A method for determining silicon carbide crystal growth parameters based on active learning

Abstract

The application provides a silicon carbide crystal growth parameter determination method based on active learning, and relates to the technical field of crystal growth. The method comprises the following steps: constructing a numerical simulation model corresponding to a silicon carbide crystal growth process; extracting a working condition parameter sample of the silicon carbide crystal growth process by using a Latin hypercube algorithm; obtaining a characteristic position temperature corresponding to the working condition parameter sample by using the numerical simulation model; constructing an active learning Gaussian process regression model based on the working condition parameter sample and the characteristic position temperature through prediction uncertainty iterative updating; and determining the growth parameter of the silicon carbide crystal by using the active learning Gaussian process regression model. The embodiment of the application is favorable for greatly reducing the calculation cost and time cost of experiments and multi-physical field numerical simulation, and improving the accuracy and efficiency of the determination process of the silicon carbide crystal growth parameter under complex working conditions.

Description

Technical Field

[0001] This invention relates to the field of crystal growth technology, and in particular to a method for determining silicon carbide crystal growth parameters based on active learning. Background Technology

[0002] Silicon carbide (SiC) is a third-generation wide-bandgap semiconductor material with high breakdown electric field, high thermal conductivity, high saturated electron drift velocity, excellent chemical stability and good radiation resistance, and has broad application prospects in the field of high-power electronic devices.

[0003] Currently, the Physical Vapor Transport (PVT) method is generally used to prepare SiC single crystals. In this method, an axial temperature gradient is formed inside the crucible of the growth furnace, which causes the SiC raw material at the bottom of the crucible to sublimate into gaseous components under high temperature conditions. Driven by the temperature difference, the gaseous components are transported to the low-temperature region at the top, and finally deposited and recrystallized on the surface of the SiC seed crystal to form a SiC ingot with a certain thickness.

[0004] However, since SiC crystal growth is usually carried out in a high-temperature, low-pressure, and closed reaction environment, it is difficult to directly observe the real-time changes in the temperature field inside the growth furnace. At the same time, since SiC crystal growth involves many parameters, including heating current and voltage, physical and structural parameters of graphite parts, physical and structural parameters of insulation layer, powder amount, etc., which correspond to a variety of working conditions and have different effects on crystal quality, studying a large number of parameters to optimize crystal quality requires a large number of experiments, which is extremely costly and inefficient. Summary of the Invention

[0005] This invention provides a method for determining silicon carbide crystal growth parameters based on active learning, which can solve the problems of high experimental cost and low efficiency in the determination process of silicon carbide crystal growth parameters in related technologies.

[0006] To address the aforementioned problems, this invention discloses a method for determining silicon carbide crystal growth parameters based on active learning. The method includes: constructing a numerical simulation model corresponding to the silicon carbide crystal growth process; extracting operating parameter samples of the silicon carbide crystal growth process using the Latin hypercube algorithm; obtaining the characteristic location temperature corresponding to the operating parameter samples using the numerical simulation model; constructing an active learning Gaussian process regression model based on the operating parameter samples and the characteristic location temperature through iterative updates of prediction uncertainty; and determining the growth parameters of the silicon carbide crystal using the active learning Gaussian process regression model.

[0007] Compared with related technologies, the embodiments of the present invention have the following advantages: The active learning-based method for determining silicon carbide crystal growth parameters provided in this invention constructs a numerical simulation model corresponding to the silicon carbide crystal growth process and uses the Latin hypercube algorithm to extract operating condition parameter samples of the silicon carbide crystal growth process. This allows for efficient screening of representative operating condition parameter samples that can characterize the multidimensional operating condition regularity within the entire operating condition parameter value space, enabling small-sample calculations to replace complex operating condition calculations. Then, the numerical simulation model is used to calculate the characteristic location temperature corresponding to the operating condition parameter samples. Based on the operating condition parameter samples and characteristic location temperatures, an active learning Gaussian process regression model is constructed through iterative updates of prediction uncertainty. This facilitates the continuous supplementation of effective operating condition parameter samples, efficiently improving the temperature prediction accuracy of the active learning Gaussian process regression model. Finally, the active learning Gaussian process regression model is used to determine the growth parameters of the silicon carbide crystal in real time. This significantly reduces the computational and time costs of experiments and multiphysics numerical simulations, and improves the accuracy and efficiency of determining silicon carbide crystal growth parameters under complex operating conditions. Attached Figure Description

[0008] Figure 1 This is a flowchart of a method for determining silicon carbide crystal growth parameters based on active learning, provided in an embodiment of the present invention. Figure 1 ; Figure 2 This is a cross-sectional structural schematic diagram of an induction heating growth furnace provided in an embodiment of the present invention; Figure 3 This is a flowchart of a method for determining silicon carbide crystal growth parameters based on active learning, provided in an embodiment of the present invention. Figure 2 ; Figure 4 This is a flowchart of a method for determining silicon carbide crystal growth parameters based on active learning, provided in an embodiment of the present invention. Figure 3 ; Figure 5 This is a schematic diagram of the temperature field distribution in a growth furnace provided in an embodiment of the present invention; Figure 6 This is a logic block diagram of a working condition parameter provided in an embodiment of the present invention; Figure 7 This is a flowchart of a method for determining silicon carbide crystal growth parameters based on active learning, provided in an embodiment of the present invention. Figure 4 ; Figure 8 This is a logical block diagram of a parameter temperature dataset provided in an embodiment of the present invention; Figure 9 This is a flowchart of a method for determining silicon carbide crystal growth parameters based on active learning, provided in an embodiment of the present invention. Figure 5 ; Figure 10This is a performance variation graph of an active learning Gaussian process regression model provided in an embodiment of the present invention; Figure 11 This is a comparison chart of the actual temperature values ​​and the model-predicted temperature values ​​at the center of the top of the crucible and the center of the bottom of the heating cylinder, provided by an embodiment of the present invention. Figure 12 This is a flowchart of a method for determining silicon carbide crystal growth parameters based on active learning, provided in an embodiment of the present invention. Figure 6 ; Figure 13 This is a flowchart of a method for determining silicon carbide crystal growth parameters based on active learning, provided in an embodiment of the present invention. Figure 7 ; Figure 14 This is a logic block diagram of a silicon carbide crystal growth parameter determination device based on active learning provided in an embodiment of the present invention.

[0009] Explanation of reference numerals in the attached figures: 11-Heating cylinder; 12-Crucible; 13-Crucible lid; 14-Silicon carbide seed crystal; 15-Insulation layer; 16-Induction coil; 17-Silicon carbide powder. Detailed Implementation

[0010] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0011] Method Implementation Examples Currently, the most widely used method in SiC single crystal preparation is the physical vapor transport method. This method utilizes the axial temperature gradient (high temperature at the bottom and low temperature at the top) formed inside the crucible of the growth furnace to cause the SiC raw material at the bottom of the crucible to sublimate into gaseous components under high temperature conditions. Driven by the temperature difference, the gaseous components are transported to the low temperature region at the top and eventually deposited and recrystallized on the surface of the SiC seed crystal. As the growth process continues, a SiC ingot with a certain thickness gradually forms on the surface of the seed crystal.

[0012] In terms of heating methods, SiC raw materials are generally heated in two ways: induction heating and resistance heating. Induction heating involves inputting high-frequency alternating current into an induction coil, causing the crucible and surrounding graphite components to generate induced heat. This heat is then transferred to the SiC powder inside the crucible via heat conduction and radiation, thus achieving sublimation growth. Resistance heating involves passing current through a heating element (such as a graphite heating element or resistance wire), utilizing the Joule effect of the heating element material to directly generate heat. This heat is then transferred to the SiC powder inside the crucible via heat conduction and radiation, thus achieving sublimation growth. During SiC crystal growth, the temperature field distribution within the furnace directly affects the gas-phase mass transport behavior and the formation and evolution of defects within the crystal, thus playing a decisive role. However, since crystal growth is usually carried out in a high-temperature, low-pressure, and closed reaction environment, it is difficult to directly observe the real-time changes in the temperature field within the growth furnace, which increases the difficulty of process optimization and mechanism research. Meanwhile, since silicon carbide crystal growth involves many parameters, including current and voltage for induction or resistance heating, physical and structural parameters of graphite parts, physical and structural parameters of insulation layer, powder amount, etc., which correspond to a variety of working conditions and have different effects on crystal quality, studying these numerous parameters to optimize crystal quality requires a large number of experiments, which is extremely costly and inefficient.

[0013] Numerical simulation technology is widely used because it can calculate all temperature and flow field information during SiC crystal growth. However, due to the complexity of the SiC crystal growth process, accurate numerical simulation often requires consideration of the coupling effects of multiple physics fields, including electromagnetic, heat transfer, and component transport numerical models. This requires a significant amount of time to achieve computational convergence, and numerous calculations are needed under complex conditions to obtain accurate patterns, resulting in low research efficiency. Existing crystal growth optimization methods also face high cost and efficiency issues when optimizing crystal growth interfaces or stress defects, regardless of whether experimental or numerical simulation methods are used, due to the complexity of the operating conditions. Experimentally, it is usually necessary to continuously adjust structural and process parameters through numerous experiments and repeated verification, which is not only time-consuming and costly but also yields limited optimization results. While numerical simulation can study temperature field changes by adjusting parameters, the large number of structural and process parameters involved makes it difficult for traditional single-factor or multi-factor analysis methods to quickly find the optimal solution, also requiring significant computation time and resulting in low optimization efficiency. Therefore, existing optimization methods for SiC single crystal growth using the PVT method often suffer from the following problems: (1) Crystal growth experiments are difficult to obtain useful information, have complex operating conditions, and are costly: In the process of growing SiC crystals by physical vapor transport, SiC powder sublimates into a gas phase only when the temperature in the growth furnace reaches 2100℃~2300℃ and the pressure is low, and is then transported to the SiC seed crystal for crystallization under the action of the temperature gradient. Due to the excessively high internal temperature and the presence of opaque graphite parts and insulation layers, it is impossible to observe the internal temperature field, flow field, and crystal growth process. Since SiC crystal growth is greatly affected by the temperature field, flow field, and pressure field, many parameters are involved internally. Different parameters have different effects on the temperature field and flow field of crystal growth, thus affecting the quality of crystal growth. Then, studying these numerous parameters to optimize the quality of crystal growth requires a large number of experiments, which incurs extremely high experimental costs.

[0014] (2) Existing numerical simulations of crystal growth are time-consuming and inefficient when considering the effects of multiple physics: Numerical simulation technology can analyze the temperature field and flow field during crystal growth by constructing corresponding numerical models, and study the influence of the temperature field and flow field on the interface shape or stress defects of crystal growth. Due to the complex physical phenomena such as electromagnetic, heat transfer and component transport involved in the growth of SiC crystals by PVT method, existing numerical simulation technology often requires multiple models or multiple software programs to calculate when considering the coupling effect of multiple physics. In order to make the calculation accurate, a lot of time is required to achieve calculation convergence. Moreover, under a large number of complex working conditions, a large number of calculation examples are required to obtain accurate laws, resulting in low research efficiency.

[0015] (3) Traditional crystal growth optimization methods are simple and have low efficiency: Due to the complexity of the working conditions, when optimizing the crystal growth interface or stress defects, from the experimental level, a large number of experiments can be conducted to continuously adjust the structural parameters, process parameters, etc. to optimize the crystal quality. However, this requires a lot of experimental costs and time, and often the results are minimal. From the numerical simulation level, structural parameters, process parameters, etc. can be adjusted on the numerical model and simulated to study the optimized temperature field. However, due to the large number of structural parameters and process parameters, traditional single or multi-factor modifications are difficult to accurately find the optimal value. This also requires a lot of computational costs and time, and the results are also low.

[0016] To address the aforementioned problems, this invention provides a flowchart of a method for determining silicon carbide crystal growth parameters based on active learning, as shown in the following embodiments. Figure 1 The method may specifically include the following steps: Step S101: Construct a numerical simulation model corresponding to the silicon carbide crystal growth process.

