138
M. B. Ross et al.
3.3.4 Dielectric Core—Metal Shell Particles
So far we have only discussed essentially spherical metal particles with various
dielectric coatings. In order to cover a large fraction of the solar spectrum, geometries
that allow for large shifts in the LSPR wavelength must be used. One example of this
is the dielectric core—metal shell geometry. The polarizability of this geometry is
given by:
ω = V
(λ m − λ d )(λ c + 2λ m ) + f (λ c − λ m )(λ d + 2λ m )
(λ m + 2λ d )(λ c + 2λ m ) + 2 f (λ m − λ d )(λ c − 2λ m )
,
(3.7)
where λ c , λ m and λ d are the dielectric functions of the core, metal and surrounding
dielectric respectively. The fill fraction, f, is the fraction of the volume occupied by
the core: f = (r c /r m ) 3 . As the fraction approaches one, the resonance condition in
terms of λ m moves to more negative values, and the LSPR red-shifts.
SiO 2 -core-silver-shell, type G, particles have been introduced into DSSCs, where
they show a broad absorption band from approximately 450–700 nm [49]. Incorporating 22 vol. % of these core-shell particles resulted in an increase in overall cell
efficiency from 2.7 to over 4 %. The authors note that the core-shell particles reduce
the dye available surface area by 21 % and dye adsorption by the same amount. With
this considered, the near-field enhancement of dye absorption for the 22 vol. % is
over 1.8 [49]. Upon inclusion of 33 vol. % core-shell particles, the efficiency of the
cell decreased, possibly due to a reduction in the dye accessible surface area [49].
3.3.5 Polarization-Dependent Resonances in Anisotropic Particles
Asymmetry in the geometry of a nanoparticle gives rise to polarization-dependent
resonances. These can vary from highly anisotropic particles, such as prisms and
rods, to more isotropic ones, like cubes and dodecahedra. As a simple example,
let us consider a rod, which typically has two distinct resonances. The longitudinal
resonance occurs when the polarization of light is parallel to the long axis of the
particle, and is always red of the sphere resonance. The transverse resonance occurs
when the polarization is parallel to the short axis and occurs at approximately the
same frequency as the sphere resonance. The polarizability of a rod-like prolatespheroid is given by:
ω = V
λ m − λ d
λ d + L(λ m − λ d )
,
(3.8)
where L is a depolarization factor that takes the form:
L Long =
1 − e 2
e 2
−1 +
1
2e
ln
1 + e
1 − e
,
(3.9)
M. B. Ross et al.
3.3.4 Dielectric Core—Metal Shell Particles
So far we have only discussed essentially spherical metal particles with various
dielectric coatings. In order to cover a large fraction of the solar spectrum, geometries
that allow for large shifts in the LSPR wavelength must be used. One example of this
is the dielectric core—metal shell geometry. The polarizability of this geometry is
given by:
ω = V
(λ m − λ d )(λ c + 2λ m ) + f (λ c − λ m )(λ d + 2λ m )
(λ m + 2λ d )(λ c + 2λ m ) + 2 f (λ m − λ d )(λ c − 2λ m )
,
(3.7)
where λ c , λ m and λ d are the dielectric functions of the core, metal and surrounding
dielectric respectively. The fill fraction, f, is the fraction of the volume occupied by
the core: f = (r c /r m ) 3 . As the fraction approaches one, the resonance condition in
terms of λ m moves to more negative values, and the LSPR red-shifts.
SiO 2 -core-silver-shell, type G, particles have been introduced into DSSCs, where
they show a broad absorption band from approximately 450–700 nm [49]. Incorporating 22 vol. % of these core-shell particles resulted in an increase in overall cell
efficiency from 2.7 to over 4 %. The authors note that the core-shell particles reduce
the dye available surface area by 21 % and dye adsorption by the same amount. With
this considered, the near-field enhancement of dye absorption for the 22 vol. % is
over 1.8 [49]. Upon inclusion of 33 vol. % core-shell particles, the efficiency of the
cell decreased, possibly due to a reduction in the dye accessible surface area [49].
3.3.5 Polarization-Dependent Resonances in Anisotropic Particles
Asymmetry in the geometry of a nanoparticle gives rise to polarization-dependent
resonances. These can vary from highly anisotropic particles, such as prisms and
rods, to more isotropic ones, like cubes and dodecahedra. As a simple example,
let us consider a rod, which typically has two distinct resonances. The longitudinal
resonance occurs when the polarization of light is parallel to the long axis of the
particle, and is always red of the sphere resonance. The transverse resonance occurs
when the polarization is parallel to the short axis and occurs at approximately the
same frequency as the sphere resonance. The polarizability of a rod-like prolatespheroid is given by:
ω = V
λ m − λ d
λ d + L(λ m − λ d )
,
(3.8)
where L is a depolarization factor that takes the form:
L Long =
1 − e 2
e 2
−1 +
1
2e
ln
1 + e
1 − e
,
(3.9)