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Modeling and simulation of sublimation growth of SiC bulk single crystals. (English) Zbl 1081.35117

Summary: We present a transient mathematical model for the sublimation growth of silicon carbide (SiC) single crystals by the physical vapor transport (PVT) method. The model of the gas phase consists of balance equations for mass, momentum, and energy, as well as reaction-diffusion equations. Due to physical and chemical reactions, the gas phase is encompassed by free boundaries. Nonlinear heat transport equations are considered in the various solid components of the growth system.
Discontinuous and nonlocal interface conditions are formulated to account for temperature steps between gas and solid as well as for diffuse-gray radiative heat transfer between cavity surfaces. An axisymmetric induction heating model is devised using a magnetic scalar potential. For a nonlinear evolution problem arising from the model, a finite volume scheme is stated, followed by a discrete existence and uniqueness result. We conclude by presenting and analyzing results of transient numerical experiments relevant to the physical growth process.

MSC:

35Q72 Other PDE from mechanics (MSC2000)
80A20 Heat and mass transfer, heat flow (MSC2010)
80M25 Other numerical methods (thermodynamics) (MSC2010)
76M12 Finite volume methods applied to problems in fluid mechanics
74N05 Crystals in solids
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