Lattice Boltzmann Modeling of the Dissolution Process of Silicon into Germanium using a Simplified Crystal Growth Technique

Numerical simulations were carried out to explain the behavior exhibited in experimental work on the dissolution process of silicon into a germanium melt. The experimental work utilized a material configuration similar to that used in the Liquid Phase Diffusion (LPD) and Melt-Replenishment Czochralski (Cz) growth systems. The numerical simulations were carried out under the assumption of 2D. The mathematical model equations were developed using Lattice Boltzmann Method (namely the BGK approximation was adopted). Measured concentration profiles and dissolution height from the samples processed with and without the application of magnetic field show that the amount of silicon transported into the melt is slightly higher in the samples processed under magnetic field, and there is a difference in dissolution interface shape indicating a change in flow structure. This change in flow structure was predicted by the present LB model. In the absence of magnetic field a flat stable interface is observed. In the presence of an applied field, however, the dissolution interface remains flat in the center but curves back into the source material near the edge of the wall. This indicates a far higher dissolution rate at the edge of the silicon source.