[0017] Step S102: Extract the operating parameters of the silicon carbide crystal growth process using the Latin hypercube algorithm.

[0018] Step S103: Using the numerical simulation model, obtain the characteristic location temperature corresponding to the working condition parameter sample.

[0019] Step S104: Based on the operating condition parameter samples and the temperature at the characteristic location, construct an active learning Gaussian process regression model by iteratively updating the prediction uncertainty.

[0020] Step S105: Use the active learning Gaussian process regression model to determine the growth parameters of silicon carbide crystals.

[0021] The method for determining silicon carbide crystal growth parameters based on active learning provided in this invention can be applied to any electronic device capable of numerical simulation. This electronic device may include, but is not limited to, mobile terminals such as laptops, personal digital assistants (PDAs), handheld devices, and computing devices, as well as fixed terminals such as digital TVs and desktop computers.

[0022] In some embodiments, silicon carbide crystal refers to silicon carbide single crystal grown using the PVT method.

[0023] The growth parameters of silicon carbide crystals refer to the operating conditions and / or characteristic temperature involved in the growth of silicon carbide crystals using the PVT method.

[0024] Reference Figure 2 This diagram illustrates a cross-sectional structure of an induction heating growth furnace according to an embodiment of the present invention. The growth furnace includes a heating cylinder 11, a crucible 12, a crucible cover 13, a silicon carbide seed crystal 14, a heat insulation layer 15, an induction coil 16, and silicon carbide powder 17. The induction heating growth furnace generates induced heat in the crucible 12 and its external heating cylinder 11 by passing high-frequency alternating current through the induction coil 16. The heat is then transferred to the silicon carbide powder 17 inside the crucible 12 via conduction and radiation, and continues to rise under the insulation effect of the heat insulation layer 15. When the temperature reaches a certain level, the silicon carbide powder 17 sublimates, forming a gaseous component, which is transported to the cooler crucible cover 13. The silicon carbide seed crystal 14, located on the crucible cover 13, is deposited and recrystallized. As the growth process continues, the silicon carbide seed crystal 14 gradually forms a silicon carbide ingot of a certain thickness.

[0025] In some embodiments, the crucible, heating cylinder, and crucible lid may be made of graphite. The insulation layer may be made of insulating felt.

[0026] In step S101, the electronic device can construct a numerical simulation model based on the fundamental principles of silicon carbide crystal growth using the PVT method. In some embodiments, refer to Figure 3The heating methods for silicon carbide powder include induction heating and resistance heating. The numerical simulation model constructed by the electronic device in step S101 includes an electromagnetic thermal coupling numerical simulation model and a resistance heating numerical simulation model. The construction of the numerical simulation model corresponding to the silicon carbide crystal growth process in step S101 includes: Step S1011: Establish a heat transfer model based on the heat transfer mode of silicon carbide crystals grown by the PVT method.

[0027] Step S1012: Establish an electromagnetic induction model based on electromagnetic field theory.

[0028] Step S1013: Calculate the volumetric heat generation rate of the solid components in the growth furnace.

[0029] Step S1014: Construct a numerical simulation model of silicon carbide electromagnetic thermal coupling.

[0030] Step S1015: Calculate the volumetric heat generation rate of the heater based on the heating power and the heater volume.

[0031] Step S1016: Construct a numerical simulation model of silicon carbide resistance heating.

[0032] Specifically, for induction heating applications, in step S101, the electronic device can construct a silicon carbide electromagnetic-thermal coupling numerical simulation model through steps S1011 to S1014. For resistance heating applications, in step S101, the electronic device can construct a silicon carbide resistance heating numerical simulation model through steps S1011, S1015, and S1016.

[0033] Specifically, in step S1011, the electronic device can construct a numerical heat transfer model based on the heat transfer forms of heat conduction and heat radiation present in the growth furnace during the growth of silicon carbide crystal by the PVT method. The numerical heat transfer model includes heat transfer control equations based on heat conduction and radiation transfer equations based on heat radiation.

[0034] The heat transfer control equations satisfied by each solid component in the growth furnace are as follows: (1) in, This represents the Hamiltonian differential operator, used for mathematical operations on spatial gradients and divergences; Thermal conductivity of a solid component, expressed in W·m. -1 ·K -1 ; This represents the thermodynamic temperature corresponding to a spatial location in the computational domain, in Kelvin (K). This represents the temperature gradient, used to characterize the rate of change of temperature at various spatial points within the computational domain with respect to spatial coordinates.

[0035] Solid components include, for example Figure 2 The heating cylinder 11, crucible 12, crucible lid 13, silicon carbide seed crystal 14, insulation layer 15, induction coil 16, and silicon carbide powder 17 are shown.

[0036] When radiant energy in the growth furnace passes through a semi-transparent participating medium, it may be absorbed, scattered, and emitted by the medium, thus changing its spatial position. Along a specific direction The radiation transfer equation is: (2) in, Represents a spatial position vector within a semi-transparent participating medium; and These are unit vectors representing the incident and outgoing directions of radiation, respectively. Indicates the direction of radiation propagation The travel length, in meters (m); Indicates position along The spectral radiance in the direction, expressed in W·m 2 ·sr 1 ; The absorption coefficient of a semi-transparent participating medium is expressed in m. -1 ; The scattering coefficient of a semi-transparent participating medium is expressed in m. -1 ; Represents the refractive index of a semi-transparent participating medium; This represents the Stefan-Boltzmann constant, with units of W·m. -2 ·K -4 , ; The local thermodynamic temperature of the semi-transparent participating medium is expressed in K. Indicates direction Scattered to direction The scattering phase function; Represents the solid angle in space, with the unit being steradian degrees (sr).

[0037] In some embodiments, the semi-transparent participating medium refers to the inert gas filled in the growth furnace, which may include, but is not limited to, argon, helium, etc.

[0038] In step S1012, for induction heating, an electromagnetic induction model is established based on electromagnetic field theory. Specifically, based on the fundamental theory of electromagnetic fields, the governing equations for the induction heating process in cylindrical coordinates are established as the electromagnetic induction model. (3) (4) (5) In formula (4), This represents the alternating excitation current density applied to the induction coil region; This represents the circumferential induced eddy current density generated in solid components outside the induction coil in the growth furnace under the influence of the induced magnetic field.

[0039] in, This represents the radial coordinate in a cylindrical coordinate system, with units of meters (m). This represents the axial coordinate in a cylindrical coordinate system, in meters (m). Indicates time, in seconds; This represents the equivalent magnetic permeability of the medium inside the growth furnace, expressed in ohms (H). m -1 ; This represents the angular frequency of the alternating excitation current, measured in rad. s -1 ; This represents the magnetic vector potential per unit circumferential length under axisymmetric conditions, with units of Wb. m -1 ; Represents magnetic vector potential The in-phase spatial amplitude component, in Wb m -1 ; Represents magnetic vector potential The orthogonal out-of-phase spatial amplitude components, in Wb m -1 ; The electrical conductivity of a solid-state component is expressed in saturation (S). m -1 ; This represents the circumferential tangential current density, with units of A. m -2 ; This represents the magnitude of the excitation current density in the induction coil, measured in amperes (A). m -2 .

[0040] It should be noted that the cylindrical coordinate system used in this invention is constructed with the central axis of the growth furnace as the z-axis and the radial direction of the growth furnace as the r-axis; the origin of the z-axis can be customized. In some embodiments, the origin of the z-axis is the bottom center point of the growth furnace, and the origin of the r-axis is set on the central axis of the growth furnace.

[0041] In step S1013, the electronic device can derive the volumetric heat generation rate of the solid components in the growth furnace according to the above formulas (3) to (5): (6) in, Indicates the spatial location of solid components Volumetric heat production rate at a given location, in W. m -3 .

[0042] In step S1014, firstly, the electronic device derives the spatial position of the semi-transparent participating medium based on formula (2). Net radiative volume heat source term at the location: (7) in, Indicates the spatial position of a semi-transparent participating medium. The net radiative volume heat source term at the location, in W. m -3 .

[0043] Then, the electronic device couples the volumetric heat generation rate of formula (6) and the net radiative volumetric heat source term of formula (7) according to the computational domain. It substitutes the volumetric heat generation rate of formula (6) into the heat transfer control equation of formula (1) to obtain the solid domain electromagnetic thermal coupling numerical simulation model. It also substitutes the net radiative volumetric heat source term of formula (7) into the heat transfer control equation of formula (1) to obtain the gas domain electromagnetic thermal coupling numerical simulation model. The solid domain electromagnetic thermal coupling numerical simulation model and the gas domain electromagnetic thermal coupling numerical simulation model together constitute the silicon carbide electromagnetic thermal coupling numerical simulation model.

[0044] The numerical simulation model for electromagnetic-thermal coupling in the solid domain is as follows: (8) The numerical simulation model for electromagnetic-thermal coupling in the gas domain is as follows: (9) in, The thermal conductivity of a semi-transparent media is expressed in W·m. -1 ·K -1 .

[0045] In step S1015, for resistance heating, the electronic device can calculate the volumetric heat generation rate of the heater based on the heating power and the heater volume. The volumetric heat generation rate of the heater is: (10) in, Indicates the spatial location of the heater Volumetric heat production rate at a given location, in W. m -3 ; This indicates heating power, measured in W. This indicates the volume of the heater, in meters (m). 3 Heating power refers to the rated total heating power of the heater, and heater volume refers to the effective heating volume of the heater.

[0046] In step S1016, firstly, the electronic device derives the spatial position of the semi-transparent participating medium based on formula (2). The net radiative volume heat source term at the location is specifically expressed as shown in the aforementioned formula (7).

[0047] Then, the electronic device couples the volumetric heat generation rate of formula (10) and the net radiative volumetric heat source term of formula (7) according to the computational domain partition, substitutes the volumetric heat generation rate of formula (10) into the heat transfer control equation of formula (1) to obtain the solid domain resistance heating numerical simulation model, and substitutes the net radiative volumetric heat source term of (7) into the heat transfer control equation of formula (1) to obtain the gas domain resistance heating numerical simulation model; the solid domain resistance heating numerical simulation model and the gas domain resistance heating numerical simulation model together constitute the silicon carbide resistance heating numerical simulation model.

[0048] The numerical simulation model for solid-domain resistance heating is as follows: (11) The numerical simulation model for gas domain resistance heating is as follows: (12) To address the issues of complex operating conditions, high experimental costs, and the need for extensive experiments or numerical simulations to study crystal growth patterns in the PVT method for growing silicon carbide crystals, in step S102, the electronic device can use the Latin hypercube algorithm to extract operating parameter samples of the silicon carbide crystal growth process. This allows for the creation of various combinations of operating parameters based on the required parameters. By using the Latin hypercube algorithm to extract a subset of operating parameters as operating parameter samples, representative operating parameter samples capable of characterizing multidimensional operating conditions can be efficiently selected within the entire operating parameter value space. This enables small-sample calculations to replace complex operating condition calculations, reducing the computational load of numerical simulations and lowering the costs of physical experiments and numerical simulations. Simultaneously, it improves the accuracy of the characteristic location temperature obtained from the numerical simulation model based on the operating parameter samples, as well as the modeling accuracy of the active learning Gaussian process regression model constructed based on the operating parameter samples and the characteristic location temperature.

[0049] In this process, the number of operating condition parameter samples extracted by the electronic device in step S102 is at least 2. Each set of operating condition parameter samples includes parameter values ​​for at least two operating condition parameters.

[0050] In step S103, firstly, the electronic device can modify the model parameters in the numerical simulation model constructed in step S101 based on the operating condition parameter samples extracted in step S102, and then perform numerical simulation calculations using the modified numerical simulation model to obtain the temperature field results corresponding to the set of operating condition parameter samples. Then, the electronic device determines the characteristic location temperature corresponding to the set of operating condition parameter samples from the temperature field results. It can be understood that through step S103, the electronic device can obtain the characteristic location temperature corresponding to each set of operating condition parameter samples extracted in step S102.

