simultaneous enhancement of conductivity and seebeck ... · seebeck coefficient. the side gate...
TRANSCRIPT
Simultaneous enhancement of conductivity and Seebeck coefficient in an organic MotttransistorYoshitaka Kawasugi, Kazuhiro Seki, Yusuke Edagawa, Yoshiaki Sato, Jiang Pu, Taishi Takenobu, Seiji Yunoki,Hiroshi M. Yamamoto, and Reizo Kato Citation: Applied Physics Letters 109, 233301 (2016); doi: 10.1063/1.4971310 View online: http://dx.doi.org/10.1063/1.4971310 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/109/23?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Apparatus for measuring Seebeck coefficient and electrical resistivity of small dimension samples using infraredmicroscope as temperature sensor Rev. Sci. Instrum. 84, 054903 (2013); 10.1063/1.4805016 Simultaneous measurement of the Seebeck coefficient and thermal conductivity in the cross-sectional directionof thermoelectric thick film J. Appl. Phys. 112, 104511 (2012); 10.1063/1.4766911 First principles study of Seebeck coefficients of doped semiconductors ZnTe1−xFx and ZnTe1−yNy J. Appl. Phys. 111, 033701 (2012); 10.1063/1.3679569 Huge Seebeck coefficients in nonaqueous electrolytes J. Chem. Phys. 134, 114513 (2011); 10.1063/1.3561735 Controlled doping of phthalocyanine layers by cosublimation with acceptor molecules: A systematic Seebeck andconductivity study Appl. Phys. Lett. 73, 3202 (1998); 10.1063/1.122718
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 134.160.214.55 On: Tue, 06 Dec 2016
04:47:08
Simultaneous enhancement of conductivity and Seebeck coefficientin an organic Mott transistor
Yoshitaka Kawasugi,1,a) Kazuhiro Seki,2,3 Yusuke Edagawa,4 Yoshiaki Sato,1 Jiang Pu,4
Taishi Takenobu,5 Seiji Yunoki,2,3,6 Hiroshi M. Yamamoto,1,7 and Reizo Kato1
1Condensed Molecular Materials Laboratory, RIKEN, Wako, Saitama 351-0198, Japan2Computational Condensed Matter Physics Laboratory, RIKEN, Wako, Saitama 351-0198, Japan3Computational Materials Science Research Team, RIKEN Advanced Institute for Computational Science(AICS), Kobe, Hyogo 650-0047, Japan4Department of Applied Physics, Waseda University, Tokyo 169-8555, Japan5Department of Applied Physics, Nagoya University Furo-cho, Chikusa-ku, Nagoya, 464-8601, Japan6Computational Quantum Matter Research Team, RIKEN, Center for Emergent Matter Science (CEMS),Wako, Saitama 351-0198, Japan7Research Center of Integrative Molecular Systems (CIMoS), Institute for Molecular Science, Okazaki,Aichi 444-8585, Japan
(Received 30 August 2016; accepted 17 November 2016; published online 5 December 2016)
We report on the electrical conductivity and Seebeck coefficient of an electric-double-layer
transistor based on an organic Mott insulator. The measurements were performed along the two
in-plane crystallographic axes (a and c) of the same device. While the Seebeck coefficient along the
a-axis was decreased by electron or hole doping, the value along the c-axis was increased by hole
doping. This is in contrast to the general trade-off relation between the conductivity and the Seebeck
coefficient. The simultaneous enhancement of the conductivity and the Seebeck coefficient is attrib-
uted to pseudogap formation in the hole-doped state, where a steep slope of the density of states
emerges at the chemical potential because of the electron interaction. Published by AIP Publishing.[http://dx.doi.org/10.1063/1.4971310]
Thermoelectric devices, which directly convert heat into
electricity, have recently attracted considerable attention as
energy-harvesting applications. Thermoelectric efficiency is
given by the dimensionless figure of merit ZT, which is
defined as
ZT ¼ rS2T
j; (1)
where r is the electrical conductivity, S is the Seebeck coef-
ficient, and j denotes the thermal conductivity at tempera-
ture T. All these parameters depend on the carrier density
and generally have trade-off relations, for example, the
Seebeck coefficient decreases when the conductivity is
enhanced by carrier doping. However, such a trade-off rela-
tion can be violated and a high ZT is expected under specific
conditions. According to the Mott formula,1 S in metals or
degenerate semiconductors is expressed as
S ¼ p2
3
k2BT
�eð Þ@ ln r Eð Þ@E
� �E¼EF
; (2)
where EF is the Fermi energy and �e is the electron charge.
