Numerical modeling of crystal growth under strong magnetic fields: An application to the travelling heater method

Abstract

The article presents a 3-D numerical simulation study for the growth of single crystal semiconductors under strong magnetic fields. In such high fields, the magnetic body force components, which also depend on the flow velocity components present numerical challenges particularly in terms of convergence of iterations. To remedy such difficulties, a novel numerical approach was introduced in an in-house 3-D finite volume-based computer code. As an application, the Travelling Heater Method (THM) was selected for the growth of CdTe crystals under a static vertical magnetic field. The governing equations of the model, which also include the electric charge balance equation in terms of the induced electric potential and the applied magnetic field intensity, are solved numerically. Evolution of the growth interface is simulated with the help of a moving grid algorithm in a block-structured finite-volume code. The convergence rate of iterations is significantly improved by treating a part of the magnetic body force terms implicitly in the iteration loop. Consequently, the magnetic field as high as 15.0 kG did not lead to any convergence problems. Simulation results are presented for the flow, concentration, temperature, and electric potential fields in the liquid solution. Results show that, in spite of the initially assumed-axisymmetric boundary conditions, three-dimensional transport structures develop as soon as the growth process begins. Application of the magnetic field suppresses convection in the solution, and the magnitude of the maximum flow velocity decreases monotonically with the increasing magnetic field intensity.