Numerical Simulation of Convective Flow of the Melt in the Classical Czochralski Method, in ACRT and CACRT. Part 1. Simulation of Forced Convection

摘要

A procedure is described for the numerical solution of the time-dependent Navier-Stokes equations governing the forced convection flow in a crystal-growth crucible. Five digital simulations of the classical Czochralski crystal-pulling process show the excellent agreement of the calculations with the experimental data of Carruthers and Nassau. Moreover, for the Accelerated Crucible-Rotation Technique (ACRT) and its application to the Czochralski method (CACRT), the first numerical simulations are presented assuming the fluid model to be the 1:1 glycerine-water mixture of moderate kinematic viscosities. The program can also deal with low viscosities typical for semiconductors and liquid metals. This is demonstrated by simulations of the classical Czochralski, the ACRT and the CACRT arrangements with the viscosity of liquid copper. The influence of the temperature distribution on these flow phenomena will be studied in part 2. 227 figures. (ERA citation 08:005741)