Interacting Steps With Finite-Range Interactions: Analytical Approximation and Numerical Results

TL;DR

This paper develops an analytical model for the distribution of terrace widths in interacting step systems, incorporating finite-range interactions, and validates it with simulations and experiments, revealing minimal effects of extended interactions.

Contribution

It introduces an analytical approximation for terrace-width distribution considering finite-range interactions and validates it through numerical and experimental comparisons.

Findings

Next-nearest neighbor interactions cause modest changes in distribution.

Including interactions beyond next-nearest neighbors has negligible effects.

The model helps extract potential parameters from experimental data.

Abstract

We calculate an analytical expression for the terrace-width distribution $P(s)$ for an interacting step system with nearest and next nearest neighbor interactions. Our model is derived by mapping the step system onto a statistically equivalent 1D system of classical particles. The validity of the model is tested with several numerical simulations and experimental results. We explore the effect of the range of interactions $q$ on the functional form of the terrace-width distribution and pair correlation functions. For physically plausible interactions, we find modest changes when next-nearest neighbor interactions are included and generally negligible changes when more distant interactions are allowed. We discuss methods for extracting from simulated experimental data the characteristic scale-setting terms in assumed potential forms.