Silicon wafers for solar cells by horizontal ribbon growth

In this paper, we present a set of models that describe the principal components of the Horizontal Ribbon Growth process - mainly, the interaction between fluid flow and heat transfer, the crystallization dynamics, and the effect of impurities on the morphology of the interface. Fluid-flow and heat-transfer models show the relationship between the pulling rate and the thickness of the silicon film. A crystallization model is developed to find the concentration distribution of impurities - aluminum in this case - in the melt and in the ribbon. We find that, because of low growth velocities, there is no formation of a solute-enriched boundary layer and that a 50-fold reduction of aluminum impurities can be expected. Finally, we use the Mullins-Sekerka stability theory to show that aluminum impurities at the proposed levels do not destabilize the interface upon applied perturbations.