A numerical simulation study for the Czochralski growth process of Si under magnetic field

The article presents results of the numerical simulations carried out for the transport phenomena occurring during the Czochralski crystal growth process. Due to computational constraints, the simulations were kept limited to axisymmetric geometries. The simulation model gives special attention to the crystal–melt interface and oxygen transport, and treats the crystal–melt interface according to Stefan’s balance, by explicitly moving the grids. Oxygen evaporation at the free surface is expressed by balancing the corresponding fluxes. Marangoni convection due to temperature gradients is also incorporated into the model. The role of an applied axial magnetic field in controlling fluid flow, interface shape, and oxygen levels is studied in detail. The effect of crystal and crucible rotations is also examined under the influence of the magnetic field. Simulation results show that the application of an axial magnetic field leads to flatter interfaces and lower oxygen concentration levels, but makes the oxygen distribution non-uniform at the crystal–melt interface.