140
M. B. Ross et al.
efficiencies have been reached with a combination of Al substrate and Au nanoparticles [52]. Additionally, nucleated silver nanoparticles showed a large increase in
scattering resulting in a ∪5 % increase in photocurrent [53]. The nucleated large
particles were essentially 200 nm Ag particles covered in many smaller 20–40 nm
particles. The small particles scatter red light and the large particles scatter blue light,
maximizing the total scattered radiation into the cell. Though this study was formulated for thin film silicon cells, similar principles with different particles involving
absorption and field concentration could be incorporated into DSSCs.
To elucidate some of possibilities for local field enhancement offered by various
nanoparticle shapes (Fig. 3.8), we have calculated the optical response of silver cubes,
prisms and rods within the discrete dipole approximation (See [54, 55] for details
and [56] for an overview). For simplicity, the particles were not coated in a capping
layer in the simulation. The cubes have a rounding on the corners of 10 % of the
edge length, which is comparable to what is seen experimentally. They offer strong
enhancement in the UV for particles with an edge length of less than 60 nm, with
the 40 nm edge length cubes offering field enhancements above 200. The prisms also
have a radius of curvature on the corners of 10 % of the edge length. Increasing the
aspect ratio of the prism (edge length: thickness) rapidly red-shifts the resonance and
causes a large increase in the field enhancement from approximately 1,000 for 5:1
prisms, to 4,500 for 15:1 and larger. The enhancement for rods is even more dramatic,
reaching nearly 20,000 for 8:1 (length:width) aspect ratio rods. It is clear from these
brief calculations that massively-enhanced fields can be observed across the entire
solar spectrum by modifying the geometry of the nanoparticles in a system.
3.4.1 Ensembles
Thus far we have only discussed nanoparticle attributes on a single particle level.
However, nanoparticles are usually implemented in ensembles where proximity allows for optical-mode coupling. The coupling of these modes leads to very large field
enhancement in the gaps between particles. Many applications have arisen because
of this strong enhancement, particularly in the field of surface enhanced Raman scattering (SERS), where the Raman scattering scales with the fourth power of the local
electric field (
E 4 /E 4
0
). This has resulted in reports of enhancement factors of up
to 10 10 [57, 58]. As of yet, there have been no reports of particle dimers or aggregates being used systematically to enhance absorption in DSSCs. To demonstrate
the possible increase in dye absorption provided by dimerized particle structures, we
have calculated the electric field enhancement around a dimer of 20 nm radius silver
spheres with a 2 nm TiO 2 capping layer. Even with the presence of the capping layer,
the field enhancement can be increased from 160 in the case where the particles
are separated by 5 nm, to 360 when they are separated by 1 nm. The approximate
factor of two change in enhancement due to the gap is much smaller than arises
in Raman scattering, which means that dimers with small gaps are less important
in solar energy than in Raman, however the results in Fig. 3.9 suggest that dimer
M. B. Ross et al.
efficiencies have been reached with a combination of Al substrate and Au nanoparticles [52]. Additionally, nucleated silver nanoparticles showed a large increase in
scattering resulting in a ∪5 % increase in photocurrent [53]. The nucleated large
particles were essentially 200 nm Ag particles covered in many smaller 20–40 nm
particles. The small particles scatter red light and the large particles scatter blue light,
maximizing the total scattered radiation into the cell. Though this study was formulated for thin film silicon cells, similar principles with different particles involving
absorption and field concentration could be incorporated into DSSCs.
To elucidate some of possibilities for local field enhancement offered by various
nanoparticle shapes (Fig. 3.8), we have calculated the optical response of silver cubes,
prisms and rods within the discrete dipole approximation (See [54, 55] for details
and [56] for an overview). For simplicity, the particles were not coated in a capping
layer in the simulation. The cubes have a rounding on the corners of 10 % of the
edge length, which is comparable to what is seen experimentally. They offer strong
enhancement in the UV for particles with an edge length of less than 60 nm, with
the 40 nm edge length cubes offering field enhancements above 200. The prisms also
have a radius of curvature on the corners of 10 % of the edge length. Increasing the
aspect ratio of the prism (edge length: thickness) rapidly red-shifts the resonance and
causes a large increase in the field enhancement from approximately 1,000 for 5:1
prisms, to 4,500 for 15:1 and larger. The enhancement for rods is even more dramatic,
reaching nearly 20,000 for 8:1 (length:width) aspect ratio rods. It is clear from these
brief calculations that massively-enhanced fields can be observed across the entire
solar spectrum by modifying the geometry of the nanoparticles in a system.
3.4.1 Ensembles
Thus far we have only discussed nanoparticle attributes on a single particle level.
However, nanoparticles are usually implemented in ensembles where proximity allows for optical-mode coupling. The coupling of these modes leads to very large field
enhancement in the gaps between particles. Many applications have arisen because
of this strong enhancement, particularly in the field of surface enhanced Raman scattering (SERS), where the Raman scattering scales with the fourth power of the local
electric field (
E 4 /E 4
0
). This has resulted in reports of enhancement factors of up
to 10 10 [57, 58]. As of yet, there have been no reports of particle dimers or aggregates being used systematically to enhance absorption in DSSCs. To demonstrate
the possible increase in dye absorption provided by dimerized particle structures, we
have calculated the electric field enhancement around a dimer of 20 nm radius silver
spheres with a 2 nm TiO 2 capping layer. Even with the presence of the capping layer,
the field enhancement can be increased from 160 in the case where the particles
are separated by 5 nm, to 360 when they are separated by 1 nm. The approximate
factor of two change in enhancement due to the gap is much smaller than arises
in Raman scattering, which means that dimers with small gaps are less important
in solar energy than in Raman, however the results in Fig. 3.9 suggest that dimer