Record High Thermoelectric Powerfactor in Single and FewLayer MoS2
Kedar Hippalgaonkar1, 2, 3, †, Ying Wang1, †, Yu Ye1, †, Hanyu Zhu1, Yuan Wang1, 2, Joel
Moore2, 4, Xiang Zhang1, 2, *
1
NSF Nano-scale Science and Engineering Center (NSEC), 3112 Etcheverry Hall,
University of California, Berkeley, California 94720, USA
2
Material Sciences Division, Lawrence Berkeley National Laboratory (LBNL), 1
Cyclotron Road, Berkeley, CA 94720, USA
3
Institute of Materials Research and Engineering, Agency for Science Technology and
Research, Singapore, 117602
4
Department of Physics, University of California, Berkeley, California 94720 USA
† These authors contributed equally.
*Correspondence and requests for materials should be addressed to X. Z. (email:
xiang@berkeley.edu)
i Abstract:
The quest for high-efficiency heat-to-electricity conversion has been one of the major
driving forces towards renewable energy production for the future. Efficient
thermoelectric devices require careful material engineering such as high voltage
generation from a temperature gradient, and high electrical conductivity while
maintaining a low thermal conductivity. Significant progress in the thermoelectric
performance of materials has been made by exploring the ultralow thermal conductivity
at high temperature1, reducing the thermal conductivity by nanostructuring2, resonant
doping3 and energy-dependent scattering4. For a given thermal conductivity and
temperature, thermoelectric powerfactor is determined by the electronic structure of the
material. Low dimensionality (1D and 2D) opens new routes to high powerfactor due to
their unique density of states of confined electrons and holes5, 6. Emerging 2D transition
metal dichalcogenide (TMDC) semiconductors represent a new class of thermoelectric
materials not only from their discretized density of states7, 8, but especially due to their
large effective masses and high carrier mobilities9–13, different from gapless semimetallic graphene14, 15. Here we report a measured powerfactor of MoS2 as large as 8.5
mWm−1K−2 at room temperature, the highest among all thermoelectric materials and
twice that of commercial thermoelectric material Bi2Te3. For the first time, the
measurement of the thermoelectric properties of monolayer MoS2 allows us to determine
the quantum confined 2D density of states near the conduction band edge, which cannot
be measured by electrical conductivity alone. The demonstrated record high powerfactor
in 2D TMDCs holds promise for efficient thermoelectric energy conversion.
ii An ideal thermoelectric material behaves as an electron-crystal and phonon-glass, allowing a
large temperature gradient across it while conducting electricity efficiently to generate a
thermoelectric voltage16. Recently, 2D transition metal dichalcogenides (TMDCs) have
shown their unique valley-dependent electronic and optical properties 9, 12, 17–21, and also have
been theoretically predicted as superior thermoelectric materials22. The theoretical analysis
has been centered on low thermal conductivity23, with a recent calculation suggesting
favorable electronic properties of TMDCs resulting in an enhanced Seebeck effect24. Recent
experiments studied the photo-thermoelectric effect and the large Seebeck coefficient of
monolayer MoS2, both of which are at low carrier densities that limits its powerfactor for
thermoelectric applications25, 26. In this letter, we examine thermoelectric transport in
monolayer and few-layer MoS2 at high carrier densities and observe a record powerfactor S2σ
as large as 8.5 mWm−1K−2, where S is the Seebeck coefficient, σ is the electrical
conductivity. We attribute this high powerfactor to the large conduction-band effective mass
and electron mobility. Compared with commercial thermoelectric materials, Bi2Te3 and its
alloys constituted of Sn, Pb and Se, the observed powerfactor of 2D MoS2 is two times larger,
and to our best knowledge, is the highest value reported so far at room temperature among all
thermoelectric materials. Moreover, for the first time, we develop a unique technique to
determine the 2D confined density of states by measuring the thermoelectric properties of
monolayer MoS2, which cannot be accomplished by measuring electrical conductivity alone.
2D TMDCs with highest powerfactors are promising thermoelectric materials for applications
such as Peltier cooling devices.
We first measure Seebeck coefficient and electrical conductivity of 2D MoS2 as a function of
carrier concentration tuned by a back gate (Fig. 1, see Methods for detailed measurement
setup). The electron concentration is given by n = Cox/e·(Vg – VT), where Cox is the
capacitance between the channel and the back gate, e is the electron charge, Vg and VT are the
iii gate and threshold voltage, respectively. The measured electrical conductivities and Seebeck
coefficients of monolayer, bilayer and trilayer MoS2 follow behavior similar to an
extrinsically doped semiconductor (Fig. 2a). The Seebeck voltage is proportional to the
asymmetry of occupied density of states around the Fermi level in the energy diagram4, 27.
