130
M. B. Ross et al.
example, Standridge, et al. showed that the observed overall cell efficiency decreased
by 40 % when the thickness of the TiO 2 capping layer was increased from 2.0 nm to
4.9 nm [18].
To demonstrate the effect of capping layer thickness, Mie theory [19] can be used
to calculate the optical properties of a spherical nanoparticle with a 20 nm radius silver
core and a TiO 2 shell of varying thickness (Fig. 3.3). The absorption efficiency of the
bare silver particle has a maximum value of nine, indicating that the absorption crosssection of the particle is nine times larger than the area of the particle (Fig. 3.3a). To
put this in perspective, typical DSSC dye molecules have absorption cross-sections
which are smaller than their geometric cross-sections [20], generally of the order
of one Å 2 . The typical density of molecules on the surface of the titania is between
0.5 and 1 dye molecule per nm 2 [21]. The effective cross-section of a dye molecule
adsorbed to the nanoparticle surface is approximately:
C eff =
|E|
2
C dye ,
(3.3)
where ≈ ∼ indicates averaging over the surface of the nanoparticle and C dye is the
absorption cross-section of an isolated dye molecule. The surface-average fields
for silver/titania nanoparticles are shown in Fig. 3.3b, it is clear that the surfaceaveraged fields decrease dramatically with increased TiO 2 thickness which, alongside
experimental observations [18], suggests that near-field enhancement is the primary
enhancement mechanism.
To demonstrate the increase in the effective dye cross-section due to the nearfield, Fig. 3.3d shows the result of Eq. (3.3) for a dye with a frequency independent
absorption cross-section of 0.01 nm 2 multiplied by the number of dye molecules
on the surface N dye (assuming one molecule per nm 2 ). For the bare silver particle,
N dye is 5,000 and the total cross-section of all of the dye molecules increases from
50 nm 2 to 7,500 nm 2 , in line with the 150× increase predicted by the strong localfield. The reduction in field enhancement with increasing TiO 2 thickness is partially
compensated by the increase in the surface area of the nanoparticle, which increases
with radius. For a 12 nm layer of TiO 2 , N dye is 13,000 and the total dye absorption
cross section increases from 130 nm 2 to 2,500 nm 2 .
3.2.2 Calculating Solar Enhancement
Above, we note that the cross-section of a plasmonically enhanced dye is just the
product of the surface-averaged near-field on the plasmonically active component
and the non-enhanced dye cross-section. To calculate the solar-weighted dye enhancement factor, the product of the dye absorption spectrum, the solar spectrum
and the local-field strength must be integrated over a relevant fraction of the solar
spectrum:
M. B. Ross et al.
example, Standridge, et al. showed that the observed overall cell efficiency decreased
by 40 % when the thickness of the TiO 2 capping layer was increased from 2.0 nm to
4.9 nm [18].
To demonstrate the effect of capping layer thickness, Mie theory [19] can be used
to calculate the optical properties of a spherical nanoparticle with a 20 nm radius silver
core and a TiO 2 shell of varying thickness (Fig. 3.3). The absorption efficiency of the
bare silver particle has a maximum value of nine, indicating that the absorption crosssection of the particle is nine times larger than the area of the particle (Fig. 3.3a). To
put this in perspective, typical DSSC dye molecules have absorption cross-sections
which are smaller than their geometric cross-sections [20], generally of the order
of one Å 2 . The typical density of molecules on the surface of the titania is between
0.5 and 1 dye molecule per nm 2 [21]. The effective cross-section of a dye molecule
adsorbed to the nanoparticle surface is approximately:
C eff =
|E|
2
C dye ,
(3.3)
where ≈ ∼ indicates averaging over the surface of the nanoparticle and C dye is the
absorption cross-section of an isolated dye molecule. The surface-average fields
for silver/titania nanoparticles are shown in Fig. 3.3b, it is clear that the surfaceaveraged fields decrease dramatically with increased TiO 2 thickness which, alongside
experimental observations [18], suggests that near-field enhancement is the primary
enhancement mechanism.
To demonstrate the increase in the effective dye cross-section due to the nearfield, Fig. 3.3d shows the result of Eq. (3.3) for a dye with a frequency independent
absorption cross-section of 0.01 nm 2 multiplied by the number of dye molecules
on the surface N dye (assuming one molecule per nm 2 ). For the bare silver particle,
N dye is 5,000 and the total cross-section of all of the dye molecules increases from
50 nm 2 to 7,500 nm 2 , in line with the 150× increase predicted by the strong localfield. The reduction in field enhancement with increasing TiO 2 thickness is partially
compensated by the increase in the surface area of the nanoparticle, which increases
with radius. For a 12 nm layer of TiO 2 , N dye is 13,000 and the total dye absorption
cross section increases from 130 nm 2 to 2,500 nm 2 .
3.2.2 Calculating Solar Enhancement
Above, we note that the cross-section of a plasmonically enhanced dye is just the
product of the surface-averaged near-field on the plasmonically active component
and the non-enhanced dye cross-section. To calculate the solar-weighted dye enhancement factor, the product of the dye absorption spectrum, the solar spectrum
and the local-field strength must be integrated over a relevant fraction of the solar
spectrum: