Letterpubs.acs.org/JPCL

Single-Crystal Pentacene Valence-Band Dispersion and Its
Temperature Dependence
Yasuo Nakayama,*,† Yuta Mizuno,‡ Masataka Hikasa,† Masayuki Yamamoto,‡ Masaharu Matsunami,§
Shinichiro Ideta,§ Kiyohisa Tanaka,§ Hisao Ishii,‡,∥ and Nobuo Ueno‡†

Department of Pure and Applied Chemistry, Graduate School of Science and Technology, Tokyo University of Science, 2641
Yamazaki, Noda 278-8510, Japan‡
Graduate School of Advanced Integration Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan§UVSOR Facility, Institute for Molecular Science (IMS), National Institutes of Natural Sciences, 38 Nishigo-Naka, Myodaiji, Okazaki444-8585, Japan∥
Center for Frontier Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, JapanS Supporting Information*

ABSTRACT: The electronic structures of the highest occupied molecular orbital(HOMO) or the HOMO-derived valence bands dominate the transport nature of positive
charge carriers (holes) in organic semiconductors. In the present study, the valence-bandstructures of single-crystal pentacene and the temperature dependence of their energy−
momentum dispersion relations are successfully demonstrated using angle-resolved
ultraviolet photoelectron spectroscopy (ARUPS). For the shallowest valence band, theintermolecular transfer integral and eﬀective mass of the holes are evaluated as 43.1 meV
and 3.43 times the electron rest mass, respectively, at room temperature along the
crystallographic direction for which the widest energy dispersion is expected. The
temperature dependence of the ARUPS results reveals that the transfer integral values (holeeﬀective mass) are enhanced (reduced) by ∼20% on cooling the sample to 110 K.

Cthin-ﬁlm samples of pentacene using angle-resolved ultraviolet
photoelectron spectroscopy (ARUPS).9−13 Although suchinformation on the band structures provides a fundamental
basis for the transport nature,14,15 it is generally not suﬃcientfor comprehensive reproduction of the experimental values ofcharge-carrier mobility in thin-ﬁlm devices because of strong
disturbances in device performance by structural imperfections,such as grain boundaries.16−18 Therefore, single crystals withminimized structural imperfections are suitable benchmarks for
relating electronic structures directly with the electric responses
exhibited by actual devices.
For single crystals of pentacene, many studies have estimatedthe charge-carrier mobility in ﬁeld-eﬀect transistor (FET)
devices, with reported values of as great as 5 cm2V−1s−1.19−29
Moreover, theoretical calculations have predicted the formationof widely dispersed valence band derived from the highest
occupied molecular orbital (HOMO).30−32 However, althoughexperimental characterization of the valence bands of thepentacene single crystal (Pn-SC) has been attempted,33−35 theE−K dispersion structures have not yet been observed
experimentally. One reason for this situation is ascribed tothe experimental diﬃculty of so-called “sample charging”, whichharge carrier transport in semiconducting molecular solids
is a central question in the pursuit of organic electronic
devices with superior eﬃciencies. In particular, the mobility ofcharge carriers is regarded as a criterion not only of theappropriateness of a material for usage as a good semiconductor
but also to distinguish the probable mechanism of transport,that is, bandlike or hopping transport. In this context,
molecules exhibiting large mobility values attract attention
from the viewpoints of both fundamental science and device
applications. Moreover, because the molecular solids areconstructed with weak van der Waals bonding, the charge
carriers inside the solids generally undergo strong coupling withintra- and intermolecular vibrations. Accordingly, knowledge
about the temperature dependence of the electronic structures
is essential to clearly deﬁne the transport nature of the charge
carriers as Holstein−Peierls-type small polarons in organic
semiconducting materials.1−6
The present target molecule pentacene (C22H14) is one of
the most well-studied organic semiconductor materials.
Signiﬁcantly large mobility values of the positive charges(holes) were reported in thin-ﬁlm (1.5 cm2V−1s−1)7 and singlecrystal (over 10 cm2V−1s−1)8 phases of pentacene, implying thatthe transport mechanism should be interpreted as bandlike
rather than intermolecular hopping. As the electronic origin of
the transport behavior, valence bands showing energy−
momentum (E−K) dispersion relations have been proven on© XXXX American Chemical Society

