crucible rotation speed, 3-10 rpm; the horizontal rotation speed of the crystal rod sidewall is set to be consistent with the crystal rod rotation speed, 3-10 rpm; the crystal rod pulling adopts a moving grid, and the moving speed is consistent with the crystal rod pulling speed, 3-35 mm / h; the crystal rod wall is an insulated boundary condition (the current component in the interface normal direction is zero); the magnetic flux and current at the solid / liquid interface are conserved (the current components in the interface normal direction are equal).

[0015] Furthermore, in step S2, the LES large eddy model and the SST turbulence model are selected to simulate the direct pulling process, and the temperature-flow field distribution and the changes in the solid / liquid interface of the solution are analyzed to obtain basic information about the normal direct pulling process.

[0016] Furthermore, in step S3, the evolution law of the solid / liquid interface of the solution is analyzed by examining the interaction between the external magnetic field and the temperature-flow field of the solution.

[0017] Furthermore, the applied magnetic field includes a horizontal magnetic field and a vertical magnetic field, with a magnetic field strength of 0.1-0.5T.

[0018] Furthermore, in step S4, based on the numerical simulation results and combined with process parameter data, a deep reinforcement learning model is constructed, and a multivariate multi-objective optimization algorithm is used to establish a mapping relationship between process parameters, interface data, and impurity concentration.

[0019] Furthermore, high-speed photography and image recognition techniques are used to acquire melt pool interface data such as crystal morphology and crystal curvature. This melt pool interface data reflects the stability of the solid / liquid interface of the melt, aiming to convert abstract images into repeatable data. The process parameters include the applied magnetic field strength, Czochralski temperature, Czochralski speed, furnace pressure, Czochralski time, crucible rotation speed, and seed crystal rotation speed.

[0020] Furthermore, in step S5, the process involves a closed-loop iteration of "prediction-verification-optimization". Based on the prediction of the learning model, experimental verification is performed, the process is optimized, and then fed back into the model for further training and prediction. This process is iterated repeatedly to form a closed-loop optimization model. The optimal process parameters are selected as the control scheme for stabilizing the solid / liquid interface, resulting in 8N high-purity indium.

[0021] Compared with the prior art, the present invention has the following advantages:

[0022] (1) This invention establishes a mathematical model of multi-physics field and multi-phase indium Czochralski purification process, and obtains the temperature-flow field distribution and its interaction with the external magnetic field in key stages such as crystal pulling, shoulder formation and equal diameter. This solves the problem of unclear understanding of the temperature and flow field distribution law in the melt in actual production.

[0023] (2) This invention simulates the direct pulling process using the LES large eddy model and the SST turbulence model, and clarifies the role of the external magnetic field in suppressing melt flow and stabilizing the solid / liquid interface of the melt, providing a solution for actual stable production;

[0024] (3) This invention establishes a mapping relationship between process parameters, interface data, and impurity concentration, providing a theoretical basis for subsequent research on the influence of process parameters on the evolution of the solid / liquid interface of the solution, stability control, and impurity distribution behavior;

[0025] (4) The crystal Czochralski process learning model formed by the present invention has a closed-loop iteration of process “prediction-verification-optimization”, which can be used for the optimization and precise control of process parameters, promote the quality improvement and upgrading of high-purity indium, obtain 8N high-purity indium, and has important guiding role in actual production. Attached Figure Description

[0026] Figure 1 This is a flowchart of the present invention based on numerical simulation to optimize the control of the solid / liquid interface in the indium Czochralski purification process;

[0027] Figure 2 This is a simulated geometric model established in the embodiments of the present invention;

[0028] Figure 3 This refers to the solid / liquid interface changes during different stagnation times in the crystal-leading stage of this invention.

[0029] Figure 4 This describes the temperature field distribution at different stages of the shoulder-laying phase in an embodiment of the present invention.

[0030] Figure 5 This describes the temperature field, flow field distribution, and solid / liquid interface morphology during the constant diameter stage in this embodiment of the invention.

[0031] Figure 6 This is the temperature distribution cloud of the magnetic field-stabilized solid / liquid interface flow field in an embodiment of the present invention. Detailed Implementation

[0032] To more clearly illustrate the purpose, technical solutions, and advantages of the embodiments of the present invention, the present invention will be further described below in conjunction with the accompanying drawings and embodiments. The scope of protection of the present invention is not limited to the embodiments mentioned herein.

[0033] The following description, with reference to the figures, illustrates this embodiment. This embodiment of the invention provides a method for optimizing the solid / liquid interface control in indium Czochralski purification based on numerical simulation. Based on multiphysics numerical simulation, a stable solid / liquid interface process control scheme is obtained by establishing a mapping relationship between an external magnetic field and process parameters, interface data, and impurity concentration. The method includes the following steps, see... Figure 1 :

[0034] S1. Obtain raw data on the properties of the Czochralski furnace and indium, calculate the geometric model and mesh, and establish a multi-physics, multi-phase mathematical model.

