Continuum description of profile scaling in nanostructure decay

Dionisios Margetis; Michael J. Aziz; Howard A. Stone

doi:10.1103/PhysRevB.69.041404

Continuum description of profile scaling in nanostructure decay

Dionisios Margetis, Michael J. Aziz, Howard A. Stone

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10 Scopus citations

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>0 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)^1/3,(c) distinct solutions are found for different g₃/g₁, and (d) for conical shapes, the profile peak scales as (g₃/g₁<1)^−1/6.These results compare favorably with kinetic simulations.

Original language	English (US)
Journal	Physical Review B - Condensed Matter and Materials Physics
Volume	69
Issue number	4
DOIs	https://doi.org/10.1103/PhysRevB.69.041404
State	Published - Jan 26 2004
Externally published	Yes

All Science Journal Classification (ASJC) codes

Electronic, Optical and Magnetic Materials
Condensed Matter Physics

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10.1103/PhysRevB.69.041404

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title = "Continuum description of profile scaling in nanostructure decay",

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>0 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)1/3,(c) distinct solutions are found for different g3/g1, and (d) for conical shapes, the profile peak scales as (g3/g1<1)−1/6.These results compare favorably with kinetic simulations.",

author = "Dionisios Margetis and Aziz, {Michael J.} and Stone, {Howard A.}",

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T1 - Continuum description of profile scaling in nanostructure decay

AU - Margetis, Dionisios

AU - Aziz, Michael J.

AU - Stone, Howard A.

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AB - 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>0 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)1/3,(c) distinct solutions are found for different g3/g1, and (d) for conical shapes, the profile peak scales as (g3/g1<1)−1/6.These results compare favorably with kinetic simulations.

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Continuum description of profile scaling in nanostructure decay

Abstract

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