Kinetics of step bunching during growth: A minimal model

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.

arXiv comment8 pages, 10 figures

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• Impurity-induced step interactions: a kinetic Monte-Carlo study
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• Scaling laws for step bunching on vicinal surfaces: the role of the dynamical and chemical effects
• Anti-Coarsening and Complex Dynamics of Step Bunches on Vicinal Surfaces during Sublimation
• Bunch width versus macrostep height: A quantitative study of the effects of step-step repulsion