Numerical Investigation of Effect of Temperature Profile Imposed on the Crucible Surface on Oxygen Incorporated at the Crystal Melt Interface for 450 mm Diameter Silicon Single Crystal Growth in Presence of CUSP Magnetic Field Using Czochralski Technique

Abstract

Numerical investigation has been carried out to study the effect of thermal boundary condition on turbulent melt flow and oxygen transfer inside a crucible used to grow 450 mm diameter silicon single crystal using Czochralski method. Two types of thermal boundary conditions, namely, isothermal crucible surface and experimentally measured temperatures on the crucible surface have been imposed on the crucible wall and crucible bottom. Melt motion owing to buoyancy, surface tension variation at the free melt surface as well as crystal and crucible rotation has been considered. Effect of CUSP magnetic field has also been investigated. Melt having aspect ratio of 1 and 0.5, representing high and moderate level of melt inside the crucible have been considered. K-epsilon turbulent model with low Reynolds number formulation has been used for turbulence modelling. Melt motion governed by natural convection, Marangoni convection and crystal as well as crucible rotation shows higher oxygen concentration at melt crystal interface for aspect ratio of 1, when experimental temperature profile is imposed at the crucible wall. For melt aspect ratio of 0.5, natural convection and Marangoni convection dependent melt show higher oxygen concentration for isothermal crucible wall boundary condition. Marangoni convection in absence of rotation of crystal and crucible leads to low oxygen concentration zone near the crystal outer surface, the size of which is larger for melt aspect ratio of 0.5. Maximum turbulent viscosity values for aspect ratio of 1, in case of experimental temperature at the crucible are higher compared to isothermal case, which is just the opposite of the trend for aspect ratio of 0.5. Imposing a CUSP magnetic field leads to similar distribution of turbulent viscosity for both types of thermal boundary conditions, irrespective of the type of thermal boundary condition. Oxygen concentration at the melt crystal interface is found to be higher in presence of CUSP magnetic field. Value of maximum turbulent viscosity for the two boundary condition are similar for melt aspect ratio of 1.0. Crucible surface temperature profile for aspect ratio of 1, on actual melt aspect ratio of 0.5 predicts lower oxygen concentration at melt crystal interface. Values and distribution of turbulent viscosity is however the same for both temperature profiles.