Application of porous interface on segregation in Czochralski crystal growth

The aim of this paper is to develop a model for the solute segregation in Czochralski crystal growth based on similarity solution. In this model, the effect of crystal growth rate for the wide range of Schmidt (Sc) numbers on boundary layer is considered. We utilize a variable R=V0/νω which represents the ratio of growth velocity (V0) to stirring velocity (νω). Since both crystal rotation rate and growth velocity are almost varied in order to control the growth process, the parameter R can be used as a scale of optimization for the various growth conditions. The analyses show that the effective segregation coefficient (keff) is related to the parameter R. In the end, the results are utilized in the Czochralski configuration to determine the equilibrium segregation coefficient (k0) and Sc number evaluated and compared with experimental data.