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Fast prediction of fluid flow and thermal fields during the growth of bulk silicon single crystals by the ‘Vertical Magnetic Field Applied Czochralski (VMCz) Method’ was successfully achieved by the application of Physics Informed Neural Networks (PINNs) without any answer-labeled training data generated by a numerical simulation. The PINNs’ results are in good agreement with those of the numerical simulation. The prediction time by PINNs was significantly reduced; to less than 0.1 seconds compared with about 30 minutes required by the numerical simulation. Moreover, being mesh-free techniques, PINNs do not require mesh reconstruction to accommodate the change in the growth melt volume during growth. This shows that PINNs have great potential, as real-time simulation techniques, for future applications in various areas.

Silicon carbide (SiC) is a power semiconductor used to supply and control the electric power source. Top-Seeded Solution Growth (TSSG) method is a promising technique for producing high-quality SiC single crystals. In order to achieve a high- and uniform-growth rate in this growth technique, however, the complex fluid flow developing in the growth melt/solution, mainly induced by the electromagnetic field of the induction-heating coils, free surface tension gradient, and buoyancy, must be well-controlled. Our previous studies have shown that the applications of a static magnetic field and seed rotation are effective in controlling the components of this melt flow and the associated control parameters were optimized effectively using the Bayesian optimization. In this study, we analyze the optimal state determined by the Bayesian optimization in more detail and it is found that the separation of the Marangoni flow near the seed edge leads to a non-uniform growth rate. In addition, the most sensitive region of the melt flow is determined by using an explainable machine learning technique based on a convolutional neural network and the sensitivity map obtained by SmoothGrad. This machine learning technique automatically predicts the preferred melt flow pattern that would lead to high-quality crystal growth. The interpretations by the explainable machine learning technique used in the present study are consistent with those of previous studies carried out on the optimization of the TSSG method.

We have developed a reinforcement learning (RL) model to control the melt flow in the radio frequency (RF) top-seeded solution growth (TSSG) process for growing more uniform SiC crystals with a higher growth rate. In the study, the electromagnetic field (EM) strength is controlled by the RL model to weaken the influence of Marangoni convection. The RL model is trained through a two-dimensional (2D) numerical simulation of the TSSG process. As a result, the growth rate under the control of the RL model is improved significantly. The optimized RF-coil parameters based on the control strategy for the 2D melt flow are used in a three-dimensional (3D) numerical simulation for model validation, which predicts a higher and more uniform growth rate. It is shown that the present RL model can significantly reduce the development cost and offers a useful means of finding the optimal RF-coil parameters.

Three-dimensional numerical simulations were conducted for the Top-Seeded Solution Growth (TSSG) process of silicon carbide (SiC) crystals. We investigated the influence of coils frequency and peak current, and an applied rotating magnetic field (RMF) on the melt flow developing in this system. Numerical simulation results show that the Marangoni flow in the melt becomes stronger at higher coils frequencies due to the decreasing coils-induced electromagnetic field strength. Results also show that the use of external RMF may improve supersaturation uniformity along the seed if it is properly adjusted with respect to the coils-induced electromagnetic field strength. Furthermore, it is predicted that the application of RMF and seed rotation in the same direction may enhance supersaturation below the seed.