A method for growing gallium oxide based on an explainable machine learning optimized guided mode method

Abstract

This invention relates to the field of semiconductor single crystal material growth technology, and more particularly to a method for optimizing gallium oxide (EFG) growth using the guided mode method based on interpretable machine learning. The method includes the following steps: constructing a process parameter-temperature gradient mapping database for gallium oxide crystal growth; constructing an ensemble learning framework model to achieve parallel optimization using multiple algorithms; employing a multi-dimensional evaluation strategy to ultimately select the prediction model with the highest matching degree to the preset process standard; using the SHAP method to compare the feature importance in the optimal prediction model; inputting the parameter set into the prediction model to accurately obtain the axial temperature gradient distribution characteristics of the crystal; and using optimization algorithms to perform solution space optimization on the prediction results to select parameter combinations that simultaneously meet the axial temperature gradient control requirements. This invention provides an innovative solution for optimizing the EFG (guided mode method) crystal growth process based on machine learning-based intelligent thermal field prediction technology.

Description

Technical Field

[0001] This invention relates to the field of semiconductor single crystal material growth technology, and in particular to a method for growing gallium oxide based on interpretable machine learning-optimized guided mode method. Background Technology

[0002] Gallium oxide single crystal ( β Ga₂O₃, as a typical representative of fourth-generation semiconductor materials, has demonstrated significant application value in high-voltage power electronic devices and deep-ultraviolet photodetectors due to its ultra-wide bandgap characteristics. This material system, with its excellent physical properties, has become a research hotspot in the field of wide-bandgap semiconductors. To address the challenges of component volatilization and low thermal conductivity during material preparation, the industry currently widely employs the guided-mode method for large-size single-crystal growth. This technical approach effectively solves the thermodynamic control problems in the crystal growth process.

[0003] Although the guided-mode method has made breakthrough progress in the fabrication of large-size gallium oxide single crystals, its industrial application is still limited by the optimization challenges of the process thermodynamic system. Specifically, this manifests as: Imbalance in thermal gradient control—crystal growth kinetics are highly sensitive to axial temperature gradients. Excessive gradient amplitude or distorted distribution can lead to significant local stress accumulation, causing crystal interface instability and inducing macroscopic cracks or melt fracture. Simultaneously, it exacerbates the probability of microstructural defects such as dislocation multiplication and twin formation, directly affecting the electrical reliability of wafer-level materials. The contradiction of thermal field scalability—facing the industrialization needs of 6-inch and larger crystals, the complexity of thermal field design due to multi-physics coupling increases dramatically. To achieve uniform heat flow distribution at large-diameter growth interfaces, the furnace thermal field structure, insulation system, and gas flow mass transfer efficiency must be optimized simultaneously, placing stringent requirements on the precision of thermal field temperature control.

[0004] Traditional numerical simulation-based EFG (Expanded Modeling) thermal field analysis methods have significant limitations: the modeling process requires multiple rounds of iterative modeling and repeated calculations, resulting in significant computational resource consumption and a lengthy cycle. More critically, the process system involves multi-physics coupling parameters (such as heating power, crucible position, and thermal conductivity of the insulation layer), and there are strong coupling effects between these parameters. Adjusting a single parameter can trigger a chain reaction of reconstructions in key thermodynamic boundary conditions such as the heat flux density field and temperature gradient field. This complex nonlinear correlation mechanism makes it difficult to determine the optimal parameter optimization path for controlling the thermal field distribution, ultimately leading to a significant deviation between the simulation results and the axial temperature gradient distribution required for actual EFG crystal growth, making it difficult to accurately reproduce the three-dimensional temperature gradient distribution characteristics required by the EFG method.

[0005] In view of the above-mentioned problems, this invention provides a method for optimizing the mode-guided growth of gallium oxide based on interpretable machine learning to optimize the furnace structure and achieve thermal system optimization for gallium oxide growth by EFG, thus providing an effective technical solution for improving the quality of gallium oxide single crystal growth. Summary of the Invention

[0006] The purpose of this invention is to provide a method for optimizing the mode-guided growth of gallium oxide based on interpretable machine learning, which provides an innovative solution for optimizing the EFG (mode-guided growth) crystal growth process.

