Spatial–temporal stability analysis of faceted growth with application to horizontal ribbon growth

Abstract

Spatial–temporal stability analysis has been applied to a solidification model that includes both isotropic and non-isotropic kinetics. In agreement with previous temporal stability analyses, it was shown that the kinetics associated with the propagation of steps across a facet can stabilize solidification processes that would normally be thermally unstable. In cases where the solidification is unstable, it was also shown that pulling the solid with a tangential velocity can cause a transition from “absolute” instability where perturbations cause growth at all locations to “convective” instability where a perturbation grows as it propagates, but at any fixed location disturbances decay away after the perturbation passes. These results were applied to understand instabilities in the floating silicon method (FSM), which is a particular type of horizontal ribbon growth. It was shown that increasing pull-speeds in FSM leads to increasingly unstable thermal growth conditions, but the combination of the kinetics of faceted growth and the tangential pull velocity can stabilize the process. As the pull speed increases, however, the process becomes increasingly sensitive to perturbation.