Quantum Chemical Analysis of Electronic Structure and n- and p-Type Charge Transport
in Perfluoroarene-Modified Oligothiophene Semiconductors
Sharon E. Koh,†Bernard Delley,‡Julia E. Medvedeva,§,|Antonio Facchetti,†
Arthur J. Freeman,*,§Tobin J. Marks,*,†and Mark A. Ratner*,†
Department of Chemistry and Materials Research Center, Northwestern UniVersity, EVanston, Illinois 60208,
Paul Scherrer Institut, CH-5232 Villigen, PSI Switzerland, and Department of Physics and Astronomy and the
Materials Research Center, Northwestern UniVersity, EVanston, Illinois 60208
ReceiVed: July 28, 2006
Density-functional theory (DFT) is employed to investigate the structural, electronic, and transport properties
of several isomeric fluoroarene-oligothiophene-based semiconductors. Three oligothiophene systems varying
in the perfluoroarene group positions within the molecule are studied to understand the electronic structure
leading to the observed mobility values and to the n- or p-type behavior in these structures. Analyses of both
intermolecular interactions in dimers and extended interactions in crystalline structures afford considerable
insight into the electronic properties and carrier mobilities of these materials, as well as the polarity of the
charge carriers. From the calculated carrier effective masses, we find that sterically governed molecular planarity
plays a crucial role in the transport properties of these semiconductors. Our calculations correlate well with
experimentally obtained geometries, highest-occupied molecular orbital (HOMO)/lowest-unoccupied molecular
orbital (LUMO) energies, and the experimental carrier mobility trends among the systems investigated.
Conducting soft materials are important for the development
of organic-based electronics and optoelectronics.1-3However,
many fundamental questions concerning how charge is trans-
ported through functional organic molecular solids are currently
unresolved. For instance, why certain molecular materials have
particular majority charge-carriers (electrons or holes) and how
molecular and crystal structure parameters influence the relative
magnitudes of carrier mobility are far from being completely
understood.2,4,5For these materials to achieve full potential
requires better understanding of both molecular properties and
intermolecular interactions. It is well-known that the carrier
mobility of organic conductors depends crucially on the
geometry of molecular packing and that the carrier sign may
be altered through introduction of substituents on the conjugated
core.6-8In this regard, thiophene-based conductors are of great
interest because of their attractive properties, including chemical/
thermal stability, synthetic tailorability, solubility/processability,
and relatively large carrier mobility.9-15The transport properties
of the oligothiophene skeletons have been shown to be strikingly
sensitive to the nature of the skeletal functionalization.7,8,16For
instance, by the introduction of electron-withdrawing fluoro-
carbon substitutents, the energies of unoccupied orbitals can
be lowered, making n-type transport channels available.7,8,17-24
To date, most organic semiconductors have been found to be
p-type charge transporters.25-40However, carriers of both signs
are critically needed for organic CMOS (complementary metal
oxide semiconductor) to increase operating speeds and to reduce
In the quest for n-type organic conductors, recent research
in this laboratory has focused on fluorocarbon-oligothiophene
isomers containing variously positioned perfluorinated-arene and
alkyl substituents.14,15,17,41Experimentally, we have used field-
effect transistor (FET) measurements to observe substantial
mobilities and n-type carrier dominance, a striking variance from
the p-type transport typical of unfunctionalized and hydrocarbon-
functionalized oligothiophenes.7,8,17,28,42-45This contribution
provides theoretical investigations of perfluoroarene-modified
oligothiophenes that are of interest because of their unusual
semiconducting properties; in particular, relatively large carrier
mobilities combined with favorable reduction properties result-
ing in n-type transport.17,41Here, we focus on the electronic
and structural properties of three electrically and crystallo-
graphically characterized mixed-polarity molecules with per-
fluoroarene groups sequentially located in different skeletal
positions; each molecule contains six rings, two perfluoroarene
units, and four thiophene rings (see Figure 1). As Table 1 shows,
both TFTFT and FTF exhibit large FET mobilities, with the
latter exhibiting n-type transport. The archetypical p-type
conductor 6T is also investigated for comparison.46To under-
stand the effect of the molecular structure on the electronic and
transport properties (i.e., the majority carrier sign inversion and
variation in the carrier mobility magnitudes) in the three
perfluoroarene-modified thiophene semiconductors, the elec-
tronic and geometric structures were investigated using two
density functional theory (DFT) methods. First, a molecular
quantum chemical approach focused on understanding frontier
orbital interactions and charge density distributions arising from
pairwise intermolecular interactions, starting from the crystal
packing of dimers and idealized π-π stacked models. Second,
we study electronic properties of the corresponding crystalline
structures with an infinite three-dimensional network by cal-
culating their electronic band structures, conduction/valence
band topologies, and electron/hole effective masses. The latter
* To whom correspondence should be addressed.