[0051] Reference Figure 4 For induction heating, step S103, which involves using the numerical simulation model to obtain the characteristic location temperature corresponding to the operating condition parameter sample, includes: Step S1031: Extract single working condition parameter samples sequentially from the working condition parameter samples.

[0052] Specifically, the electronic device sequentially extracts single operating condition parameter samples from the operating condition parameter samples extracted in step S102. In some embodiments, the order in which the operating condition parameter samples are extracted may be the order in which the electronic device extracts the operating condition parameter samples in step S102.

[0053] Step S1032: Modify the model parameters in the numerical simulation model.

[0054] Specifically, the electronic device can modify the model parameters in the numerical simulation model constructed in step S101 based on the operating condition parameter samples extracted in step S1031.

[0055] Step S1033: Solve the electromagnetic induction model to obtain the volumetric heat generation rate of the solid component.

[0056] Specifically, the electronic device can prioritize step S1033 to solve the electromagnetic induction model and obtain the volumetric heat generation rate of the solid components in the growth furnace.

[0057] Step S1034: Solve the numerical simulation model to obtain the temperature field results.

[0058] Specifically, the electronic device can further solve the numerical simulation model based on the volumetric heat generation rate of the solid component obtained through step S1033 to obtain the temperature field results corresponding to the operating condition parameter samples extracted through step S1031.

[0059] Step S1035: Has all operating condition parameter samples been traversed?

[0060] Specifically, the electronic device confirms whether all operating condition parameter samples extracted in step S102 have been traversed. If all operating condition parameter samples extracted in step S102 have been traversed, then step S1036 is executed. If all operating condition parameter samples extracted in step S102 have not been traversed, then step S1031 is executed again, until all operating condition parameter samples extracted in step S102 have been traversed.

[0061] Step S1036: End numerical simulation calculation.

[0062] Specifically, the electronic device ends the numerical simulation calculation after iterating through all the operating condition parameter samples extracted in step S102.

[0063] In this embodiment of the invention, the characteristic location temperature refers to the temperature at a predetermined characteristic location in the growth furnace.

[0064] In some embodiments, the characteristic locations include the center of the crucible top, the center of the heating cylinder bottom, the center of the seed crystal, and the edge of the seed crystal. The characteristic location temperatures obtained by the electronic device in step S103 include the temperature at the center of the crucible top, the temperature at the center of the heating cylinder bottom, the temperature at the center of the seed crystal, and the temperature at the edge of the seed crystal. The axial temperature gradient of the growth furnace can be calculated based on the temperatures at the center of the crucible top and the center of the heating cylinder bottom, reflecting the component transport rate, the sublimation rate of the powder, and the crystallization rate at the seed crystal. The radial temperature gradient of the seed crystal can be calculated based on the temperatures at the center and the edge of the seed crystal, reflecting the different crystallization rates of the seed crystal in the radial direction. These are key parameters characterizing the crystallization interface shape and defects of silicon carbide crystals.

[0065] As a first example, refer to Figure 5 , Figure 5 Specifically, the temperature field results of the part located on the left side of the central axis in the growth furnace are shown. The characteristic position temperatures obtained by the electronic device through step S103 include: the temperature at the center of the top of the crucible (2420K), the temperature at the center of the bottom of the heating cylinder (2406K), the temperature at the center of the seed crystal (2426K), and the temperature at the edge of the seed crystal (2428K).

[0066] In some embodiments, in step S104, firstly, the electronic device constructs a training dataset based on the sets of operating condition parameter samples extracted in step S102 and the feature location temperatures corresponding to each set of operating condition parameter samples. The training dataset includes the sets of operating condition parameter samples extracted in step S102 and the feature location temperatures corresponding to each set of operating condition parameter samples obtained in step S103. Then, in each round of training, the electronic device inputs the operating condition parameter samples from the training dataset into the Gaussian process regression model to be trained, and determines the effectiveness of the Gaussian process regression model on the target operating condition parameter samples based on the predicted temperature output by the Gaussian process regression model and the feature location temperatures corresponding to the set of operating condition parameter samples. The corresponding loss value is determined; based on the loss value, the model parameters of the Gaussian process regression model to be trained are adjusted, and step S102 is executed again to obtain candidate operating condition parameter samples. Based on the prediction uncertainty of the candidate operating condition parameter samples, new operating condition parameter samples are determined from the candidate operating condition parameter samples. Then, step S103 is executed again to obtain the feature location temperature corresponding to the new operating condition parameter samples. Based on the new operating condition parameter samples and the feature location temperature corresponding to the new operating condition parameter samples, the training dataset is updated, and the Gaussian process regression model to be trained is trained again based on the updated training dataset until the loss value meets the preset convergence condition, thus obtaining the actively learned Gaussian process regression model. Among them, the new operating condition parameter samples are at least one set of candidate operating condition parameter samples with high prediction uncertainty.

[0067] Specifically, the preset convergence condition can be a preset loss threshold for the Gaussian process regression model to be trained. If the loss value of the Gaussian process regression model to be trained does not meet the preset convergence condition, for example, if the loss value is greater than the preset loss threshold, then the next round of training is performed. If the loss value of the Gaussian process regression model to be trained meets the preset convergence condition, for example, if the loss value is less than or equal to the preset loss threshold, then training can be stopped, and the actively learned Gaussian process regression model is obtained.

[0068] This invention addresses the problem of long computation time and low efficiency in existing numerical simulations of crystal growth when considering multiphysics effects. It constructs an active learning Gaussian process regression model based on operating parameter samples and characteristic location temperatures. This model establishes a nonlinear mapping relationship between operating parameters and characteristic location temperatures. Subsequently, by inputting any operating parameter sample to be detected into the active learning Gaussian process regression model, the accurate characteristic location temperature can be quickly predicted. This reduces the high computational cost of repeatedly calling multiphysics coupling models. While ensuring the accuracy of the numerical simulation results, it helps to shorten the computation time of the numerical simulation process and improve the efficiency of numerical simulation of silicon carbide crystal growth.

[0069] In some embodiments, the growth parameters include the characteristic location temperature corresponding to the sample of operating conditions to be detected; in step S105, the electronic device can input any set of samples of operating conditions to be detected into the active learning Gaussian process regression model, and use the predicted temperature output by the active learning Gaussian process regression model based on the sample of operating conditions to be detected as the characteristic location temperature corresponding to the sample of operating conditions to be detected, thereby quickly predicting the characteristic location temperature inside the growth furnace, with a prediction speed that is 10 times faster than that of traditional numerical simulation. 6 This significantly improves computational efficiency and reduces computational costs.

[0070] In some embodiments, the growth parameters include target operating parameters corresponding to the target temperature at the pre-set characteristic position. In step S105, the electronic device can construct a particle swarm optimization algorithm based on an active learning Gaussian process regression model. It can quickly invert and optimize the target operating parameters corresponding to the target temperature at the characteristic position according to the pre-set target temperature at the characteristic position. Thus, under the constraint of the target temperature at the characteristic position, the operating parameters of the silicon carbide crystal growth process can be optimized in a targeted manner. This solves the problem of the single and low efficiency of traditional crystal growth optimization methods. It is beneficial to shorten the debugging cycle of operating parameters, reduce the number of physical sintering experiments, accurately match the design requirements of the temperature field in the crystal growth region, improve the optimization efficiency of operating parameters and the control accuracy of the temperature field in the growth furnace, and thus improve the growth quality and process stability of silicon carbide crystals.

[0071] The active learning-based method for determining silicon carbide crystal growth parameters provided in this invention constructs a numerical simulation model corresponding to the silicon carbide crystal growth furnace and uses the Latin hypercube algorithm to extract operating parameter samples of the silicon carbide crystal growth process. This allows for efficient screening of representative operating parameter samples that can characterize the multidimensional operating condition characteristics within the entire operating parameter value space, enabling small-sample calculations to replace complex operating condition calculations. The numerical simulation model then calculates the characteristic temperature corresponding to the operating parameter samples. Based on the operating parameter samples and characteristic temperature, an active learning Gaussian process regression model is constructed through iterative updates of prediction uncertainty. This facilitates the continuous replenishment of effective operating parameter samples, efficiently improving the temperature prediction accuracy of the active learning Gaussian process regression model. Finally, the active learning Gaussian process regression model is used to determine the silicon carbide crystal growth parameters in real time. This significantly reduces the computational and time costs of experiments and multiphysics numerical simulations, and improves the accuracy and efficiency of determining silicon carbide crystal growth parameters under complex operating conditions.

[0072] In an optional embodiment, step S102, which involves extracting the operating parameter samples of the silicon carbide crystal growth process using the Latin hypercube algorithm, includes: Step S1021: Determine at least two operating parameters corresponding to the silicon carbide crystal growth process.

[0073] Step S1022: Determine the value range corresponding to each of the operating condition parameters.

[0074] Step S1023: Based on the value range of each operating condition parameter and the parameter dimension of the operating condition parameter, extract the operating condition parameter samples of the silicon carbide crystal growth process using the Latin hypercube algorithm.

[0075] In this embodiment of the invention, when the electronic device extracts operating parameter samples of the silicon carbide crystal growth process using the Latin hypercube algorithm, it can first determine at least two operating parameters corresponding to the silicon carbide crystal growth process through step S1021, then determine the value range corresponding to each operating parameter through step S1022, and finally extract operating parameter samples of the silicon carbide crystal growth process using the Latin hypercube algorithm according to the value range and parameter dimension of each operating parameter through step S1023. Thus, it can not only efficiently screen representative operating parameter samples that can characterize the multidimensional operating condition regularity in the entire operating parameter value space, realizing small sample calculation instead of complex operating condition calculation, but also realize uniform sampling on the parameter dimension of different operating parameters, providing a uniformly distributed and sufficiently representative data basis for the subsequent construction of the active learning Gaussian process regression model, thereby improving the accuracy of the characteristic position temperature obtained by numerical simulation model based on the operating parameter samples and the modeling accuracy of the active learning Gaussian process regression model constructed based on the operating parameter samples and characteristic position temperatures.

[0076] The electronic device determines the operating parameters in step S1021 as those that affect the temperature field distribution in the growth furnace during the silicon carbide crystal growth process. In step S1021, the electronic device can determine the operating parameters from at least one of the physical property parameters of the growth furnace, the process parameters of the growth furnace, and the structural parameters of the growth furnace.

[0077] Among them, physical property parameters are used to characterize the inherent physicochemical properties of solid components in the growth furnace, determine the heat transfer performance and electromagnetic induction heating characteristics of the solid components, and provide basic physical property input variables for numerical simulation models. Physical property parameters may include, but are not limited to, the thermal conductivity and electrical conductivity of solid components.

[0078] Process parameters are used to characterize the controllable and adjustable conditions of the actual operation of the growth furnace. By equivalently controlling the amplitude of the heat source and the spatial arrangement of the solid components, the total amount of endogenous heat source and the temperature gradient distribution of the growth furnace can be controlled. Process parameters may include, but are not limited to, heating power and the arrangement parameters of the solid components within the growth furnace. Among them, the amplitude of the heat source refers to the heat generation intensity level of the heat source per unit volume, which is a macroscopic quantitative characterization of the volumetric heat generation rate.

[0079] Structural parameters characterize the geometric features of assemblies and openings related to temperature field distribution in the growth furnace. On the one hand, they define the spatial boundary of the numerical simulation computational domain; on the other hand, they indirectly alter the overall temperature field distribution within the growth furnace by leveraging heat leakage from openings and heat transfer effects between assembly gaps. Structural parameters may include, but are not limited to, the assembly spacing dimensions between solid components and the geometric dimensions of various openings within solid components.

[0080] In an alternative embodiment, refer to Figure 6 The operating parameters include the physical properties, process parameters, and structural parameters of the growth furnace. The physical properties include the thermal conductivity index of the insulation material forming the insulation layer, the thermal conductivity of the heating substrate, and the electrical conductivity of the heating substrate. The process parameters include the heating power and the location of the heat source. The structural parameters include the distance from the top flange to the top of the crucible lid, the diameter of the top hole in the crucible, and the diameter of the bottom hole in the heating substrate.