Hence, with increasing electron concentration, the magnitude of the Seebeck coefficient drops
as the Fermi level is pushed closer to the conduction band minimum (See Methods for
measurement details). The measured powerfactor, S2σ, increases correspondingly with
applied gate voltage Vg (Fig. 2b). The bilayer device exhibits the largest powerfactor S2σ =
8.5 mWm−1K−2 at Vg = 104 V corresponding to a high electron concentration n2D ~ 1.06×1013
cm−2. The powerfactor is expected to reach a peak and then drop for higher carrier
concentrations, as the increasing in electrical conductivity is offset by the decreasing Seebeck
coefficient4. However, for our MoS2 samples, the powerfactor does not peak, as the optimum
value is expected to occur at an even higher gate voltage corresponding to an electron
concentration of n2D ~ 1.31×1013 cm−2, equivalent to a bulk concentration of n3D ~ 1×1020
cm−3, which is limited by the electrical breakdown of the gate oxide28. To the best of our
knowledge, 8.5 mWm−1K−2 is the highest room-temperature powerfactor of all thermoelectric
materials reported so far.
The largest powerfactor is observed in the bilayer exceeding that of the monolayer and
trilayer samples. In order to understand this, let us assume that all devices in the conducting
state asymptotically transport through the 2D density of states. This is reasonable at high
carrier concentration, and the density of states near the Fermi level can be written as
gsgvm*EF/2πħ2, where gs =2 and gv = 2 are the spin and valley degeneracies at the Fermi
energy, EF, respectively7, 21, 22, m* is the band-mass and ħ is the reduced Planck’s constant.
For extended states in the conduction band, the Mott relation can be used to estimate the
iv Seebeck coefficient as S =
π2
E 27
kB
. Then, EF ∝ n2D/m* results in S ∝ m*/n2D. σ = n2D.e.µ;
3e EF
hence the powerfactor, S2σ ∝ (m*)2·µ/n2D. Therefore, for a given electron concentration (i.e.,
fixed (Vg-VT)), the powerfactor is expected to scale with the mobility µ and effective mass
m*. The effective mobility of our device is determined by a standard transistor measurement
(see Supplementary Information for details). The measured effective mobilities at room
temperature are 37 cm2V−1s−1 for the monolayer, 64 cm2V−1s−1 for the bilayer and 31
cm2V−1s−1 for the trilayer. We can therefore ascribe the powerfactor as scaling with the
measured mobility (Fig. 2b). Of course, any contribution due to localized states in the
bandgap may not follow this behavior. For few-layer MoS2, extrinsic effects can be different
such as screening and scattering from the underlying dielectric substrate12, and the level of
impurities in individual samples8, thus the device mobilities vary and are lower than
theoretical estimates29. Like MoS2, other TMDCs are expected to simultaneously have large
band effective masses and mobilities10,13 leading to high values of powerfactor, thus
highlighting their uniqueness as potential thermoelectric materials.
Interestingly, we found that measurement of the gate-dependent Seebeck coefficient provides
a direct way to probe the electronic density of states in monolayer MoS2. The conduction
band minimum of monolayer MoS2 sits at the K-point, while for the bilayer and trilayer, the
sideband in the ΓK-direction begins to contribute to transport29, 30. Therefore we consider
experimental Seebeck of the monolayer with a clearly defined conduction band effective
mass of m*=0.45m0 where m0 is the free electron mass, based on a parabolic conduction band
approximation29–31(dotted black curve in Fig. 3a). At 300 K, for n2D > 1.4x1012 cm-2, we
consider metal-like behavior with carriers behaving as a degenerate gas through the MoS2
channel, which is confirmed by the temperature-dependence conductance measurement (see
v Supplementary Information). Here, the diffusive thermopower using the Mott relation is
expected to hold and is given by27:
S=
−π 2 2 1 " d σ %
kT $
'
3e B σ # dE & E
(1)
F
where kB = 86.2 µeVK−1 is the Boltzmann constant. It can be simplified in terms of the
electron concentration as:
S=
−π 2 2 1 dσ e " dn %
kT
$ '
3e B σ dVg Cox # dE & E
(2)
F
The gate-dependent conductivity, σ(Vg), is determined experimentally as is the differential
transconductivity, dσ/dVg. The four-probe conductivity, σ 4p = γc.σ 2p is measured after
calibrating the contact resistance by obtaining the contact ratio, γc (see Supplementary
Information). We then utilize the experimentally measured Seebeck coefficient at 300 K (Fig.
