Multiscale Kinetic Monte-Carlo for Simulating Epitaxial Growth

TL;DR

This paper introduces a fast kinetic Monte-Carlo algorithm for simulating epitaxial surface growth, significantly reducing computational time by allowing larger adatom steps, especially effective at moderate temperatures and high diffusion-to-flux ratios.

Contribution

The authors develop a multiscale kinetic Monte-Carlo method that accelerates epitaxial growth simulations by enabling larger adatom steps, improving efficiency over traditional methods.

Findings

Achieves nearly tenfold speed-up in simulations

Effective at moderate temperatures and large D/F ratios

Maintains accuracy while reducing computational cost

Abstract

We present a fast Monte-Carlo algorithm for simulating epitaxial surface growth, based on the continuous-time Monte-Carlo algorithm of Bortz, Kalos and Lebowitz. When simulating realistic growth regimes, much computational time is consumed by the relatively fast dynamics of the adatoms. Continuum and continuum-discrete hybrid methods have been developed to approach this issue; however in many situations, the density of adatoms is too low to efficiently and accurately simulate as a continuum. To solve the problem of fast adatom dynamics, we allow adatoms to take larger steps, effectively reducing the number of transitions required. We achieve nearly a factor of ten speed up, for growth at moderate temperatures and large D/F.