Growth morphologies of crystal surfaces

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Abstract
We have expanded our earlier Monte Carlo model [Phys. Rev. A 38, 2447 (1988); J. Crystal Growth 100, 313 (1990)] to three dimensions and included reevaporation after accommodation and growth on dislocation-induced steps. We found again that, for a given set of growth parameters, the critical size, beyond which a crystal cannot retain its macroscopically faceted shape, scales linearly with the mean free path in the vapor. However, the three-dimensional (3D) the systems show increased shape stability compared to corresponding 2D cases. Extrapolation of the model results to mean-free-path conditions used in morphological stability experiments leads to order-of-magnitude agreement of the predicted critical size with experimental findings. The stability region for macroscopically smooth (faceted) surfaces in the parameter space of temperature and supersaturation depends on both the surface and bulk diffusion. While surface diffusion is seen to smooth the growth morphology on the scale of the surface diffusion length, bulk diffusion is always destabilizing.