[0081] Among these factors, the thermal conductivity index of the insulation material determines the heat insulation capacity of the insulation layer, affecting the overall temperature field distribution inside the furnace by changing the heat dissipation rate of the furnace sidewall; the thermal conductivity of the heating substrate determines the heat transfer rate of the heating substrate along the radial and axial directions, directly controlling the uniformity of the internal temperature of the heating substrate; the electrical conductivity of the heating substrate determines the eddy current generation efficiency of the heating substrate under alternating electromagnetic fields, thereby changing the volumetric heat generation rate. The heating power, as the input power of the induction coil or the heater, is converted into an equivalent volumetric heat generation rate after power conversion efficiency, used to determine the total load of the endogenous heat source inside the furnace; the location of the heat source can change the magnetic vector potential distribution in the furnace space, which can both control the distribution area of ​​the heat source in the growth furnace and affect the temperature gradient of the growth furnace along the radial and axial directions. The distance from the top flange surface to the top of the crucible lid, the diameter of the top hole of the crucible, and the diameter of the bottom hole of the heating substrate together determine the spatial geometric boundaries corresponding to the r-axis and z-axis in the cylindrical coordinate system. Changes in the diameter of the top hole of the crucible and the bottom hole of the heating substrate will change the heat leakage loss in the growth furnace, and ultimately disturb the temperature field distribution in the growth furnace.

[0082] In some embodiments, the insulation material constituting the insulation layer can be a soft felt material; the heating substrate includes graphite material; the heating power refers to the power input to the induction coil or the power input to the heater; the heat source placement includes the placement of the induction coil or the placement of the crucible, wherein the placement of the induction coil refers to the coordinates of the axial center point of the induction coil in a cylindrical coordinate system, and the placement of the crucible refers to the coordinates of the axial center point of the crucible in a cylindrical coordinate system. The openings at the top of the crucible and at the bottom of the heating substrate are both infrared temperature measurement holes. If the aperture of the openings is too large, heat leakage will occur, thus affecting the temperature field distribution in the growth furnace.

[0083] As an example, the operating parameters determined by the electronic device in step S1021 include the physical property parameters, process parameters, and structural parameters of the growth furnace. The physical property parameters include the thermal conductivity index of the soft felt material used for the insulation layer, and the thermal conductivity and electrical conductivity of the graphite materials used for the crucible, crucible lid, and heating cylinder. In the induction heating scenario, the process parameters include the power input to the induction coil and the placement of the induction coil; in the resistance heating scenario, the structural parameters include the power input to the heater and the placement of the crucible, including the distance from the top flange of the growth furnace to the top of the crucible lid, the diameter of the top hole in the crucible, and the diameter of the bottom hole in the heating cylinder.

[0084] In step S1022, the electronic device can determine the value range of each operating condition parameter based on the structure of the growth furnace, the range of material property variations of the solid component, and the process window suitable for growing silicon carbide crystals using the PVT method. Specifically, the value range of structural parameters can be determined based on the structure of the growth furnace, the value range of physical property parameters can be determined based on the range of material property variations of the solid component, and the value range of process parameters can be determined based on the process window suitable for growing silicon carbide crystals using the PVT method.

[0085] In some embodiments, the first value range corresponding to the thermal conductivity index of the insulation material is [1.1, 2.7] W·m. -1 ·K -1 The second range of values ​​for the thermal conductivity of the heating substrate is [0.5, 3.5] W·m. -1 ·K -1 The third value range corresponding to the conductivity of the heating substrate is [70000, 90000] S·m -1 The fourth value range corresponding to the heating power is [14, 16] kW, the fifth value range corresponding to the heat source placement position is [70, 90] mm, the sixth value range corresponding to the distance from the top flange surface to the top of the crucible cover is [410, 450] mm, the seventh value range corresponding to the diameter of the hole at the top of the crucible in the growth furnace is [10, 40] mm, and the eighth value range corresponding to the diameter of the hole at the bottom of the heating substrate in the growth furnace is [2, 40] mm.

[0086] In step S1023, the electronic device can extract samples of operating parameters for the silicon carbide crystal growth process using the Latin hypercube algorithm, based on the value range and parameter dimension of each operating parameter, while meeting the requirements of data characteristic. This helps to improve the model accuracy of the active learning Gaussian process regression model built based on the operating parameter samples and characteristic position temperatures, while reducing the computational load of numerical simulation and improving the efficiency of numerical simulation of the silicon carbide crystal growth process.

[0087] In an optional embodiment, step S1023, which involves extracting samples of operating parameters for the silicon carbide crystal growth process using the Latin hypercube algorithm based on the value range corresponding to each operating parameter and the parameter dimension of the operating parameter, includes: Step A11: Based on the parameter dimensions of the operating condition parameters, construct a multi-dimensional parameter space with the value ranges corresponding to various operating condition parameters as boundaries.

[0088] Step A12: Using the Latin hypercube algorithm, the multidimensional parameter space is divided into layers according to the operating parameters.

[0089] Step A13: Randomly select samples within each stratum and randomly combine the sampling results from each stratum to obtain the working condition parameter samples.

[0090] In this embodiment of the invention, during the extraction of operating parameter samples of the silicon carbide crystal growth process, the electronic device can first construct a multidimensional parameter space with the value range of various operating parameters as the boundary through step A11, based on the parameter dimension of the operating parameters. Then, through step A12, the multidimensional parameter space is layered according to the operating parameters using the Latin hypercube algorithm. Finally, through step A13, samples are randomly extracted from each layer, and the extraction results of each layer are randomly combined to obtain the operating parameter samples. This not only helps to improve the uniformity of the distribution of operating parameter samples in the entire operating parameter value space and the representativeness of the operating parameter samples, but also enables the use of a small number of operating parameter samples to cover the regular characteristics of multidimensional operating conditions, effectively reducing the number of calculation cases and computational overhead of subsequent multiphysics numerical simulations.

[0091] In step A11, the electronic device can construct a multidimensional parameter space with the number of dimensions equal to the number of types of operating parameters, using the value range corresponding to each type of operating parameter as the upper and lower boundaries of the parameter dimension corresponding to that type of operating parameter. The multidimensional parameter space can cover all feasible combinations of operating parameters, and any coordinate point within the multidimensional parameter space corresponds to a valid combination of operating parameters. This allows for defining the global solution interval for the operations in step A12, which involves layering the multidimensional parameter space according to operating parameters, and for the operations in step A13, which involve extracting operating parameter samples.

[0092] In step A12, the electronic device can use the Latin hypercube algorithm to divide the multidimensional parameter space into sub-layer intervals that are equal to and do not overlap with the total number of operating condition parameter samples along the value range corresponding to each parameter dimension of the multidimensional parameter space, in combination with the pre-set total number of operating condition parameter samples to be extracted.

[0093] In step A13, the electronic device can randomly extract parameter values ​​from each sub-layer interval obtained by dividing each parameter dimension. After extracting parameter values ​​for all parameter dimensions, the extracted parameter values ​​from different parameter dimensions can be randomly assigned and combined to form a complete set of operating condition parameter samples. Repeating the above extraction and combination operations of operating condition parameter samples can obtain all the operating condition parameter samples that need to be extracted. This sampling method can avoid the concentration of each set of operating condition parameter samples in local intervals of the multidimensional parameter space, which is conducive to improving the uniformity of the distribution of operating condition parameter samples in the entire multidimensional parameter space, taking into account the representativeness and randomness of the operating condition parameter sample extraction, and improving the accuracy of the characteristic location temperature obtained by numerical simulation model based on the operating condition parameter samples, as well as the modeling accuracy of the active learning Gaussian process regression model constructed based on the operating condition parameter samples and characteristic location temperatures.

[0094] In an optional embodiment, step S1023, which involves extracting samples of operating parameters for the silicon carbide crystal growth process using the Latin hypercube algorithm based on the value range corresponding to each operating parameter and the parameter dimension of the operating parameter, includes: Step A21: Determine at least two discrete parameter values ​​from the range of values ​​corresponding to the operating condition parameters.

[0095] Step A22: Determine the index identifier corresponding to each of the discrete parameter values.

[0096] Step A23: Construct a multi-dimensional index space based on the index identifiers corresponding to the discrete parameter values ​​under each of the aforementioned operating conditions.

[0097] Step A24: Using the Latin hypercube algorithm, the multidimensional index space is layered according to the operating parameters.

[0098] Step A25: Randomly extract index identifiers within each layer, and randomly combine the extraction results from each layer to obtain an index combination.

[0099] Step A26: Map the index identifiers in the index combination to the discrete parameter values ​​corresponding to the index identifiers to obtain the operating condition parameter samples.

[0100] In this embodiment of the invention, during the extraction of operating parameter samples from the silicon carbide crystal growth process, the electronic device can first determine at least two discrete parameter values ​​from the range of values ​​corresponding to the operating parameters in step A21. Then, in step A22, it can determine the index identifier corresponding to each discrete parameter value. Next, in step A23, it can construct a multidimensional index space. Then, in step A24, it can layer the multidimensional index space according to the operating parameters. Then, in step A25, it can obtain the index combination. Finally, in step A26, it can obtain the operating parameter samples. The index identifiers are used to replace the specific parameter values ​​to complete the construction, layering, and indexing of the multidimensional index space. Combinatorial random sampling can reduce computational redundancy caused by the direct participation of multi-dimensional floating-point parameter values ​​in calculations, simplify the computational logic of the Latin hypercube algorithm, and constrain the range of values ​​of the operating condition parameter samples by using pre-determined discrete parameter values. This improves the uniformity, randomness, and representativeness of the distribution of operating condition parameter samples in the entire multi-dimensional parameter space, reduces invalid computation, and helps to further optimize the data quality of operating condition parameter samples. This improves the accuracy of the characteristic location temperature obtained by numerical simulation model based on the operating condition parameter samples, as well as the modeling accuracy of the active learning Gaussian process regression model built based on the operating condition parameter samples and characteristic location temperatures.

[0101] In step A21, the electronic device can determine at least two discrete parameter values ​​from the range of values ​​corresponding to the operating condition parameters. The operating condition parameters can be represented as N. x From the operating condition parameter N x The discrete parameter values ​​within the corresponding range can be represented as N. iy i=1,…,N x For example, the operating parameters include heating power, and the fourth value range corresponding to the heating power is [14, 16] kW. Therefore, the discrete parameter values ​​determined from the range corresponding to the heating power can include 14 kW, 14.5 kW, 15.0 kW, 15.5 kW, and 16 kW. If the discrete parameter values ​​under all operating parameters are combined, the number of groups that need to be calculated is... The computational load required is extremely large. However, the embodiments of the present invention utilize the Latin hypercube algorithm for sampling through steps A22 to A26 below. Under the premise of meeting the requirements of data characteristics, a small number of working condition parameter samples are uniformly extracted to reduce the computational load. This can improve the extraction efficiency of working condition parameter samples, reduce the computational power consumption of subsequent numerical simulation calculations, optimize the data quality of the sample dataset constructed based on working condition parameter samples and characteristic location temperatures, and thus improve the modeling accuracy of the active learning Gaussian process regression model.

[0102] In step A22, the electronic device can assign an index identifier corresponding one-to-one with each discrete parameter value determined in step A21. For example, N can be used.iy As an index identifier for discrete parameter values.

[0103] In step A23, the electronic device can construct a multi-dimensional index space based on the index identifiers corresponding to the discrete parameter values ​​under each operating condition parameter. The number of dimensions in the multi-dimensional index space is equal to the number of types of operating condition parameters. Each dimension in the multi-dimensional index space consists of the index identifiers of all discrete parameter values ​​under the operating condition parameter corresponding to that dimension.

[0104] In step A24, the electronic device can use the Latin hypercube algorithm to divide the multidimensional index space into layers according to the operating parameters. Specifically, the electronic device can, for each parameter dimension of the multidimensional index space, combine the pre-set total number of operating parameter samples to be extracted, and uniformly divide the index sub-layers along the index identifier in a single dimension to achieve the layering of the multidimensional index space.