[0007] One of the technical solutions adopted to achieve the objective of this invention is: a method for growing gallium oxide based on interpretable machine learning-optimized guided mode method, comprising the following steps: Historical data of multidimensional process parameters were collected, and the corresponding crystal axial temperature gradient was obtained simultaneously to form the original dataset. The multidimensional process parameters were constructed as feature vectors, and the crystal axial temperature gradient was set as the regression label to construct a process parameter-temperature gradient mapping database for gallium oxide crystal growth. An ensemble learning framework model is constructed, dividing multidimensional process parameters into training and testing sets. The feature vectors of the multidimensional process parameters in the training set are used as model input, and the target value of the crystal axial temperature gradient is used as the supervision signal for model training, achieving parallel optimization of multiple algorithms. A multi-dimensional evaluation strategy was adopted. The evaluation index parameters between the temperature gradient prediction values ​​and the measured values ​​of each candidate model were calculated using test set data. The comprehensive performance of the model was quantified by longitudinal and horizontal comparisons. Finally, the prediction model with the highest matching degree to the preset process standard was selected. The SHAP method is used to compare the feature importance in the optimal prediction model; The specific steps are as follows: (1) Sample the feature set; (2) Convert the set vector into actual feature values ​​through feature mapping and calculate the corresponding model prediction output; (3) Calculate the weight coefficient of each feature set based on the SHAP kernel function formula; (4) Construct a weighted linear regression model, using the sampled feature set vector as the independent variable, the SHAP kernel function value as the sample weight, and the model prediction value as the dependent variable; (5) The linear regression coefficients obtained after model training are the SHAP estimates of each feature.

[0008] The parameter set is input into the prediction model to accurately obtain the axial temperature gradient distribution characteristics of the crystal. The optimization algorithm is used to optimize the solution space of the prediction results and select the parameter combination that simultaneously meets the axial temperature gradient control requirements.

[0009] Preferably, the multidimensional process parameters include the radius of the crucible, the height of the crucible, the thickness of the crucible lid, the length of the iridium mold, the width of the iridium mold, the width of the capillary slit, the height of the crystal, the coil current, the number of coil turns, and the height of the upper insulation layer.

[0010] Preferably, after collecting the original dataset, outliers are removed using the Z-scores method.

[0011] Preferably, the multidimensional process parameters are divided into a training set and a test set in an 8:2 ratio.

[0012] Preferably, the models in the ensemble learning framework include: Random Forest (RF), Extreme Gradient Boosting (XGBoost), and Category Boosting (Catboost).

[0013] Preferably, 5-fold cross-validation is used during model training to reduce the risk of overfitting and obtain the optimal hyperparameter values ​​for each regression model.

[0014] Preferably, the evaluation metrics of the multi-dimensional evaluation strategy include: mean squared error (MSE), root mean square error (RMSE), mean absolute error (MAE), and goodness of fit (R-squared).

[0015] Preferably, the smaller the mean square error, root mean square error, and mean absolute error, the better the model performance and the greater the goodness of fit. The goodness of fit ranges from 0 to 1.

[0016] Preferably, through SHAP analysis, the top five characteristic quantities affecting the magnitude of the crystal temperature gradient are: the height of the crystal, the width of the iridium mold, the thickness of the crucible lid, the height of the upper insulation layer, and the number of turns of the coil.

[0017] Preferably, the optimization algorithm is a genetic algorithm, and the optimization objective is to minimize the temperature gradient of the crystal.

[0018] The beneficial effects of this invention are: The method of this invention provides an innovative solution for optimizing the EFG (mode-guided growth method) crystal growth process based on machine learning-based intelligent thermal field prediction technology.

[0019] The method of this invention breaks through the bottleneck of traditional thermal field analysis by constructing a dual-engine model of "numerical simulation-data-driven": First, multi-dimensional parameter sensitivity analysis is used to reveal the coupling mechanism of multiple parameters such as power and geometric configuration in thermal field control. A high-fidelity thermal field dataset is constructed based on numerical simulation, and feature engineering modeling is performed by combining ensemble learning algorithms to achieve high-precision prediction of the temperature field. Finally, the reverse design capability of process parameters is formed, and the combination of process parameters that satisfy the axial temperature gradient of the crystal is obtained by iterative optimization algorithm through genetic algorithm optimization.

