Island nucleation in the presence of step edge barriers: Theory and applications

TL;DR

This paper presents a new theoretical model for nucleation on two-dimensional islands considering step edge barriers, providing more accurate predictions than traditional rate equations, with applications to multilayer growth and specific material systems.

Contribution

The authors develop a residence time-based theory for nucleation that accurately accounts for strong step edge barriers, improving upon conventional rate equation approaches.

Findings

New expression for nucleation rate derived

Application to Pt(111) estimates barrier height

Theory explains size distribution of top terraces

Abstract

We develop a theory of nucleation on top of two-dimensional islands bordered by steps with an additional energy barrier $\Delta E_S$ for descending atoms. The theory is based on the concept of the residence time of an adatom on the island,and yields an expression for the nucleation rate which becomes exact in the limit of strong step edge barriers. This expression differs qualitatively and quantitatively from that obtained using the conventional rate equation approach to nucleation [J. Tersoff et al., Phys. Rev. Lett.72, 266 (1994)]. We argue that rate equation theory fails because nucleation is dominated by the rare instances when two atoms are present on the island simultaneously. The theory is applied to two distinct problems: The onset of second layer nucleation in submonolayer growth, and the distribution of the sizes of top terraces of multilayer mounds under conditions of strong step edge barriers. Application to homoepitaxial growth on Pt(111) yields the estimate $\Delta E_S \geq 0.33$ eV for the additional energy barrier at CO-decorated steps.