[0105] In step A25, the electronic device can randomly extract index identifiers within each index sub-layer. After the index identifier extraction is completed, the extraction results of each index sub-layer can be randomly combined to obtain an index combination. By repeating the above extraction and combination operations to form an index combination, all the index combinations that need to be extracted can be obtained.

[0106] In step A26, the electronic device can map the index identifier in each index combination obtained in step A25 to the discrete parameter value corresponding to the index identifier based on the one-to-one correspondence between the discrete parameter values ​​and index identifiers determined in step A22, thereby obtaining the operating condition parameter sample.

[0107] As an example, refer to Figure 7 Step S102, which involves extracting the operating parameter samples of the silicon carbide crystal growth process using the Latin hypercube algorithm, may include the following steps: Step A31: Determine at least two operating parameters corresponding to the silicon carbide crystal growth process.

[0108] The specific implementation of step A31 can be found in the detailed description of step S1021, and will not be repeated here.

[0109] Step A32: Determine the value range corresponding to each working condition parameter.

[0110] The specific implementation of step A32 can be found in the detailed description of step S1022, and will not be repeated here.

[0111] Step A33: Determine at least two discrete parameter values ​​from the range of values ​​corresponding to the operating condition parameters.

[0112] The specific implementation of step A33 can be found in the detailed description of step A21, and will not be repeated here.

[0113] Step A34: Determine the index identifier corresponding to each discrete parameter value.

[0114] The specific implementation of step A34 can be found in the detailed description of step A22, and will not be repeated here.

[0115] Step A35: Construct a multidimensional index space.

[0116] Specifically, the electronic device can construct a multidimensional index space based on the index identifiers corresponding to the discrete parameter values ​​under each operating condition parameter, using the same method as in step A23.

[0117] Step A36: Use the Latin hypercube sampling algorithm to uniformly extract the required number of index combinations.

[0118] Specifically, the electronic device can first use the Latin hypercube algorithm in the same way as step A24 to divide the multidimensional index space into layers according to the operating parameters, and then randomly extract index identifiers in each layer in the same way as step A25, and randomly combine the extraction results of each layer to obtain the required number of index combinations.

[0119] Step A37: Map the index identifiers in the index combination to the discrete parameter values ​​corresponding to the index identifiers to obtain the working condition parameter samples.

[0120] The specific implementation of step A37 can be found in the detailed description of step A26, and will not be repeated here.

[0121] In an optional embodiment, step S104, which involves constructing an active learning Gaussian process regression model based on the operating condition parameter samples and the characteristic location temperature through iterative updates of prediction uncertainty, includes: Step S1041: If the index parameters of the Gaussian process regression model to be trained do not meet the target performance index, construct a parameter temperature dataset based on the working condition parameter sample and the feature location temperature.

[0122] Step S1042: Divide the parameter temperature dataset into a training dataset and a test dataset.

[0123] Step S1043: Train the Gaussian process regression model to be trained using the training dataset.

[0124] Step S1044: Use the test dataset to test the trained Gaussian process regression model to obtain the index parameters of the Gaussian process regression model to be trained.

[0125] Step S1045: If the index parameters meet the target performance index, the Gaussian process regression model to be trained is determined as an active learning Gaussian process regression model.

[0126] In this embodiment of the invention, during the construction of an active learning Gaussian process regression model, if the index parameters of the Gaussian process regression model to be trained do not meet the target performance index, step S1041 is used to construct a parameter temperature dataset based on the operating condition parameter samples and the temperature at the feature location. Then, steps S1042 and S1043 are used to partition the dataset and iteratively train the Gaussian process regression model to be trained. Step S1044 is used to test the trained Gaussian process regression model to obtain the current index parameters of the Gaussian process regression model to be trained. If the index parameters meet the target performance index, the Gaussian process regression model to be trained can be determined as an active learning Gaussian process regression model. This is beneficial for continuously optimizing the fitting performance of the Gaussian process regression model to be trained, improving the prediction accuracy of the active learning Gaussian process regression model, and improving the construction efficiency of the active learning Gaussian process regression model.

[0127] Before step S1041, firstly, a Gaussian process regression model to be trained is constructed. The Gaussian process regression model to be trained can be a basic Gaussian process regression model (GPR). Then, the index parameters corresponding to the Gaussian process regression model to be trained and the target performance index corresponding to the index parameters are set. After that, a data standardizer is established and an active learning iterative loop is started. The data standardizer is used to standardize the input parameters of the model to transform the input parameters into standardized data with a mean of 0 and a standard deviation of 1, thereby improving the training speed of the Gaussian process regression model to be trained and preventing the large magnitude or excessively large value of a single-dimensional parameter from dominating the model's fitting results.

[0128] In some embodiments, the indicator parameters include the root mean square error (RMSE) and the coefficient of determination (R²). 2 The target performance metrics include a first target performance metric corresponding to the root mean square error (RMSE) and a second target performance metric corresponding to the coefficient of determination (CCD). The closer the RMSE is to 0, the smaller the model error, and the closer the CCD is to 1, the better the model fit. For example, the first target performance metric can be 0.05, and the second target performance metric can be 0.95.

[0129] If the root mean square error of the Gaussian process regression model to be trained is less than or equal to the first target performance index, and the coefficient of determination of the Gaussian process regression model to be trained is greater than or equal to the second target performance index, it indicates that the index parameters of the Gaussian process regression model to be trained meet the target performance index; if the root mean square error of the Gaussian process regression model to be trained is greater than the first target performance index, and / or the coefficient of determination of the Gaussian process regression model to be trained is less than the second target performance index, it indicates that the index parameters of the Gaussian process regression model to be trained do not meet the target performance index.

[0130] If the index parameters of the Gaussian process regression model to be trained do not meet the target performance index, the electronic device can construct a parameter temperature dataset based on the operating condition parameter samples and the feature location temperature in step S1041. Here, constructing the parameter temperature dataset in step S1041 refers to: creating a new parameter temperature dataset based on the operating condition parameter samples and the feature location temperature, or updating an existing parameter temperature dataset based on the operating condition parameter samples and the feature location temperature.

[0131] In a scenario where a new parameter temperature dataset is created based on operating condition parameter samples and feature location temperatures, electronic devices can use the operating condition parameter samples as input parameters X to the model, and the feature location temperatures corresponding to the operating condition parameter samples as the target output parameters Y of the model. Subsequently, the input parameters X and the target output parameters Y corresponding to each input parameter X are organized in a table to form the parameter temperature dataset. The parameter temperature dataset includes each set of operating condition parameter samples and the feature location temperatures corresponding to the operating condition parameter samples.

[0132] In some embodiments, refer to Figure 8 Each set of input parameters X includes the physical properties, process parameters, and structural parameters of the growth furnace. The physical properties include the thermal conductivity index of the insulation material, the thermal conductivity of the heating substrate, and the electrical conductivity of the heating substrate. The process parameters include the heating power and the location of the heat source. The structural parameters include the distance from the top flange to the top of the crucible lid, the diameter of the hole at the top of the crucible, and the diameter of the hole at the bottom of the heating substrate. The corresponding target output parameters Y include the temperature at the center of the crucible top, the temperature at the center of the heating cylinder bottom, the temperature at the center of the seed crystal, and the temperature at the edge of the seed crystal.

[0133] In step S1042, firstly, the electronic device uses a data normalizer to standardize the input parameters (i.e., operating condition parameter samples) in the parameter temperature dataset. Then, the electronic device can divide the operating condition parameter samples and feature location temperature data pairs in the parameter temperature dataset constructed in step S1041 into a training dataset and a test dataset according to a preset ratio (e.g., 1:1). The training dataset is used to train the Gaussian process regression model to be trained in step S1043, and the test dataset is used to test the trained Gaussian process regression model to be trained in step S1044 to obtain the index parameters of the Gaussian process regression model to be trained, so as to objectively characterize the fitting effect of the Gaussian process regression model to be trained on the parameter temperature dataset.

[0134] It is understandable that the training dataset includes a portion of the operating condition parameter samples from the parameter temperature dataset and the corresponding feature location temperatures; the test dataset includes another portion of the operating condition parameter samples from the parameter temperature dataset and the corresponding feature location temperatures.

[0135] In step S1043, in each round of training, the electronic device inputs the standardized operating condition parameter samples from the training dataset into the Gaussian process regression model to be trained. Based on the predicted temperature output by the Gaussian process regression model and the feature location temperature corresponding to that set of operating condition parameter samples, the loss value corresponding to the Gaussian process regression model to be trained is determined. The model parameters of the Gaussian process regression model to be trained are adjusted according to the loss value, and the next round of training is performed until the loss value meets the preset convergence condition, at which point the operation corresponding to step S1044 is executed. It can be understood that the parameter dimension of the predicted temperature output by the Gaussian process regression model to be trained is the same as the parameter dimension of the feature location temperature.

[0136] In step S1044, the electronic device can use the test dataset to test the Gaussian process regression model to be trained after step S1043, calculate the root mean square error and the coefficient of determination, and obtain the current index parameters of the Gaussian process regression model to be trained.

[0137] Subsequently, the electronic device can determine whether the index parameters of the Gaussian process regression model to be trained meet the target performance index based on the index parameters obtained in step S1044. If the index parameters of the Gaussian process regression model to be trained do not meet the target performance index, the electronic device can execute step S1041 to update the existing parameter temperature dataset based on the operating condition parameter samples and feature location temperatures. The specific implementation in this scenario can be found in the detailed description of steps B11 to B13. If the index parameters meet the target performance index, the electronic device can execute step S1045 to determine the Gaussian process regression model to be trained as an actively learned Gaussian process regression model.

[0138] In an optional embodiment, step S1041, which involves constructing a parameter temperature dataset based on the operating condition parameter samples and the feature location temperature when the index parameters of the Gaussian process regression model to be trained do not meet the target performance index, includes: Step B11: If the index parameters of the Gaussian process regression model to be trained do not meet the target performance index, the Latin hypercube algorithm is used to extract candidate operating condition parameter samples for the silicon carbide crystal growth process.

[0139] Step B12: Determine the prediction uncertainty of each group of candidate operating condition parameter samples, and sort the prediction uncertainties of each group of candidate operating condition parameter samples.

[0140] Step B13: Update the parameter temperature dataset based on at least two candidate operating condition parameter samples ranked first in prediction uncertainty and the feature location temperature corresponding to the candidate operating condition parameter samples.

[0141] In step S1041, which is a scenario where the existing parameter temperature dataset is updated based on the operating condition parameter samples and the temperature at the feature location, the electronic device can update the parameter temperature dataset through the operations corresponding to steps B11 to B13.

[0142] Specifically, in step B11, the electronic device can extract at least two sets of operating condition parameter samples for the silicon carbide crystal growth process as candidate operating condition parameter samples when the index parameters of the Gaussian process regression model to be trained do not meet the target performance index. In some embodiments, the method by which the electronic device extracts candidate operating condition parameter samples for the silicon carbide crystal growth process using the Latin hypercube algorithm is the same as the method described in step S102; in some embodiments, the method by which the electronic device extracts candidate operating condition parameter samples for the silicon carbide crystal growth process using the Latin hypercube algorithm is the same as the method described in steps S1021 to S1023, and will not be described again here to avoid repetition.

[0143] In step B12, firstly, the electronic device obtains the characteristic location temperature corresponding to each candidate operating condition parameter sample using the same method as in step S103; then, the electronic device inputs the candidate operating condition parameter sample into the Gaussian process regression model to be trained, and obtains the predicted temperature and prediction variance output by the Gaussian process regression model to be trained based on the candidate operating condition parameter sample; then, the electronic device uses the prediction variance output by the Gaussian process regression model to be trained as the prediction uncertainty of the candidate operating condition parameter sample; by iterating through all candidate operating condition parameter samples, the prediction uncertainty of all candidate operating condition parameter samples can be obtained.

