Capture numbers in rate equations and scaling laws for epitaxial growth

Frédéric Gibou, Christian Ratsch, Russel Caflisch

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Article number155403
Pages (from-to)1554031-1554034
Number of pages4
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume67
Issue number15
StatePublished - Apr 2003

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Scaling laws
Epitaxial growth
scaling laws
Adatoms
Nucleation
adatoms
nucleation
scaling
approximation

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Capture numbers in rate equations and scaling laws for epitaxial growth. / Gibou, Frédéric; Ratsch, Christian; Caflisch, Russel.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 67, No. 15, 155403, 04.2003, p. 1554031-1554034.

Research output: Contribution to journalArticle

Gibou, F, Ratsch, C & Caflisch, R 2003, 'Capture numbers in rate equations and scaling laws for epitaxial growth', Physical Review B - Condensed Matter and Materials Physics, vol. 67, no. 15, 155403, pp. 1554031-1554034.
Gibou, Frédéric ; Ratsch, Christian ; Caflisch, Russel. / Capture numbers in rate equations and scaling laws for epitaxial growth. In: Physical Review B - Condensed Matter and Materials Physics. 2003 ; Vol. 67, No. 15. pp. 1554031-1554034.
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