Island Distance in One-Dimensional Epitaxial Growth

Abstract

The typical island distance $\ell$ in submonlayer epitaxial growth depends on the growth conditions via an exponent $γ$. This exponent is known to depend on the substrate dimensionality, the dimension of the islands, and the size $i^*$ of the critical nucleus for island formation. In this paper we study the dependence of $γ$ on $i^*$ in one--dimensional epitaxial growth. We derive that $γ= i^*/(2i^* + 3)$ for $i^*\geq 2$ and confirm this result by computer simulations.