Math. Model. Nat. Phenom.
Volume 10, Number 4, 2015Micro-nanophenomena
|Page(s)||97 - 110|
|Published online||15 July 2015|
Step Growth and Meandering in a Precursor-Mediated Epitaxy with Anisotropic Attachment Kinetics and Terrace Diffusion
1 Department of Mathematics, Western
Kentucky University, Bowling
2 Applied Physics Institute, Western Kentucky University, Bowling Green, KY 42101
Corresponding author. E-mail: firstname.lastname@example.org
Step meandering instability in a Burton-Cabrera-Frank (BCF)-type model for the growth of an isolated, atomically high step on a crystal surface is analyzed. It is assumed that the growth is sustained by the molecular precursors deposition on a terrace and their decomposition into atomic constituents; both processes are explicitly modeled. A strongly nonlinear evolution PDE for the shape of the step is derived in the long-wave limit and without assuming smallness of the amplitude; this equation may be transformed into a convective Cahn-Hilliard-type PDE for the step slope. Meandering is studied as a function of the precursors diffusivity and of the desorption rates of the precursors and adatoms. Several important features are identified, such as: the interrupted coarsening, “facet” bunching, and the lateral drift of the step perturbations (a traveling wave) when the terrace diffusion is anisotropic. The nonlinear drift introduces a disorder into the evolution of a step meander, which results in a pronounced oscillation of the step velocity, meander amplitude and lateral length scale in the steady-state that emerged after the coarsening was interrupted. The mean values of these characteristics are also strongly affected by the drift.
Mathematics Subject Classification: 35R37 / 35Q74 / 37N15 / 65Z05 / 74H10 / 74H55
Key words: epitaxial crystal growth / step flow / meandering instability / molecular precursors / anisotropic diffusion / nonlinear pde model / convective Cahn-Hilliard equation
© EDP Sciences, 2015
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