2a) (for Vg>-20V) to extract the density of states from Equation (2). Within an energy range
of ~kBT (~26 meV at room temperature) near the conduction band bottom EC, we would
expect the carriers to move freely, thus defining the mobility edge. In this energy bandwidth
near the mobility edge at EC, the density of states is a rapid-varying function (red dotted line
in Fig. 3a). The density of states asymptotically approaches the fixed 2D density of states
! dn $
g g m * 2m *
= 3.75 ×1014 eV −1cm −2 (solid
& = s v 2 =
" dE % EF
2π 
π 2
(DOS) due to the conduction band given by #
blue line in Fig. 3a).
By analyzing the conductivity as a function of temperature for different electron
concentrations, from 1.4×1012 cm−2 to 8.5×1012 cm−2, MoS2 is seen to undergo an insulatorto-metal transition as the temperature increases, consistent with other reports10, 11, 31 (see
vi Supplementary Information). The insulator-to-metal transition temperature (TIMT) is extracted
from the evolution of conductivity as a function of temperature and is defined as the
temperature at which the measured conductivity changes from increasing with temperature to
a metal-like decrease with temperature. We thus elucidate the electronic phase diagram of
transport in MoS2 (Fig. 3b) where TIMT is plotted as a function of the carrier concentration.
The mechanism of electrical transport in the insulating phase is still under debate and
depends on the level of impurities in the samples.8, 12, 31 We find that the electrical
conductivity fits a Mott Variable-Range-Hopping (m-VRH) model (See Supplementary
Information). Here, electrons at the Fermi Level below the mobility edge (at Ec) are
localized, but are able to hop from one localized site to another due to the gradient field or
interaction with phonons 32, 33. The conductivity is expected to follow a relation in
temperature given by: σ ∝ exp(-(T0/T)v), where v = 1/3 in a 2D system. Concurrently, the
measured Seebeck coefficient as a function of back-gate voltage for temperatures from 100 K
to 300 K (Fig. 3c) shows a monotonic increase with temperature. Using Zyvagin’s formula
for the m-VRH model, S ∝ T(d-1)/(d+1), where d is the dimensionality34–36; for 2D, S ∝ T1/3. The
experimentally measured Seebeck coefficient fits very well to a cube-root dependence on
temperature, with S→0 as T→0 (inset of Fig. 3c). If the carriers were thermally activated, as
is the case for transport in crystalline semiconductors, the conductivity would follow an
exponential relationship with temperature and the measured Seebeck coefficient would
decrease as a function of temperature37,38. However, in our case, the measured Seebeck
coefficient increases with temperature, indicating that electronic transport is not thermally
activated. Similar m-VRH transport phenomenon has also recently been observed in CVDgrown MoS2 for the insulating phase26. Note that at all temperatures, the experimental
Seebeck at a fixed carrier concentration (Vg-VT) is considered.
vii In conclusion, our experiments report the thermoelectric properties of exfoliated monolayer,
bilayer and trilayer MoS2, and we observe record powerfactors as large as 8.5 mWm−1K−2 at
room temperature. This is twice higher than commercially used bulk Bi2Te3 therefore
making 2D TMDCs promising candidates for planar thermoelectric applications. The
enhanced powerfactor is attributed to a unique combination of high mobility and high
effective mass. For the first time, we demonstrate a unique experimental methodology to
determine the 2D electronic density of states (DOS) from the measurement of the
thermoelectric properties. Our device configuration allows us to tune the carrier concentration
in 2D MoS2, which is difficult in bulk materials hence providing important insights into
thermoelectric transport in these layered materials. The high powerfactor in layered TMDCs
provides an exciting avenue to enhance thermoelectric efficiencies and galvanize the growth
of thermoelectric devices in the near future.
Methods
Sample preparation and characterization
Exfoliated samples are obtained using the scotch-tape method by cleaving a bulk
molybdenite. We exfoliate the samples onto 275 nm thermally grown SiO2 on a highly doped
p-Si substrate. MoS2 flakes are visible on the sample under an optical microscope and the
monolayer, bilayer or trilayer samples are selected based on characterization due to optical
contrast photoluminescence imaging and Raman Spectroscopy (see Supplementary
Information).
