Journal of Crystal Growth, Vol.380, 43-50, 2013
Combined-convection segregation coefficient and related Nusselt numbers
In Czochralski growth, forced convection is always accompanied by natural convection. Hence, an effective segregation coefficient, which accounts for both forced and buoyancy-induced convection, was recently proposed. This combined-convection coefficient is presented here in dimensionless form, k(CC) (Nu(FC), Nu(NC), Pe), where Nu(FC) and Nu(NC) are Nusselt numbers for forced and natural convection and Pe is Peclet number for convection due to freezing. Several Nu-number correlations, relevant for Czochralski growth, are presented. The seminal diffusion coefficients of dopants in molten Si, reported by Kodera, are revisited. Kodera's calculations were done using the BPS model, which does not account for buoyancy-induced flow. In a part of Koclera's experiments, natural convection was significant, and has "inflated" Kodera's coefficients D [cm(2)/s]. The k(CC) correlation is applied to Kodera's data to provide more precise values of D. The impact of buoyancy-induced flow on CZ segregation is demonstrated. (C) 2013 Elsevier B.V. All rights reserved