Melt motion in floating-zone process for single crystal growth with an axial magnetic field

The bulk flow of molten silicon in the floating-zone process with an applied axial magnetic field, for a dislocation-free single crystal, is studied by using asymptotic expansion. Centrifugal force, crystal growth speed, buoyancy, thermocapillarity and electromagnetic body force are the driving forces involved in the floating-zone process for growing single crystal. The strong, DC magnetic field eliminates the inertial effect of the melt motion and confines the viscous effect in the thin boundary layers; the modified Navier-Stokes equations are linearlized by the presence of the axial magnetic field. With the shape of the molten silicon pool calculated through the force balance on the free surface, the individual motion driven by each factor is investigated separately.Conductive and convective heat transfer are both studied and later compared to find that the convection does not alter the temperature distribution in the melt significantly. Finite differences, boundary elements and numerical integration are the numerical schemes used in this problem.U of I OnlyETDs are only available to UIUC Users without author permissio