†Department of Chemistry and Materials Research Center.
‡Paul Scherrer Institut.
§Department of Physics and Astronomy and the Materials Research
|Current address: Department of Physics, University of Missouri-Rolla,
Rolla, MO 65409.
J. Phys. Chem. B 2006, 110, 24361-24370
10.1021/jp064840x CCC: $33.50 © 2006 American Chemical Society
Published on Web 11/11/2006
approach contrasts with most of the band structure studies of
organic conductors performed to date which have predominantly
been limited to one-dimensional analyses in reciprocal space
(because of the inherent structural complexity of most molecular
The band structure calculations reported here suggest, for each
of the three perfluoroarene-modified oligothiophene semicon-
ductors, similar transport properties for both hole and electron
carriers. It will be shown that molecular geometry and packing
dictate the π-π overlap connected with the crystallographic
direction of the highest transport observed in most organic
conductors, as well as in the present calculations. Importantly,
our calculations agree well with experimentally obtained crystal
structure geometries, electrochemically measured redox poten-
tials, and the observed mobility trends.
II. Computational Methods
Density functional theory (DFT) has been found to be an
accurate formalism for calculating the chemical and structural
properties of many molecular systems, including organic
conductors.52-58The DFT methodology has also been shown
to predict accurate band structure diagrams, bandwidths, and
densities of states for conventional inorganic semiconductors
and to provide reliable trends for organic conductors.59-61
Despite the well-known overbinding effects of pure DFT
functionals which result in underestimations of the energy band
gaps, full band structure analyses can provide information on
the band topology for the top of the valence band and the bottom
of the conduction band and thus illuminate features such as
carrier effective masses, carrier mobilities, and transport sym-
metries that are difficult to extract from simple dimer models.
The two methods used in this study are detailed below.
A. Molecular Approach. Monomer and dimer calculations
were performed with DFT using the Q-Chem 2.1 program62with
the B3LYP hybrid functional63,64and a 6-31G* basis set.
Optimized monomer geometries were compared to those
obtained experimentally via X-ray diffraction.17Three dimer
models were investigated: the true dimer, a modified dimer,
and the perfect dimer models (see Figure 2). In the true dimer
model, the atomic geometry is extracted directly from the
crystallographically determined unit cell. In the FTF and TFT
systems, the true dimer is significantly slipped from a cofacial
arrangement, with two neighbor half-molecules overlapping.
Therefore, a modified dimer was investigated for FTF and TFT
where two-half-molecules interact with one full molecule. In
the perfect dimer, optimized monomers are used to construct
the dimer with two monomers spaced at the crystallographically
determined cofacial distance (see Figure 3a for cofacial packing).
This distance is 3.2 Å for FTF, 3.4 Å for TFTFT, and 3.36 Å
Single-point energy calculations were performed for all dimer
structures, retaining the crystal geometry in the two models
referred to here as the true dimer and the modified dimer and
freezing the cofacial spacing in the third model, the perfect
dimer. DFT calculations were performed in Q-Chem 2.1 and
Jaguar 5.0.65Orbital plots were calculated using single-point
energy calculations with Spartan ’04 for Windows,62,66using
DFT with a B3LYP functional63,64and 6-31G* basis set.
B. Band Structure Calculations. Electronic structure cal-
culations were performed with DMol33.853,67using DFT with
the Perdew-Wang exchange-correlation functional68,69and a
DND basis set.67The lattice parameters and the atomic positions
were taken from experimentally determined crystal structures
(see Figure 3b for crystallographic packing).17For sexithiophene
(6T), the structural parameters were taken from the Cambridge
Crystal Database.70,71For all systems under investigation, the
internal geometries were optimized by total energy and atomic
force minimization; during the relaxation, the volume of the
corresponding unit cell was fixed to the experimental value.
The results showed that the binding energies changed ∼1%,
while, as expected, the band gap values became smaller upon
optimization, ranging from 0.09 to 0.21 eV.