Received: January 11, 2017
Accepted: February 27, 2017
Published: February 27, 20171259

DOI: 10.1021/acs.jpclett.7b00082
J. Phys. Chem. Lett. 2017, 8, 1259−1264

Letter

The Journal of Physical Chemistry Letterscommonly hinders accurate characterization by standard
photoelectron spectroscopy techniques on single-crystal
samples of organic semiconductors. This problem can beovercome with the assistance of enhanced photoconductivity
under laser light illumination during photoelectron spectroscopy measurements, and the valence-band dispersion structures ofthe single crystal samples of several organic semiconductormaterials have been successfully resolved in this way.36−41 For
the Pn-SC, ﬁne analyses of inner-shell electronic states haverecently been accomplished by means of photoconductivityassisted high-resolution X-ray photoelectron spectroscopy(XPS).42 Nevertheless, the E−K dispersion of the valencebands has not yet been resolved by ultraviolet photoelectron
spectroscopy experiments using standard excitation photon
energies (e.g., 21.2 eV), even with the assistance of enhanced
photoconductivity.
In this study, we successfully demonstrated the valence-band
dispersion structures of the Pn-SC for the ﬁrst time using
photoconductivity-assisted ARUPS. Adopting low-energy (10eV) photons as the excitation source enabled us to unveil the“bulk” band beneath the surface. The E−K dispersion of thevalence band was clearly resolved along the crystallographic
direction for which the widest bandwidth has been theoretically
predicted. In addition, the evolution of the valence-bandstructures upon cooling the sample temperature from room
temperature to 110 K was also examined. The transfer integral
and eﬀective mass values for the conducting holes wererevealed at these temperatures based on the present
experimental results.
Single-crystal samples of pentacene were produced using
previously described procedures.34 Quasi-parallelogram-shaped
plates (ca. 3 mm × 2 mm) of Pn-SCs were selected andattached to pieces of conductive carbon tape. Subsequently,
silver paste was added at the peripheries of the crystals for goodelectrical contact. The surface index of the present sample was
identiﬁed as (001) face by grazing incidence X-ray diﬀraction(GIXD) analysis at BL-46XU of SPring-8.43 The orientation of
the crystal lattice of the Pn-SC sample was determined by theanisotropic character of the crystal shape,44 as illustrated in
Figure 1b. Thus a slight misalignment of the sample azimuthal
angle in the range of ±5° was inevitable, which may result in
deviation of the reciprocal lattice point by ∼0.5 nm−1 at theboundary of the surface Brillouin zone (SBZ). Because the PnSC samples were exposed to ambient air for at least for 1 h andused as-is for ARUPS measurements, oxide species of a few
percent population were likely formed at the crystal surface.42,45
ARUPS measurements were carried out at BL7U in UVSOR,
IMS.47 In the present work, the excitation photon energy wasset at 10 eV. The probing depth of these measurements is
expected to be deeper than the layer distance of the Pn-SC(1.41 nm)46 because of the relatively long inelastic mean path(∼2 nm) of electrons of their kinetic energy <10 eV.48−50 The
photoelectron emission angle was varied along the Γ−M′
direction of the Pn-SC (Figure 1c), for which the widest energy
dispersion has been theoretically predicted.30 The sample was
illuminated by continuous wave laser (405 nm, 30 mW) torelieve positive charging of the sample surface after photoelectron ejection.36 The sample temperature without any
intentional heating or cooling was 309 K, which we deﬁne asroom temperature (RT) in this work. The sample was slowly
cooled (approximately −1 K per 3 min) to trace thetemperature dependence of the valence-band structures.

Figure 1. (a) Molecular structure of pentacene. (b) Schematic
illustration of the molecular arrangement and unit cell of the PnSC(001) surface46 with the typical parallelogram-shape of the Pn-SCs.44(c) Surface Brillouin zone of Pn-SC. The direction of the ARUPS
measurements is indicated by the gray arrow. (d) ARUPS spectra of
Pn-SC taken toward the Γ−M′ direction at RT. The vertical bars are
guides for the eyes to indicate the peak positions of spectral
components. The measurement geometry is illustrated in the inset.

