Three-dimensional simulation of vertical zone-melting crystal growth: symmetry breaking to multiple states

For the first time three dimensional simulation is conducted for vertical z one-melting crystal growth, simultaneously considering the time-dependent f luid flow, heat transfer, and moving interfaces. The numerical method is ba sed on an efficient finite-volume method with front tracking. The growth of 2-cm diameter GaAs in a quartz ampoule is used as an example. Under an axi symmetric operation, the two-dimensional solution can bifurcate subcritical ly to three-dimensional ones as the convection or superheating increases. T he three-dimensional modes, which can have either one- or two-fold symmetry , depend on the equilibrium aspect ratio of the molten zone. Under normal g ravity, the axisymmeric mode exists only for low superheating. Furthermore, the multiple slates, including other multi-fold modes, are path dependent, which are further illustrated though the dynamics of heating and cooling o perations. (C) 2000 Elsevier Science B.V. All rights reserved.