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Island-Size Distributions for Submonolayer Epitaxy: Rate Equations and Beyond

Published online by Cambridge University Press:  10 February 2011

D.D. Vvedensky ,
R.E. Caflisch ,
M.F. Gyure ,
B. Merriman ,
S. Osher ,
C. Ratsch  and
J.J. Zinck
D.D. Vvedensky
Affiliation:
The Blackett Laboratory, Imperial College, London SW7 2BZ, United Kingdom Department of Mathematics, University of California, Los Angeles, CA 90095-1555 SHRL Laboratories LLC, 3011 Malibu Canyon Road, Malibu, CA 90265
R.E. Caflisch
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90095-1555
M.F. Gyure
Affiliation:
SHRL Laboratories LLC, 3011 Malibu Canyon Road, Malibu, CA 90265
B. Merriman
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90095-1555
S. Osher
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90095-1555
C. Ratsch
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90095-1555 SHRL Laboratories LLC, 3011 Malibu Canyon Road, Malibu, CA 90265
J.J. Zinck
Affiliation:
SHRL Laboratories LLC, 3011 Malibu Canyon Road, Malibu, CA 90265
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Abstract

The scanning tunnelling microscope has revolutionized the quantitative analysis of epitaxial phenomena. This, in turn, has spawned a huge theoretical effort aimed at analyzing various aspects of the morphology of growing surfaces. One of the most important general approaches to have emerged from this effort is based on the application of scaling concepts to epitaxial island-size distributions in the regime of submonolayer coverage prior to coalescence. We first discuss the analytical basis for scaling solutions to rate equations. In the limit of irreversible aggregation, a solution is obtained in terms of the capture numbers which agrees with previous work. For reversible aggregation, we identify a new quantity that may be regarded as a continuous analogue of a critical island size. We then examine the influence of spatial correlations by introducing a method for modeling epitaxial phenomena in terms of the motion of island boundaries, which is implemented numerically using the level set method. This island dynamics model is continuous in the lateral directions, but retains atomic scale discreteness in the growth direction. Several choices for the island boundary velocity are discussed and computations of the island dynamics model using the level set method are presented.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 528: Symposia AA – Mechanisms & Principals of Epitaxial Growth in Metallic Systems , 1998 , 261
Copyright
Copyright © Materials Research Society 1998

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