Numéro |
J. Phys. I France
Volume 5, Numéro 8, August 1995
|
|
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Page(s) | 1065 - 1086 | |
DOI | https://doi.org/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 SchimschakIFF, 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
, where
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
. This case is solved exactly, and the terrace
lengths are shown to have a Poisson distribution.
© Les Editions de Physique 1995