Drift-Induced Step Instabilities Due to the Gap in the Diffusion Coefficient

TL;DR

This paper investigates how differences in adatom diffusion coefficients across structures on Si(111) surfaces cause step instabilities like wandering and bunching under drift, with implications for surface patterning.

Contribution

It introduces a model considering diffusion coefficient gaps at steps and analyzes their effects on step instabilities, supported by Monte Carlo simulations.

Findings

Step wandering occurs with step-down drift when a diffusion gap exists.

Step bunching occurs regardless of drift direction if lower side diffusion is faster.

Strong step-step repulsion suppresses bunching, allowing groove formation.

Abstract

On a Si(111) vicinal face near the structural transition temperature, the $1 \times 1$ structure and the $7 \times 7$ structure coexist in a terrace: the $1 \times 1$ structure is in the lower side of the step edge and the $7 \times 7$ structure in the upper side. The diffusion coefficient of adatoms is different in the two structures. Taking account of the gap in the diffusion coefficient at the step, we study the possibility of step wandering induced by drift of adatoms. A linear stability analysis shows that the step wandering always occurs with step-down drift if the diffusion coefficient has a gap at the step. Formation of straight grooves by the step wandering is expected from a nonlinear analysis. The stability analysis also shows that step bunching occurs irrespective of the drift direction if the diffusion in the lower side of the step is faster. The step bunching disturbs the formation of grooves. If step-step repulsion is strong, however, the step bunching is suppressed and the straight grooves appear. Monte Carlo simulation confirms these predictions.