Abstract
The effective viscosity (μeff) has a crucial turbulent effect in the fluid flow. In this work, μeff is proposed and applied to the Burton, Prim, and Slichter (BPS) and Ostrogorsky-Muller (OM) analytical models to estimate the solute boundary layer in Czochralski (CZ) growth of silicon. A series of numerical simulations for CZ silicon growth are performed, with different crystal rotation rates (ranging from 1 to 50 rpm), in order to obtain different convective flow regimes. The results revealed 3.6% as the average predicted error (where, μeff was employed as an input) for the boundary layer thickness between the modified models. Furthermore, the modified OM model was also verified to describe the radial distribution of solute boundary layer, and to demonstrate the capturing efficiency of the characteristic points at melt/crystal interface. Aiming at practical purposes, Gr/Re2 was proposed as a criterion to obtain the weak lateral segregation of impurities in the crystal growth process.
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