Document DOI: 10.1209/epl/i1998-00171-0
Europhys. Lett, 41 (4), pp. 443-448 (1998)
A simple model of epitaxial growth
M. Biehl, W. Kinzel and S. Schinzer
Institut für Theoretische Physik, Julius-Maximilians-Universität Würzburg Am Hubland, D-97074 Würzburg, Germany
(received 28 August 1997; accepted in final form 5 January 1998)
PACS. 81.10Aj - Theory and models of crystal growth; physics of
crystal growth, crystal morphology and orientation.
PACS. 05.70Ln - Nonequilibrium thermodynamics, irreversible processes.
PACS. 68.55
- Thin film structure and morphology.
Abstract:
A discrete solid-on-solid model of epitaxial growth
is introduced which, in a simple manner, takes into account the
effect of an Ehrlich-Schwoebel barrier at step edges as well as the
local relaxation of incoming particles. Furthermore, a fast step edge
diffusion is included in 2+1 dimensions. The model exhibits the
formation of pyramid-like structures with a well-defined constant
inclination angle. Two regimes can be clearly distinguished: in an initial phase (I)
a definite slope is selected while the number of pyramids remains unchanged.
Then a coarsening process (II) is observed
which decreases the number of islands according to a power law in time.
Simulations support self-affine scaling of the growing surface in both regimes.
The roughness exponent is 
in all cases. For growth in
1+1 dimensions we obtain dynamic exponents z = 2 (I) and z = 3 (II).
Simulations for d=2 seem to be consistent with z= 2 (I) and
z= 2.3 (II), respectively.
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