Island Distance in One-Dimensional Epitaxial Growth

TL;DR

This paper derives and confirms a formula for how the typical island distance in one-dimensional epitaxial growth depends on the critical nucleus size, providing insights into the growth process under various conditions.

Contribution

The paper presents a new analytical expression for the exponent relating island distance to critical nucleus size in 1D epitaxial growth, supported by computer simulations.

Findings

Derived the formula b3 = i^*/(2i^* + 3) for i^*  2.

Confirmed the analytical result with computer simulations.

Provides a deeper understanding of island formation in 1D 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 $i^*$ of the critical nucleus for island formation. In this paper we study the dependence of $\gamma$ on $i^*$ in one--dimensional epitaxial growth. We derive that $\gamma = i^*/(2i^* + 3)$ for $i^*\geq 2$ and confirm this result by computer simulations.