142
M. B. Ross et al.
3.4.2 Excited State Lifetime of Plasmons
The utility of plasmonically enhanced DSSCs relies on the premise that electron
injection from the dye to the TiO 2 occurs on a timescale that is more rapid than the
lifetime of the plasmon. There have been many studies on electron injection dynamics
(see [60] for a review), with many reports suggesting that the charge injection occurs
on the sub-100 fs timescale. However, there have been reports of injection half-times
ranging from sub-3 fs [61] to 200 ps [62]. For small nanoparticles (in the quasi-static
limit, where there is minimal scattering), the excited state lifetime of a LSPR is
related to the full-width at half-maximum (∂) via
T = 2/ ∂,
(3.12)
the minimum non-radiative contribution to ∂ depends on the frequency of the LSPR
and is given by:
∂(π) = 2λ i (π)
dλ r (π)
dπ
−1
(3.13)
In Eq. 3.13, λ r and λ i are the real and imaginary parts of the dielectric function
of the metal. Dephasing times calculated using Eqs. 3.12 and 3.13 for silver and
gold are shown in Fig.3.10. For particles that cannot be considered in the quasistatic regime (for spheres, a radius of about 30 nm) there is a contribution to ∂ from
radiative effects, such as scattering, which reduces the lifetime of the state. There
are several noteworthy features of Fig. 3.10, the first is that the lifetime of LSPRs on
silver particles is at least twice that of gold across all frequencies, and the second is
that interband transitions result in very low lifetimes at high frequencies.
There have also been reports that the injection dynamics depend on the nature of
the excited state of the dye, with singlet injection dynamics on the N719 dye occurring
on time scales almost two orders of magnitude faster than triplet injection [63]. In
this case, a combination of finely tuning the plasmon resonance of nanoparticles and
dye engineering could assist in promoting singlet excitation to aid electron injection
dynamics.
3.4.3 Metal Losses
It is well known that metal nanoparticles get hot under irradiation, a characteristic
that has resulted in their use in fields as diverse as tumor therapy [64]. The rate of
energy loss inside a metal particle (due to scattering of the electrons on phonons)
is the product of the imaginary part of the dielectric constant of the metal and the
volume integral of the internal electric field strength (see [65, Sect. 80]):
dq
dt
=
π
2
λ i (π)
E(π)
2 dV
(3.14)
M. B. Ross et al.
3.4.2 Excited State Lifetime of Plasmons
The utility of plasmonically enhanced DSSCs relies on the premise that electron
injection from the dye to the TiO 2 occurs on a timescale that is more rapid than the
lifetime of the plasmon. There have been many studies on electron injection dynamics
(see [60] for a review), with many reports suggesting that the charge injection occurs
on the sub-100 fs timescale. However, there have been reports of injection half-times
ranging from sub-3 fs [61] to 200 ps [62]. For small nanoparticles (in the quasi-static
limit, where there is minimal scattering), the excited state lifetime of a LSPR is
related to the full-width at half-maximum (∂) via
T = 2/ ∂,
(3.12)
the minimum non-radiative contribution to ∂ depends on the frequency of the LSPR
and is given by:
∂(π) = 2λ i (π)
dλ r (π)
dπ
−1
(3.13)
In Eq. 3.13, λ r and λ i are the real and imaginary parts of the dielectric function
of the metal. Dephasing times calculated using Eqs. 3.12 and 3.13 for silver and
gold are shown in Fig.3.10. For particles that cannot be considered in the quasistatic regime (for spheres, a radius of about 30 nm) there is a contribution to ∂ from
radiative effects, such as scattering, which reduces the lifetime of the state. There
are several noteworthy features of Fig. 3.10, the first is that the lifetime of LSPRs on
silver particles is at least twice that of gold across all frequencies, and the second is
that interband transitions result in very low lifetimes at high frequencies.
There have also been reports that the injection dynamics depend on the nature of
the excited state of the dye, with singlet injection dynamics on the N719 dye occurring
on time scales almost two orders of magnitude faster than triplet injection [63]. In
this case, a combination of finely tuning the plasmon resonance of nanoparticles and
dye engineering could assist in promoting singlet excitation to aid electron injection
dynamics.
3.4.3 Metal Losses
It is well known that metal nanoparticles get hot under irradiation, a characteristic
that has resulted in their use in fields as diverse as tumor therapy [64]. The rate of
energy loss inside a metal particle (due to scattering of the electrons on phonons)
is the product of the imaginary part of the dielectric constant of the metal and the
volume integral of the internal electric field strength (see [65, Sect. 80]):
dq
dt
=
π
2
λ i (π)
E(π)
2 dV
(3.14)