Measurement technique and electrical contact
The heating element is a resistive metal line, through which a DC current, IDC, up to 20 mA is
applied. The heat generated from the heater line creates a temperature gradient across the
TMDC sample, given by Q ∝ I2DCRhtr ∝ ΔT. The electrodes patterned on two sides of the
sample function both as probes for electrical measurements and for local temperature
viii measurement. For each electrode, the resistance is given by Rhot/cold ∝ ΔThot/cold. Then, the
temperature difference across the device is calibrated as ΔT = ΔThot−ΔTcold, where ΔRhot/cold =
αhot/coldΔTholt/cold obtained at every global temperature, where the slope αhot/cold is determined
experimentally. The open circuit voltage across the device, VOC, as a function of heating
current is then determined, from which the Seebeck coefficient of the device can be deduced
as S = −VOC/ΔT.
In order to minimize the electrical contact resistance, we use Ti/Au films evaporated with
electron beam evaporation. Titanium has been known to have good Fermi level alignment
with monolayer MoS2 42. In order to improve the contact quality, we annealed the sample insitu at 475 K for one hour in the cryostat prior to performing measurements. After annealing,
all of our I-V curves are linear, indicating ohmic contact and hence none of the transport
characteristics can be ascribed to Schottky behavior. We have characterized the contact
resistance of the Ti/Au contacts and found the ratio of four-probe to two-probe conductance
at all temperatures (see Supplementary Information). It has been reported that the contact
resistance contribution to measured total resistance at room temperature can be as large as
50% at 100 K with Ti/Au contacts42. In our case, we define the ratio of the four-probe to the
two-probe conductivity as the contact ratio, γc, which is 2 at 300 K and 2.5 at 100 K. Hence,
our estimation of the intrinsic electrical conductivity of the layered MoS2 is underestimated
due to included contact resistance. The Seebeck measurements are not affected by the contact
quality since it is measured in an open-circuit configuration. However, the measured S is a
sum of the sample and the contacts (Ti/Au). Since the metallic Seebeck is < 1 µVK-1 at all
temperatures, it does not affect our measurements and we do not consider it in our
measurements. All measurements were performed in vacuum at 2×10−6 torr. For lower gate
voltages close to the threshold voltage VT, the channel resistance becomes too high and we
ix are unable to measure the Seebeck coefficient accurately. The maximum gate voltage VG
applied for all devices is limited by the electrical breakdown of the gate oxide.
x Figures
Figure 1: Device Configuration for Seebeck coefficient and electrical conductivity
measurement of MoS2 (a) Schematic of the simultaneous measurement of the Seebeck
coefficient and the electrical conductivity. The illustration shows monolayer MoS2, placed on
thermally grown SiO2 on a p+ silicon substrate. Two-probe electrical conductivity was
measured by passing a current through the device (IDS) and measuring the drain-source
voltage (VDS) at each temperature. In order to measure the Seebeck coefficient S = −VOC/ΔT,
current was passed through the heater to generate a temperature gradient,
∇T
while the open
circuit voltage (VOC) was measured. (b) Scanning electron micrograph of an actual device as
described in (a). Note, the hall-bar electrodes were used to obtain the ratio of the two-probe to
the four-probe electrical conductivities, γc = σ4p/σ2p to estimate the contribution due to contact
resistance at each temperature. For the monolayer sample, γc = 1.98 at 300 K with
temperature dependent ratios shown in the Supplementary Information.
xi Figure 2: Thermoelectric characterization of 2D MoS2 at room temperature. (a)
Electrical conductivities, (closed markers) and Seebeck Coefficients, S (open markers) as a
function of gate voltage at 300 K for monolayer (green circles), bilayer (red squares) and
trilayer MoS2 (blue triangles). As the carrier concentration n ∝ (Vg−VT) increases, σ increases
and the magnitude of S decreases. S is negative, which confirms that the sample is n-type. (b)
Powerfactor, S2σ as a function of Vg. The bilayer device with a larger effective mobility of
64 cm2V−1s−1 exhibits larger powerfactor of 8.5 mWm−1K−2 at room temperature, twice that
of commercially used bulk Bi2Te3.