[0035] S2. Based on historical experimental data, set boundary conditions to simulate the key processes of indium Czochralski purification, including crystal pulling, shoulder formation, and equal diameter formation.

[0036] S3. Coupled multiphysics field analysis to analyze the changes in the solid / liquid interface of the solution during the Czochralski process;

[0037] S4. Construct a deep reinforcement learning model to establish the mapping relationship between process parameters, interface data, and impurity concentration;

[0038] S5. The process adopts a closed-loop iteration of "prediction-verification-optimization" to obtain synergistically controllable process parameters.

[0039] In step S1 of this embodiment, data on the Czochralski furnace is acquired, including the heater, crucible, seed crystal, and the geometry and dimensions of the furnace body; indium physical properties are acquired, including melting point, latent heat, density, thermal conductivity, specific heat capacity, and viscosity; mathematical models are established, including a fluid transport model, electromagnetic field control equations, and a heat transfer model; wherein the fluid transport model includes mass conservation, momentum conservation, and large eddy simulation control equations; the heat transfer model includes the change in total energy during the fluid heat transfer process, the enthalpy change rate equation, and the solid internal heat transfer equation.

[0040] In the embodiments, the established geometric model is as follows: Figure 2 As shown, the number of grids in the computational domain is 1,383,200.

[0041] In this embodiment, electromagnetic braking is used to control the flow. The magnetic field simulation involves fundamental electromagnetic theory, specifically Maxwell's equations, which consist of four equations that explain the relationship between electricity and magnetism. Their differential form is as follows:

[0042]

[0043] Formula (1) is Gauss's electric field law: the divergence of the electric field is proportional to the charge density at that point, which describes the relationship between charge and electric field.

[0044] Formula (2) is Gauss's law of magnetic fields: the divergence of a magnetic field is zero everywhere. This means that the magnetic flux through any closed surface is zero, i.e., magnetic monopoles do not exist.

[0045] Formula (3) is Faraday's law: the curl of the induced electric field is equal to the rate of change of the magnetic induction intensity, which shows that a magnetic field that changes with time can induce an electric field.

[0046] Formula (4) is the Ampere-Maxwell law: the curl of the induced magnetic field is equal to the sum of the current density and the rate of change of the electric field strength, that is, the magnetic field can be generated by the current or by the electric field that changes with time.

[0047] In this embodiment, the total energy during fluid heat transfer is divided into internal energy e and kinetic energy. The rate of change of total energy is:

[0048]

[0049] enthalpy is Equation for the rate of change of enthalpy:

[0050]

[0051] Where r is the heat source and Rad is radiant heat.

[0052] Heat transfer equation inside a solid:

[0053]

[0054] Where α = k / cp, thermal diffusivity = thermal conductivity / specific heat.

[0055] In step S2 of the embodiment, the data is based on experimental and production multidimensional historical data, including the composition of the indium raw material used for Czochralski purification, Czochralski speed, Czochralski temperature, Czochralski time, crucible rotation speed, seed crystal rotation speed, furnace pressure, and the indium composition of the experimental results.

[0056] The LES large eddy model was selected to simulate the crystal formation and shoulder formation process, while the LES large eddy model and the SST turbulence model were used to simulate the constant diameter process.

[0057] In this embodiment, the boundary conditions for the crystal pulling process are as follows: the initial temperature of the seed crystal is 300K; the thermal field of the molten pool is the temperature field calculated using the full-size thermal field before mapping; the thermal boundary condition is Heat Flux calculated using the full-size thermal field; the molten pool surface is a free-slip boundary condition; the horizontal rotation speed of the sidewalls and bottom is set to be the same as the crucible rotation speed, 10 rpm; the horizontal rotation speed of the crystal rod sidewall is set to be the same as the crystal rod rotation speed, 10 rpm; the crystal rod pulling adopts a moving mesh, and the moving speed is the same as the crystal rod pulling speed, 25 mm / h. The solid / liquid interface changes during different stagnation times in the crystal pulling process are as follows: Figure 3 As shown, the solid / liquid interface increases with the increase of the dwell time, and as the seed crystal is pulled, the solid / liquid interface gradually shrinks and moves upward.

[0058] In this embodiment, the boundary conditions for the shoulder-forming process are as follows: the molten pool thermal field is the temperature field calculated using the full-size thermal field before mapping; the thermal boundary condition uses Heat Flux calculated using the full-size thermal field; the molten pool surface is a free-slip boundary condition; the sidewalls and bottom are set with a horizontal rotation speed consistent with the crucible rotation speed, 10 rpm; the crystal rod sidewalls are set with a horizontal rotation speed consistent with the crystal rod rotation speed, 10 rpm; the crystal rod pulling uses a moving mesh, with a moving speed consistent with the crystal rod pulling speed, 35 mm / h. The temperature field distribution at different stages of the shoulder-forming process is as follows. Figure 4 As shown, with increasing time, the solid / liquid interface extends outwards, its maximum diameter increases, forming an inverted conical shoulder. This also causes changes in the position and morphology of the solid / liquid interface.

