Efficient thermal field optimization of PVT simulations for SiC single crystal growth

The physical vapor transport (PVT) method is the most commonly applied growth technique for bulk SiC single crystals. Nowadays, the increasing demand of SiC substrates inevitably requires the adaption of PVT reactors to larger boule diameters. Since the boule quality and the single-crystal yield are primarily dependent on the thermal field inside the growth chamber and its stability, the control and optimization of the thermal conditions are the most crucial aspects to address. In this respect, the temperature difference along the seed, in the source and between source and seed, in addition to the growth temperature, are of particular interest. Due to the quasi-closed nature of the PVT system, in-situ measurements are hardly feasible, making numerical simulations the primary tool for analyzing the thermal field. But, since the high computational demand of these simulations restricts the number of cases that can be practically evaluated, numerical in-depth investigations are constrained. Attributed to this, the present study demonstrates an efficient way for constrained multi-objective optimization of the thermal field of PVT simulations by leveraging the correlation within the data through singular value decomposition (SVD). A 6-inch inductively heated PVT reactor is taken as a representative example and is optimized by combining machine learning models with numerical simulation data and optimization algorithms. In general, this approach enables the identification of optimal process parameters and reactor configurations, while revealing inherent tradeoffs between objectives and operational limitations, regardless of the PVT furnace operation principle (resistive or inductive) or seed crystal diameter (6-inch, 8-inch, etc.). Furthermore, it allows for an in-depth analysis of optimal settings, parameter sensitivities, interdependencies and solution robustness.