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 $\gamma$. 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 $\gamma =i^{\ast }/(2i^{\ast }+3)$ for $i^{\ast }\ge 2$ and confirm this result by computer simulations.

5 pages, 3 figures, uses revtex, psfig, 'Note added in proof' appended

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