A continuum description of the energetics and evolution of stepped surfaces in strained nanostructures

TL;DR

This paper develops a continuum model for the evolution of stepped surfaces in strained nanostructures, emphasizing the role of surface steps and strain in surface stability, shape evolution, and island formation.

Contribution

It introduces a novel continuum framework based on surface steps and strain effects, bridging atomistic insights with macroscopic surface evolution modeling.

Findings

Surface step formation energy depends on strain sign.

No energetic barrier for island nucleation during deposition.

Surface orientations tend toward strain-dependent natural configurations.

Abstract

As a departure from existing continuum approaches for describing the stability and evolution of surfaces of crystalline materials, this article provides a description of surface evolution based on the physics of the main feature imposed by the discrete nature of the material, namely, crystallographic surface steps. It is shown that the formation energy of surface steps depends on the sign of extensional strain of the crystal surface, and this behavior plays a crucial role in surface evolution. The nature of this dependence implies that there is no energetic barrier to nucleation of islands on the growth surface during deposition, and that island faces tend toward natural orientations which have no counterpart in unstrained materials. This behavior is expressed in terms of a small number of parameters that can be estimated through atomistic analysis of stepped surfaces. The continuum framework developed is then applied to study the time evolution of surface shape of an epitaxial film being deposited onto a substrate. The kinetic equation for mass transport is enforced in a weak form by means of a variational formulation [...].