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Continuum description of profile scaling in nanostructure decay Dionisios Margetis,1
 

Summary: Continuum description of profile scaling in nanostructure decay
Dionisios Margetis,1
Michael J. Aziz,2
and Howard A. Stone2
1
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
2
Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
Received 5 November 2003; published 26 January 2004
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 /g1, and d for conical
shapes, the profile peak scales as (g3 /g1) 1/6
. These results compare favorably with kinetic simulations.
DOI: 10.1103/PhysRevB.69.041404 PACS number s : 68.35.Md, 61.46. w, 61.50.Ah
The drive toward smaller features in devices has fuelled
much interest in low-temperature kinetic processes such as

  

Source: Aziz, Michael J.- School of Engineering and Applied Sciences, Harvard University
Margetis, Dionisios - Institute for Physical Science and Technology & Department of Mathematics, University of Maryland at College Park

 

Collections: Materials Science; Mathematics; Physics