Lattice gas models of coherent strained epitaxy

TL;DR

This paper introduces a method to map coherently strained epitaxial systems onto lattice gas models with discrete variables, enabling efficient simulations of atomic interactions and self-organization phenomena.

Contribution

It presents an exact mapping technique from a continuous atomic model to a lattice gas model, facilitating the use of Monte Carlo methods for strained epitaxial systems.

Findings

Efficient Monte Carlo simulations for strained epitaxy models.

Application of the formalism to 1D and 2D systems.

Analysis of self-organization of clusters on vicinal surfaces.

Abstract

The harmonic Frenkel-Kontorova model is used to illustrate with an exactly solvable example a general technique of mapping a coherently strained epitaxial system with continuous atomic displacements onto a lattice gas model (LGM) with only discrete variables. The misfit strain of the original model is transformed into cluster interatomic interactions of the LGM. The clusters are contiguous atomic chains of all lengths but the interaction strength for long chains is exponentially small. This makes possible the application of efficient Monte Carlo techniques developed for discrete variables both in kinetic and equilibrium simulations. The formalism developed can be applied to 1D as well as to 2D systems. As an illustrative example we consider the problem of self-organization of 1D size calibrated clusters on the steps of the vicinal surfaces.