https://doi.org/10.1007/s100510070019
Scaling regimes for second layer nucleation
Fachbereich Physik, Universität GH Essen, 45117 Essen, Germany
Received:
4
September
2000
Published online: 15 December 2000
Nucleation on top of two-dimensional islands
with step edge barriers is investigated
using scaling arguments. The nucleation rate is expressed in
terms of three basic time scales: the time interval between
deposition events, the residence time of atoms on the island,
and the encounter time required for 
atoms forming
a stable nucleus to meet. Application to the problem of second layer
nucleation on growing first layer islands yields a sequence of
scaling regimes with different scaling exponents relating
the critical island size, at which nucleation takes place, to the
diffusion and deposition rates.
Second layer nucleation is fluctuation-dominated, in the sense
that the typical number of atoms on the island is small compared
to , when the first layer island density exponent
χ satisfies 
.
The upper critical nucleus size,
above which the conventional
mean field theory of second layer nucleation is valid,
increases with decreasing dimensionality.
In the related case
of nucleation on top of multilayer mounds fluctuation-dominated
and mean field like regimes coexist for arbitrary values of the
critical nucleus size 
.
PACS: 68.35.Fx – Diffusion; interface formation / 81.15.Aa – Theory and models of film growth / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