xii Figure 3. Electronic Density of States (DOS) determined by Thermoelectric Transport
measurement in monolayer MoS2. (a) DOS as a function of energy. The expected
(schematic) 2D DOS from the discretized conduction band is illustrated as blue steps. The
parabolic approximation is calculated as the dotted black line with an effective mass of m* =
0.45 m0. The red line is the measured density of states obtained from fitting the Mott relation
in Equation (2) with experimental Seebeck coefficients in Fig. 2a at 300K. At this
temperature, for n > 1.4×1012 cm−2 (see Supplementary Information), transport is metal-like
and the density of states asymptotes to the 2D DOS from the conduction band (horizontal
solid blue line). Here, the trapped states are filled and the band tail is within an energy
bandwidth of ~ kBT from the mobility edge at the conduction band, EC (b) the phase diagram
for thermoelectric transport as a function of temperature and electron concentration. For the
insulating phase, T > TIMT, the Seebeck coefficient increases slowly, S ∝ T (Mott formula for
xiii extended states) while for conducting phase, T > TIMT, S ∝ T1/3 (m-VRH for localized states). (c) Experimental Seebeck Coefficient for monolayer MoS2 as a function of temperature and
applied back-gate voltage. The magnitude of Seebeck decreases (increases) with Vg
(temperature). In the inset we show measured Seebeck at a fixed carrier concentration n =
Cox/e·(Vg−VT), which follows a function of T1/3, indicating Mott Variable-Range Hopping
dominates transport. In the phase diagram (Fig. 3c), the trend of the Seebeck coefficient S ∝
T1/3 in the insulating phase is illustrated.
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xvii Supplementary Information for Record High Thermoelectric
Powerfactor in Single and Few-Layer MoS2
Kedar Hippalgaonkar1, 2, 3, †, Ying Wang1, †, Yu Ye1, †, Hanyu Zhu1, Yuan Wang1, 2, Joel
Moore2, 4, Xiang Zhang1, 2, *
1
NSF Nano-scale Science and Engineering Center (NSEC), 3112 Etcheverry Hall,
University of California, Berkeley, California 94720, USA
2
Material Sciences Division, Lawrence Berkeley National Laboratory (LBNL), 1
Cyclotron Road, Berkeley, CA 94720, USA
3
Institute of Materials Research and Engineering, Agency for Science Technology and
Research, Singapore, 117602
4
Department of Physics, University of California, Berkeley, California 94720 USA
† These authors contributed equally.
*Correspondence and requests for materials should be addressed to X. Z. (email:
xiang@berkeley.edu)
xviii MoS2 layer number characterization The monolayer, bilayer and trilayer MoS2 samples are selected and identified based on characterization from optical contrast, photoluminescence images and Raman spectroscopy. The separation between Raman-­‐active modes the A1g and E12g decreases as the layer thickness decreases from three layers to one layer, as has been reported in literature. 1–3 The separation of the A1g and E12g peaks are 18 cm-­‐1 for the monolayer, 22 cm-­‐1 for the bilayer and 24 cm-­‐1 for the trilayer (Fig. S1a). Moreover, the monolayer MoS2 exhibits strong photoluminescence, due to the direct bandgap transition (Fig. S1b).4 Figure S1 (a) Thickness dependence of the Raman spectrum of MoS2. The Raman spectrum of MoS2 has two prominent peaks: an in-­‐plane (E12g) mode and an out-­‐of-­‐plan (A1g) mode. As MoS2 becomes monolayer these two modes evolve with thickness. The in-­‐plane mode upshifts to 386 cm−1 and the out-­‐of-­‐plane downshifts to 404 cm−1. The difference of these two modes (~18 cm−1) can be used as a reliable identification for monolayer MoS2. (b) Confocal image of a monolayer MoS2 thermoelectric device. The monolayer MoS2 shows strong photoluminescence, due to the direct bandgap property. The red channel is the photoluminescence channel, indicating the shape of monolayer MoS2. The green channel is the scattering channel of the incident laser, indicating the geometry of the device. xix Field-­‐effect Mobility: The mobility of MoS2 is determined following standard procedure using field-­‐effect transistor with a fixed drain-­‐source voltage, Vds=10 mV. Here, the drain-­‐source current, Ids ∝ Vg and the mobility is given by: µ =
dI ds L 1 1
where L and W are the MoS2 channel length and width respectively, dVg W Vds Cox