[0144] Among them, the prediction uncertainty of the candidate operating condition parameter sample represents the spatial distance between the candidate operating condition parameter sample and the training sample of the Gaussian process regression model to be trained. The greater the prediction uncertainty, the stronger the difference between the candidate operating condition parameter sample and the training sample in the current training dataset, and the higher the information gain.

[0145] Then, the electronic equipment can sort all the candidate operating condition parameter samples extracted in step B11 according to the magnitude of the prediction uncertainty.

[0146] In step B13, the electronic device can add at least two candidate operating condition parameter samples with the highest prediction uncertainty and the characteristic location temperature corresponding to these candidate operating condition parameter samples to the existing parameter temperature dataset, thereby updating and expanding the parameter temperature dataset.

[0147] The active learning-based method for determining silicon carbide crystal growth parameters provided in this invention employs an active learning strategy when the index parameters of the Gaussian process regression model to be trained do not meet the target performance index. This strategy selectively filters and iteratively expands the parameter temperature dataset by extracting candidate operating condition parameter samples through the Latin hypercube algorithm, prioritizing the addition of operating condition parameter samples with higher prediction uncertainty and greater information gain. This helps to accelerate the convergence speed of the Gaussian process regression model to be trained, improve the training efficiency of the Gaussian process regression model to be trained, and simultaneously improve the prediction accuracy of the finally constructed active learning Gaussian process regression model.

[0148] As an example, refer to Figure 9 Step S104, which involves constructing an active learning Gaussian process regression model based on the operating condition parameter samples and the temperature at the characteristic location through iterative updates of prediction uncertainty, may specifically include the following steps: Step B21: Build the Gaussian process regression model to be trained.

[0149] The Gaussian process regression model to be trained can be the basic Gaussian process regression model. After building the Gaussian process regression model to be trained, the index parameters corresponding to the Gaussian process regression model to be trained can be set as root mean square error and coefficient of determination, and the first objective performance index corresponding to root mean square error can be set to 0.05, and the second objective performance index corresponding to coefficient of determination can be set to 0.95; then, a data normalizer is built, and an active learning iterative loop is started.

[0150] Step B22: Construct a parameter temperature dataset, standardize the data, and divide it into a training dataset and a test dataset.

[0151] Specifically, firstly, the electronic device can construct a parameter temperature dataset in the same way as in step S1041; then, the electronic device can use a data normalizer to standardize the input parameters in the parameter temperature dataset; then, the electronic device can divide the working condition parameter samples and feature location temperature data pairs in the parameter temperature dataset into a training dataset and a test dataset according to a preset ratio.

[0152] Step B23: Train the Gaussian process regression model to be trained using the training dataset, and test the Gaussian process regression model to be trained using the test dataset.

[0153] Specifically, the electronic device can be trained using the training set data based on the Gaussian process regression model to be trained and the pre-set initial kernel function hyperparameters of the model, in the same way as step S1043. Then, the Gaussian process regression model to be trained can be tested using the test dataset in the same way as step S1044, and the root mean square error and coefficient of determination can be calculated to obtain the index parameters of the Gaussian process regression model to be trained.

[0154] Step B24: Determine whether the Gaussian process regression model to be trained has reached the target performance index.

[0155] Specifically, in step B23, the electronic device tests the trained Gaussian process regression model using the test dataset to obtain the index parameters of the Gaussian process regression model. Then, the electronic device compares the index parameters with the first target performance index and the second target performance index. If the root mean square error of the Gaussian process regression model is less than or equal to the first target performance index, and the coefficient of determination of the Gaussian process regression model is greater than or equal to the second target performance index, the electronic device determines that the Gaussian process regression model has reached the target performance index, and can proceed to step B28. If the root mean square error of the Gaussian process regression model is greater than the first target performance index, and / or the coefficient of determination of the Gaussian process regression model is less than the second target performance index, the electronic device determines that the Gaussian process regression model has not reached the target performance index, and can proceed to step B25.

[0156] Step B25: Extract candidate operating condition parameter samples using the Latin hypercube algorithm.

[0157] The specific implementation of step B25 can be found in the detailed description of step B11, and will not be repeated here.

[0158] Step B26: Determine the prediction uncertainty of each group of candidate operating condition parameter samples.

[0159] Step B27: Sort the prediction uncertainties of each group of candidate operating condition parameter samples.

[0160] The specific implementation methods for steps B26 and B27 can be found in the detailed description of step B12, and will not be repeated here. After step B27, the electronic device can execute step B23 again: First, update the parameter temperature dataset in the same way as in step B23; then, continue data standardization in the same way as in step B22; and perform the operations of dividing the training dataset and the test dataset, as well as the operations corresponding to subsequent steps B23 and B24, until the Gaussian process regression model to be trained reaches the target performance index.

[0161] Step B28: Output the active learning Gaussian process regression model.

[0162] When the Gaussian process regression model to be trained reaches the target performance index, the electronic device can identify the Gaussian process regression model to be trained as an actively learned Gaussian process regression model and output the actively learned Gaussian process regression model.

[0163] Reference Figure 10 The graph shows the performance variation of the active learning Gaussian process regression model. The horizontal axis represents the number of training samples. The vertical axis of the left graph represents the root mean square error (RMSE) of the temperature at the center of the crucible top (Tu) and the temperature at the center of the heating cylinder bottom (Td). The vertical axis of the right graph represents the coefficient of determination (R²) of the temperature at the center of the crucible top (Tu) and the temperature at the center of the heating cylinder bottom (Td). 2 ,from Figure 10 As can be seen, with the increase of the number of training samples in active learning, the root mean square error (RMSE) gradually decreases to close to 0, and the coefficient of determination (R²) decreases. 2 As the value gradually approaches 1, this indicates that the accuracy of the actively learned Gaussian process regression model is gradually improving.

[0164] Furthermore, referring to Figure 11 The graphs compare the actual and model-predicted temperatures at the center of the crucible top (Tu) and the center of the heating cylinder bottom (Td). The left graph shows the actual temperature (Tu) at the center of the crucible top, and the right graph shows the actual temperature (Td) at the center of the heating cylinder bottom. The horizontal axis of both graphs represents the actual temperature, and the vertical axis represents the predicted temperature obtained from the active learning Gaussian process regression model. Figure 11 As can be seen, the actual temperature value and the predicted temperature value are basically distributed near the reference line y=x, indicating that the predicted temperature value of the active learning Gaussian process regression model is very close to the actual temperature value, thus indicating that the prediction performance and prediction accuracy of the active learning Gaussian process regression model are high.

[0165] In an optional embodiment, the growth parameters include the characteristic location temperature corresponding to the operating condition parameter sample to be detected; step S105, which uses the active learning Gaussian process regression model to determine the growth parameters of the silicon carbide crystal, includes: Step S1051: Input the sample of the working condition parameters to be detected into the active learning Gaussian process regression model.

[0166] Step S1052: Obtain the predicted temperature output by the active learning Gaussian process regression model.

[0167] Step S1053: Use the predicted temperature as the characteristic location temperature corresponding to the working condition parameter sample to be detected.

[0168] In application scenarios where growth parameters include the characteristic location temperature corresponding to the sample of operating conditions to be detected, electronic devices can determine the growth parameters of silicon carbide crystals through the operations corresponding to steps S1051 to S1053. The characteristic location temperature can be quickly output directly using the trained active learning Gaussian process regression model, abandoning the traditional calculation mode of solving temperature data by full numerical simulation. While ensuring the accuracy and reliability of the predicted results of characteristic location temperature, the complexity of the solution process of characteristic location temperature is reduced, the solution time of characteristic location temperature is shortened, and the efficiency of obtaining growth parameters of silicon carbide crystals is improved.

[0169] In step S1051, the electronic device can input the sample of the operating condition parameter to be detected as an input parameter into the active learning Gaussian process regression model, and use the active learning Gaussian process regression model to predict the predicted temperature corresponding to the sample of the operating condition parameter to be detected; in step S1052, the electronic device can obtain the predicted temperature output by the active learning Gaussian process regression model, and use the predicted temperature as the feature location temperature corresponding to the sample of the operating condition parameter to be detected in step S1053.

[0170] Among them, the sample of operating parameters to be detected is: during the growth process of silicon carbide crystal, the sample of real-time operating parameters during the growth process of silicon carbide crystal is extracted by the Latin hypercube algorithm using a method similar to step S102.

[0171] As an example, in application scenarios where growth parameters include the temperature at the characteristic location corresponding to the sample of the operating condition parameters to be detected, refer to... Figure 12 Step S105, which involves using the active learning Gaussian process regression model to determine the growth parameters of silicon carbide crystals, includes: Step C11: Input the sample of operating parameters to be detected into the active learning Gaussian process regression model.

[0172] Specifically, the electronic device can input the sample of the operating condition parameter to be detected into the active learning Gaussian process regression model in the same way as in step S1051.

[0173] Step C12: Standardize the sample of operating parameters to be tested.

[0174] Specifically, in some embodiments, a data normalizer can be integrated into the active learning Gaussian process regression model. After the operating condition parameter sample to be detected is input into the active learning Gaussian process regression model through step C11, the electronic device can use the data normalizer to standardize the operating condition parameter sample to be detected, which is beneficial to further improve the accuracy of the predicted temperature output by the active learning Gaussian process regression model for the operating condition parameter sample to be detected.

[0175] Step C13: Obtain the predicted temperature output by the active learning Gaussian process regression model.

[0176] Specifically, the electronic device can obtain the predicted temperature output by the active learning Gaussian process regression model using the same method as in step S1052.

[0177] Step C14: Output the temperature at the characteristic location.

[0178] Specifically, electronic devices can use the predicted temperature output by the actively learned Gaussian process regression model as the characteristic location temperature corresponding to the working condition parameter sample to be detected, and output the characteristic location temperature for subsequent applications such as silicon carbide crystal growth process control and growth state analysis.

[0179] In an optional embodiment, the growth parameters include target operating condition parameters corresponding to the target temperature at a pre-set characteristic location; step S105, which uses the active learning Gaussian process regression model to determine the growth parameters of the silicon carbide crystal, includes: Step S1054: Initialize the particle swarm in the multidimensional parameter space corresponding to the operating parameters, wherein each particle in the particle swarm corresponds to a set of operating parameters.

[0180] Step S1055: Update the velocity and position of the particles in the particle swarm.

[0181] Step S1056: For any particle in the particle swarm, input the operating parameters corresponding to the particle into the active learning Gaussian process regression model to obtain the predicted temperature corresponding to the particle.

[0182] Step S1057: If the difference between the predicted temperature and the target temperature at the feature location is greater than or equal to a preset threshold, update the velocity and position of the particles in the particle swarm again, and re-acquire the predicted temperature corresponding to the particles until the difference between the predicted temperature and the target temperature at the feature location is less than the preset threshold.

[0183] Step S1058: If the difference between the predicted temperature and the target temperature at the feature location is less than the preset threshold, the operating condition parameter corresponding to the predicted temperature is determined as the target operating condition parameter.

[0184] In application scenarios where growth parameters include target operating parameters corresponding to pre-set target temperatures at characteristic locations, electronic devices can determine the growth parameters of silicon carbide crystals through operations corresponding to steps S1054 to S1058. This enables rapid optimization to obtain the optimal target operating parameters based on the required target temperatures at characteristic locations. On the one hand, this can reduce the optimization cycle of target operating parameters and improve the efficiency of solving target operating parameters. On the other hand, based on the prediction accuracy of the active learning Gaussian process regression model, the reliability of the target operating parameters determined through the embodiments of the present invention is improved.

[0185] The characteristic position target temperature refers to the characteristic position temperature that needs to be reached during the growth of silicon carbide crystals. By adjusting the operating parameters of the growth furnace to the target operating parameters, the actual characteristic position temperature during the growth of silicon carbide crystals can be made close to the characteristic position target temperature.

