A three-dimensional numerical study of Marangoni convection in a floating full zone

The article presents a three-dimensional computational study for the transport phenomena occurring during the growth of Si-doped Ge crystals by the Floating-Zone (FZ) technique. Numerical simulations were performed to examine the role of the Marangoni convection in a Full-zone configuration under zero gravity. The effects of crystal rotation and zone aspect ratio were also considered in the model. The field equations of the liquid phase and the associated boundary conditions were discretised by the finite difference method, and solved by the HSMAC (Highly Simplified Marker And Cell) method. Results show that the flow and temperature fields are initially two-dimensional with two pairs of vortexes of the same size, as time proceeds, however the flow field becomes three-dimensional in spite of assumed axisymmetric boundary conditions. The concentration field becomes three-dimensional much earlier than the flow field. The float zone aspect ratio has a prominent effect on the critical Marangoni number at which three-dimensional flow structures occur, and as well as on the azimuthal wave number and the uniformity of the solute concentration along the crystal growth interface in the melt. It was also shown that the application of a crystal rotation is very beneficial in obtaining a moreuniform solute concentration distribution along the growth interface.