Kinetics of step bunching during growth: A minimal model

TL;DR

This paper introduces a minimal stochastic model to analyze step bunching during growth on vicinal surfaces, revealing different coarsening behaviors depending on terrace diffusion rates and providing analytical insights for the case of infinite diffusion.

Contribution

It presents a new minimal stochastic model capturing the kinetics of step bunching and analytically describes stationary bunch properties at infinite diffusion.

Findings

For $d > 0$, coarsening exponent $eta \,\simeq\, 0.38$

For $d=0$, linear coarsening with $eta=1$ observed

Analytic description of stationary bunches at $d=0$

Abstract

We study a minimal stochastic model of step bunching during growth on a one-dimensional vicinal surface. The formation of bunches is controlled by the preferential attachment of atoms to descending steps (inverse Ehrlich-Schwoebel effect) and the ratio $d$ of the attachment rate to the terrace diffusion coefficient. For generic parameters ($d > 0$) the model exhibits a very slow crossover to a nontrivial asymptotic coarsening exponent $\beta \simeq 0.38$. In the limit of infinitely fast terrace diffusion ($d=0$) linear coarsening ($\beta$ = 1) is observed instead. The different coarsening behaviors are related to the fact that bunches attain a finite speed in the limit of large size when $d=0$, whereas the speed vanishes with increasing size when $d > 0$. For $d=0$ an analytic description of the speed and profile of stationary bunches is developed.