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Modification of BCF theory due to step motion

Crystal growth kinetics from the vapor phase or from solution can be described by the diffusion of growth species to the echelon of equidistant steps present at vicinal surfaces. Diffusion takes place in a thin boundary layer adjacent to the interface. Present theories of this process neglect a convective transport mechanism in the boundary layer. In this work, we reexamine this zero-flow assumption. We consider the difference in the densities between the mother phase and the growing crystalline phase as the driving force for the flow. This force is localized at the step positions when only lateral growth of the steps is permitted. In such a case a highly nonuniform flow pattern is obtained. It consists of two vortices with the line between these vortices corresponding to a flow directed towards the step. This nonuniform part of the flow is found to extend into the mother phase up to an inter- step distance. This is the region where diffusion in the horizontal direction takes place. Consequently, the results suggest the importance of convective transport in the boundary layer. Finally, a constant horizontal flow, far from the surface, is predicted.