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.