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Effect of Step Stiffness and Diffusion Anisotropy on the Meandering of a Growing Vicinal Surface

Thomas Frisch and Alberto Verga
Phys. Rev. Lett. 96, 166104 – Published 28 April 2006
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    Abstract

    We study the step meandering instability on a surface characterized by the alternation of terraces with different properties, as in the case of Si(001). The interplay between diffusion anisotropy and step stiffness induces a finite wavelength instability corresponding to a meandering mode. The instability sets in beyond a threshold value which depends on the relative magnitudes of the destabilizing flux and the stabilizing stiffness difference. The meander dynamics is governed by the conserved Kuramoto-Sivashinsky equation, which display spatiotemporal coarsening.

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    • Received 10 February 2006

    DOI:https://doi.org/10.1103/PhysRevLett.96.166104

    ©2006 American Physical Society

    Authors & Affiliations

    Thomas Frisch* and Alberto Verga†

    • Institut de Recherche sur les Phénomènes Hors Équilibre, UMR 6594, CNRS, Université de Provence, Marseille, France

    • *Electronic address: frisch@irphe.univ-mrs.fr
    • †Electronic address: Alberto.Verga@irphe.univ-mrs.fr

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    Issue

    Vol. 96, Iss. 16 — 28 April 2006

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    • Figure 1
      Figure 1
      Sketch of the Si(001) vicinal surface showing the alternation of terraces and steps Sa and Sb. Lines on terraces indicate the privileged diffusion directions. Da, Db and γ˜a, γ˜b are the surface diffusion and step stiffness coefficients, respectively; xan, xbn and ξan(y,t), ξbn(y,t) are step positions and the corresponding perturbations.Reuse & Permissions
    • Figure 2
      Figure 2
      Stability diagram in the plane (f0,δ0), for α0>1. The thick gray line f0=f0c given by Eq. (9), separates the unstable region (right side), from the stable one (left side). The dispersion relation σ(q) with its two branches is shown in each region.Reuse & Permissions
    • Figure 3
      Figure 3
      Spacetime plot of u(y,t) with nondimensional y and t axes, given by the numerical solution of the CKS equation. The coarse graining of structures leads to a superposition of parabolas, with a size ⟨u2⟩1/2∼t. In the long time state all the parabolas tend to have unity curvature at their maximum, and width increasing as t.Reuse & Permissions
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