[0186] In step S1054, the electronic device can generate initial particles by uniformly distributing points in a multidimensional parameter space based on the rules of the Latin hypercube algorithm. The operating parameters corresponding to each initial particle are all limited to the range of values ​​corresponding to those operating parameters. The construction method of the multidimensional parameter space can be referred to the detailed description of step A11 above, and will not be repeated here.

[0187] In step S1055: First, the electronic device can update the velocity and position of the particles in the particle swarm, where the particle velocity and position are: (13) (14) in, This represents the velocity of the i-th particle in the particle swarm at time t+1. Let represent the velocity of the i-th particle in the particle swarm at time t; This represents the position of the i-th particle in the particle swarm at time t; This represents the historical best position of the i-th particle in the particle swarm. This represents the global historical best position of the entire particle swarm; This represents the inertia weight, with a value ranging from 0.4 to 0.9. and Indicates the learning factor; and This represents a uniformly random number whose value ranges from 0 to 1. This represents the iteration step size, with a preferred value of 1.

[0188] In step S1056, for any particle in the particle swarm, the electronic device can first use a data normalizer to standardize the operating parameters corresponding to the current particle, then input the standardized operating parameters into the active learning Gaussian process regression model, and use the predicted temperature output by the active learning Gaussian process regression model as the predicted temperature corresponding to the particle.

[0189] In some embodiments, when the predicted temperature corresponding to the current particle is obtained, the electronic device can compare the predicted temperature with the preset target temperature of the characteristic position, and calculate the absolute value of the difference between the predicted temperature and the target temperature of the characteristic position as the difference between the predicted temperature and the target temperature of the characteristic position.

[0190] In some embodiments, given the predicted temperature corresponding to the current particle, the electronic device can calculate the minimum of the squared residual between the predicted temperature and the target temperature at the characteristic location, and use the minimum of the squared residual as the difference between the predicted temperature and the target temperature at the characteristic location.

[0191] Specifically, firstly, the electronic device can construct an objective function based on the predicted temperature and the target temperature at the characteristic location. The objective function is as follows: (15) in, Represent the objective function; Indicates the target temperature at the characteristic location, in Kelvin (K). This indicates the predicted temperature, expressed in Kelvin (K).

[0192] As an example, the target temperature at the characteristic location includes the target temperature at the center of the top of the crucible and the target temperature at the center of the bottom of the heating cylinder. Correspondingly, the predicted temperature includes the predicted temperature at the center of the top of the crucible and the predicted temperature at the center of the bottom of the heating cylinder. In this scenario, the objective function is: (16) in, This indicates the target temperature at the center of the top of the crucible, in Kelvin (K). This indicates the predicted temperature at the center of the top of the crucible, in Kelvin (K). This indicates the target temperature at the center of the bottom of the heating element, in Kelvin (K). This indicates the predicted temperature at the center of the bottom of the heating element, expressed in Kelvin (K).

[0193] Then, the electronic device can use the value of the objective function calculated by the above formula (15) as the difference between the predicted temperature and the target temperature at the feature location.

[0194] If the difference between the predicted temperature and the target temperature at the characteristic position is greater than or equal to a preset threshold, it indicates that the operating parameters corresponding to the current particle cannot make the actual characteristic position temperature during the silicon carbide crystal growth process approach the target temperature at the characteristic position, and the electronic device can execute step S1057; if the difference between the predicted temperature and the target temperature at the characteristic position is less than a preset threshold, it indicates that the operating parameters corresponding to the current particle can make the actual characteristic position temperature during the silicon carbide crystal growth process approach the target temperature at the characteristic position, and the electronic device can execute step S1058.

[0195] The preset threshold can be set according to the temperature control accuracy of the silicon carbide crystal growth process, and the embodiments of the present invention do not impose specific limitations on it.

[0196] In step S1057: First, the electronic device can update the motion speed and position of the particles in the particle swarm using the same method as in step S1055; then, the electronic device can reacquire the predicted temperature corresponding to the particle using the same method as in step S1056, until the difference between the predicted temperature and the target temperature at the feature position is less than a preset threshold, and then execute step S1058.

[0197] In step S1058, the electronic device can determine the operating parameters corresponding to the current particle as the target operating parameters if the difference between the predicted temperature and the target temperature at the feature position is less than a preset threshold.

[0198] In some embodiments, refer to Figure 13 In application scenarios where growth parameters include target operating condition parameters corresponding to pre-set target temperatures at characteristic locations, step S105, which involves using the active learning Gaussian process regression model to determine the growth parameters of silicon carbide crystals, includes: Step C21: Particle swarm initialization.

[0199] Specifically, the electronic device can initialize the particle swarm in the multidimensional parameter space corresponding to the operating parameters using the same method as in step S1054, wherein each particle in the particle swarm corresponds to a set of operating parameters.

[0200] Step C22: Update the velocity and position of particles in the particle swarm.

[0201] Specifically, the detailed implementation of step C22 can be found in the detailed description of step S1055, and will not be repeated here.

[0202] Step C23: Obtain the predicted temperature corresponding to the particle.

[0203] Specifically, the detailed implementation of step C23 can be found in the detailed description of step S1056, and will not be repeated here.

[0204] Step C24: Construct the objective function based on the predicted temperature and the target temperature at the characteristic location.

[0205] Specifically, given the predicted temperature of the current particle, the electronic device can first construct an objective function as shown in formula (15) based on the predicted temperature and the target temperature at the characteristic position; then, the electronic device can use the value of the objective function calculated by formula (15) as the difference between the predicted temperature and the target temperature at the characteristic position.

[0206] Step C25: Determine whether the differences have converged.

[0207] Specifically, if the difference between the predicted temperature and the target temperature at the feature location is greater than or equal to a preset threshold, the electronic device can determine that the difference has not converged and repeat steps C22 to C25 until the difference converges; if the difference between the predicted temperature and the target temperature at the feature location is less than the preset threshold, the electronic device can determine that the difference has converged and execute step C26.

[0208] Step C26: The iteration ends, and the target operating condition parameters are output.

[0209] Specifically, when the difference converges, the electronic device can end the iterative calculation of the particle swarm, determine the operating parameters corresponding to the current particle as the target operating parameters and output them. Subsequently, during the silicon carbide crystal growth process, by adjusting the actual operating parameters to the target operating parameters, the actual characteristic position temperature during the silicon carbide crystal growth process can be made close to the target temperature of the characteristic position. This is beneficial for accurately controlling the growth temperature of the silicon carbide crystal, reducing crystal defects, and improving the quality of the finished silicon carbide crystal.

[0210] Referring to Table 1, a comparison of the target operating condition parameters determined through the embodiments of the present invention with the target values ​​of the operating condition parameters corresponding to the target temperatures at characteristic locations in actual scenarios is shown. The target temperatures at characteristic locations include the target temperature (Tu) at the center of the crucible top (2555.5K) and the target temperature (Td) at the center of the heating cylinder bottom (2547.5K). The target operating condition parameters determined through steps S1054 to S1058 in the embodiments of the present invention include: the thermal conductivity index (Cts) of the soft felt material used for the insulation layer, the thermal conductivity (Ctg) and electrical conductivity (Ceg) of the graphite materials used for the crucible, crucible lid, and heating cylinder, the power input to the induction coil (P), the placement position of the induction coil (Dxg), the distance from the top flange surface to the top of the crucible lid (Lfg), the diameter of the hole at the top of the crucible (Du), and the diameter of the hole at the bottom of the heating cylinder (Dd). The values ​​of the target operating condition parameters are 1.47 W·m. -1 ·K -1 0.62 W·m -1 ·K -1 73525 S·m -1 The parameters are 15.1kW, 81.7mm, 450mm, 25mm, and 2mm. After inputting the above target operating condition parameters into the active learning Gaussian process regression model, the predicted temperatures output by the active learning Gaussian process regression model include the predicted temperature (Tu) at the center of the top of the crucible (2555.5K) and the predicted temperature (Td) at the center of the bottom of the heating cylinder (2547.5K). The temperature error between these predicted temperatures and the target temperatures at the characteristic locations is 0%, indicating that the target operating condition parameters determined through the embodiments of the present invention have high accuracy.

[0211] Table 1

[0212] In an optional embodiment, step S101, which involves constructing a numerical simulation model corresponding to the silicon carbide crystal growth process, includes: Step S1017: Construct the heat transfer control equation corresponding to the growth furnace based on the heat conduction form in the growth furnace.

[0213] Step S1018: Construct the radiation transfer equation corresponding to the growth furnace based on the form of thermal radiation in the growth furnace.

[0214] Step S1019: Construct the volumetric heat production rate equation corresponding to the heating method of the growth furnace.

[0215] Step S1020: Based on the heat transfer control equation, the radiation transfer equation, and the volumetric heat generation rate equation, construct a numerical simulation model corresponding to the silicon carbide crystal growth process.

[0216] In this embodiment of the invention, the electronic device can construct a numerical simulation model through the operations corresponding to steps S1017 to S1020, which can completely reproduce the heat transfer law inside the growth furnace from three heat transfer dimensions: heat conduction, heat radiation, and heating method. This improves the simulation accuracy of the numerical simulation model for the actual temperature field distribution inside the furnace, which is beneficial for providing reliable data support for the subsequent construction of the active learning Gaussian process regression model. This simultaneously improves the modeling accuracy of the active learning Gaussian process regression model and the determination accuracy of the growth parameters of silicon carbide crystal.

[0217] The specific implementation of steps S1017 and S1018 can be found in the detailed description of step S1011, the specific implementation of step S1019 can be found in the detailed description of steps S1012 to S1013 and step S1015, and the specific implementation of step S1020 can be found in the detailed description of steps S1014 and S1016, which will not be repeated here.

[0218] In summary, the active learning-based method for determining silicon carbide crystal growth parameters provided in this invention first constructs a numerical simulation model based on the fundamental principles of PVT induction heating or resistance heating for silicon carbide crystal growth. Then, it uses Latin hypercube to uniformly extract a subset of operating parameters that characterize the regularity of these parameters from complex multidimensional operating conditions, performs numerical simulation, and constructs a small-sample parameter temperature dataset. Next, it expands the parameter temperature dataset based on active learning and uses a Gaussian process regression model to construct an active learning Gaussian process regression model for rapid temperature prediction. Finally, it introduces a particle swarm optimization algorithm to optimize the optimal target operating parameters in real time based on the required temperature gradient. This method achieves small-sample calculations instead of complex operating condition calculations, real-time prediction of characteristic location temperatures based on the samples of operating parameters to be detected, and real-time optimization of target operating parameters based on temperature requirements. This significantly reduces the computational and time costs of experiments and multiphysics numerical simulations, and improves the accuracy and efficiency of determining silicon carbide crystal growth parameters under complex operating conditions. It provides a highly accurate and efficient optimization method for real-time calculation and optimization of PVT induction heating or resistance heating silicon carbide crystals under complex operating conditions.

[0219] Device Examples Reference Figure 14 The diagram illustrates a logic block diagram of a silicon carbide crystal growth parameter determination device based on active learning provided by the present invention. The device may include: The first building module 1401 is used to build a numerical simulation model corresponding to the silicon carbide crystal growth process; The sample extraction module 1402 is used to extract the working condition parameter samples of the silicon carbide crystal growth process using the Latin hypercube algorithm. The acquisition module 1403 is used to acquire the characteristic location temperature corresponding to the working condition parameter sample using the numerical simulation model. The second construction module 1404 is used to construct an active learning Gaussian process regression model based on the working condition parameter samples and the characteristic location temperature by iteratively updating the prediction uncertainty. The determination module 1405 is used to determine the growth parameters of silicon carbide crystals using the active learning Gaussian process regression model.

[0220] Optionally, the sample extraction module includes: The first determination submodule is used to determine at least two operating parameters corresponding to the silicon carbide crystal growth process. The second determining submodule is used to determine the value range corresponding to each of the operating condition parameters; The extraction submodule is used to extract samples of operating parameters for the silicon carbide crystal growth process based on the value range and parameter dimension of each operating parameter using the Latin hypercube algorithm.