[0020] The method of this invention shortens the thermal field design cycle by more than 70% and reduces the cost of a single growth experiment by 45%, providing an intelligent thermal field control paradigm for the industrial growth of 6-inch EFG single crystals. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a schematic diagram of the process for growing gallium oxide based on the interpretable machine learning optimization method according to the present invention; Figure 2 This is a schematic diagram of the equipment for growing single-crystal gallium oxide using the EFG method according to the present invention. Figure 3 This is a flowchart illustrating the design of the prediction and evaluation model based on machine learning in this invention. Figure 4 This is a flowchart illustrating the design process of the present invention based on the genetic optimization algorithm. Figure 5 The graph shows the evaluation results of different models of this invention; Figure 6 This is a graph showing the contribution of the characteristic quantities of this invention to the crystal temperature gradient. Figure 7 The diagram shows the distribution of thermal stress in the crystal before and after optimization in this invention. Detailed Implementation

[0023] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments: like Figure 1 The diagram shows a flowchart of the method for growing gallium oxide based on the mode-guided method optimized by interpretable machine learning according to the present invention. The method for growing gallium oxide based on the mode-guided method optimized by interpretable machine learning includes the following steps: Historical data of multidimensional process parameters were collected, and the corresponding crystal axial temperature gradient was obtained simultaneously to form the original dataset. The multidimensional process parameters were constructed as feature vectors, and the crystal axial temperature gradient was set as the regression label to construct a process parameter-temperature gradient mapping database for gallium oxide crystal growth. The model training phase employs an ensemble learning framework to achieve parallel optimization of multiple algorithms: An ensemble learning framework model is constructed, dividing the multi-dimensional process parameters into training and testing sets. The feature vectors of the multi-dimensional process parameters in the training set are used as model input, and the target value of the crystal axial temperature gradient is used as the supervision signal for model training, thus achieving parallel optimization of multiple algorithms. Model selection stage: A multi-dimensional evaluation strategy is adopted. The evaluation index parameters between the temperature gradient prediction values ​​and the measured values ​​of each candidate model are calculated through test set data. The comprehensive performance of the model is quantified by longitudinal and horizontal comparison. Finally, the prediction model with the highest matching degree with the preset process standard is selected. The SHAP method is used to compare the feature importance in the optimal prediction model; Input the parameter set (actual parameters) into the prediction model to accurately obtain the axial temperature gradient distribution characteristics of the crystal. Use the optimization algorithm to optimize the solution space of the prediction results and select the parameter combination that simultaneously meets the axial temperature gradient control requirements.

[0024] The multidimensional process parameters include the radius of the crucible, the height of the crucible, the thickness of the crucible lid, the length of the iridium mold, the width of the iridium mold, the width of the capillary slit, the height of the crystal, the coil current, the number of coil turns, and the height of the upper insulation layer.

[0025] The dataset consists of 2000 sets of one-to-one mappings of process parameters and temperature gradients, and requires preprocessing. After collecting the original dataset, outliers are removed using the Z-scores method.

[0026] The multidimensional process parameters were divided into training and testing sets in an 8:2 ratio.

[0027] The models in the ensemble learning framework include: Random Forest (RF), Extreme Gradient Boosting (XGBoost), and Category Boosting (Catboost).

[0028] The model training process uses 5-fold cross-validation to reduce the risk of overfitting and obtain the optimal hyperparameter values ​​for each regression model.

[0029] The evaluation metrics of the multi-dimensional evaluation strategy include: mean squared error (MSE), root mean squared error (RMSE), mean absolute error (MAE), and goodness of fit (R-squared).

[0030] The smaller the mean square error, root mean square error, and mean absolute error, the better the model performance. The greater the goodness of fit, the better the model performance. The goodness of fit ranges from 0 to 1.

[0031] SHAP analysis revealed that the top five characteristics affecting the magnitude of the crystal temperature gradient are: crystal height, iridium mold width, crucible lid thickness, upper insulation layer height, and coil number of turns.

[0032] The optimization algorithm uses a genetic algorithm, and the optimization objective is to minimize the temperature gradient of the crystal.

[0033] Example 2 like Figure 2The diagram shows the equipment for growing single-crystal gallium oxide using EFG according to the present invention.

[0034] The main components of the EFG equipment include: 1-lower insulation layer, 2-iridium crucible, 3-coil, 4-iridium mold, 5-melt, 6-capillary slit, 7-crucible lid, 8-crystal, 9-upper insulation layer, 10-seed crystal rod.

[0035] The main growth process is as follows: First, the iridium crucible is heated by induction heating to a temperature higher than the melting point of gallium oxide, causing it to melt completely. The melt is then transported to the top of the iridium mold through capillary action and evenly covers the surface. Next, the seed crystal rod is slowly lowered to a height of 3-5 mm above the mold for 5-10 minutes of preheating. Once the seed crystal and melt are fully bonded, the crystal pulling process is initiated. To eliminate seed crystal defect propagation, a necking process is implemented by increasing the heating power to improve crystal quality. Subsequently, the power is reduced to enter the shoulder expansion growth stage, allowing the crystal to extend laterally and cover the mold surface, followed by constant-diameter growth. After the entire process is completed, the crystal is removed after gradient cooling to room temperature, ultimately yielding a complete neptunium oxide single crystal.

