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Continuum imit of a tep Flow odel 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. ur goal is to derive a consistent contin uummodel for the ev olutionof the lm surface. Away from peaks and valleys, the surface height solves a Hamilton- acobi equation (H E). he peaks are free boundaries for this H E. heir evolution must be speci ed by boundary conditions re ecting the microscopic physics of nucleation. e investigate this boundary condition by numerical simulation of the step ow dynamics using a simple n ucleationlaw. ur results rev ealthe presence of sp ecial structures in the pro le near a peak; we discuss the relationship between these structures and the contin uumequation. e further address the importance of ev aporationfor 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 696: Symposium N – Current Issues in Heteroepitaxial Growth--Stress Relaxation and Self Assembly , 2001 , T1.7
Copyright
Copyright © Materials Research Society 2002

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