Exciton and Charge Dynamics in Polymer Solar Cells Studied by Transient Absorption Spectroscopy - Organic Solar Cells: Materials and Device Physics - page 128

Fig. 5.20 Log-log plots of
the bimolecular
recombination rate c at
1000 nm (solid lines) and
700 nm (broken lines)asa
function of a time t and b the
carrier density n. Adapted
with permission from [ 20 ].
Copyright 2010 American
Chemical Society

(a)

-12

10

-13

10 -7 -6 -5 -4 -3

10 10 10 10 10

Time / s

(b)

-12

10

-13

10

17 16 15

10 10 10

n / cm −3

a

c ð n Þ¼ aa
n

n
n 0

ð 5 : 4 Þ

As mentioned above, a is equal to *0.5 for the localized polaron band at 1000 nm
and unity for the delocalized polaron band at 700 nm. Therefore, as shown in
Fig. 5.20 , the bimolecular recombination rate is time-dependent c(t) for the
localized polaron band at 1000 nm, which decreases from 10 -12 to 10 -13 cm 3 s -1
over the time range from 10 -6 to 10 -3 s, while it is time-independent
c = an 0 -1 & 10 -12 cm 3 s -1 for the delocalized polaron band at 700 nm. Fig-
ure 5.21 shows the temperature dependence of the bimolecular recombination rate
of (a) localized polarons at 1000 nm and (b) delocalized polarons observed at
700 nm over the carrier density range from 10 16 to 10 17 cm -3 . For the localized
polarons, the activation energy estimated from the slope in the Arrhenius plots is
as large as 0.097-0.178 eV, which depends on the carrier density. On the other
hand, the activation energy for the delocalized polarons is as low as *0.078 eV
and independent of the carrier density. We therefore assign the localized polarons
to trapped polarons and the delocalized polarons to trap-free polarons.
For localized polarons, the time-dependent trap-limited bimolecular recombi-
nation rate c(t) varies from 10 -12 to 10 -13 cm 3 s -1 depending on time or carrier
density, as shown in Fig. 5.20 , which is consistent with previous reports [ 67 , 68 ,
71 , 72 ]. The time-dependent bimolecular recombination rate is due to trap depths
depending on the carrier density: the trap depth deepens with time because of
lower carrier density, resulting in the slower bimolecular recombination rate on
longer time scales [ 31 , 68 , 70 ]. As shown in Fig. 5.20 b, the slope of log-log plots
of c(n) against n is almost unity. In other words, c(n) can be expressed by
c(n) & c 0 n. Thus, Eq. ( 5.2 ) is rewritten as