| Magnetic fields have been used to suppress fluid flow during melt growth of semiconductors. In this study the effect of orientation of magnetic fields and container shapes on flow suppression is investigated. Based on the critical Rayleigh numbers calculated for all container shapes except cylinders using linear stability analysis, it was shown that horizontal fields suppress flow to a larger extent than vertical fields for all flows except longitudinal rolls. Suppression by vertical fields was uniform for all flows, while suppression by horizontal fields depended on the flow pattern. The orthogonality and completeness of the eigenfunction set for the linear problem for both cases were shown. Weakly nonlinear analysis showed that subcritical instabilities would not exist for this problem. Numerical studies for cylindrical containers, where depending upon the aspect ratio either axi- or anti-symmetric rolls prevail in the absence of magnetic fields, showed that vertical magnetic fields suppress all flow fields at all aspect ratios without altering the flow pattern. Horizontal fields suppressed axisymmetric rolls more effectively than vertical fields, but suppressed antisymmetric rolls less effectively than vertical ones. This resulted in a switch from axisymmetric flows to antisymmetric flows at onset when the magnitude of the field was increased, rendering the field less effective than the vertical one.; Crystal growth with a planar solid-liquid interface is desirable in order to achieve optimum material properties of semiconductors. Earlier studies on the effect of fluid flow on the morphological stability of the interface have shown an absence of coupling for non-faceted growth [Coriell, Sekerka, and others, Journal of Crystal Growth, 49, 13 (1980)]. However, for faceted growth, recent studies conducted by Coriell, Chernov and others (Met. Matls. Trans., 27A, 687 (1996)] show that kinetic anisotropy is responsible for the stabilizing effects of a shear flow. In this study, the same model is used to analyze the morphological stability of a vicinal crystal-melt interface taking into account both anisotropic interface kinetics and solutally-driven convection. Coupling was shown to occur only when the instability set in as an overstable mode, and that too only for certain ranges of wavenumbers. Of the various patterns, 2-D roll cells with the step motion perpendicular to the axis of the cell were found to have the largest effect. |
