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Title:
Capture numbers in rate equations and scaling laws for epitaxial growth
Authors:
Gibou, Frédéric; Ratsch, Christian; Caflisch, Russel
Affiliation:
Departments of Mathematics & Computer Science, Stanford University, Stanford, California 94305-2125
Publication:
Physical Review B, vol. 67, Issue 15, id. 155403 (PhRvB Homepage)
Publication Date:
04/2003
Origin:
APS
PACS Keywords:
Theory and models of film growth, Methods of crystal growth; physics of crystal growth
Abstract Copyright:
(c) 2003: The American Physical Society
DOI:
10.1103/PhysRevB.67.155403
Bibliographic Code:
2003PhRvB..67o5403G

Abstract

In this paper, we present a detailed exposition of the functional form of capture numbers that we found using an extended-island model. Our results suggest that the assumption σs=σ1 for all s is only valid up to a time that scales like O(R-1/2). After this time, a better approximation is σs=as+b+small correction and we show that in the limit R→∞, σs→as+b. We link the functional form to the amount of nucleation of new islands on the surface and explain the differences between what is obtained with our extended-island model to what is obtained with a point-island model. Finally, we use our results to derive scaling laws for the adatom and total number densities. We found that the scaling in R remains unchanged, but that the time evolution is influenced by the functional form of the capture numbers.
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