Numerical simulation of the horizontal Bridgman growth. Part III: Calculation of the interface

Abstract

SUMMARYWe study the transient motion of the solidification front during the growth of semiconductor crystals in the horizontal Bridgman geometry. The calculation is based on a two-dimensional flow. We use finite elements which deform with the motion of the interface. The energy equation is coupled with the isothermal constraint of the interface in an implicit transient algorithm. Several examples show the oscillatory motion of the interface caused by the periodic flow of the melt, and they reveal the importance of the growth rate on the shape of the interface.

Theory of transport processes in single crystal growth from the melt

“…This approach has been used in investigations of buoyancy-driven convection in idealized geometries (McLaughlin and Orszag, 1982;Curry et al, 1984;Sackinger et al, 1988a). Crochet and coworkers have studied the oscillations in the convection of a prototype of the horizontal Bridgman method for twodimensional motion without (Crochet et al, 1983; and including (Wouters et al, 1987) the melt/crystal interface. Crochet et al (1987b) computed three-dimensional motions by direct simulation of the nonlinear, time-dependent equations.…”

Flow fields and interface shapes during horizontal Bridgman growth of fluorides

“…Some of the phenomena occurring in horizontal melting and solidification systems have been previously studied. One of the initial comprehensive computational analyses of these material processing methods, involving the two-dimensional horizontal solidification of a low Prandtl number melt (mimicking GaAs), is described in [13,14]. This study, which accounted for buoyancy-driven flows alone, reported transitions from (quasi) steady-state flows to time-dependent convective patterns at a critical Rayleigh number, which depends on the value of the Prandtl number and on the melt's geometry.…”