On the creation of a drop-like static meniscus, appropriate for single crystal ribbon growth, with specified half thickness, using EFG technique

Abstract

In this paper a theoretical procedure for the creation of a stable static drop-like (concave) meniscus, appropriate for the growth of a single crystal ribbon (with specified half thickness), by edge-defined film-fed growth (EFG) technique, is presented. The method is based on explicit formulas, established as mathematical theorems, which locate the controllable part of the pressure difference across the free surface of the meniscus. In fact, the method consists in a set of calculus, which leads to the determination of the melt column height between the shaper top level and the crucible melt level in function of the pressure of the gas flow (introduced into the furnace for release the heat).The procedure is presented in general and it is numerically illustrated, revealing even situation when only convex-concave appropriate meniscus can be created. The novelty is that for the second order plan symmetric Young-Laplace equation three boundary conditions are specified (instead of two) and that value of the controllable part of the pressure difference is found for which the boundary conditions are satisfied.