Optimization of semiconductor melts
Günter Bärwolff, Michael Hinze · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2006
In the present paper we investigate optimal control of semiconductor melts in zone-melting and Czochralski growth configurations. The flow is governed by the Boussinesq approximation of the Navier-Stokes system. The control goal consists in tracking of a prescribed flow field. As control action boundary heating in terms of Dirichlet and Neumann-type boundary conditions is considered. Optimal control strategies are characterized in terms of the first-order optimality conditions. On the numerical level these optimality conditions are solved by a damped Picard iteration. We present numerical experiments in two and three spatial dimensions for the crystal (Bi0.25Sb0.75)2 Te2, which is formed by a composition of bismuth point fifty antimony one point fifty tellurium two, as well as for Si (Silicium).