[0059] In this embodiment, the boundary conditions for the constant diameter process are as follows: the molten pool thermal field maps to the temperature field calculated from the full-size thermal field beforehand; the thermal boundary condition uses Heat Flux calculated from the full-size thermal field; the molten pool surface is a free-slip boundary condition; the sidewalls and bottom are set with horizontal rotation speeds consistent with the crucible rotation speed, 5 rpm and 10 rpm; the crystal rod sidewalls are set with horizontal rotation speeds consistent with the crystal rod rotation speed, 5 rpm and 10 rpm; the crystal rod pulling uses a moving mesh, with a moving speed consistent with the crystal rod pulling speed, 10 mm / h and 30 mm / h. Different electrical conductivities are set for the indium crystal and liquid states; the molten pool wall and liquid surface are insulating boundary conditions; the crystal rod wall is an insulating boundary condition (the current component in the interface normal direction is zero); the magnetic flux and current at the solid / liquid interface are conserved (the current components in the interface normal direction are equal). The transient temperature field and flow field distributions for each stage of the constant diameter process are shown in [reference needed]. Figure 5 (a) The flow within the crucible is highly complex. As the crystal is pulled out, the temperature change within the molten pool is significant. The temperature begins to decrease at the center and bottom of the crucible, and solidification even occurs. At the solid / liquid interface, there are two additional small eddies. The generation of these eddies can disrupt the stability of the solid / liquid interface, potentially leading to a reduction in the diameter of the crystal rod or even breakage. The temperature distribution and solid / liquid interface morphology at different speeds are shown in the figure. Figure 5 (b) As the pulling speed increases, the interface gradually bulges upward. Because the crystal cannot solidify quickly enough, the central part of the solidification front shifts upward, indicating that heat transfer in the vertical direction of the central region is hindered; the flow field vectors at different crucible rotation speeds are as follows: Figure 5 (c) The main flow inside the crucible is characterized by two large eddies on the left and right. As the crucible speed increases, small eddies appear below the liquid surface, which is not conducive to crystal growth.

[0060] In step S3 of the embodiment, an external magnetic field, temperature field, and flow field are coupled. When no electromagnetic field is applied, the turbulence is mainly concentrated in the central region and exhibits an elliptical distribution. After the electromagnetic field is applied, the turbulence viscosity exhibits a symmetrical distribution from left to right. Figure 6The temperature distribution cloud formed at the solid / liquid interface when the magnetic field strength is 0.3T shows that the temperature tends to be symmetrically distributed. It can be seen that applying a vertical magnetic field hinders heat transfer along the vertical direction, suppresses the flow intensity of the melt, and stabilizes the melt. A reasonable magnetic field is conducive to stabilizing the flow field and optimizing the temperature distribution.

[0061] In step S4 of the embodiment, based on the numerical simulation results, interface data of the curvature of the melt crystal is obtained by high-speed photography and image recognition. Combined with process parameter data, a deep reinforcement learning model is constructed. Using a multivariate multi-objective optimization algorithm, a mapping relationship between process parameters (external magnetic field strength, Czochralski temperature, Czochralski speed, furnace pressure, Czochralski time, crucible rotation speed, seed crystal rotation speed) - crystal curvature - impurity concentration is established.

[0062] In step S5 of Example, the experimental verification is carried out based on the prediction of the Czochralski purification learning model, the process is optimized, and then fed back into the model for further training and prediction. The process is iterated repeatedly to form a closed-loop optimization model, and the optimal process parameters are selected as the control scheme for stabilizing the solid / liquid interface.

[0063] In the embodiment, 6N and above indium were used as raw materials, and the optimal parameters were adopted. The process was carried out through four stages: the first stage was at a temperature of 300-600℃ for 1 hour; the second stage was at a temperature of 120-130℃ for 0.05-0.1 hours; the third stage was at a temperature of 130-140℃ for 0.5-1 hours; and the fourth stage was at a temperature of 150-160℃ for 4-5 hours, so as to stably obtain 8N high-purity indium.

[0064] 1. Purity testing

[0065] The high-purity indium obtained in the examples was subjected to GDMS purity analysis. The purity of all elements (73 impurity elements) was below the instrument detection limit, meeting the requirements of the 8N high-purity indium industry standard. Some key elements are shown in Table 1:

[0066] Table 1 Results of some key elements

[0067]

[0068] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make many modifications and variations based on the concept of the present invention without creative effort, and all such modifications and variations should be within the scope of protection defined by the claims.