Figure 1d shows ARUPS spectra of the Pn-SC taken at RT.
The electron emission angles θ of 0° and ∼33° correspond tothe Γ and M′ points in the SBZ, respectively. The abscissa istaken on an electron binding energy (BE) scale with respect to
the Fermi level. Spectral proﬁles in the BE range of 0.5−1.5 eV,
which are attributed to the valence band (highest occupied
states) of the Pn-SC, exhibit characteristic transformations withrespect to θ. In the normal emission condition (θ = 0°), two
spectral components are resolved in close proximity to eachother at BEs of <1 eV. By changing the emission angle, thesecomponents coalesce at around θ = 10°, split into two again byθ = 20°, and are further separated at larger θ. This variation
represents the energy dispersion of the valence bands of the PnSC.
The ARUPS spectra of Figure 1d are represented on the E−
K∥ plane (K∥ is the surface parallel component of the electronwavenumber) as shown in Figure 2a, where the electronic band
structures are replicated as an undulation of the photoelectron
intensity. The shape of the valence-band structures revealed by
ARUPS measurements excellently reproduces the theoreticalprediction.30 Notably, the trend of the present dispersion
relation, namely, the expansion of the energy split of the twobands when moving toward the edge of the SBZ along its
diagonal direction, is in contrast with that of the thin-ﬁlm phaseof pentacene.11
The E−K∥ dispersion relations of the Pn-SC valence bands
were mapped as plotted in Figure 2b in which the energetic
positions are determined through curve ﬁtting of the individual
ARUPS spectra corresponding to the respective θ (for details,
see Supporting Information Figure S1). At the Γ point, thespectra in the valence-band region are resolved into three
spectral components. The upper two components are
attributed to the two valence bands originating from the
HOMOs of the two pentacene molecules in the unit cell of the
Pn-SC, whereas the third component of a dispersionlesscharacter may be ascribed to inelastic scattering of photo1260

DOI: 10.1021/acs.jpclett.7b00082
J. Phys. Chem. Lett. 2017, 8, 1259−1264

Letter

The Journal of Physical Chemistry Letters

the Fermi level at the M′ and Γ points, respectively, and the BEof the ﬁrst band top is even smaller than that of the second
band, as indicated in Table 1. Hence, the valence band
maximum (VBM) is located at the M′ point rather than Γ,which is also in agreement with the theoretical work.30
Figure 3 shows the ARUPS spectra of the Pn-SC taken atlower temperatures. The overall appearance of the spectral
images does not change signiﬁcantly, which corroborates theabsence of notable phase transitions of the Pn-SC in thepresent temperature range.46 It is interesting to note that thepresent E−K∥ dispersion width and behaviors exhibit close
resemblance to those of the “bulk-phase” pentacene monolayer(see Supporting Information Figure S2).10 Using the 1D-TB
approximation, Ec and t for the ﬁrst and second bands were
evaluated, as listed in Table 1, where the lattice constant values
at each temperature are approximated by simple linear
interpolation of the reported crystallographic data.46 The
VBM position is still at the M′ point of the ﬁrst band at thelower temperatures. This ﬁnding indicates that when the charge
carrier density is not too high, conductive holes injected fromelectrodes into the Pn-SC are located in the ﬁrst valence bandwith a narrower energetic dispersion rather than in the second
band with a wider dispersion.
Whether charge-carrier transport in the Pn-SC is bandlike or
hopping transport has been under debate. One necessary
condition for bandlike transport is |4t| > kBT (kB: Boltzmann
constant; T: temperature), which is fulﬁlled at RT in thepresent case even for the narrower ﬁrst band. In the bandlike
transport framework, the mobility of a charge carrier is given as
a function of its eﬀective mass m*. From the energy−timeuncertainty relation, the lowest limit of the drift mobility μD ofthe charge carriers is given by their m* as51

Figure 2. (a) Γ−M′ ARUPS spectral image taken at RT mapped on
the E−K∥ plane. The band calculation results30 are also plotted as
cross marks. (b) Binding energy positions of the three valence-band
components derived through least-squares ﬁtting of the ARUPS
spectra plotted as a function of the electron wavenumber parallel tothe surface. The sizes of the symbols represent the intensities of therespective spectral components. The 1D tight-binding (1D-TB) ﬁtting
curves for the ﬁrst and second valence bands are shown as thick lines.

