Exciton and Charge Dynamics in Polymer Solar Cells Studied by Transient Absorption Spectroscopy - Organic Solar Cells: Materials and Device Physics - page 119

mixing between singlet and triplet excitons. Higher exciton states in conjugated
polymers are likely to be more mixed with CT states, resulting in a relatively
longer electron-hole separation, and hence a smaller electron exchange integral
2 J. The small energy gap of 2 J between the singlet and triplet states would
promote the interconversion between them. For a very small exchange integral,
hyperfine interaction (HFI) between the electron and nuclear spins generally plays
an important role in the interconversion mechanism. In organic radicals, the HFI
energy is typically in the order of *5 mT, which corresponds to an intercon-
version time of several nanoseconds [ 39 , 40 ]. This is consistent with an inter-
conversion time of *1 ns reported for poly(3-octylthiophene) in a xylene solution
[ 38 ]. Thus, the ultrafast triplet formation on a short time scale of picoseconds
suggests that the interconversion mechanism is different from the normal inter-
system crossing from the lowest singlet exciton.
Fission of singlet excitons into two triplet exciton pairs is spin conserving and
hence spin-allowed [ 23 ]. Singlet fission is primarily induced by spin dipole-dipole
interaction while the normal intersystem crossing is induced by the spin-orbit
coupling [ 41 ]. Triplet formation from singlet fission has been reported for
molecular crystals [ 42 - 47 ], and also for conjugated polymer films [ 48 - 50 ]. The
energy of the two triplet pair state 1 (TT) is approximated by twice the energy of
isolated triplet excitons (2E T1 ). This is in good approximation for molecular
crystals with weak intermolecular interactions. Thus, 2E T1 is generally considered
to be the threshold energy for singlet fission. Assuming that the energy difference
between the lowest singlet and triplet states DE ST is 0.7 eV for RRa-P3HT, which
is a typical value for various amorphous conjugated polymers [ 51 , 52 ], the energy
level of the lowest triplet exciton state (E T1 ) is roughly estimated to be 1.6 eV for
RRa-P3HT amorphous films. Therefore, the threshold energy for singlet fission is
estimated to be 3.2 eV for RRa-P3HT, which is slightly higher than the excitation
energy (3.1 eV). In other words, the singlet fission by one photon excitation at
400 nm is thermodynamically unfavorable for RRa-P3HT. Indeed, no distinct
triplet signal is observed for RRa-P3HT films immediately after the laser excita-
tion under lower excitation intensities. On the other hand, singlet fission is ther-
modynamically possible from a higher singlet exciton state generated by the
singlet exciton-exciton annihilation (singlet fusion). If triplet excitons are gener-
ated from singlet fission, the back recombination of the two triplet pair state 1 (TT)
to the singlet exciton state is also spin-allowed, and therefore expected to be much
faster than the normal spin-forbidden transition from isolated triplet excitons to the
ground state. As shown in Fig. 5.12 , the lifetime of triplet signals observed for
RRa-P3HT is as short as 300 ps, which is much faster than that of ''isolated''
triplet excitons (*7 ls). This rapid decay is ascribed to the recombination of
triplet exciton pairs to the singlet exciton state. We therefore conclude that triplet
excitons observed for RRa-P3HT films are mainly generated through the singlet
fission from a higher singlet exciton state produced by the singlet exciton-exciton
annihilation (singlet fusion followed by singlet fission into triplet exciton pairs).
Note that no triplet formation is observed for RR-P3HT crystalline films even
though singlet fission is thermodynamically possible from a higher singlet exciton