Computation of Strained Epitaxial Growth in Three Dimensions by Kinetic Monte Carlo

TL;DR

This paper presents a numerical Kinetic Monte Carlo method for simulating three-dimensional heteroepitaxial growth with strain effects, revealing instability and island formation at high misfit levels.

Contribution

It introduces an efficient computational approach combining elastic strain modeling with KMC for 3D epitaxial growth simulation, including novel approximations for speed.

Findings

Layer-by-layer growth becomes unstable at high misfit.

Strain induces three-dimensional island formation.

The method efficiently captures elastic effects in growth simulations.

Abstract

A numerical method for computation of heteroepitaxial growth in the presence of strain is presented. The model used is based on a solid-on-solid model with a cubic lattice. Elastic effects are incorporated using a ball and spring type model. The growing film is evolved using Kinetic Monte Carlo (KMC) and it is assumed that the film is in mechanical equilibrium. The strain field in the substrate is computed by an exact solution which is efficiently evaluated using the fast Fourier transform. The strain field in the growing film is computed directly. The resulting coupled system is solved iteratively using the conjugate gradient method. Finally we introduce various approximations in the implementation of KMC to improve the computation speed. Numerical results show that layer-by-layer growth is unstable if the misfit is large enough resulting in the formation of three dimensional islands.