EPL

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 ${\rm-a}$ - 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 $\alpha =1$ 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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