Multiple-Relaxation-Time Lattice Boltzmann method for thermosolutal convection in Czchralski silicon crystal growth

A multiple-relaxation-time lattice Boltzmann Method (MRT-LBM) is established to study the thermosolutal mixed convection with multi-physical parameters in the process of silicon crystal growth. The experimental results show that the proposed model for solving the thermosolutal convection has correctness and rapidity in Czchralski (Cz) crystal growth. The melt temperature distribution and the oxygen concentration distribution under different Xe numbers are studied in this paper, which come to the conclusion that the high Reynolds (Re) numbers are helpful to improve the uniformity of the thermosolutal distribution, but it cannot reduce the oxygen concentration effectively. Analysis of the oxygen concentration distributions under the different Cusp magnetic field intensities show that the external magnetic field can force the oxygen concentration gathered at the crucible wall and inhibit the content of oxygen impurity. The oxy gen concentration decreases with the increase of Hartmann (Ha) numbers at the solid-liquid interface, which indicates that the strong magnetic field can reduce the oxygen content of the crystal.