Explainable machine learning for the analysis of transport phenomena in top-seeded solution growth of SiC single crystal

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 highand 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.