The choice of the pressure of the gas flow and the melt level in silicon tube growth

Abstract

In this paper it is shown that a stable and convex static meniscus, appropriate for the growth of a single crystal silicon tube with specified inner and outer radius, can be created by the choice of the pressure of the gas flow introduced in the furnace (in order to release the heat) and the choice of the melt column height between the horizontal crucible melt level and the shaper top level. The presented method use explicit formulas established for the exact solution of the axisymetric Young-Laplace equation (no approximation with arcs of constant curvature) for materials for which $0<\alpha_{c}<\displaystyle\frac{\pi}{2}-\alpha_{g}<\displaystyle\frac{\pi}{2}$ ($\alpha_{g}$ is the growth angle, $\alpha _{c}$ is the contact angle). The procedure is numerically illustrated for silicon tubes of different sizes. The effect of the shaper radii choice is also discussed. The setting of thermal conditions which assure that for the obtained static meniscus the solidification conditions are satisfied at the ``right'' places is not considered in this paper.