Provided that r(E) is proportional to the density of states
N(E), S is proportional to 1/N(E) and @N(E)/@E at EF.
Therefore, the trade-off relation between r and S may be
overcome if @N(E)/@E is sufficiently large. Indeed, the
simultaneous enhancement of r and S resulted in a high
power factor rS2 in the Heusler alloys Fe2VAl1�xGex, which
have a dip of N(E) near EF.2 Such a dip structure of N(E) is
called a pseudogap.
We recently reported on the pseudogap in an electric-
double-layer transistor (EDLT) based on an organic Mott
insulator j-(BEDT-TTF)2Cu[N(CN)2]Cl (abbreviated to
j-Cl).3 j-Cl is a quasi-two-dimensional organic Mott insula-
tor, which comprises the alternating layers of conducting
BEDT-TTFþ0.5 radical cations and insulating Cu[N(CN)2]Cl�
counteranions (Fig. 1(a)). According to band calculations,
j-Cl is expected to be a metal because the highest occupied
molecular orbital (HOMO) band of BEDT-TTF is three-
quarters filled. However, the strong dimerization of BEDT-
TTF makes it effectively half-filled. The strong onsite (on-
dimer) Coulomb repulsion in the half-filled band makes the
electrons be aligned commensurately with the lattice potential,
thereby resulting in the Mott insulating state. When electrons
or holes were doped into the organic Mott insulator, the com-
mensurability was reduced, and the effect of the electron inter-
action was weakened, resulting in a marked decrease in the
resistivity. However, the pseudogap remained at specific k-
points under hole doping. The pseudogap emerged as a result
of interactions between carriers at EF. Therefore, a small N(E)
and large @N(E)/@E around EF are expected in the pseudogap
state. In this letter, we demonstrate that r and S can be
increased simultaneously in an organic Mott insulator by car-
rier doping. The simultaneous increase is probably because of
the large enhancement of @N(E)/@E due to pseudogap
formation.
Thin single crystals of the organic Mott insulator j-Cl
were electrochemically synthesized. A crystal was laminated
on a polyethylene naphthalate (PEN) substrate, on whicha)Electronic mail: [email protected]
0003-6951/2016/109(23)/233301/4/$30.00 Published by AIP Publishing.109, 233301-1
APPLIED PHYSICS LETTERS 109, 233301 (2016)
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 134.160.214.55 On: Tue, 06 Dec 2016
04:47:08
18-nm-thick Au electrodes and heaters had previously been
evaporated. The j-Cl crystal was shaped into a cross along
the crystallographic a- and c-axes, which are usually parallel
to the diagonals of the rhombic crystal, using a pulsed laser
beam with a wavelength of 532 nm (Fig. 1(b)). The crystal
axes were determined by its diamond shape before laser-
cutting, where the longer diagonal is a-axis and shorter
diagonal is c-axis. This crystal orientation is also confirmed
by the signs of Seebeck coefficients themselves.4 The
EDLT device was fabricated by mounting an ion gel on the
cross-shaped crystal and the Au side gate electrode. We
employed poly(vinylidene fluoride-co-hexafluoropropylene)
[PVDF-HFP] with 58% w/w 1-butyl-3-methylimidazolium
tetrafluoroborate [BMIM-BF4] as the ion gel. Details of the
electrolysis and crystal lamination are described in our previ-
ous papers. The temperature was controlled using a Physical
Property Measurement System (Quantum Design) and the
thermal electromotive force was measured with a nanovolt-
meter (Agilent 34420A). The measurements were performed
at temperatures between 60 and 160 K where the resistance
was moderate (R< 105 X) and the ion gel was frozen, with
steps of 20 K (cooling and warming rates: 2 K/min). At lower
temperatures where the resistance was higher, the DV vs DTplots tended to deviate from the linear relation, namely, the
reliability of the Seebeck measurements deteriorated. The
gate voltage Vg was applied in the following order: �1.2,
�0.9, �0.6, �0.3, 0, 0.3, 0.6, 0.9, 1.2, 1.3, and 1.4 V. While
the gate voltage was varied, the sample was warmed to
220 K. For the Seebeck measurements, the thin Au lines
(width: 2 lm, thickness: 18 nm) patterned on the substrate
were employed as heaters to generate a temperature gradient.
For details of the Seebeck measurements, see supplementary
material. The thermovoltage DV linearly increased with the
temperature difference DT, giving the Seebeck coefficient Sas the slope as shown in Fig. 1(c).
