Three-dimensional characteristics of turbulent flow and heat transfer in Czochralski silicon melt with different cusp magnetic field configurations

Abstract

Three-dimensional unsteady simulations are performed for the turbulent flow and heat transfer in a Czochralski silicon melt for 300 mm crystal growth. The influence of the horizontal symmetry plane in the cusp magnetic field on the melt flow, temperature field, and crystal/melt interface is systematically analyzed. The numerical results show that the melt velocity and its fluctuation near the interface decrease, while the temperature and its fluctuation increase gradually with the downward horizontal symmetry plane position. For each horizontal symmetry plane position, the oscillation frequencies of melt temperature and velocity consist of a basic frequency and its integer multiple frequencies. Thermal waves with a regular shape rotate on the melt-free surface, and the rotational direction is consistent with the crucible rotation. The interface shape is strongly associated with the heat transfer near the interface, which depends on the melt flow direction and velocity magnitude as well as the temperature gradient below the crystal. In addition, the oscillation of interface temperature is affected by the melt flow below the crystal, changing from high-frequency small fluctuation to low-frequency large fluctuation with the horizontal symmetry plane moving down.