Computational Study of Heat Transfer on Molten Silicon During Directional Solidification for Solar Cell Applications

Abstract

Computational modeling is an essential tool in modern crystal growth technology and development which is extensively used for promotion of directional solidification of silicon growth processes. The fluctuation of melt flow in the crucible has significant effects on segregation of impurity concentration and the formation of micro - defects in the grown Si multi-crystals. The control of grains as well as the grain boundaries is particularly important to the crystal quality and thus the solar cell efficiency. The numerical study is performed in the framework of the incompressible Navier-Stokes equation in the Boussinesq approximation with convection-conduction equations. The computations are made in two dimensional (2D) axisymmetric model by the finite-element numerical technique. The melt flow properties like velocity field, convective heat flux in molten silicon system are accurately simulated and analyzed at constant Prandtl number for two various Rayleigh numbers Ra= 100 and Ra=1000. In which, we found that Ra=1000 is critical Raleigh number for molten silicon. The main goal is to reduce the grain boundaries, dislocation density and increase the average grain size in whole multi-crystalline silicon ingots through controlling the turbulent melt flow patterns to laminar.