Three-dimensional modeling of melt flow and interface shape in the industrial liquid-encapsulated Czochralski growth of GaAs

The heat transport in the melt and in the crystal including the interface shape was numerically investigated by local, fully three-dimensional (3D), time-dependent simulations for an industrially sized liquid-encapsulated Czochralski setup for growing GaAs crystals with 150 mm diameter. The thermal boundary conditions for the local 3D simulations were obtained from global quasi-steady 2D simulations. It was found that the type of thermal boundary conditions (fixed temperature or heat flux) has a strong influence on the 3D results of the interface shape and on the melt convection. Furthermore, a high sensitivity of the interface deflection on the temperature at the bottom wall of the crucible is observed. For a control of the interface shape the use of two types of magnetic fields (horizontal and vertical) was considered. It was found that a horizontal magnetic field has a bigger influence on the interface shape than a vertical magnetic field. (C) 2004 Elsevier B.V. All rights reserved.