A continuum model for the Liquid Phase Diffusion growth of bulk SiGe single crystals

In this article, we present a computational model for the growth of SixGe1−x single crystals by Liquid Phase Diffusion (LPD) from the germanium-rich side of the binary SixGe1−x phase diagram. The model accounts for some important physical features of the LPD growth process of SixGe1−x such as a growth-zone design on the thermal field, the buoyancy induced convective flow and its effect on the growth process, the evolution of growth interface, and the variation of growth velocity with time. Two- and three-dimensional numerical simulations were carried out. Simulation results show that the natural convection in the solution is very strong during the initial stages of the growth process, and gets weaker as the growth progresses. Diffusion becomes the dominant mass transport mechanism during the rest of the growth process. Computed growth interface shapes and growth velocities agree with experimental observations.