Modeling anisotropic shape evolution in large scale melt growth systems has been reported in the literature over the past 10-15 years. However, in most cases relevant studies were concerned with interface attachment kinetics and associated faceting of melt/crystal interfaces in confined-growth (e.g. vertical Bridgman) systems (e.g. [1,2]). Very little attention has been given to Czocralski grown crystals which may exhibit anisotropy in the shape of both the melt/crystal and crystal/gas interfaces. Relevant studies include a two-dimensional capillary model used to analyze the cross-sectional shape of certain oxides [3], an axisymmetric thermal model linking shifts in the balance of heat transfer mechanisms with experimentally observed changes in morphology of sillenites [4], and most recently a three-dimensional analysis of the impact of interface-attachment kinetics on the cross-sectional shape of Bismuth Germanium Oxide (BGO) [5].

In this contribution we will present our efforts in developing and implementing efficient (e.g. Lattice-Boltzmann-Model based) algorithms for the three-dimensional numerical modeling of oxide single crystal growth via the CZ method. We will discuss the status of our algorithms with a specific emphasis on the application of appropriate boundary conditions at the partially faceted melt/crystal interface, at the melt/gas interface and along the three-phase contact line where melt, crystal and gas phases meet. Results to be presented include a discussion of the combined impact of interface attachment and growth angle anisotropy on the shape of the growing crystal.

This Research was supported by THE ISRAEL SCIENCE FOUNDATION founded by The Academy of Sciences and Humanities.

[1] O. Weinstein and S. Brandon, J. Crystal Growth 284, 235 (2005).

[2] C.W. Lan and C.J. Chen, J. Crystal Growth 303, 287 (2007).

[3] I.S. Pet’kov and B.S. Red’kin, J. Crystal Growth 131, 598 (1993).

[4] J.C. Rojo, C. Marin, J.J. Derby and E. Diéguez, J. Crystal Growth 183, 604 (1998).

[5] O. Weinstein and W. Miller, J. Crystal Growth 312, 989 (2010).

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1. Combined interface attachment kinetics and transport phenomena in large scale solution growth systems
2. Solidification of multicrystalline silicon - phase field studies of micro-structures