Abstract:
Step meandering due to a deterministic morphological instability on vicinal surfaces during growth is studied. We investigate nonlinear dynamics of a step model with asymmetric step kinetics, terrace and line diffusion, by means of a multiscale analysis. We give the detailed derivation of the highly nonlinear evolution equation on which a brief account has been given [6]. Decomposing the model into driving and relaxational contributions, we give a profound explanation to the origin of the unusual divergent scaling of step meander (where F is the incoming atom flux). A careful numerical analysis indicates that a cellular structure arises where plateaus form, as opposed to spike-like structures reported erroneously in reference [6]. As a robust feature, the amplitude of these cells scales as t 1/2, regardless of the strength of the Ehrlich-Schwoebel effect, or the presence of line diffusion. A simple ansatz allows to describe analytically the asymptotic regime quantitatively. We show also how sub-dominant terms from multiscale analysis account for the loss of up-down symmetry of the cellular structure.
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Received 4 May 2000 and Received in final form 8 September 2000
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Gillet, F., Pierre-Louis, O. & Misbah, C. Non-linear evolution of step meander during growth of a vicinal surface with no desorption. Eur. Phys. J. B 18, 519–534 (2000). https://doi.org/10.1007/s100510070042
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DOI: https://doi.org/10.1007/s100510070042