perturbation by the molecular environment. Only a few studies have discussed the
influence of this perturbation on the transport behavior of P3HT. Usually requiring
atomistic resolution, systems of up 10
4 thiophenes have been treated in this fashion,
for example, in order to explore the density of states of P3HT in dependence on the
polymorph and regioregularity or at interfaces [13, 49].
In amorphous systems, localization of charge carriers has been reported to result
from fluctuations of the electrostatic potential rather than from breaks in conjugation [107]. Furthermore, an exponentially decaying tail of the density of states was
found.
In crystalline systems, P3HT backbones are fully conjugated and a charge can be
assumed to delocalize over an entire oligomer [108] (for a more detailed discussion
see Sect. 5.1). The internal contribution to the ionization potential does not change
from segment to segment and the energetic disorder is mostly due to a locally
varying electrostatic potential.
The distributions in hole site energies, i.e., the differences between the energies
of the system when a selected molecule is in the cationic or neutral state excluding
the constant internal contribution related to the gas-phase ionization potential, are
reproduced in Fig. 8 according to [13], together with the fits to a Gaussian function.
It was shown that both the width σ and the mean hUi of the distribution depend on
the side-chain packing and polymer regioregularity. As expected, 100% regioregular
P3HT always has narrower site energy distributions than the 90% P3HT. Interestingly, the hole becomes less stable upon side-chain melting in the 100% regioregular
P3HT (the distribution shifts to more negative numbers by 0.1 eV), whereas it is
stabilized by side chain melting in the 90% regioregular P3HT.
One can attribute the changes in the energetic density of states (DOS) to specific
structural features [13]. The width in the distributions is governed by
regioregularity, with CC-100 and CA-100 having virtually identical widths of
σ ¼ 45 and 51 meV, respectively. CC-90 and CA-90 are energetically more disordered with σ ¼ 74 and 75 meV, respectively. The magnitude of the disorder
compares well with the width of the DOS as extracted from time-of-flight experiments [16, 17], where values for σ of 56 and 71 meV, respectively, have been
proposed from a fit of the field-dependence of the mobility as obtained within the
Gaussian disorder model [109]. In [16], σ did not vary significantly between 94%
and 98% regioregular P3HT. However, an increase in DOS width of around 30 meV
can drastically impact charge mobility in the case of a one-dimensional connected
hopping network, which can be assumed to appropriately reflect conditions in
crystalline lamellae.
On the level of chain ordering, the increase in energetic disorder can also be
related to the increase in paracrystallinity along the π-stacking direction [13]. Considering that the hole–quadrupole interactions associated with thiophene dimers are
the leading contributors to site energies here, this origin for the increase in σ is fully
justified and explains the similar energetic disorder computed for CC-100 and
162
C. Poelking et al.
influence of this perturbation on the transport behavior of P3HT. Usually requiring
atomistic resolution, systems of up 10
4 thiophenes have been treated in this fashion,
for example, in order to explore the density of states of P3HT in dependence on the
polymorph and regioregularity or at interfaces [13, 49].
In amorphous systems, localization of charge carriers has been reported to result
from fluctuations of the electrostatic potential rather than from breaks in conjugation [107]. Furthermore, an exponentially decaying tail of the density of states was
found.
In crystalline systems, P3HT backbones are fully conjugated and a charge can be
assumed to delocalize over an entire oligomer [108] (for a more detailed discussion
see Sect. 5.1). The internal contribution to the ionization potential does not change
from segment to segment and the energetic disorder is mostly due to a locally
varying electrostatic potential.
The distributions in hole site energies, i.e., the differences between the energies
of the system when a selected molecule is in the cationic or neutral state excluding
the constant internal contribution related to the gas-phase ionization potential, are
reproduced in Fig. 8 according to [13], together with the fits to a Gaussian function.
It was shown that both the width σ and the mean hUi of the distribution depend on
the side-chain packing and polymer regioregularity. As expected, 100% regioregular
P3HT always has narrower site energy distributions than the 90% P3HT. Interestingly, the hole becomes less stable upon side-chain melting in the 100% regioregular
P3HT (the distribution shifts to more negative numbers by 0.1 eV), whereas it is
stabilized by side chain melting in the 90% regioregular P3HT.
One can attribute the changes in the energetic density of states (DOS) to specific
structural features [13]. The width in the distributions is governed by
regioregularity, with CC-100 and CA-100 having virtually identical widths of
σ ¼ 45 and 51 meV, respectively. CC-90 and CA-90 are energetically more disordered with σ ¼ 74 and 75 meV, respectively. The magnitude of the disorder
compares well with the width of the DOS as extracted from time-of-flight experiments [16, 17], where values for σ of 56 and 71 meV, respectively, have been
proposed from a fit of the field-dependence of the mobility as obtained within the
Gaussian disorder model [109]. In [16], σ did not vary significantly between 94%
and 98% regioregular P3HT. However, an increase in DOS width of around 30 meV
can drastically impact charge mobility in the case of a one-dimensional connected
hopping network, which can be assumed to appropriately reflect conditions in
crystalline lamellae.
On the level of chain ordering, the increase in energetic disorder can also be
related to the increase in paracrystallinity along the π-stacking direction [13]. Considering that the hole–quadrupole interactions associated with thiophene dimers are
the leading contributors to site energies here, this origin for the increase in σ is fully
justified and explains the similar energetic disorder computed for CC-100 and
162
C. Poelking et al.