Comparison between analytical and numeric determination of the interface curvature during dewetted Bridgman crystal growth

The effect of the crystal-crucible gap on the curvature of the solid-liquid interface, in the dewetted Bridgman method, has been studied for a set of non-dimensional parameters representative of classical semiconductor crystal growth. Using COMSOL Multiphysics 3.3, the equation of energy, in which thermal conductivity varies as a function of temperature, has been solved in the stationary case, to find the shape of the solid-liquid interface. The analysis shows that the shape of the interface depends on the thickness of the gap, the thickness of the crucible, and the thermal conductivities of the liquid, solid and crucible. These dependences were compared with those obtained through an analytical formula for the interface curvature, based on simple heat fluxes arguments. The main conclusion is that the solid-liquid interface curvature can be adjusted by the thickness of the gap. In some cases the curvature can be reversed from convex to concave. (C) 2007 Elsevier B.V. All rights reserved.