Qualitative Characterization of Solute Boundary Layer in Industrial Czochralski Growth of Silicon.

The effective viscosity (μ_eff) has a crucial turbulent effect in the fluid flow. In this work, μ_eff 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, μ_eff 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. [ABSTRACT FROM AUTHOR]