First, we show the experimental results for r and S. The
gate-induced carriers were confined at the surface of the
j-Cl crystal. However, the bulk (thickness �40 nm) was also
conducting at the temperatures studied here (Fig. S2 of
supplementary material). To focus on the gate-induced sur-
face states, the surface conductivity rs is shown here. On the
other hand, we show the bare Seebeck coefficient to
overview its gate dependence because the estimation of the
surface value is more ambiguous than that of the conductiv-
ity. We attempt to estimate the surface Seebeck coefficient
in the latter part of this paper. Figures 1(d) and 1(e) show the
gate voltage and temperature dependencies of the surface
conductivity along the a- and c-axes (rsa and rsc), respec-
tively. Without a gate voltage, the resistivity was semicon-
ducting (Fig. S2 of supplementary material). Both a positive
and negative gate voltage enhanced the surface conductivity
(ambipolar transistor), where the minimum conductivity was
observed at Vg¼þ0.3 V. The gate-induced conducting sur-
face was metallic down to approximately 100 K. Comparing
the two crystallographic axes, rsc was more asymmetric
upon doping. On the assumption that the gate-induced car-
riers are confined in a single BEDT-TTF layer (1.5 nm), rs
was approximately 200 S/cm (a-axis, Vg¼�1.2 V, and
T¼ 100 K).
Figure 2 shows the gate voltage and temperature depen-
dencies of S for the heat flow along the a (Sa)- and c (Sc)-
axes. As shown in Fig. 2(a), the sign of Sa (Sc) was positive
(negative) in accordance with the bulk j-Cl.4 The effect of
doping on S strongly depended on the crystallographic direc-
tion. While jSaj was reduced monotonically by both electron
and hole doping, as in the case of typical semiconductors,
jScj was enhanced by hole doping. The contour plots in Figs.
2(b) and 2(c) clearly show this tendency at all the tempera-
tures studied here and also the slight increase of Sc by a small
amount of electron doping. The original data used to obtain
the contour plots are shown in Fig. S3 (supplementary
material).
We discuss these results by considering the electronic
state of j-Cl and its doping dependence. According to the
Boltzmann equation approach,5 ra and Sa (a¼ a, c) are given
as
ra ¼ e2 K0½ �aa; Sa ¼1
�eð ÞTK�1
0 K1
� �aa; (3)
where Kn (n¼ 0, 1) is defined as
FIG. 1. (a) Molecular arrangement of the conducting BEDT-TTF layer of
j-Cl (top view). Each conducting layer is separated by the closed-shell insu-
lating anion Cu[N(CN)2]Cl� along the b-axis (not shown). (b) Optical image
of a sample. The crystallographic axes were assigned from the sign of the
Seebeck coefficient. The side gate electrode (area: �600� 600 lm2) was
evaporated 300 lm away from the j-Cl crystal. (c) Thermovoltage DV vs.
the temperature difference DT at 160 K and Vg¼ 0 V. (d), (e) Contour plots
of the gate-induced conductivity rs along the a- and c-axes, respectively.
Here, rs is defined as rðVgÞ � rðVg ¼ 0:3VÞ, where Vg¼ 0.3 V is the charge
neutrality point.
233301-2 Kawasugi et al. Appl. Phys. Lett. 109, 233301 (2016)
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 134.160.214.55 On: Tue, 06 Dec 2016
04:47:08
Kn¼ 2Xm;k
sm kð Þvm kð Þvm kð ÞT �@f Eð Þ@E
� �E¼Em kð Þ
Em kð Þn: (4)
Here, Em(k) is the electron band dispersion of the band index
m at momentum k measured from the chemical potential,
vmðkÞ ¼ ðvamðkÞ; vc
mðkÞÞT
is the velocity vector with vamðkÞ
¼ @EmðkÞ=@ð�hkaÞ being the group velocity, smðkÞ is the qua-
siparticle lifetime, and f(E) is the Fermi distribution function.
The Mott formula Eq. (2) is based on the Sommerfeld expan-
sion of Eq. (3) which is valid when EF � kBT. These equa-
tions indicate that both r and S strongly depend on the Fermi
velocity vm(kF), where kF is the Fermi momentum defined by
Em(kF)¼ 0. Figure 3(a) shows the Fermi surface of the sim-
plest tight-binding model for undoped j-Cl without the elec-
tron interaction. When the electron interaction is considered,
no Fermi surface is expected because the ground state is the
Mott insulating state.3 However, the conducting states under
doping and/or at high temperatures are essentially deter-
mined by the original non-interacting band structure, which
can be modified by the electron correlation effect. The
electron-like Fermi sheet (blue part in Fig. 3(a)) has a moder-
ate energy dispersion along the a-axis, resulting in a small
group velocity along the a-axis. Therefore, it dominantly
contributes to rc and Sc. Likewise, the hole-like Fermi
pocket (red part in Fig. 3(a)) contributes more to ra and Sa
than to rc and Sc. In-plane anisotropy in S with a positive Sa
and a negative Sc has indeed been observed in various
j-BEDT-TTF salts, and the sign and the temperature depen-
dence of S were explained by the Boltzmann equation
approach based on the tight-binding band calculations.6,7
Therefore, to understand qualitatively the experimental
results, we assume that rc and Sc (ra and Sa) are governed
mostly by the electron-like Fermi sheet (hole-like Fermi
pocket).