The electronic band structures were calculated along the high-
symmetry directions in the corresponding standard Brillouin
zone of the designated crystal system. For better comparison
among the systems and because of the peculiar space orientation
of the molecules, additional band structure calculations were
performed including other directions in reciprocal space. Densi-
ties of states were calculated using the tetrahedron method72
and a 8 × 8 × 4 k-point mesh (see Figure 1 for molecular
structures for FTF, TFTFT, TFT, and 6T). Finally, both the
hole and electron effective masses were calculated according
Here, m* is the effective mass, E is the band energy, and k is
the wavevector. Note that the estimation of curvature can be
dependent on different numerical methods for estimating the
second derivative of energy with respect to k-space. Here we
use a variation of the three-point method commonly used for
estimating second derivatives.
In the discussion below, differences in structural and elec-
tronic properties are compared for FTF, TFTFT, and TFT in
both optimized gas phases and crystalline structures. Dimer
interactions are evaluated using three different models to
understand intermolecular interactions. Additionally, band struc-
ture calculations are used to understand the extended polycrys-
talline networks of these organic semiconductors. From these
calculations, the electronic structure properties defining charge
transport are then evaluated.
A. Energetics and Structural Properties of Monomers.
DFT-optimized gas-phase structures generally correspond well
with the experimental crystallographic data. For the systems
herein, we find that DFT overestimates the C-S bond lengths
within the thiophene ring (0.02 Å) and the conjugated C-C
bonds lengths within the thiophene ring (0.01 Å), while the C-C
single bond lengths between rings are underestimated by <0.008
Å. In comparison to the computed geometry, the experimental
dihedral angles in FTF are smaller between the two cis-
thiophene rings by 5.5° but are slightly larger between the
perfluoroarene groups and the two sets of cis-thiophene groups
(by 1.5°). For TFTFT, the dihedral angles are all slightly (1-
7°) greater in the experimental crystal geometry. For TFT, the
Figure 1. Molecular structures examined in this study.
24362 J. Phys. Chem. B, Vol. 110, No. 48, 2006
Koh et al.
dihedral angle between the two perfluoroarene groups is
measured to be 53.9(0.32)° in the crystal structure17versus 52.6°
in the optimized structures. All other dihedral angles in the
crystal geometry are greater (by 2-7°) than in the optimized
single-molecule structure of TFT.
Orbital contour plots for the three molecules in both optimized
gas-phase and crystal geometries reveal that both highest-
occupied molecular orbitals (HOMOs) and lowest-unoccupied
molecular orbitals (LUMOs) consist of linear combinations of
individual thiophene and perfluoroarene groups. The HOMOs
reside predominately in the thiophene rings and show the typical
cis-butadiene HOMO pattern (Figure 4); there is some, minimal,
contribution from the perfluorarene segments. The LUMOs, on
the other hand, are more delocalized with more equal contribu-
tion from both the thiophene and perfluoroarene groups.
Substantial contributions from the sulfur atoms are also seen in
TABLE 1: Experimental Electrochemical Data (eV), Where Electron Affinity (EA) and Ionization Potentials (IP) Are
Estimated via Redox Potentials Measured versus SCE,17,41Experimental Mobilities (measured in field-effect transistors), Where
the Temperature Reported is the Deposition Temperature (TD) of the Organic Film, and Computed Band Gaps (eV)a
experimental electrochemistry data17(eV)
calculated band gaps (eV)
FET µ (TDin °C)
4 × 10-5(60)c
not active (90)
aNote that the gaps calculated for the band structure were with a pure DFT (LDA) functional and the molecular calculations were with a hybrid
functional.bn-type conductor.cp-type conductor.
Figure 2. Schematics of (a) the true dimers from the crystal, (b) the modified dimers from the crystal, and (c) the perfect π-π overlap dimers.
Perfluoroarene-Modified Oligothiophene Semiconductors
J. Phys. Chem. B, Vol. 110, No. 48, 2006 24363
the LUMO orbital plots, whereas the fluorine atoms make little
direct contribution to either HOMO or LUMO orbitals (in
keeping with the traditional role of fluorine as an inductive
substituent). Additionally, the carbon-centered orbitals of the
perfluoroarene fragments in TFTFT and TFT show significantly
more charge density localization than FTF. HOMO/LUMO
energies from the crystal geometries exhibit slightly larger
energy gaps than in the optimized gas-phase structures by 0.082
eV for FTF, 0.109 eV for TFTFT, and 0.190 eV for TFT.