Claims

1. A method for controlling the solid / liquid interface of the solution in the Czochralski purification process based on numerical simulation optimization, characterized in that, Based on multiphysics numerical simulation, a process control scheme for a stable solution solid / liquid interface is obtained by establishing a mapping relationship between an external magnetic field and process parameters, interface data, and impurity concentration. The scheme includes the following steps: S1. Obtain raw data on the properties of the Czochralski furnace and indium, calculate the geometric model and mesh generation, and establish a mathematical model; the mathematical model includes a fluid transport model, electromagnetic field control equations, and heat transfer model. S2. Based on historical experimental data, boundary conditions were set to simulate the key processes of indium Czochralski purification, including seeding, shoulder formation, and equal diameter determination. The LES large eddy model and SST turbulence model were selected to simulate the Czochralski process, analyzing the temperature-flow field distribution and the changes in the solid / liquid interface of the melt. The boundary conditions included: the furnace outer wall as an adiabatic boundary condition; the furnace cavity pressure set to 0.1-0.5 Pa; face-to-face radiation between the graphite and quartz crucibles and the heating element; heat conservation at the crucible-molten pool interface; convective boundary conditions between the molten pool surface and the gas; the input power of the heating element as the heat source; and the molten pool wall and surface as insulating boundary conditions. The initial seed crystal temperature was 300-600 K. The thermal boundary condition was calculated using the full-size thermal field Heat field model. Flux, the molten pool surface is a free-slip boundary condition, the sidewalls and bottom are set with a horizontal rotation speed consistent with the crucible rotation speed, 3~10 rpm, the crystal rod sidewalls are set with a horizontal rotation speed consistent with the crystal rod rotation speed, 3~10 rpm, the crystal rod pulling adopts a moving grid, the moving speed is consistent with the crystal rod pulling speed, 3~35 mm / h, the crystal rod wall is an insulating boundary condition, the current component in the interface normal direction is zero, the magnetic flux and current at the solid / liquid interface are conserved, and the current components in the interface normal direction are equal; S3. Coupled multiphysics field analysis to analyze the changes in the solid / liquid interface of the solution during the Czochralski process; S4. Construct a deep reinforcement learning model to establish the mapping relationship between process parameters, interface data, and impurity concentration; S5. The process adopts a closed-loop iteration of "prediction-verification-optimization" to obtain synergistically controllable process parameters.

2. The control method according to claim 1, characterized by: In step S1: data on the Czochralski furnace is obtained, including the heater, crucible, seed crystal, furnace geometry and dimensions; indium physical properties are obtained, including melting point, latent heat, density, thermal conductivity, specific heat capacity and viscosity.

3. The control method according to claim 2, characterized in that: The fluid transport model includes mass conservation, momentum conservation, and large eddy simulation control equations; the heat transfer model includes the change in total energy during the fluid heat transfer process, the enthalpy change rate equation, and the heat transfer equation within the solid.

4. The control method according to claim 1, characterized by: In step S2, the experimental historical data is the data obtained from the Czochralski purification process experiment, which includes the indium raw material composition, process parameters and experimental results. This includes the indium raw material composition for crystal Czochralski, Czochralski speed, Czochralski temperature, Czochralski time, crucible rotation speed, seed crystal rotation speed, furnace pressure and the indium composition of the experimental results.

5. The control method according to claim 1, characterized by: In step S3, the evolution law of the solid / liquid interface of the solution is analyzed by the interaction of the external magnetic field on the temperature-flow field of the solution.

6. The control method according to claim 5, characterized in that: The applied magnetic field includes a horizontal magnetic field and a vertical magnetic field, with a magnetic field strength of 0.1-0.5T.

7. The control method according to claim 1, characterized by: In step S4, based on the numerical simulation results, high-speed photography and image recognition are used to obtain melt pool interface data of crystal morphology and crystal curvature. Combined with process parameter data, a deep reinforcement learning model is constructed, and a multivariate multi-objective optimization algorithm is used to establish a mapping relationship between process parameters, interface data and impurity concentration. The stability of the solid / liquid interface of the melt is reflected by the data of the molten pool interface; the process parameters include the applied magnetic field strength, Czochralski temperature, Czochralski speed, furnace pressure, Czochralski time, crucible rotation speed, and seed crystal rotation speed.

8. The control method according to claim 1, characterized by: In step S5, the process undergoes a closed-loop iteration of "prediction-verification-optimization". The prediction is verified by experiments based on the learning model, and then the process is optimized. The results are fed back into the model for further training and prediction. This process is iterated repeatedly to form a closed-loop optimization model. The optimal parameters are selected as the process control scheme for stabilizing the solid / liquid interface of the solution, resulting in 8N high-purity indium.

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