J. Phys. I France
Volume 1, Numéro 1, January 1991
Page(s) 19 - 42
DOI: 10.1051/jp1:1991114
J. Phys. I France 1 (1991) 19-42

Continuum models of crystal growth from atomic beams with and without desorption

J. Villain

DRF/MDN, Centre d'Etudes Nucléaires de Grenoble, 85X, F-38041 Grenoble Cedex, France

(Received 9 April 1990, revised 13 September 1990, accepted 25 September 1990)

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 lenghtscales 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 $\partial/\partial x$ and $\partial/\partial y$. The exponents are calculated in a Flory-type approximation. In particular the roughness exponent is found to be $\chi=(5-d)/3$ in d dimensions.

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