Molecular orbital contour plots for the dimers [denoted as
(FTF)2, (TFTFT)2, and (TFT)2] in the enforced perfect π-π
overlap model reveal significant intermolecular orbital overlap
between the LUMO oribitals in both (FTF)2and (TFTFT)2.
This is especially significant between corresponding C‚‚‚C and
the S‚‚‚S pairs in the two cofacial molecules, which exhibit
intermolecular contacts of 3.2 and 3.4 Å, respectively. In
(TFT)2, orbital overlap is far smaller than in (FTF)2 and
(TFTFT)2because of the pronounced twist from planarity in
the molecular geometry, which leads to a far larger interplanar
spacing. See Figure 5 for example of contour plot of the (FTF)2
dimer in the perfect model.
B. Bandwiths in Dimers: Tight-Binding Model. In a simple
tight-binding model picture, bandwidths arising from orbital
splittings directly determine the mobility (increased bandwidth
leads to increased mobility). This bandwidth follows from the
tight-binding model picture where the monomer HOMO and
LUMO orbitals split upon formation of an interacting dimer
(see Figure 6).73Orbital splittings are defined by the absolute
energy difference between the HOMO and HOMO-1 (2?HOMO)
and the LUMO and LUMO+1 (2?LUMO) orbital energies (see
Figure 2). Computed bandwidths are 4?74and are summarized
in Table 2.
1. True Dimers. Dimers with the atomic positions taken
directly from the corresponding crystal geometry were also
evaluated (Figure 2a). In (TFTFT)2, there is little slippage in
the packing, with a slight displacement in the parallel planes
between the two molecules in the dimer. The bandwidths
obtained for (TFTFT)2 are 0.164 (HOMO) and 0.272 eV
(LUMO). In both (FTF)2and (TFT)2, the monomer cofacility
is slipped, reducing the interaction. For (FTF)2, bandwidths of
0.284 (HOMO) and 0.112 eV (LUMO) are computed, while
(TFT)2 has bandwidths of 0.224 (HOMO) and 0.096 eV
(LUMO) (Table 2). In 6T, the herringbone pattern of the
molecular structures are perpendicular, leading to reduction in
perfect π-π overlap. The bandwidths obtained for (6T)2are
0.276 (HOMO) and 0.271 eV (LUMO).
Figure 3. Experimental crystal packing diagrams17for the molecules examined in this study: projections showing the (a) cofacial packing and (b)
24364 J. Phys. Chem. B, Vol. 110, No. 48, 2006
Koh et al.
2. Modified Dimers. The interactions within (FTF)2 and
(TFT)2were further investigated with a modified dimer model,
using two half molecules interacting with a full molecule in
the corresponding crystal lattice packing (Figure 2b). The
scission points of the half molecules were capped with hydrogen
A comparison of the energy splitting patterns traced from
the monomers to the modified dimers reveals that the presence
of the two half molecules results in the appearance of additional
orbitals having energies both lying within 0.001 hartree (0.027
eV), Figure 2 (designated as HOMO-1a and HOMO-1b for
the HOMO levels and similarly LUMO+1a and LUMO+1b
for the LUMO). Here, the HOMO-1a and LUMO+1a have
orbital energy values close to the HOMO and LUMO orbitals.
Bandwidths were calculated from the HOMO/HOMO-1a and
LUMO/LUMO+1a energy differences. As expected, the band-
widths of the modified dimers are increased by 1-3 and 6-8
times for the HOMO and LUMO, respectively, as compared to
the true dimers, see Table 2, showing the significance of the
interactions: (FTF)2 is found to have bandwidths of 0.878
(HOMO) and 0.852 eV (LUMO), and (TFT)2has bandwidths
of 0.262 (HOMO) and 0.612 eV (LUMO) (Table 2).
3. Perfect Dimers. To understand the perfect π-π stacked
system for the three molecules under investigation, orbital
energy calculations on fully eclipsed dimers with incrementally
varied z-axis spacings (distances between the cofacial molecular
π-π stacking) were also performed (Figure 2c). Bandwidths
were found to decrease exponentially with respect to the distance
between the two molecules. As z becomes greater than 5 Å,
the two molecules in the dimer behave essentially like two
isolated monomers with orbital energies corresponding to those
of the monomer.
