Asymptotic step profiles from a nonlinear growth equation for vicinal surfaces

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.

4 pages, 5 included figures. Typo in Eq.(5) corrected, section headlines added and Ref.[12] updated

References in corpus (1)

• Coarsening in surface growth models without slope selection

Cited by in corpus (9)

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• Nonlinear evolution of the step meandering instability of a growing crystal surface
• Anisotropic dynamics of a vicinal surface under the meandering step instability