A simple model of epitaxial growth

Institut für Theoretische Physik, Julius-Maximilians-Universität Würzburg Am Hubland, D-97074 Würzburg, Germany

Received: 28 August 1997
Accepted: 5 January 1998

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.