Bandwidths (4?) reported from this model are for crystallo-
graphically determined π-π cofacial distances [(FTF)23.2 Å,
(TFTFT)23.4 Å, and (TFT)23.36 Å]. Bandwidths are estimated
to be 1.688 (HOMO) and 1.198 eV (LUMO) for (FTF)2and
1.414 (HOMO) and 1.306 eV (LUMO) for (TFTFT)2. In
(TFT)2, the large dihedral angle between the two perfluoroarene
groups leads to small bandwidths: 0.544 (HOMO) and 0.380
eV (LUMO). The corresponding bandwidths for (6T)2are found
to be 1.258 (HOMO) and 1.244 eV (LUMO). Bandwidths
obtained via this orbital splitting analysis are summarized in
C. Band Structures of the Crystals. Band structures were
investigated by evaluating band dispersion along standard
Brillouin zones and additional directions in the reciprocal space
for all four systems: FTF (triclinic), TFTFT (monoclinic), TFT
(orthorhombic), and 6T (monoclinic). Using the standard
Brillouin zone directions, we found less dispersion than with
Figure 4. Monomer molecular orbital contour plots of the HOMO and LUMO orbitals of FTF, TFTFT, and TFT.
Figure 5. Example orbital plot. A contour plot of (FTF)2in the perfect
dimer model. The molecular orbital contour plot reveals the overlap in
Figure 6. Energy splittings used to determine bandwidths. Cartoon
of a monomer evolving into a dimer band diagram. The left most dimer
model corresponds to the band diagram for the dimers in the perfect
and true dimer models. The dimer band diagram on the right
corresponds to the modified dimer model. Here, orbital splitting
corresponds to 2? and Egap to the HOMO/LUMO energy gap (Hd
HOMO, L)LUMO). Note that in this model the bandwidth is 4?.74
Perfluoroarene-Modified Oligothiophene Semiconductors
J. Phys. Chem. B, Vol. 110, No. 48, 2006 24365
the inclusion of additional directions in reciprocal space in the
band structure plots, where larger energy dispersion of both the
conduction and valence bands is found for all structures
investigated, but it most pronounced in the FTF system. This
additional band dispersion is the result of a more thorough
sampling in the reciprocal space of the molecular packing
(Figure 7). Thus, we may conclude that more directions, as
compared to the standard directions in the Brillouin zone, are
required to obtain accurate band dispersions and, therefore, to
describe more accurately the charge-transport properties through
analysis of the effective masses at the conduction and valence
band edges. Herein, we discuss the findings in band structure
plots taken from the additional reciprocal space evaluation as
seen in Figure 8; the results are summarized in Table 3.
The effective mass values calculated at the conduction band
edge (CBE) and valence band edge (VBE) predict the following
mobility trends: FTF > TFT > TFTFT > 6T. It is expected
that the geometric twist in TFT should lead to a much lower
charge transport; however, this is not seen in the comparison
of effective mass calculation at the CBE and VBE. Overall band
dispersion, as monitored by the bandwidths seen in the band
structure plots (Figure 8), is smaller in TFT than in the other
three systems (FTF, TFTFT, and 6T) (Table 3). Apart from
TFT, the trend otherwise agrees with the measured FET
mobility trends where FTF is predicted to have higher mobilities
than TFTFT and 6T, which is greater than TFT. The
magnitudes of the hole versus electron effective masses do not
show significant enough differences to estimate theoretically
the favoring of n- vs p-type charge transport. According to these
calculations, it appears these systems would be ambipolar;
however, all of the fluorinated-arene systems appear to favor
hole transport, and 6T is predicted to have favored electron
transport. To understand better the directional mobilities within
the crystal packing, plots of the planes in real space corre-
sponding to the directions calculated in reciprocal space were
made using the program Mercury75-77(Figures 9 and 10).
Bandwidths from the HOMO/LUMO tight-binding model
dimer splitting cannot be directly compared to the calculated
band structures because of the degenerate nature of the conduc-
tion bands found in TFTFT, TFT, and 6T. It should also be
noted in the band structure calculations that the bandwidths of
the valence and conduction bands are from multiple split bands.