[0036] To construct a process parameter-temperature gradient mapping database for gallium oxide crystal growth, ten multi-dimensional process parameters were collected, including crucible radius (45-47 mm), crucible height (45-47.5 mm), crucible lid thickness (1-4 mm), iridium mold length (55-57 mm), iridium mold width (5-15 mm), capillary slit width (0.5-1 mm), crystal height (5-100 mm), coil current (20-28 A), coil turns (100-150 turns), and upper insulation layer height (81-141.5 mm). These parameters served as features in the dataset. Simultaneously, the corresponding crystal axial temperature gradient distribution range of 0-18 K / mm was acquired and used as regression labels in the data.

[0037] Figure 3 This is a flowchart illustrating the design of the prediction and evaluation model based on machine learning in this invention.

[0038] The model's dataset is divided into multidimensional process parameters and temperature gradients. The multidimensional process parameters are constructed as feature vectors, and the temperature gradient index is set as the regression label. The Z-scores method is used to remove outliers. Specifically, a Z-score threshold is set; for example, a threshold of 3 is chosen, meaning values ​​exceeding 3 standard deviations are considered outliers.

[0039] The dataset was divided into training and test sets in an 8:2 ratio. Three ensemble learning models—RF, XGBoost, and Catboost—were used for predictive analysis. For the training set, 5-fold cross-validation was used to reduce the risk of overfitting, obtaining the optimal hyperparameter values ​​for each regression model. Then, the test set data was used for predictive analysis. The model performance was evaluated using MSE, RMSE, MAE, and R-squared metrics. After selecting the best model, SHAP analysis was performed to identify key process factors.

[0040] Figure 4 This is a flowchart illustrating the design process of the present invention based on the genetic optimization algorithm.

[0041] To obtain optimal process parameters, the optimization objective is to minimize the temperature gradient of gallium oxide crystals. A genetic algorithm is used to achieve this optimization goal. Through genetic operations such as selection, crossover, and mutation, the population continuously evolves, approaching the optimal solution. For parameter settings, the Non-Dominated Sorting Genetic Algorithm (NSGA-II) is selected as the solver, with a population size of 100, a maximum number of iterations of 50, crossover probabilities of 0.9, and mutation probabilities of 0.2. The encoding method is floating-point real-number encoding. In the actual optimization process, evaluating whether the algorithm has effectively converged is a crucial prerequisite for judging the reliability of the optimization. Therefore, the changes in the number of non-dominated solutions and the convergence of the Pareto front spacing are monitored during the optimization process. Combined with the Pareto solution set distribution at different generations, the search efficiency and convergence behavior of the optimization process are comprehensively analyzed.

[0042] Figure 5 The following are evaluation results of different models of the present invention: a) is the result diagram of the three models for MAE evaluation, b) is the result diagram of the three models for MSE evaluation, c) is the result diagram of the three models for RMSE evaluation, and d) is the result diagram of the three models for R-squared evaluation.

[0043] The smaller the MSE, RMSE, and MAE values, the better the model performance; the larger the R-squared value, the better the model performance. R-squared ranges from 0 to 1. To evaluate the model's suitability, error information was collected after running each model 500 times. It can be seen that among the RF, XGBoost, and Catboost models, Catboost has the smallest MSE, RMSE, and MAE, and the largest R-squared. Based on the optimal model evaluation scheme, Catboost is selected as the best predictive model.

[0044] Figure 6 This is a graph showing the contribution of the characteristic quantities of this invention to the crystal temperature gradient.

[0045] To further reveal the model's decision-making process and verify the contribution of each input feature to the prediction results, the SHAP method was employed. This method, derived from cooperative game theory, can quantitatively calculate the contribution of each feature to the result of a single prediction sample, thus visually demonstrating the model's internal decision-making mechanism. SHAP analysis revealed that the top five features affecting the crystal temperature gradient are: crystal height, iridium mold width, crucible lid thickness, upper insulation layer height, and coil turn count.

[0046] Figure 7 The diagram shows the distribution of thermal stress in the crystal before and after optimization in this invention.

