Turbulent Convection in a Czochralski Silicon Melt

Abstract

The individual and combined effects of buoyancy, crystal rotation, and crucible rotation are reported in this paper for axisymmetrically averaged melt convection in a large Czochralski crystal growth system for silicon. These body force effects are characterized by the respective parameters of Grashof number, Gr, rotational Reynolds number, Rer, and the Marangoni number, Ma. The range investigated consists of 108 ≤ Gr ≤ 1010, 103 ≤ Re ≤ 3 × 104, and 103 ≤ Ma ≤ 104, which is appropriate for the real Czochralski system. The studies are based on a multizone, adaptive, finite volume calculation. Validations of the numerical procedures are presented, including a grid convergence study. The effects of buoyancy and rotation on melt convection are discussed in detail. When the crystal and crucible both rotate at the same speed, but in opposite directions, without buoyancy, the effect of the crucible rotation is stronger. The rotation induces turbulence, contrary to what the literature suggests. For the combined effects, the intensity of turbulence and the average Nusselt number at the crucible wall are largest when buoyancy is slightly dominant over rotation. High rotation rates generate temperature oscillations in the presence of high Grashof numbers. Because of the consequence of oscillation for crystal quality, a dynamic adjustment of the rotation rate might be necessary in order to obtain desirable growth conditions.