# Kinetics of step bunching during growth: A minimal model

Source: [Kinetics of step bunching during growth: A minimal model](<https://www.sota2.com/research/paper/68fa26862c2a3760193bac08>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T11:26:10.053Z

Authors: Frantisek Slanina, Joachim Krug, Miroslav Kotrla

Published: 2004-09-13T15:44:12.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0409324>)

[PDF](<https://arxiv.org/pdf/cond-mat/0409324.pdf>)