A Two-Region Diffusion Model for Current-Induced Instabilities of Step Patterns on Vicinal Si(111) Surfaces

TL;DR

This paper introduces a two-region diffusion model to analyze current-induced step instabilities on vicinal Si(111) surfaces, revealing new insights into step bunching and wandering phenomena driven by local surface reconstruction differences.

Contribution

The study develops a novel two-region diffusion model that captures local surface reconstruction effects and maps these to traditional models, providing a physical basis for current-induced instabilities.

Findings

Negative kinetic coefficient when diffusion in step region exceeds terrace diffusion

Step wandering driven by step edge diffusion, not Mullins-Sekerka instability

Numerical simulations match experimental step pattern alignments

Abstract

We study current-induced step bunching and wandering instabilities with subsequent pattern formations on vicinal surfaces. A novel two-region diffusion model is developed, where we assume that there are different diffusion rates on terraces and in a small region around a step, generally arising from local differences in surface reconstruction. We determine the steady state solutions for a uniform train of straight steps, from which step bunching and in-phase wandering instabilities are deduced. The physically suggestive parameters of the two-region model are then mapped to the effective parameters in the usual sharp step models. Interestingly, a negative kinetic coefficient results when the diffusion in the step region is faster than on terraces. A consistent physical picture of current-induced instabilities on Si(111) is suggested based on the results of linear stability analysis. In this picture the step wandering instability is driven by step edge diffusion and is not of the Mullins-Sekerka type. Step bunching and wandering patterns at longer times are determined numerically by solving a set of coupled equations relating the velocity of a step to local properties of the step and its neighbors. We use a geometric representation of the step to derive a nonlinear evolution equation describing step wandering, which can explain experimental results where the peaks of the wandering steps align with the direction of the driving field.