Eur. Phys. J. B 18, 519-534 (2000)
https://doi.org/10.1007/s100510070042

Non-linear evolution of step meander during growth of a vicinal surface with no desorption

LSP, UJF-Grenoble 1, BP 87, 38402 Saint Martin d'Hères, France

Corresponding author: ^a olivier.pierre-louis@ujf-grenoble.fr

Received: 4 May 2000
Revised: 8 September 2000
Published online: 15 December 2000

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 , 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.