Island Distance in One-Dimensional Epitaxial Growth

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