Numerical simulation of temperature fields during the sublimation growth of SiC single crystals, using WIAS-HiTNIHS

Abstract

We present numerical computations of the temperature fields in axisymmetric growth apparatus for sublimation growth of silicon carbide (SiC) bulk single crystals by physical vapor transport (PVT) (modified Lely method). The results are computed using our software WIAS-HiTNIHS, the WIAS High Temperature Numerical Induction Heating Simulator; pronunciation: $hit-nice, by solving the energy balance in the entire growth apparatus, taking into account the heat conduction in the solid parts as well as in gas cavities, and also accounting for the radiative heat transfer between the surfaces of the gas cavities. The insulation in a PVT growth apparatus usually consists of graphite felt, where the fibers are aligned in one particular direction, resulting in an anisotropic thermal conductivity. We show that neglecting this anisotropy can overestimate the SiC crystal's temperature by 70 K or underestimate the required heating power by 800 W. r

PDE-Driven Shape Optimization: Numerical Investigation of Different Descent Directions and Projections Using Penalization and Regularization

“…4]. More precisely, the software WIAS-HiTNIHS 1 , originally designed for the solution of more general PDE occurring when modeling conductive-radiative heat transfer and electromagnetic heating [2], has been adapted for use in the present context. WIAS-HiTNIHS is based on the program package pdelib [1], it employs the grid generator Triangle [11] to produce constrained Delaunay triangulations of the domains, and it uses the sparse matrix solver GSPAR [3] to solve the linear system arising from the finite volume scheme.…”

A Penalization and Regularization Technique in Shape Optimization Problems

“…Step For all the numerical examples discussed subsequently, we stopped the iteration and returned (g fin , p fin ) : [9,12], has been adapted for use in the present context.…”