Capture numbers in rate equations and scaling laws for epitaxial growth

Frédéric Gibou, Christian Ratsch, Russel Caflisch

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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 1 2003

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ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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