Three-dimensional time dependent modelling of the marangoni convection in zone melting configurations for GaAs

Abstract The growth by the floating-zone method of GaAs crystals having diameters >8 mm can be carried out only under microgravity conditions because of the limitations set by hydrostatic pressure. Furthermore, the advantages of this method can only be used if unsteady Marangoni convection (MC) causing unsteady growth conditions can be avoided. In this paper we make a quantitative study of the MC in floating zone configurations by a numerical modelling for a large range of Prandtl numbers, 7 × 10 -3 2 . Results are presented of flow configurations and critical values of the Marangoni number defining the onset of unsteady flow. These values were compared with experimental results achieved by our own investigations for GaAs melts (Pr = 0.068) and by other investigators for Mo (Pr = 0.025) and Si (Pr = 0.02). Good agreement is obtained between the results of the three-dimensional time-dependent numerical simulations and model experiments of this work and in the literature. An extrapolation to the results of scheduled microgravity experiments on GaAs is made at the end of the paper. It shows that unsteady MC will probably occur for zone diameters ≥ 15 mm in the crystal growth of GaAs if no precautions are taken.