[0047] An optimized Pareto front distribution was selected, with the following process parameters: crucible radius (range 45.32 mm), crucible height (45 mm), crucible lid thickness (3.52 mm), iridium mold length (54 mm), iridium mold width (5 mm), capillary slit width (0.5 mm), crystal height (10 mm), coil current (28 A), number of coil turns (114 turns), and upper insulation layer height (90.2 mm). To better evaluate crystal quality, thermal stress was simulated. Figure 7 In Figure 'a', the thermal stress distribution of the crystal before optimization is shown. The maximum thermal stress of the crystal is ~2.4 MPa. Figure 7 The thermal stress distribution of the crystal after optimization (b) is shown. The maximum thermal stress of the crystal is ~1.2 MPa, indicating that the quality of the crystal has been significantly improved after optimization.

[0048] The above description is merely a preferred embodiment of the present invention, and should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A method for optimizing growth of gallium oxide based on explainable machine learning guided mode method, characterized by, Includes the following steps: Historical data of multidimensional process parameters were collected, and the corresponding crystal axial temperature gradient was obtained simultaneously to form the original dataset. The multidimensional process parameters were constructed as feature vectors, and the crystal axial temperature gradient was set as the regression label to construct a process parameter-temperature gradient mapping database for gallium oxide crystal growth. An ensemble learning framework model is constructed, dividing multidimensional process parameters into training and testing sets. The feature vectors of the multidimensional process parameters in the training set are used as model input, and the target value of the crystal axial temperature gradient is used as the supervision signal for model training, achieving parallel optimization of multiple algorithms. A multi-dimensional evaluation strategy was adopted. The evaluation index parameters between the temperature gradient prediction values ​​and the measured values ​​of each candidate model were calculated using test set data. The comprehensive performance of the model was quantified by longitudinal and horizontal comparisons. Finally, the prediction model with the highest matching degree to the preset process standard was selected. The SHAP method is used to compare the feature importance in the optimal prediction model; The parameter set is input into the prediction model to accurately obtain the axial temperature gradient distribution characteristics of the crystal. The optimization algorithm is used to optimize the solution space of the prediction results and select the parameter combination that simultaneously meets the axial temperature gradient control requirements.

2. The method for growing gallium oxide based on an explainable machine learning optimized leaky mode method according to claim 1, characterized in that, The multidimensional process parameters include the radius of the crucible, the height of the crucible, the thickness of the crucible lid, the length of the iridium mold, the width of the iridium mold, the width of the capillary slit, the height of the crystal, the coil current, the number of coil turns, and the height of the upper insulation layer.

3. The method for growing gallium oxide based on interpretable machine learning optimization of the guided mode method according to claim 1, characterized in that, After collecting the original dataset, outliers were removed using the Z-scores method.

4. The method for growing gallium oxide based on interpretable machine learning optimization of the guided mode method according to claim 1, characterized in that, The multidimensional process parameters were divided into training and testing sets in an 8:2 ratio.

5. The method for growing gallium oxide based on interpretable machine learning optimization of the guided mode method according to claim 1, characterized in that, The models in the ensemble learning framework include: Random Forest (RF), Extreme Gradient Boosting (XGBoost), and Category Boosting (Catboost).

6. The method for growing gallium oxide based on an explainable machine learning optimized leaky mode method according to claim 5, characterized in that The model training process uses 5-fold cross-validation to reduce the risk of overfitting and obtain the optimal hyperparameter values ​​for each regression model.

7. The method for growing gallium oxide based on an explainable machine learning optimized leaky mode method according to claim 1, characterized in that, The evaluation metrics for the multi-dimensional evaluation strategy include: mean squared error, root mean square error, mean absolute error, and goodness of fit.

8. The method for growing gallium oxide based on interpretable machine learning optimization of the guided mode method according to claim 7, characterized in that, The smaller the mean square error, root mean square error, and mean absolute error, the better the model performance. The greater the goodness of fit, the better the model performance. The goodness of fit ranges from 0 to 1.

9. The method for growing gallium oxide based on interpretable machine learning optimization of the guided mode method according to claim 1, characterized in that, SHAP analysis revealed that the top five characteristics affecting the magnitude of the crystal temperature gradient are: crystal height, iridium mold width, crucible lid thickness, upper insulation layer height, and coil number of turns.

10. The method for growing gallium oxide based on an explainable machine learning optimized leaky mode method according to claim 1, characterized in that, The optimization algorithm uses a genetic algorithm, and the optimization objective is to minimize the temperature gradient of the crystal.

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