R. Srinivasan et al. / Surface Science 490 ꢀ2001) 308±314
313
studied for hemispheroids. The intensity of the
dipolar surface plasmon resonance of spherical
nanoparticles is expected to rise with particle vol-
ume until the particle size becomes signi®cant with
respect to the wavelength of light. At this point
retardation eects cause the dipolar surface plas-
mon to red-shift and decline in intensity. Simul-
taneously, quadrupole and higher order multipoles
begin to contribute signi®cantly to surface plas-
mon eects. This can be seen clearly in the ab-
sorbance and extinction spectra of spherical Ag
nanoparticles larger than about 100 nm diame-
ter [36±38]. While the dipole resonance red-shifts
with increasing particle size, the quadruapole and
higher multipoles remain close to the wavelength
of the original dipole resonance.
The size at which the maximum SHG intensity
occurs can be employed to probe the kinetics of
Au nanoparticle growth. Volmer±Weber growth
kinetics during vacuum deposition have been
thoroughly studied. However, the existence of ad-
sorption isotherms and electrocatalytic eects,
which may be more important than relative in-
terfacial energies, make electrochemical particle
growth more complex. Clearly the exchange cur-
rent density for both the anodic and cathodic re-
actions will be much higher on Au than on Si.
For these reasons, a phenomenological kinetic
analysis is performed based on
ꢀa 0:06) [28]. This indicates that the lateral par-
À
ticle growth rate is independent of the AuꢀCN)
2
concentration, suggesting that an excess of AuꢀI)
species is available for nanoparticle growth. These
results demonstrate the utility of SHG as an in situ
probe of particle growth.
The origin of the relative SHG intensities at the
maxima in Fig. 1 mainly re¯ects dierences in the
nucleation density, although the aspect ratios may
also have some eect. The average nucleation
densities from AFM images at the SHG maxima
À5
À4
for 3 Â 10 and 10 M KAuꢀCN)
2
relative to
À5
those for 10 M KAuꢀCN) are 2.0 and 3.2, re-
2
spectively. Similarly, the relative SHG enhance-
ments at the corresponding maxima in Fig. 1 are
1.6 and 3.1, respectively. Thus, the relative nucle-
ation density closely matches the relative SHG
enhancement. However, this may not be generally
be the case. Previous results suggest that in some
cases Au nanoparticle aspect ratio may also aect
the relative SHG intensities [27].
Acknowledgements
This research has been supported by NSF grant
CTS-9527497. Thanks to George C. Schatz and
Richard P. van Duyne for helpful discussions.
References
a
À b
Lateral growth rate / HF AuꢀCN ;
ꢀ4
2
[
[
[
[
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