In our previous report, the calculations based on the
cluster perturbation theory, which takes into account the
electron correlation effect, revealed that the Mott insulating
state became metallic and N(E) at the chemical potential was
increased by either electron or hole doping.3 However, the
evolution of N(E) with doping was quite asymmetric. The
pseudogap emerged at the center of the electron-like Fermi
sheets under hole doping but was almost absent in electron
doping. Figure 3(b) shows N(E) for 17% hole doping (which
roughly corresponds to a gate voltage of �1 V [Ref. 3]) in
the Brillouin zone enclosed by lines C-M-Z (blue solid line)
and C-M-X (red solid line), which roughly correspond to the
electron-like Fermi sheet and the hole-like Fermi pocket,
respectively. Both 1/N(E) and @N(E)/@E are larger in the for-
mer region than in the latter region. The parameter set for
the calculations (t0=t ¼ �0:44, U/t¼ 5.5, and t¼ 65 meV,
where t and t0 are the transfer integrals between the neighbor-
ing sites and the next-neighboring sites along the c-axis,
respectively, and U is the onsite Coulomb repulsion) is
quoted from the first principles calculations for j-Cl.8
However, we have also confirmed that the pseudogap
occurred by hole doping even with a different parameter set
(t0=t ¼ �0:8, U/t¼ 7, and t¼ 55 meV from semi-empirical
calculations) and different hole doping levels.3 The marked
doping asymmetry in rc observed experimentally may be
attributed to the smaller N(E) in the hole-doped region than
in the electron-doped region, which stems from the pseudo-
gap formation on the electron-like Fermi sheet. The slight
increase in Sc for low electron doping (Vg¼þ0.6 V in Fig.
2(c)) can also be attributed to a pseudogap because the calcu-
lations predicted the presence of minor pseudogaps under
electron doping (at a different portion of the electron-like
Fermi sheet).
The simultaneous enhancement of r and S has thus been
qualitatively understood from the aspect of pseudogap for-
mation. However, the measured S shown in Fig. 2 is strongly
suppressed by the bulk crystal because the bulk is also
FIG. 2. (a) Temperature dependence of the Seebeck coefficient at Vg¼ 0,
�1.2, and þ1.2 V. The error bars denote the sum of the standard deviation
of the DV vs DT plots and the error derived from the polynomial fitting of
DT=I2heater (see Fig. S1 in supplementary material). (b), (c) Contour plots of
the absolute value of the Seebeck coefficient along the a- and c-axes,
respectively.
FIG. 3. (a) Non-interacting Fermi surface of the simplest tight-binding
model for j-Cl (t0=t ¼ �0:44) at half-filling. (b) Density of states at 30 K for
17% hole doping (t0=t ¼ �0:44, U/t¼ 5.5, and t¼ 65 meV). The blue and
red solid lines show the density of states enclosed by lines C-M-Z and
C-M-X, respectively. The dashed line denotes the total density of states in
the first Brillouin zone. The Fermi energy is located at zero energy.
233301-3 Kawasugi et al. Appl. Phys. Lett. 109, 233301 (2016)
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 134.160.214.55 On: Tue, 06 Dec 2016
04:47:08
conducting. Finally, we estimate the surface Seebeck coeffi-
cient Ss and the surface power factor rsS2s from the measured
Seebeck coefficient of two parallel connected layers, which
is described as9,10
S ¼ rbSb þ rsSs
rb þ rs
; (5)
where the suffixes b and s denote the bulk and surface. Here
we employed r and S at the maximum resistivity point
(charge neutrality point) at Vg¼þ0.3 V as rb and Sb, respec-
tively. Figure 4 shows the gate voltage dependencies of rs,
Ss, and rsS2s at 100 K along the a- and c-axes. Note that the
values of Ss at Vg¼�0.3, 0, and þ0.3 V are not shown
because of the large ambiguity due to the small rs. Instead,
the corresponding values of S at Vg¼�0.3, 0, and þ0.3 V
are shown for reference. The maximum value of Ss reached
136 6 8 lV/K (c-axis, Vg¼�1.2 V), which is comparable
with that of the materials with pudding-mold-type band
structures such as NaxCoO2 (Ref. 11) and s-type organic
conductors.12 Therefore, we obtained a relatively large rsS2s
for an organic material (95 6 7 lWm�1K�2) in the pseudo-
gap state.
