3 Plasmonically Enhanced Dye-Sensitized Solar Cells
143
Fig. 3.10 Lifetime of plasmonic states. a A typical plasmon resonance showing the strength of
the electric field and the full width at half maximum of the resonance. b The Fourier transform of
(a), showing the decay of the field strength with time. The dephasing time of 4.38 fs is related to
the FWHM of 0.3 eV via Eq. 3.12. c Dephasing times of silver and gold calculated using Eqs. 3.12
and 3.13.
This loss poses the immediate problem that the larger the strength of the internal
field (which to a first approximation is proportional to the surface field) the larger the
energy loss to the metal. Additionally, as particle size increases, the ratio of volume
to surface area increases, indicating that a larger fraction of the field will reside in
the metal than at the surface, compounding energy loss. There are two reasonably
straightforward remedies to this issue. The first is to keep the volume of individual
particles reasonably low. The second is to observe that the dye molecules obey the
same expression as the metal, except the internal field of the dye molecule is entirely
due to the surface field of the particle, and the obvious solution becomes to increase
the imaginary part of the dielectric constant of the dye to compensate for the lack of
field strength. This idea has been investigated [66], and it was noted that, although the
relationship between loss in the dye versus loss in the metal is geometry-dependent,
if the imaginary part of the dielectric function of the dye is above two, the fraction
of energy loss to the dye can approach 90 % of the total energy loss [66]. Despite
these results, dyes with low absorption cross sections (such as the N3 dye) have
been shown to be enhanced by metal nanoparticle inclusions. Some progress has
been made using hybrid electrodynamics/quantum mechanics techniques to study
plasmonically enhanced dye absorption [67], but as of yet, the dynamics of energy
transfer between nanoparticles and dye molecules remains largely unexplored.
143
Fig. 3.10 Lifetime of plasmonic states. a A typical plasmon resonance showing the strength of
the electric field and the full width at half maximum of the resonance. b The Fourier transform of
(a), showing the decay of the field strength with time. The dephasing time of 4.38 fs is related to
the FWHM of 0.3 eV via Eq. 3.12. c Dephasing times of silver and gold calculated using Eqs. 3.12
and 3.13.
This loss poses the immediate problem that the larger the strength of the internal
field (which to a first approximation is proportional to the surface field) the larger the
energy loss to the metal. Additionally, as particle size increases, the ratio of volume
to surface area increases, indicating that a larger fraction of the field will reside in
the metal than at the surface, compounding energy loss. There are two reasonably
straightforward remedies to this issue. The first is to keep the volume of individual
particles reasonably low. The second is to observe that the dye molecules obey the
same expression as the metal, except the internal field of the dye molecule is entirely
due to the surface field of the particle, and the obvious solution becomes to increase
the imaginary part of the dielectric constant of the dye to compensate for the lack of
field strength. This idea has been investigated [66], and it was noted that, although the
relationship between loss in the dye versus loss in the metal is geometry-dependent,
if the imaginary part of the dielectric function of the dye is above two, the fraction
of energy loss to the dye can approach 90 % of the total energy loss [66]. Despite
these results, dyes with low absorption cross sections (such as the N3 dye) have
been shown to be enhanced by metal nanoparticle inclusions. Some progress has
been made using hybrid electrodynamics/quantum mechanics techniques to study
plasmonically enhanced dye absorption [67], but as of yet, the dynamics of energy
transfer between nanoparticles and dye molecules remains largely unexplored.