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Continuum description of profile scaling in nanostructure decay

Dionisios Margetis·Michael J. Aziz·Howard A. Stone
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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 g_1 and step-step interaction energy g_3>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 g_3/g_1 < 1, (a) a universal equation is derived for the shape profile, (b) the layer thickness varies as (g_3/g_1)^{1/3}, (c) distinct solutions are found for different g_3/_1, and (d) for conical shapes, the profile peak scales as (g_3/g_1)^{-1/6}. These results compare favorably with kinetic simulations.

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Dionisios Margetis, Michael J. Aziz, Howard A. Stone. 2003-06-04. Continuum description of profile scaling in nanostructure decay. https://doi.org/10.1103/physrevb.69.041404

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