146
H. Ohkita
Thus, the empirical equation Eq. (6.4) can be expressed by using kinetic
parameters for TPV/TPC measurements.
n(t) = n(0)
1 +
λn(0)
λ
(λ + 1)τ n 0 n
λ
0
t
−
1
λ
(6.11)
Durrant and his co-workers demonstrated that the decay dynamics observed by
transient absorption spectroscopy is consistent with that observed by TPV/TPC
measurements [23]. At a charge density of ~10
17 cm
−3 , which corresponds to 1
sun illumination condition, both charge carriers exhibit a similar bimolecular recombination rate of ~10
−12 cm
3 s
−1 at an early time stage of <1 μs as shown in Fig. 6.18.
This is because localized polarons also contribute to charge transport owing to trap
filling. More interestingly, the recombination rate is two orders of magnitude smaller
than the Langevin recombination rate (γ L ≈ 10
−10 cm
3 s
−1 ). Here, γ L is estimated
by γ L = eμ h /ε r ε 0 with a slower charge mobility [49] of μ h ≈ 10
−4 cm
2 V
−1 s
−1
[50]. Such a slow recombination rate would be the key for highly efficient charge
collection in RR-P3HT/PCBM solar cells as described in the next section.
6.5.2 Charge Carrier Lifetime
For highly efficient charge collection, the charge carrier lifetime should be longer
than the charge collection time. The charge carrier lifetime can be estimated by
transient absorption spectroscopy as mentioned above. The carrier density has been
reported to be ~10
17 cm
−3 in RR-P3HT/PCBM blend films under 1 sun illumination.
Thus, the carrier lifetime τ n is estimated to be τ n = 14 μs from Eq. (6.8) with kinetic
parameters a and α, which are obtained by fitting analysis for the decay curve in
Fig. 6.17. On the other hand, the charge collection time τ CC is roughly estimated by
Eq. (6.12)
τ CC =
L
2
2μV
(6.12)
where L is the thickness of the active layer, μ is the charge mobility, and V is
the applied voltage, which is typically assumed to be V OC at the short circuit. For
RR-P3HT/PCBM blend films, τ CC is estimated to be τ CC = 0.8 μs for a thickness of 100 nm. In other words, the charge carrier lifetime τ n is two orders of
magnitude longer than the charge collection time τ CC . This is consistent with highly
efficient charge collection in RR-P3HT/PCBM blends. This would be true for RRP3HT/PCBM solar cells under device operation conditions. We note that the charge
carrier dynamics observed by transient absorption with pulsed laser excitations might
be different from the charge carrier dynamics under steady-state solar illumination.
H. Ohkita
Thus, the empirical equation Eq. (6.4) can be expressed by using kinetic
parameters for TPV/TPC measurements.
n(t) = n(0)
1 +
λn(0)
λ
(λ + 1)τ n 0 n
λ
0
t
−
1
λ
(6.11)
Durrant and his co-workers demonstrated that the decay dynamics observed by
transient absorption spectroscopy is consistent with that observed by TPV/TPC
measurements [23]. At a charge density of ~10
17 cm
−3 , which corresponds to 1
sun illumination condition, both charge carriers exhibit a similar bimolecular recombination rate of ~10
−12 cm
3 s
−1 at an early time stage of <1 μs as shown in Fig. 6.18.
This is because localized polarons also contribute to charge transport owing to trap
filling. More interestingly, the recombination rate is two orders of magnitude smaller
than the Langevin recombination rate (γ L ≈ 10
−10 cm
3 s
−1 ). Here, γ L is estimated
by γ L = eμ h /ε r ε 0 with a slower charge mobility [49] of μ h ≈ 10
−4 cm
2 V
−1 s
−1
[50]. Such a slow recombination rate would be the key for highly efficient charge
collection in RR-P3HT/PCBM solar cells as described in the next section.
6.5.2 Charge Carrier Lifetime
For highly efficient charge collection, the charge carrier lifetime should be longer
than the charge collection time. The charge carrier lifetime can be estimated by
transient absorption spectroscopy as mentioned above. The carrier density has been
reported to be ~10
17 cm
−3 in RR-P3HT/PCBM blend films under 1 sun illumination.
Thus, the carrier lifetime τ n is estimated to be τ n = 14 μs from Eq. (6.8) with kinetic
parameters a and α, which are obtained by fitting analysis for the decay curve in
Fig. 6.17. On the other hand, the charge collection time τ CC is roughly estimated by
Eq. (6.12)
τ CC =
L
2
2μV
(6.12)
where L is the thickness of the active layer, μ is the charge mobility, and V is
the applied voltage, which is typically assumed to be V OC at the short circuit. For
RR-P3HT/PCBM blend films, τ CC is estimated to be τ CC = 0.8 μs for a thickness of 100 nm. In other words, the charge carrier lifetime τ n is two orders of
magnitude longer than the charge collection time τ CC . This is consistent with highly
efficient charge collection in RR-P3HT/PCBM blends. This would be true for RRP3HT/PCBM solar cells under device operation conditions. We note that the charge
carrier dynamics observed by transient absorption with pulsed laser excitations might
be different from the charge carrier dynamics under steady-state solar illumination.