Theoretical Models for Crystal Growth from Atom Beams

Abstract

Continuum equations appropriate to describe crystal growth from atom beams are derived in various cases. When desorption is important, the growth is described on very long lengthscales by the Kardar-Parisi-Zhang equation, but should be corrected for shorter lengthscales where surface diffusion is the dominant mechanism. In the absence of desorption, an important effect at sufficiently low temperature comes from the fact that diffusion of incoming atoms on the surface is anisotropic on long lengthscales becaused it is biased by reflexions against terrace edges. As a result, the growth is described by a pseudo-diffusion equation. In the case of a high symmetry surface, (001) or (111), an instability arises. Finally, in the absence of diffusion bias, the growth is described by a nonlinear equation of fourth order with respect to to ∂/∂x and ∂/∂y, and the appropriate exponents are calculated in a Flory-type approximation.