A Simple Model for Anisotropic Step Growth

TL;DR

This paper introduces a simple model for anisotropic step growth on crystal surfaces, analyzing the morphology evolution with analytic and simulation methods, revealing instability and finger formation during growth.

Contribution

It presents a new, simplified model incorporating diffusion, drift, and barriers, providing detailed analysis of step morphology and instability under typical growth conditions.

Findings

Step morphology is linearly unstable, leading to finger formation.

Vertical roughness grows linearly over time.

Fingers coarsen proportionally to t^{0.33}.

Abstract

We consider a simple model for the growth of isolated steps on a vicinal crystal surface. It incorporates diffusion and drift of adatoms on the terrace, and strong step and kink edge barriers. Using a combination of analytic methods and Monte Carlo simulations, we study the morphology of growing steps in detail. In particular, under typical Molecular Beam Epitaxy conditions the step morphology is linearly unstable in the model and develops fingers separated by deep cracks. The vertical roughness of the step grows linearly in time, while horizontally the fingers coarsen proportional to $t^{0.33}$. We develop scaling arguments to study the saturation of the ledge morphology for a finite width and length of the terrace.