Solidification of a GaAs melt—Optimal control of the phase interface

A mathematical model developed for an optimal thermal control of the melt-crystal interface in vertical gradient freeze growth of GaAs is presented. The solidification process is described by a two-phase Stefan problem including convective flow in the melt. The interface between the liquid and the solid phase is modeled as a graph. The control goal consists in tracking a prescribed shape and evolution of the solid–liquid interface using the temperature at the crucible wall. In particular, the planar interface was taken as the target parameter of the model. This is achieved by minimizing an appropriate cost functional. The resulting optimization problem is solved numerically using an adjoint approach. The thermal regime found in this work provides the basis for real growth experiments which are planned in the near future.