Transient three-dimensional numerical computation for unsteady oxygen concentration in a silicon melt during a Czochralski process under a cusp-shaped magnetic field

This paper presents numerical computation for the transient oxygen concentration of a silicon melt in a Czochralski process under a cusp-shaped magnetic field. Transient three-dimensional numerical calculations were carried out for two cases of Ha = 0 and 161 for Pr = 0.013, Ra = 3.92 × 10⁵, Re_cr=1329, Re_cu = -1596 and Sc = 5.5. The SIMPLE algorithm was employed. The oxygen concentration at a fixed point has a periodic oscillation as a function of time. The local and average oxygen concentrations in the silicon melt were less with a cusp-shaped magnetic field than those without a magnetic field. The power spectral density for the oxygen concentration fluctuation was also computed.