Interplay of Quantum Size Effect, Anisotropy and Surface Stress Shapes the Instability of Thin Metal Films

TL;DR

This paper investigates how quantum size effects, surface anisotropy, and surface stress collectively influence the morphological stability of ultra-thin metal films, revealing their combined impact on film dewetting behavior.

Contribution

It introduces a comprehensive analysis of the interplay between quantum size effects, anisotropy, and surface stress on film stability using an extended Mullins equation.

Findings

Quantum size effect causes oscillations in surface energy with thickness.

Surface anisotropy and stress significantly alter stability thresholds.

The combined effects can either stabilize or destabilize thin films depending on parameters.

Abstract

Morphological instability of a planar surface ([111], [011], or [001]) of an ultra-thin metal film is studied in a parameter space formed by three major effects (the quantum size effect, the surface energy anisotropy and the surface stress) that influence a film dewetting. The analysis is based on the extended Mullins equation, where the effects are cast as functions of the film thickness. The formulation of the quantum size effect (Z. Zhang et al., PRL 80, 5381 (1998)) includes the oscillation of the surface energy with thickness caused by electrons confinement. By systematically comparing the effects, their contributions into the overall stability (or instability) is highlighted.