A numerical simulation model for the growth of {\rm Ga}_x{\rm In}_{1-x}{\rm Sb} by the travelling heater method

A numerical simulation model for the growth of {\rm Ga}_x{\rm In}_{1-x}{\rm Sb} by the traveling heater method (THM) is presented. In a thermodynamically rational mathematical model, the momentum equations including the solutal and thermal buoyancy terms, the mass transport equations in terms of the mole fractions of components, the interface mass conservation equations and the phase equilibrium equations are presented for a two-dimensional axisymmetric growth cell configuration. The cell configuration and the furnace thermal profile are adopted from the experimental setup of Amistar Research Inc.

The field equations are solved numerically by an adaptive finite element procedure as the interfaces between the solid and liquid phases change in time. The fully-implicit time integration technique is adopted to solve the transient equations, and the resulting non-linear algebraic equations are solved by the Newton–Raphson method. Numerical results show that the furnace thermal profile, the thermal as well as solutal convection in the liquid solution have significant effects on the growth process. Results are only presented for small growth times. However, it is asserted that the present simulation model could be used to simulate the entire THM growth process of ternary alloys if the required computational power is available.