Creation of a stable and convex static meniscus, which is appropriate for the growth of a single crystal ribbon with specified half thickness

A stable and convex static meniscus is appropriate for the growth of a single crystal ribbon of given half thickness, if the upper half thickness of the meniscus is equal to the ribbon half thickness and the angle between the tangent line to the meniscus and the vertical is equal to the growth angle. In this paper the material parameters, the shaper half thickness, the gas pressure above the meniscus and the half thickness of the ribbon, which has to be grown, are considered prior given. The problem that is solved is the determination of the melt column height (between the horizontal crucible melt level and the shaper top level) such that the resulting meniscus is convex, is static stable and is appropriate for the growth of the desired ribbon. The determination is numerically illustrated for silicon sheet and the dependence of the melt column height on the shaper half thickness is discussed.