Numerical simulations of Czochralski growth of single crystals

Computer-aided simulations are performed for the Czochralski growth of single crystals. Galerkin finite element method and Newton-Raphson iteration scheme are employed to solve the fully coupled momentum and energy equations.; 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 geometries and boundary conditions. Limit points in the 2-D steady-state solutions are found with respect to crystal rotation for both models. Significant differences in model predictions are found for flows affected by buoyancy. Combined rotational and buoyancy flows predicted by the HTCM are strongly affected by changes in overall system heat transfer caused by crystal diameter control.; Calculations are also performed with an integrated process model for Czochralski oxide growth in which internal thermal radiation through the crystal is approximated. Deeply convex crystal/melt interfaces are predicted which are similar in shape to those observed experimentally. Results suggest that the nature of interface inversion by crystal rotation is fundamentally different for yttrium aluminum garnet (YAG) under low and high thermal gradients. Classical "flat-interface" growth via crystal rotation is attainable for YAG growth only under low-gradient thermal conditions, while this limitation is not as stringent for the growth of gadolinium gallium garnet (GGG). Crystal cracking with large cone angle during Czochralski YAG growth is promoted by internal radiation. The depth of the melt also affects interface inversion for GGG. A new mechanism for the onset of crystal spiraling is postulated from observations of superheated crystal regions in some calculations.; A parallel implementation of Galerkin finite element method is developed to study the non-axisymmetric, time-dependent flows of Czochralski crystal growth systems. As benchmark problems, Taylor-Couette flow and baroclinic annulus wave are successfully calculated. A three-dimensional, time-dependent bulk flow model is employed to study Czochralski oxide growth systems. The results show that the transition from 2-D steady-state to 3-D transient flows strongly affects the temperature gradient near the crystal/melt interface.