However, the bandwidths can be estimated by evaluating the
width of the bands from the total density of states (TDOS);
these are summarized in Table 4. FTF does not show band
An analysis of the partial densities of states (PDOS) allows
us to clarify the origin of the charge densities contributing to
the frontier bands. We found that the majority of the charge
density contributions arise from the p-orbitals which make up
the π-conjugation, in agreement with the above molecular orbital
analysis. In general, the three systems show contributions mainly
from the conjugated carbon backbone for both the valence and
conduction bands. The sulfur p-orbitals contribute mainly to
the conduction band, and the electron-withdrawing fluorocarbon
fragments appear to make little contribution to the valence/
conduction energy level interactions, in agreement with the
molecular orbital analysis above. As expected, the calculated
band gap values are significantly underestimated. A comparison
of the band gap values for three modified structures and the 6T
structure shows a good agreement with experimental trends,17
where 6T has the smallest band gap (1.38 eV) followed in order
by FTF (1.44 eV), TFTFT (1.72 eV), and TFT (1.97 eV), see
Table 1. FTF, TFTFT, and 6T have an indirect band gap,
whereas TFT has a direct band gap.
For the perfluoroarene-oligothiophene molecules investigated,
orbital contour plots indicate that the greatest charge-density
contributions to the valence bands are from the conjugated
carbon backbone of the molecular π-system, while the sulfur
atoms contribute principally to the conduction band, in agree-
ment with previous work on thiophene oligomers.61Very little
direct charge-density contribution to the HOMOs and LUMOs
is derived from the fluorocarbon groups, although the fluorinated
components inductively stabilize the electronic levels of the
molecular systems. The analyses from the density of states
calculated from the band structures indicate similar trends in
charge density distribution within the molecular structures as
was seen in the dimer studies. Previous work showed that the
S‚‚‚S, as well as C‚‚‚C and C‚‚‚S, intermolecular interactions
are key contributors to dispersion in the bands. In particular, it
has been suggested that the sulfur-sulfur overlap leads to the
dispersion seen in the band structures and dominates the
transport properties.78In the present study, the band structure
TABLE 2: Summary of HOMO and LUMO Splittings from Molecular Orbital Calculations at the B3LYP/6-31G* Level of
true dimer from crystal (a)
modified dimer from crystal (b)
perfect π-π overlap dimer (c)
aSee Figure 2a-c for dimer configurations chosen for the molecular systems. The cofacial spacing for the perfect dimer model is as follows:
FTF (3.2 Å), TFTFT (3.4 Å), and TFT (3.36 Å)
Figure 7. Schematic of the additional points evaluated in reciprocal
space used to generate the band structure plots seen in Figure 8.
24366 J. Phys. Chem. B, Vol. 110, No. 48, 2006
Koh et al.
calculations agree with previous work revealing substantial
sulfur-sulfur interactions, also seen in the present molecular
orbital contour plots for the LUMOs. Additional investigation
is needed to probe the exact nature of the S‚‚‚S effects on the
transport properties, in particular when vibronic coupling is
The applicability of the quantum chemical tight-binding type
approach is based on the assumption that in the absence of other
effects such as polaron formation,79-82one may assume, all other
things being equal, that the greater the bandwidth, the greater
the carrier mobility (effectively, because scattering out of the
band is minimized). The general trend (see Table 2) observed
here is that FTF has a greater bandwidth than TFTFT and TFT,
in agreement with experimental data showing that FTF has a
greater carrier mobility than TFTFT, followed by TFT. In the
true dimer model, TFT appears to have larger bandwidths over
TFTFT; this is because of the crystallographic packing where
the best orbital overlap for TFTFT is along the slippage plane
(see Figure 10). The computed 6T bandwidths indicate smaller
mobilites than FTF but approximately the same as TFTFT, in
agreement with experiment.17However, the transition to n-type
conduction in FTF is not suggested by the present calculations.
In the true and modified dimer models from the crystal cell,
smaller bandwidths are observed, indicating reduced molecular
Figure 8. Band structure and density of states (DoS) plots for the semiconductors investigated. The yellow region corresponds to the band gap.
TABLE 3: Comparison of Calculated Effective Masses in
the Directions Indicated for the Semiconductors Examined
Figure 9. FTF crystal packing showing planes of high transport
probability. The red plane indicates the direction of favored n-type and
p-type transport (001 h), although the displacements in reciprocal space
differ. The abc vectors for the crystallographic repeat unit are indicated
by the red (a), green (b), and blue (c) lines.