μD ≳ 20 × (300/T ) × (m */m0)−1 [cm 2V −1s−1]

where m0 is the electron rest mass and the temperature T isgiven in Kelvins. In the present case, the m* value of the holes(mh*) derived from the curvature at the top of each band andthe lowest limits of μD are summarized in Table 1.
It is noteworthy that the ﬁeld-eﬀect mobility values of the
Pn-SC reported so far do not exceed the theoretical lowest
limits expected from inequality 2, as also listed in the
Supporting Information Table S1. This is in contrast with thecase of rubrene single crystals where the experimental
mobility52 surpasses the theoretical lower limit.36 In thiscontext, it is worth examining the validity of the hoppingtransport. In fact, based on their systematic Hall-eﬀect
measurements, Uemura et al. proposed “decoherence” of the
conducting holes in Pn-SCs, namely, that the transportmechanism cannot be simply explained as bandlike transport
but some contribution from hopping transport has to be taken
into consideration.26

electrons by impurities.36,39 The E−K dispersion of the ﬁrst andsecond bands can be reproduced well by a simple onedimensional tight-binding (1D-TB) approximation asE(K ) = Ec + 2t cos[dK ]

(2)

(1)

where Ec is a BE position of the band center, t is the transfer
integral, and d is the distance to the (11̅0) lattice point. The Ec
and t values, estimated by using the lattice constant reported by
Mattheus et al.,46 are listed in Table 1. It has to be noted thatthese values are derived solely from curvatures of the 2D
valence bands toward the steepest direction (the “−xy”
component) and thus may contain some uncertainness in theabsolute values. The ﬁrst and second bands approach closest toTable 1. Band Center Positions (Ec), Transfer Integrals (t), and Energy Positions at the Band Tops (EM′ and EΓ, respectively),hole Eﬀective Mass (mh*), Lower Limit of the Drift Mobility Values (μD), and Upper Limit of the Hopping Mobility Values(μET), of the First and Second Valence Bands of the Pn-SC Derived from the Present Temperature-Dependent ARUPS Results
Ec/eV

t/meV

EM′/eV

EΓ/eV

mh*/m0μD/cm2V−1s−1μET/cm2V−1s−1temperatureﬁrst

secondﬁrst

secondﬁrst

secondﬁrst

secondﬁrst

secondﬁrst

second

RT
212 K
110 K

0.760
0.668
0.684

0.866
0.800
0.808

−43.1
−45.7
−53.1

+86.4
+85.1
+88.2

0.674
0.576
0.578

0.694
0.630
0.632

3.43
3.26
2.81

1.71
1.75
1.70

5.7
8.7
19.3

11.4
16.2
32.0

2.8
3.6
3.3

11.4
12.4
9.2

1261

DOI: 10.1021/acs.jpclett.7b00082
J. Phys. Chem. Lett. 2017, 8, 1259−1264

Letter

The Journal of Physical Chemistry Letters

Figure 3. Γ-M′ ARUPS spectral images taken at (a) 212 and (b) 110 K mapped on the E−K∥ plane. The energy positions of the valence-band
components derived from the ARUPS data and the corresponding 1D-TB ﬁtting curves are overlaid on the images.

The upper limit of the hopping mobility μET in molecularsolids can be formulated based on the Marcus rate equation forelectron transfer as53

μET = (eL2 /kBT )kET(3)

kET = 2πt 2/ℏ × (4πλkBT )−1/2 × exp[−λ /kBT ](4)

revealed to be at the border of the SBZ on one valence bandwith a narrower E−K∥ dispersion rather than at the Γ point on
the other band with a wider dispersion. The transfer integral
and eﬀective mass values for the positive charge carriers at the
VBM were evaluated under the 1D-TB assumption as 43.1 meV
and 3.41m0, respectively, at RT, whereas these values increased
and decreased by ∼20%, respectively, at 110 K. The former
eﬀective mass value corresponds to the lowest limit of the holemobility of 5.7 cm2V−1s−1 at RT. This value suggests that thesimple bandlike transport assumption may overestimate thepractical ﬁeld-eﬀect mobility of Pn-SC FETs. On the contrary,
the highest limit of hopping mobility at RT is expected to be
2.8 cm2V−1s−1, which is insuﬃcient to explain recently reported
experimental ﬁeld-eﬀect mobility values. Accordingly, thepresent results suggest that the charge-carrier conduction
mechanism in Pn-SCs must be a hybrid case of bandlike andhopping transport frameworks.