In summary, we measured r and S along the two in-
plane crystallographic axes (a and c) of the same organic
Mott EDLT based on j-Cl. Owing to the collapse of the
Mott-Hubbard gap, ra and rc were enhanced by both elec-
tron and hole doping. However, Sc was enhanced by hole
doping, probably because of the large enhancement of
@N(E)/@E at the chemical potential caused by the electron-
interaction-driven pseudogap formation, while no such effect
was observed in the a-axis direction. As a result, rc and Sc
were simultaneously increased by hole doping, giving a rela-
tively large rsS2s . These results indicate that the pseudogap in
strongly correlated electron systems, which has attracted
considerable attention in the field of condensed matter
physics, can be applied to improve the thermoelectric prop-
erties of a material.
See supplementary material for details of the Seebeck
measurements, temperature dependence of the device con-
ductance without gate voltage, and the original data used to
obtain the contour plots in Fig. 2.
We would like to acknowledge Teijin DuPont Films
Japan Limited for providing the PEN films. Computations
have been done using HOKUSAI facility of Advanced
Center for Computing and Communication at RIKEN. This
work was supported by MEXT and JSPS KAKENHI (Grant
Nos. JP16H06346, JP16H04140, JP15K17714, JP26102012,
and JP25000003), JST ERATO, and MEXT Nanotechnology
Platform Program (Molecule and Material Synthesis).
1N. F. Mott and H. Jones, The Theory of the Properties of Metals(Clarendon Press, Oxford, 1936).
2Y. Nishino, S. Deguchi, and U. Mizutani, Phys. Rev. B 74, 115115 (2006).3Y. Kawasugi, K. Seki, Y. Edagawa, Y. Sato, J. Pu, T. Takenobu, S.
Yunoki, H. M. Yamamoto, and R. Kato, Nat. Commun. 7, 12356 (2016).4M. A. Tanatar, S. Kagoshima, T. Ishiguro, H. Ito, V. S. Yefanov, V. A.
Bondarenko, N. D. Kushch, and E. B. Yagubskii, Phys. Rev. B 62, 15561
(2000).5J. M. Ziman, Principles of the Theory of Solids, 2nd ed. (Cambridge
University Press, Cambridge, England, 1972).6T. Mori and H. Inokuchi, J. Phys. Soc. Jpn. 57, 3674 (1988).7R. C. Yu, J. M. Williams, H. H. Wang, J. E. Thompson, A. M. Kini, K. D.
Carlson, J. Ren, M.-H. Whangbo, and P. M. Chaikin, Phys. Rev. B 44,
6932 (1991).8H. C. Kandpal, I. Opahle, Y.-Z. Zhang, H. O. Jeschke, and R. Valent�ı,Phys. Rev. Lett. 103, 067004 (2009).
9P. Pichanusakorn and P. Bandaru, Mater. Sci. Eng. R 67, 19 (2010).10T. A. Cain, S.-B. Lee, P. Moetakef, L. Balents, S. Stemmer, and S. J.
Allen, Appl. Phys. Lett. 100, 161601 (2012).11K. Kuroki and R. Arita, J. Phys. Soc. Jpn. 76, 083707 (2007).12H. Yoshino, H. Aizawa, K. Kuroki, G. C. Anyfantis, G. C. Papavassiliou,
and K. Murata, Phys. B 405, S79 (2010).
FIG. 4. (a) and (b) Gate voltage Vg dependencies of the surface conductivity rs and surface Seebeck coefficient Ss along the a- and c-axes at 100 K. Note that
the values of Ss at Vg¼�0.3, 0, and þ0.3 V are not shown because of the large ambiguity due to the small rs. Instead, the corresponding values S at
Vg¼�0.3, 0, and þ0.3 V (open symbols) are shown for reference. (c) Gate voltage dependence of the surface power factor rsS2s at 100 K. Here, we assumed
that the gate-induced carriers are confined within a single BEDT-TTF layer (1.5 nm), and we estimated the values in three spatial dimensions for comparison
with other materials.
233301-4 Kawasugi et al. Appl. Phys. Lett. 109, 233301 (2016)
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 134.160.214.55 On: Tue, 06 Dec 2016
04:47:08