Buoyancy Convection During the Growth of Si_xGe_1−x by the Traveling Solvent Method (TSM)

The traveling solvent method known as TSM is a process used to produce pure and homogeneous crystals structures. TSM has been tested on many alloys producing uniform and uncontaminated single crystals. In the present study the effect of buoyancy convection on the growth of the $Si0.02Ge0.98$ crystal grown by the traveling solvent method is investigated under different heating conditions. The full Navier-Stokes equations together with the energy and solutal equations are solved numerically using the finite element technique. The model takes into consideration the losses of heat by radiation and the use of the phase diagram to determine the silicon concentration at the growth interface. Results reveal a strong convection in the solvent, which in turn is detrimental to the growth uniformity in the crystal rod. Additional numerical results show that the convective heat transfer significantly influences the solute distribution in the liquid zone and affects the growth rate substantially. Qualitative comparison of the numerical results with the experiment conducted at Dalhousie University showed a good agreement for the silicon concentration at the growth interface.