Continuum description of profile scaling in nanostructure decay
Dionisios Margetis, Michael J. Aziz, Howard A. Stone
Abstract
The relaxation of axisymmetric crystal surfaces with a single facet below the roughening transition is studied via a continuum approach that accounts for step energy g1 and step-step interaction energy g3>0. For diffusion-limited kinetics, free-boundary and boundary-layer theories are used for self-similar shapes close to the growing facet. For long times and g3/g1 < 1, (a) a universal equation is derived for the shape profile, (b) the layer thickness varies as (g3/g1)1/3, (c) distinct solutions are found for different g3/1, and (d) for conical shapes, the profile peak scales as (g3/g1)-1/6. These results compare favorably with kinetic simulations.
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