Growth of Patterned Surfaces

TL;DR

This paper investigates how patterned surfaces evolve during epitaxial growth, showing that pattern quality decays exponentially and proposing an optimal feature size for pattern longevity based on diffusion and deposition parameters.

Contribution

The study provides a theoretical and simulation-based analysis of pattern stability during epitaxial growth, introducing a criterion for optimal pattern feature size.

Findings

Pattern quality decays exponentially over time.

The lifetime of a pattern is linearly related to surface diffusion activation energy.

An optimal feature size for patterns maximizes longevity based on diffusion and deposition rates.

Abstract

During epitaxial crystal growth a pattern that has initially been imprinted on a surface approximately reproduces itself after the deposition of an integer number of monolayers. Computer simulations of the one-dimensional case show that the quality of reproduction decays exponentially with a characteristic time which is linear in the activation energy of surface diffusion. We argue that this life time of a pattern is optimized, if the characteristic feature size of the pattern is larger than $(D/F)^{1/(d+2)}$, where $D$ is the surface diffusion constant, $F$ the deposition rate and $d$ the surface dimension.