[0221] Optionally, the extraction submodule includes: The first construction unit is used to construct a multi-dimensional parameter space with the value range corresponding to various working conditions as the boundary, based on the parameter dimension of the working condition parameters. The first layering unit is used to layer the multidimensional parameter space according to the operating parameters using the Latin hypercube algorithm; The first extraction unit is used to randomly extract samples within each stratum and randomly combine the extraction results of each stratum to obtain the operating condition parameter samples.

[0222] Optionally, the extraction submodule includes: The first determining unit is used to determine at least two discrete parameter values ​​from the value range corresponding to the operating condition parameters; The second determining unit is used to determine the index identifier corresponding to each of the discrete parameter values; The second construction unit is used to construct a multi-dimensional index space based on the index identifiers corresponding to the discrete parameter values ​​under each of the aforementioned working conditions. The second layering unit is used to layer the multidimensional index space according to the operating parameters using the Latin hypercube algorithm; The second extraction unit is used to randomly extract index identifiers within each layer and randomly combine the extraction results of each layer to obtain an index combination. The mapping unit is used to map the index identifier in the index combination to the discrete parameter value corresponding to the index identifier, so as to obtain the working condition parameter sample.

[0223] Optionally, the operating parameters include the physical properties of the growth furnace, the process parameters of the growth furnace, and the structural parameters of the growth furnace; wherein, the physical properties include the thermal conductivity index of the insulation material in the growth furnace, the thermal conductivity of the heating substrate in the growth furnace, and the electrical conductivity of the heating substrate in the growth furnace; the process parameters include the heating power and the location of the heat source; and the structural parameters include the distance from the top flange surface to the top of the crucible cover in the growth furnace, the diameter of the top hole of the crucible in the growth furnace, and the diameter of the bottom hole of the heating substrate in the growth furnace.

[0224] Optionally, the second building module includes: The first construction submodule is used to construct a parameter temperature dataset based on the operating condition parameter samples and the feature location temperature when the index parameters of the Gaussian process regression model to be trained do not meet the target performance index. The parameter temperature dataset includes each group of operating condition parameter samples and the feature location temperature corresponding to the operating condition parameter samples. A sub-module is used to divide the parameter temperature dataset into a training dataset and a test dataset. The training submodule is used to train the Gaussian process regression model to be trained using the training dataset; The testing submodule is used to test the trained Gaussian process regression model using the test dataset to obtain the index parameters of the Gaussian process regression model. The third determining submodule is used to determine the Gaussian process regression model to be trained as an active learning Gaussian process regression model when the index parameters meet the target performance index.

[0225] Optionally, the first construction submodule includes: The third extraction unit is used to extract candidate operating condition parameter samples of the silicon carbide crystal growth process using the Latin hypercube algorithm when the index parameters of the Gaussian process regression model to be trained do not meet the target performance index. The third determining unit is used to determine the prediction uncertainty of each group of candidate operating condition parameter samples and to sort the prediction uncertainties of each group of candidate operating condition parameter samples. The update unit is used to update the parameter temperature dataset based on at least two candidate operating condition parameter samples ranked first in prediction uncertainty and the feature location temperature corresponding to the candidate operating condition parameter samples.

[0226] Optionally, the growth parameters include the temperature at a characteristic location corresponding to the operating condition parameter sample to be detected; the determining module includes: The first input submodule is used to input the sample of the working condition parameters to be detected into the active learning Gaussian process regression model; The first acquisition submodule is used to acquire the predicted temperature output by the active learning Gaussian process regression model; The fourth determination submodule is used to use the predicted temperature as the characteristic location temperature corresponding to the working condition parameter sample to be detected.

[0227] Optionally, the growth parameters include pre-set target operating condition parameters corresponding to the target temperature at the characteristic location; the determining module includes: An initialization submodule is used to initialize a particle swarm in a multi-dimensional parameter space corresponding to the operating parameters, wherein each particle in the particle swarm corresponds to a set of operating parameters. The update submodule is used to update the velocity and position of particles in the particle swarm; The second input submodule is used to input the operating parameters corresponding to any particle in the particle swarm into the active learning Gaussian process regression model to obtain the predicted temperature corresponding to the particle. The update submodule is further configured to update the motion speed and position of the particles in the particle swarm again when the difference between the predicted temperature and the target temperature at the feature position is greater than or equal to a preset threshold. The second input submodule is further configured to reacquire the predicted temperature corresponding to the particle until the difference between the predicted temperature and the target temperature at the feature position is less than the preset threshold. The fifth determining submodule is used to determine the operating condition parameter corresponding to the predicted temperature as the target operating condition parameter when the difference between the predicted temperature and the target temperature at the characteristic location is less than the preset threshold.

[0228] Optionally, the first building module includes: The second construction submodule is used to construct the heat transfer control equation corresponding to the growth furnace based on the heat conduction mode in the growth furnace; The third construction submodule is used to construct the radiation transfer equation corresponding to the growth furnace based on the form of thermal radiation in the growth furnace; The fourth construction submodule is used to construct the volumetric heat production rate equation corresponding to the heating method of the growth furnace. The fifth construction submodule is used to construct a numerical simulation model corresponding to the silicon carbide crystal growth process based on the heat transfer control equation, the radiation transfer equation, and the volumetric heat generation rate equation.

[0229] As the apparatus embodiment is basically similar to the method embodiment, it is described in a relatively simple manner. For relevant details, please refer to the description of the method embodiment.

[0230] This invention provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the active learning-based method for determining silicon carbide crystal growth parameters as described above.

[0231] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0232] Although preferred embodiments of the present invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present invention.

[0233] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0234] The above provides a detailed description of the method for determining silicon carbide crystal growth parameters based on active learning provided by the present invention. Specific examples have been used to illustrate the principle and implementation of the present invention. The description of the above embodiments is only for the purpose of helping to understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for determining silicon carbide crystal growth parameters based on active learning, characterized in that, The method includes: Construct a numerical simulation model corresponding to the silicon carbide crystal growth process; The Latin hypercube algorithm was used to extract operating parameter samples of the silicon carbide crystal growth process. The operating parameter samples included physical property parameters, process parameters, and structural parameters of the growth furnace. The physical property parameters included the thermal conductivity index of the insulation material in the growth furnace, the thermal conductivity of the heating substrate in the growth furnace, and the electrical conductivity of the heating substrate in the growth furnace. The process parameters included the heating power and the location of the heat source. The structural parameters included the distance from the top flange surface to the top of the crucible cover in the growth furnace, the diameter of the top hole of the crucible in the growth furnace, and the diameter of the bottom hole of the heating substrate in the growth furnace. Using the numerical simulation model, the temperature at the characteristic location corresponding to the working condition parameter sample is obtained; Based on the operating condition parameter samples and the characteristic location temperatures, an active learning Gaussian process regression model is constructed through iterative updates of prediction uncertainty. This construction includes: when the performance parameters of the Gaussian process regression model to be trained do not meet the target performance indicators, constructing a parameter temperature dataset based on the operating condition parameter samples and the characteristic location temperatures. The parameter temperature dataset includes each group of operating condition parameter samples and the corresponding characteristic location temperatures; dividing the parameter temperature dataset into a training dataset and a test dataset; training the Gaussian process regression model to be trained using the training dataset; and testing the trained Gaussian process regression model using the test dataset to obtain the Gaussian process regression model to be trained. The model's index parameters; if the index parameters meet the target performance index, the Gaussian process regression model to be trained is determined as an actively learned Gaussian process regression model; wherein, if the index parameters of the Gaussian process regression model to be trained do not meet the target performance index, constructing a parameter temperature dataset based on the operating condition parameter samples and the feature location temperature includes: if the index parameters of the Gaussian process regression model to be trained do not meet the target performance index, extracting candidate operating condition parameter samples for the silicon carbide crystal growth process using the Latin hypercube algorithm; determining the prediction uncertainty of each group of candidate operating condition parameter samples and ranking the prediction uncertainty of each group of candidate operating condition parameter samples; updating the parameter temperature dataset based on at least two candidate operating condition parameter samples with the highest prediction uncertainty and the feature location temperature corresponding to the candidate operating condition parameter samples. The growth parameters of silicon carbide crystals are determined using the active learning Gaussian process regression model. These growth parameters include pre-defined target operating parameters corresponding to the target temperature at a characteristic location. The determination of these parameters using the active learning Gaussian process regression model includes: initializing a particle swarm in a multi-dimensional parameter space corresponding to the operating parameters, where each particle in the swarm corresponds to a set of operating parameters; updating the velocity and position of the particles in the swarm; for any particle in the swarm, inputting the operating parameters corresponding to that particle into the active learning Gaussian process regression model to obtain the predicted temperature corresponding to that particle; if the difference between the predicted temperature and the target temperature at the characteristic location is greater than or equal to a preset threshold, updating the velocity and position of the particles in the swarm again, and re-obtaining the predicted temperature corresponding to the particle, until the difference between the predicted temperature and the target temperature at the characteristic location is less than the preset threshold; if the difference between the predicted temperature and the target temperature at the characteristic location is less than the preset threshold, determining the operating parameters corresponding to the predicted temperature as the target operating parameters.

2. The method according to claim 1, characterized in that, The extraction of operating parameter samples for the silicon carbide crystal growth process using the Latin hypercube algorithm includes: Determine at least two operating parameters corresponding to the silicon carbide crystal growth process; Determine the value range corresponding to each of the aforementioned operating condition parameters; Based on the value range and parameter dimension of each operating condition parameter, the Latin hypercube algorithm is used to extract operating condition parameter samples for the silicon carbide crystal growth process.

3. The method according to claim 2, characterized in that, The step of extracting operating parameter samples for the silicon carbide crystal growth process using the Latin hypercube algorithm, based on the value range and parameter dimension of each operating parameter, includes: Based on the parameter dimensions of the operating condition parameters, a multi-dimensional parameter space is constructed with the value ranges corresponding to various operating condition parameters as boundaries; The multidimensional parameter space is divided into layers according to the operating parameters using the Latin hypercube algorithm; Samples are randomly drawn from each stratum, and the results from each stratum are randomly combined to obtain the working condition parameter samples.

4. The method according to claim 2, characterized in that, The step of extracting operating parameter samples for the silicon carbide crystal growth process using the Latin hypercube algorithm, based on the value range and parameter dimension of each operating parameter, includes: Determine at least two discrete parameter values ​​from the range of values ​​corresponding to the operating condition parameters; Determine the index identifier corresponding to each of the discrete parameter values; A multi-dimensional index space is constructed based on the index identifiers corresponding to the discrete parameter values ​​under each of the aforementioned operating conditions. The multidimensional index space is layered according to the operating parameters using the Latin hypercube algorithm; Within each layer, index identifiers are randomly selected, and the selection results from each layer are randomly combined to obtain an index combination. The index identifiers in the index combination are mapped to the discrete parameter values ​​corresponding to the index identifiers to obtain the operating condition parameter samples.

5. The method according to claim 1, characterized in that, The growth parameters include the characteristic location temperature corresponding to the operating condition parameter sample to be detected; the determination of the growth parameters of the silicon carbide crystal using the active learning Gaussian process regression model includes: Input the sample of the operating condition parameters to be detected into the active learning Gaussian process regression model; Obtain the predicted temperature output by the active learning Gaussian process regression model; The predicted temperature is used as the characteristic location temperature corresponding to the sample of operating condition parameters to be detected.

6. The method according to claim 1, characterized in that, The numerical simulation model corresponding to the silicon carbide crystal growth process includes: Based on the heat conduction pattern in the growth furnace, the heat transfer control equation corresponding to the growth furnace is constructed. Based on the form of thermal radiation in the growth furnace, construct the radiation transfer equation corresponding to the growth furnace; Based on the heating method of the growth furnace, construct the volumetric heat production rate equation corresponding to the heating method; Based on the heat transfer control equation, the radiation transfer equation, and the volumetric heat production rate equation, a numerical simulation model corresponding to the silicon carbide crystal growth process is constructed.

Images