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Role of step-flow advection during electromigration-induced step bunching

Matthieu Dufay, Thomas Frisch, and Jean-Marc Debierre
Phys. Rev. B 75, 241304(R) – Published 21 June 2007
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    Abstract

    We propose a one-dimensional model based on the Burton-Cabrera-Frank equations to describe the electromigration-induced step bunching instability on vicinal surfaces. The step drift resulting from atomic evaporation and/or deposition is explicitly included in our model. A linear stability analysis reveals several stability inversions as the evaporation rate varies, while a deposition flux is shown to have a stabilizing effect.

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    • Received 1 June 2007

    DOI:https://doi.org/10.1103/PhysRevB.75.241304

    ©2007 American Physical Society

    Authors & Affiliations

    Matthieu Dufay1, Thomas Frisch2, and Jean-Marc Debierre1

    • 1Laboratoire Matériaux et Microélectronique de Provence, Aix-Marseille Université and CNRS, Faculté des Sciences et Techniques de Saint-Jérôme, Case 151, 13397 Marseille Cedex 20, France
    • 2Institut de Recherche sur les Phénomènes Hors Equilibre, Aix-Marseille Université, Ecole Centrale Marseille and CNRS, 49, rue Joliot Curie, Boîte Postale 146, 13384 Marseille Cedex 13, France

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    Vol. 75, Iss. 24 — 15 June 2007

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    Images

    • Figure 1
      Figure 1
      Schematic side view of a vicinal surface: notations and definitions. The electrical field is imposed in the step-down direction here.Reuse & Permissions
    • Figure 2
      Figure 2
      Growth rate σ as a function of the wave number k, as obtained from Eqs. (12, 13). Different evaporation rates s are considered. Nondimensional parameters are ϕ=0.2, f=0, η=−10−4, ρ=20.0, a=5×10−6.Reuse & Permissions
    • Figure 3
      Figure 3
      Stability diagram in the (s,η) plane. Solid (dotted) curves represent ηc (ηp). Nondimensional parameters are ϕ=0.2, f=0, ρ=20.0, a=10−4. For a step-up electrical field, the horizontal dashed line represents a trajectory as the evaporation rate increases.Reuse & Permissions
    • Figure 4
      Figure 4
      Critical value of the nondimensional evaporation rate s* as a function of the attachment vs diffusion parameter ρ for f=0 (log-log scales).Reuse & Permissions
    • Figure 5
      Figure 5
      Stability diagrams in the (s,f−f0) plane. Horizontal axes f=f0 correspond to zero net flux. On the left (right) side of the vertical axes, the electrical current is step-up (step-down). Solid lines represent the boundaries between stable and unstable regions. The regions below the dotted lines are unphysical (f<0). Nondimensional parameters are ϕ=0.2, ρ=1.0, a=10−4, and we set (a) η=±5.0×10−4, (b) η=±5.0×10−3.Reuse & Permissions
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