Effect of crucible geometry on the flow pattern in the magnetic field applied Czochralski process

Abstract

The effects of crucible geometry on the flow pattern and the oxygen concentration at the crystal-melt interface are studied numerically for the cusp type magnetic field applied Czochralski process. The numerically generated boundary-fitted orthogonal curvilinear coordinate systems are used with the finite difference method. The crucible geometry is found to have non-trivial effects on both the flow pattern and the oxygen concentration at the melt-crystal interface. Especially when the natural convection is dominant, the numerical results suggest that there exists a crucible shape which is advantageous over the conventional cylindrical shape in both the uniformity and the average level of oxygen concentration at the crystal-melt interface.