The flows of a Czochralski semiconductor melt predicted by a bulk-flow model are contrasted with results obtained from a hydrodynamic thermal-capillary model (HTCM) which includes realistic interfacial geometries and boundary conditions. Both models are solved using the same finite-element methodology. Simulations are performed for the model problems posed by Wheeler , which are representative of the growth of semiconductors in a small-scale Czochralski system. Limit points in the steady-state solutions are found with respect to crystal rotation for both models, and similar structures are obtained for flows driven by crystal and crucible rotation only. Significant differences in model predictions are found for flows affected by buoyancy. Combined rotational and buoyant flows predicted by the HTCM are strongly affected by changes in overall system heat transfer caused by crystal diameter control. The inability of bulk-flow models to predict these coupled effects is discussed.
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The authors gratefully acknowledge support of this research provided by the National Science Foundation PYI award program, the McKnight-Land Grant Professorship, the Minnesota Supercomputer Institute, and the University of Mm-nesota Army High Performance Computing Research Center (under the auspices of Army Research Office contract number DAALO3-89-C-0038).