Numéro
J. Phys. I France
Volume 5, Numéro 8, August 1995
Page(s) 1065 - 1086
DOI https://doi.org/10.1051/jp1:1995177
DOI: 10.1051/jp1:1995177
J. Phys. I France 5 (1995) 1065-1086

Metastability of Step Flow Growth in 1+1 Dimensions

Joachim Krug and Martin Schimschak

IFF, Theorie II, Forschungszentrum Jülich, 52425 Jülich, Germany


(Received 3 April 1995, received in final form 10 April 1995, accepted 19 April 1995)

Abstract
We introduce a "minimal" model of crystal growth in 1+1 dimensions, which includes random deposition, surface diffusion of singly bonded adatoms, and perfect step edge barriers to completely suppress interlayer transport. We show that the stable step flow regime predicted by Burton-Cabrera-Frank theories is destabilized by island formation. The transition to an asymptotic Poisson-like growth mode, in which the surface width grows indefinitely as the square root of the number of layers, occurs after a transition time $\tau\sim\ell^{-2}(D/F)^{3/4}$, where $\ell$ is the step spacing of the vicinal surface, D is the surface diffusion constant and F is the deposition rate. The Poisson regime is preceded by an intermediate scaling regime in which the surface width grows linearly with the number of layers, as has been reported in recent experiments. The relation to the Cahn-Hilliard theory for thermodynamically metastable states is outlined. Stable step flow is possible in the limit $D/F\to\infty$. This case is solved exactly, and the terrace lengths are shown to have a Poisson distribution.



© Les Editions de Physique 1995

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.