Solidification of a GaAs melt – Optimal

Abstract. We present an optimal control approach for the crystallization of a GaAs melt in a VGF configuration. The solidification process is described by a two phase Stefan problem including flow driven by convection and Lorentz forces. The interface between the liquid and the solid phase is modelled as a graph. The control goal consists in tracking a prescribed shape and evolution of the free boundary (phase interface) using the crucible temperature and/or Lorentz forces. In particular we intend to achieve a flat free boundary in order to keep the density of dislocations small, compare e.g. [8]. We achieve this goal by minimizing an appropriate cost functional. The re-sulting optimization problem is solved numerically using an adjoint approach. In the present work we apply the concept developed in [2, 3, 13] to growth from a melt to a practically relevant configuration [6]. Among other things we show that both, the control with Lorentz forces as well as the control with crucible wall temperature may be applied to achieve the control goal.