Variations of solid–liquid interface in the BGO low thermal gradients Cz growth for diffuse and specular crystal side surface

Abstract

A global analysis of heat transfer in growing BGO (Bi 4Ge 3O 12) crystals was carried out to explain the significant variation of the solid–liquid interface shape observed in practice during crystal growth. Special attention was given to the accurate treatment of radiative heat transfer in crystal and the gap between crystal and crucible wall. Crystal side surface was assumed to be transparent and diffuse or specular (Fresnel) reflective while melt was opaque. Spectral absorptivity of crystal was approximated by a three-band model. It is shown that rotationally driven vortex dominates under the solid–liquid interface during the whole growth process and no reconstruction of flow pattern, which could lead to interface inversion, takes place. As a result, in the case of diffuse crystal surfaces, the calculated deflection of the crystallization front does not exceed several millimeters and that completely disagrees with the observations. In contrast, for the specular crystal surface the solid–liquid interface turns out to be deeply convex toward the melt at the initial stage of the growth, and then, as the crystal is pulled, its convexity strongly diminishes. Such behavior is in good agreement with the experiment and mainly determined by specular reflection at the conical part of the crystal (its shoulder) while the effect of specular reflectivity of the cylindrical part and melt-free surface is significantly less. It is also shown that radiation transfer in the wavelength band of crystal opacity in conjunction with the specular reflection of radiation in the band of crystal transparency result in the appearance of “convex–concave” isotherms in the upper part of the crystal.