Capillary mechanism effect in the processing of a semiconductor single crystal rod with specified constant radius

Abstract

The purpose of this paper is the evaluation of the capillary mechanism effect, involved in the processing (from the melt) of a semiconductor single crystal rod by edge-defined film-fed growth (E.F.G.) technique. A mathematical model based method for the creation of a stable drop-like static meniscus with prescribed size and shape, a necessary requirement for the growth of a semiconductor single crystal rod with prescribed constant radius, is presented. The variation of the shape and size of the meniscus during the growth lead to the variation of the radius of the rod and generate surface non-uniformity. The presented method uses two process parameters for the creation of the desired meniscus: the melt column height (between the crucible melt level and the shaper top level) and the pressure of the gas flow introduced into the furnace for release the heat. The novelty is that for the second order axisymmetric Young-Laplace equation three boundary conditions are specified (instead of two) and that value of the controllable part of the pressure difference across the free surface is found for which the boundary conditions are satisfied. The obtained theoretical and numerical results advance the understanding of the generation of the surface non-uniformity of the grown rod, due to the capillary mechanism.