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Continuum Limit of a Step Flow Model of Epitaxial Growth

Published online by Cambridge University Press:  17 March 2011

R.V. Kohn ,
T.S. Lo  and
N.K. Yip
R.V. Kohn
Affiliation:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, U.S.A.
T.S. Lo
Affiliation:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, U.S.A.
N.K. Yip
Affiliation:
Department of Mathematics, Purdue University, West Lafay ette, IN 47907, U.S.A.
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Abstract

We examine a class of step ow models of epitaxial growth obtained from a Burton-Cabrera-Frank (BCF) type approach in one space dimension. Our goal is to derive a consistent contin uummodel for the evolutionof the film surface. Away from peaks and valleys, the surface height solves a Hamilton-Jacobi equation (HJE). The peaks are free boundaries for this HJE. Their evolution must be specified by boundary conditions reecting the micro- scopic physics of nucleation. We inv estigate this boundary condition by numerical simulation of the step ow dynamics using a simple nucleation law. Our results rev ealthe presence of special structures in the profile near a peak; we discuss the relationship between these structures and the contin uumequation. We further address the importance of evaporation for matching the local behavior near the peak to the solution of the contin uum equation.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 701: Symposium T – Statistical Mechanical Modeling in Materials Research , 2001 , T1.7.1
Copyright
Copyright © Materials Research Society 2002

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References

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