Perfluoroarene-Modified Oligothiophene Semiconductors
J. Phys. Chem. B, Vol. 110, No. 48, 2006 24367
interactions. The orbital overlap in (FTF)2and (TFT)2is greater
in the modified dimer model than in the true dimer which shows
staggering (Table 2). Although the general trends of HOMO
versus LUMO bandwidths in the modified dimer model may
not concur with observed charge polarity, the modified dimer
model may give a better indication of the real crystal interactions
since, in the crystal structure, staggering is seen where half
molecules are interacting with other half molecules for the FTF
and TFT molecular systems. When the true dimer model is
compared to the modified dimer model, the bandwidths of FTF
are seen to increase significantly in the latter, indicating good
orbital overlap, whereas in TFT, there is less increase because
of orbital overlap disruption from the twist in molecular
geometry. In the dimer models from the crystal cell, the HOMO
splitting is again seen to be greater than that of the LUMO for
(FTF)2and (TFT)2, but not for (TFTFT)2, in variance with
the perfect dimer model, but it does correspond to the wider
LUMO band seen in the calculated total DOS (Table 4). In the
perfect dimer model, greater HOMO than LUMO orbital
splittings are observed (Table 2). The greater bandwidths
calculated in the perfect dimer model arise from the assumed
idealized π-π stacking. Energy gaps, Egap, for the three models
are ordered as follows: modified dimer > true dimer > perfect
Both steric and electronic interactions are important in the
determination of molecular interactions in the π-π stacking
direction. In FTF and TFTFT, the molecules are nearly planar.
So these molecular systems stack well in the z direction and
have strong π-π stacking interactions, as indicated in the
calculations (e.g., Table 2). However, in TFT, because of the
significant torsional angle between the two central perfluoro-
arene rings, the π-π stacking interactions are much weaker.
This disruption in molecular interaction correlates well with the
lower observed charge carrier mobilities of this system. This
trend is evident in the molecular orbital picture (the bandwidths
are substantially smaller than in the other two systems). In the
band structure results, the predicted mobility, based on effective
mass, agrees with the FTF and TFTFT trends but does not
seem to consider the geometric twist in TFT and will be further
The band structure calculations agree with experimental trends
in band gaps (Eg), where Egfollows FTF < TFTFT < TFT.
However, because of the well-known overbinding effects of the
DFT functional used,83band-gap magnitudes are underestimated
by ∼0.5-0.8 eV. While DFT-derived trends should be reliable,
molecular band gaps calculated using a hybrid functional are,
as expected, in much better agreement with the experimentally
measured gaps (see Table 1).
Previous electronic structure calculations for 6T focused on
dispersion relations evaluated in four different reciprocal space
directions.78In this study, we evaluate the structure by including
additional directions in reciprocal space to attain a better
understanding of the extended electronic structure for compari-
son to the dimer calculations. In the present reciprocal space
evaluation, band dispersions are observed that agree with
previously published work by Haddon,et. al.78Evaluating the
CBE and VBE in our 6T investigation of the standard Brillouin
zones, we find the forward directions of the CBE(001 h) and the
VBE (101) to have very flat bands, while the unconventional
reciprocal space directions show the greatest dispersion in the
(1 h00) direction for the valence band and in the (010) direction
for the conduction band.
The band structures calculated for the standard Brillouin zone
directions and the sampling of reciprocal space both reveal band
degeneracy predominately in the conduction bands of TFTFT,
TFT, and 6T (energy degeneracy for particular points in
k-space): all three systems have p-type charge carrier mobilities
found experimentally through FET measurements. Band de-
generacy may occur because of the symmetry of the molecular
system leading to degenerate energy levels.84,85No band
degeneracy is seen in FTF, a system with one molecule in the
crystal unit cell. In systems with more than one molecule in
the crystal unit cell, band degeneracy, which can facilitate
phonon scattering86and hence reduce carrier mobility, is
The lowest-effective mass is found for FTF, which correlates
with the highest experimental charge carrier mobility determined
in this series. However, for the perfluorinated-oligothiophene
systems, all effective masses estimate holes lower than those
calculated for electron transport, suggesting that all three systems
studied should favor p-type carrier mobilities. For 6T, it appears
that electron transport may be favored; however, the LUMO/
conduction band levels are much higher in energy than in the
perfluorinated systems. Effective masses for holes and electrons
for all systems are on very similar numeric scales, although
these systems may appear to slightly favor hole transport, they
may also have similar transport probabilities for electrons,
indicating these systems should all be ambipolar.