where e is the elementary charge, L is the distance between
adjacent molecules (hopping length), kET is the electrontransfer rate constant, and λ is the reorganization energy. The
μET values for positive charge carriers along the Γ-M′ directionof the Pn-SC were evaluated, as listed in Table 1, where L = d/2 was applied for the present case and λ was taken fromexperimental values for thin-ﬁlm phase pentacene.54,55 These
values are fairly consistent with the reported good ﬁeld-eﬀect
mobility values (∼2 cm2V−1s−1)20,22,23,26 of Pn-SC FETs,
although the recently reported best experimental results (∼5
cm2V−1s−1)27−29 are beyond these limits. The present results
also imply that the conduction mechanism in the Pn-SC cannot
be comprehended within either the bandlike or hoppingtransport framework but that both take part in the chargecarrier transport behavior.
Finally, we discuss the possible distinction between surface
and bulk electronic bands. On the single crystal of tetracene(C18H10), a smaller member of the polyacene family, structural
relaxation at the top surface layer was reported.56 Accordingly,
the opposite valence-band dispersion behavior was predicted by
calculation for the surface-crystalline layer and the bulk;
namely, the two surface valence bands split widely at the Γpoint and approach each other along the diagonal direction of
the SBZ. As mentioned above, the probing depth of the present
measurements is deeper than the monomolecular height ofpentacene, and thus the ARUPS results in this work mainly
represent the bulk band structures of the Pn-SC. It isnoteworthy that the valence-band dispersion disappeared forsurface-sensitive ARUPS measurements on the Pn-SC samples
at higher photon energies (e.g., hν = 21.2 eV). The absence ofthe surface-band dispersion may be ascribed to the presence of
surface impurities that disturb the coherence of the charge
carriers at the surface of the Pn-SC. Attempts to characterize
the “clean surface” of the PnSC are underway to resolve thesurface valence-band structures using ARUPS measurements.
In conclusion, the electronic band structures of the Pn-SC
and their dependence on temperature were experimentallydemonstrated by ARUPS. Two valence bands, which disperse
in opposite directions, were clearly resolved. The VBM was■

ASSOCIATED CONTENT

S Supporting Information*

The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.jpclett.7b00082.
Procedures for peak separation of the ARUPS spectra,
comparison to the previous ARUPS data of the “bulkphase” pentacene ﬁlm, and comparison to the experimental mobility values (PDF)■

AUTHOR INFORMATION

Corresponding Author*E-mail: nkym@rs.tus.ac.jp.
ORCID

Yasuo Nakayama: 0000-0001-5014-6858
Notes

The authors declare no competing ﬁnancial interest.

■

ACKNOWLEDGMENTS
We thank Dr. Takuya Hosokai of National Institute ofAdvanced Industrial Science and Technology, Dr. Tomoyuki
Koganezawa of Japan Synchrotron Radiation Research Institute(JASRI), and Mr. Ryohei Tsuruta of Tokyo University of
Science for their help on the GIXD measurement that was
performed under approval of JASRI [2015A1685]. The ARUPS
experiments were conducted as the Joint Studies Programs [26530, 26-812, and 27-530] of IMS. Financial supports from
JSPS-KAKENHI Grant Numbers JP15H05498, JP16K14102,
1262

DOI: 10.1021/acs.jpclett.7b00082
J. Phys. Chem. Lett. 2017, 8, 1259−1264

Letter

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and JP25288114, G-COE/TAKUETSU Programs of Chiba
University [G-3, MEXT], Izumi Science and Technology
Foundation, and JGC-S Scholarship Foundation are gratefully
acknowledged. This work was also partially supported by the
Futaba Electronics Memorial Foundation.

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