Stability of strained heteroepitaxial systems in (1+1) dimensions

TL;DR

This paper introduces an analytical model for predicting stable phases in strained heteroepitaxial systems in (1+1) dimensions, emphasizing the roles of surface and elastic energies, and explores conditions for island array stability.

Contribution

The paper develops a simple atomistic Lennard-Jones-based analytical model to determine stable phases in strained heteroepitaxial systems, including conditions for island array formation.

Findings

Good agreement with the model using surface and elastic energy contributions

No stable island array configurations found with initial parameters

A slight model modification can stabilize island arrays

Abstract

We present a simple analytical model for the determination of the stable phases of strained heteroepitaxial systems in (1+1) dimensions. In order for this model to be consistent with a subsequent dynamic treatment, all expressions are adjusted to an atomistic Lennard-Jones system. Good agreement is obtained when the total energy is assumed to consist of two contributions: the surface energy and the elastic energy. As a result, we determine the stable phases as a function of the main ``control parameters'' (binding energies, coverage and lattice mismatch). We find that there exists no set of parameters leading to an array of islands as a stable configuration. We however show that a slight modification of the model can lead to the formation of stable arrays of islands.