We investigate the crystal growth process of an InAs-GaAs binary semiconductor by the Travelling Liquidus-Zone (TLZ) method numerically and discuss the possibility of growing a bulk In0.3Ga0.7As crystal. First, we explain this new crystal growth technique and then develop a numerical model and calculation method of the growth of binary crystals, by which the flow field in the solution, the temperature and concentration fields in both the solution and crystals, and the shape and movement of the crystal-solution interfaces are determined. We focus, in particular, on the effect of the solution zone width on the crystal growth process and the generation of supercooling in the solution in order to grow In0.3Ga0.7As. We find that a uniform In0.3Ga0.7As can be grown by the TLZ method under 1 mug conditions by adjusting the solution zone width and the temperature gradient in the solution at appropriate values, in which case buoyancy convection and supercooling induced in the solution are remarkably reduced. (C) 2004 Elsevier Ltd. All rights reserved.