A simple model of epitaxial growth

TL;DR

This paper presents a simple discrete model for epitaxial growth that captures pyramid formation, coarsening dynamics, and surface scaling behaviors, supported by simulations in 1+1 and 2+1 dimensions.

Contribution

It introduces a new discrete solid-on-solid model incorporating Ehrlich-Schwoebel barriers and step edge diffusion, revealing distinct growth regimes and scaling properties.

Findings

Formation of pyramid-like structures with constant inclination.

Identification of two growth regimes with different coarsening dynamics.

Surface roughness exponent alpha = 1 in all cases.

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 distinguished clearly: 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+1 seem to be consistent with z= 2 (I) and z= 2.3 (II) respectively.