Exciton and Charge Dynamics in Polymer Solar Cells Studied by Transient Absorption Spectroscopy - Organic Solar Cells: Materials and Device Physics - page 127

structures in RRa-P3HT:PCBM blend films cause a significant loss due to the
geminate recombination. Furthermore, the high charge mobility in
RR-P3HT:PCBM blend films can also result in the efficient dissociation of bound
radical pairs [ 60 - 66 ].

5.6.3 Trap-Free and Trap-Limited Recombination

As shown in Fig. 5.7 b, two absorption bands are clearly observed at around 700
and 1000 nm and decay slowly on a microsecond time scale. These two bands can
be ascribed to polarons: the 700 nm band to delocalized polarons and the 1000 nm
band to localized polarons. Interestingly, the delocalized polaron band at 700 nm
decays faster than the localized polaron band at 1000 nm. The delocalized polaron
band almost disappears and instead the localized polaron band is dominant at
100 ls. This is indicative of the different recombination dynamics between de-
localized polaron and localized polaron. Figure 5.19 shows the transient absorp-
tion decays at 700 and 1000 nm at different excitation intensities from 0.8 to
30 lJcm -2 . Here, the charge carrier density is calculated on the basis of the molar
absorption coefficient of each polaron. As shown in the figure, both decays can be
well fitted with an empirical power-law equation.

n 0
ð 1 þ at Þ a

n ð t Þ¼ ð 5 : 1 Þ

The exponent a for the localized polaron band at 1000 nm is *0.5, which is
consistent with previous reports [ 8 , 16 , 67 , 68 ]. As mentioned above, this
power-law decay with an exponent a \ 1 is the characteristic of bimolecular
recombination of trapped carriers having an exponential tail of polaron trap states
(trap-limited bimolecular recombination) [ 31 , 69 , 70 ]. On the other hand, the
exponent a for the delocalized polaron band at 700 nm is as high as unity, sug-
gesting trap-free bimolecular recombination.
The diffusion-limited bimolecular charge recombination dynamics is given by

dn ð t Þ
dt ¼ c ð t Þ n 2 ð t Þ

ð 5 : 2 Þ

where n(t) is the carrier density and c(t) is the bimolecular recombination rate at a
delay time t. Therefore, the bimolecular recombination rate can be expressed as a
function of time by substituting Eq. ( 5.1 ) into Eq. ( 5.2 )

c ð t Þ¼ dn ð t Þ
dt n 2 ð t Þ ¼ aa

1

ð 1 þ at Þ a 1

ð 5 : 3 Þ

n 0

Similarly, the bimolecular recombination rate can be also expressed as a function
of the carrier density by substituting Eq. ( 5.1 ) into Eq. ( 5.3 ).