Heat transfer analysis of the Bridgman-Stockbarger configuration for crystal growth

Abstract

An analytical approach describing the heat transfer during crystal growth in a Bridgman-Stockbarger configuration has been developed. All first order effects on the axial temperature distribution in a solidifying charge are treated on the basis of a one-dimensional model whose validity could be verified through comparison with a published finite difference analysis of a two-dimensional model. The present model includes an insulated region between axially aligned heat pipes and considers the effects of charge diameter, charge motion, thickness and thermal conductivity of a confining crucible, thermal conductivity change at the crystal-melt interface and non-infinite charge length. Results are primarily given in analytical form and can be used without recourse to computer work for both improved furnace design and optimization of growth conditions in a given thermal configuration.