Although the bandwidths may not be directly compared
because of the band degeneracy seen in TFTFT, TFT, and 6T,
both 6T and TFTFT show larger bandwidths for the conduction
band, indicating the capacity for n-type charge transport. We
believe the rather large conduction bandwidths of TFTFT and
Figure 10. (a) TFTFT crystal packing showing planes of highest
transport; the blue and red plane indicates the favored n- and p-type
transport (010) and (001 h), respectively. (b) TFT crystal packing showing
the plane of highest transport; the red plane indicates the favored n-
and p-type transport direction (1 h00). The abc vectors for the crystal-
lographic repeat unit are indicated by the red (a), green (b), and blue
TABLE 4: Bandwidths Computed from the Total Densities
valence band (eV)
conduction band (eV)
24368 J. Phys. Chem. B, Vol. 110, No. 48, 2006
Koh et al.
6T, although contributed by degenerate bands, indicate potential
n-type behavior under optimum processing/fabrication condi-
The large widths of the 6T conduction band are in agreement
with electronic structure calculations for polythiophene indicat-
ing that the conduction bandwidth is greater than the valence
bandwidth.61The conditions under which the organic FETs are
fabricated (and mobility and charge carrier signs are measured)
may introduce interfacial artifacts and other effects that are not
accounted for in the present calculations.87-92Chua et al.
recently reported an organic semiconductor electron affinity in
agreement with our earlier work14,15and showed, not unexpect-
edly, that removing hydroxyl trapping sites at the semiconduc-
tor-dielectric interface can be important for mobilizing n-type
FET charge carriers.93,94The present calculations indicate,
generally, that oligothiophene-fluoroarenes should exhibit am-
bipolar transport43(based on idealized behavior with perfect
molecular crystals). The experimental electron affinities obtained
from the film electrochemistry suggest little difference between
FTF and TFTFT, also shown in our theoretical models. The
effective masses also suggest that all these materials may be
ambipolar, with the carrier sign determined by the experimental
fabrication conditions and measurement schemes.
To better understand the origin of the mobility in certain
crystallographic directions, planes were plotted in real space
corresponding to the directions calculated in reciprocal space
(Figures 9 and 10). In plotting the planes that correspond to
the directions of highest-predicted mobility for the three systems,
we found that the greatest mobility is in the π-π stacking
direction. For FTF, the largest mobility predicted for both n-
and p-type carriers is in the π-π stacking direction, the (001 h)-
vector direction at different displacements in reciprocal space.
Figure 9 shows a plot of the planes for FTF. For TFTFT, the
highest-symmetry plane for both the n- and p-type regime shows
favorable transport in the π-π stacking direction, (010) and
(001 h), respectively. On the basis of the crystal packing motifs,
FTF has one defined orientation in which the long axis of the
molecule may align flat with the substrate, whereas in TFTFT,
there are several directions of orientation for this alignment.
The twist in TFT renders it difficult to discern what planes
intersect, but it appears that the π-π stacking interactions are
also important, although they are substantially disrupted by the
molecular twist, leading to lower carrier mobilities. Figure 10
shows the planes of high transport probability for TFTFT and
In summary, we find that analyses of computed orbital
splitting trends and band structure can elucidate charge-transport
behavior in these unusual isomeric molecular crystals. We find
narrow bands and comparable effective masses in both conduc-
tion and valence bands in all systems studied. This suggests
that transport is intrinsically ambipolar, with other issues
(trapping, injection, phonon coupling, and measurement tech-
nique) possibly dominating the result of any given sample set
or measurement method. Steric effects in TFT compromise
molecular planarity and render it a far poorer conductor than
planar TFTFT or FTF. This indicates (in agreement with a
simple tight-binding picture) that the extent of π-π overlap
determines the dominant transport direction.
Acknowledgment. The authors thank Drs. F. Arnold, G.
Hutchison, A. Troisi, C. Risko, K. Shuford, O. Kontsevoi, and
other members of the Ratner group for helpful discussions. We
thank Dr. S. Ohlinger from Wave function Inc. for assistance
in troubleshooting the orbital plot calculations. We thank the
NSF/MRSEC program through the Northwestern MRSEC
(DMR-0076097), as well as the ONR (N00014-02-1-0909) for
support of this research.
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