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Asymptotic step profiles from a nonlinear growth equation for vicinal surfaces

J. Kallunki·J. Krug
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Abstract

We study a recently proposed nonlinear evolution equation describing the collective step meander on a vicinal surface subject to the Bales-Zangwill growth instability [O. Pierre-Louis et al., Phys. Rev. Lett. (80), 4221 (1998)]. A careful numerical analysis shows that the dynamically selected step profile consists of sloped segments, given by an inverse error function and steepening as sqrt(t), which are matched to pieces of a stationary (time-independent) solution describing the maxima and minima. The effect of smoothening by step edge diffusion is included heuristically, and a one-parameter family of evolution equations is introduced which contains relaxation by step edge diffusion and by attachment-detachment as special cases. The question of the persistence of an initially imposed meander wavelength is investigated in relation to recent experiments.

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J. Kallunki, J. Krug. 2000-08-28. Asymptotic step profiles from a nonlinear growth equation for vicinal surfaces. https://doi.org/10.1103/physreve.62.6229

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