and Cox = εrε0/tox = 1.26×10−4 F/m2 is the oxide capacitance, where εr = 3.9 is the relative permittivity of SiO2, ε0 = 8.85x10−12 F/m is the permittivity of free space and tox =275 nm is the thickness of the thermally grown oxide. This results in an estimated field mobility of 37 cm2V-­‐1s-­‐1 for the monolayer, 64 cm2V-­‐1s-­‐1 for the bilayer and 31 cm2V-­‐1s-­‐1 for the trilayer 5,6. Since the exfoliated MoS2 are n-­‐type semiconductors, the devices turn on at negative gate voltages; VT is −20 V for the monolayer, −38 V for the bilayer and −64 V for the trilayer. The range of mobilities is consistent with previous reports of high mobility between 1-­‐100 cm2V-­‐1s-­‐1. 5,7 Here we only report the two-­‐probe mobilities for all devices. Figure S2. The measured field-­‐effect mobilities of monolayer, bilayer and trilayer as a function of back gate (Vg). The measured mobility is 37 cm2V−1s−1 for the monolayer, 64 cm2V−1s−1 for the bilayer and 31 cm2V−1s−1 for the trilayer. xx Temperature dependent contact resistance and monolayer electronic stability: Temperature-­‐dependent two-­‐probe (2p-­‐G) and four-­‐probe (4p-­‐G) conductance of monolayer MoS2 was measured to extract the contact ratio, γc = G4p/G2p at 100K, 150K, 200K, 250K and 300K. The contact ratios of our monolayer MoS2 at 100 K and 300 K (Figs. S3a and S3b respectively) are comparable to Ti/Au contacts used in literature 1. At 100K, the contact ratio drops from 10 (@Vg = −60 V) to 2.5 at high electron concentration (Vg=70 V), while at 300 K, the contact ratio remains small ~1 (@Vg = −60 V) to ~2 at high electron concentration (Vg=70 V), indicating that at higher temperatures, thermal broadening makes the bandlike density of states accessible. The two-­‐probe conductance that is measured simultaneously with the Seebeck (2p-­‐G (Voc)) is also different from the two-­‐probe (2p-­‐G) and four-­‐probe (4p-­‐G) measurements, which indicates the device changes when exposed to air and is reloaded into the cryostat (despite the same in-­‐situ annealing of 1 hour at 475 K under high vacuum). Thus, it is imperative to measure the Seebeck and electrical conductivity simultaneously for the device powerfactor as has been done in the main manuscript. Note that the numerical value of the contact ratio is only used to estimate the correct density of states in the main text, Equations (2) and (3) and not in the reported values of powerfactor. Figure S3. (a) Gate-­‐dependent two-­‐probe (red line) and four-­‐probe (blue line) conductance measurements of the monolayer MoS2 at 100 K. The contact ratio (purple star) is determined by γc = G4p/G2p; drops from 10 (@Vg = −60 V) to 2.5 at high electron concentration (Vg=70 V). (b) Gate-­‐
dependent two-­‐probe (red line) and four-­‐probe (blue line) conductance measurements of the monolayer MoS2 at 300 K. The contact ratio (purple star) is low at this higher temperature ~1 (@Vg = −60 V) to 2 at high electron concentration (Vg=70 V). xxi Comparison to other thermoelectric materials: The gate-­‐modulated Seebeck coefficient of monolayer MoS2 (shown as α in µV/K in Fig. S4a) is plotted as a function of electrical conductivity (shown as lnσ in Ω−1cm−1) in comparison to traditional thermoelectric materials. Evidently, α = m(b-­‐lnσ)8, with the slope m ≈ kB/e. A larger value of the intercept, b, indicates a larger powerfactor (α2σ). The thermoelectric performance of monolayer MoS2 is comparable with that of high-­‐performance thermoelectric materials such as Bi2Te3 and PbTe. Similarly, the monolayer MoS2 matches Bi2Te3 in the α2σ-­‐σ plot (Fig. S4b), while the bilayer MoS2 has a higher powerfactor at the same conductivity, indicating superior thermoelectric performance. The higher value of the intercept, b, is linked to the large effective mass, m* and mobility, µ of the layered MoS2 8,9. Figure S4. (a) α-­‐lnσ plot of monolayer and bilayer MoS2 in comparison of thermoelectric performance with traditional thermoelectric materials, adapted from Rowe et. al.8 (b) α2σ-­‐σ plot of monolayer and bilayer MoS2 in comparison of thermoelectric performance with traditional thermoelectric materials. The thermoelectric performance of monolayer is comparable with that of high-­‐performance thermoelectric material Bi2Te3, while the bilayer indicates superior thermoelectric performance. xxii Mott Variable Range Hopping (M-­‐VRH) for insulating phase of monolayer MoS2: Temperature and gate-­‐voltage dependent conductivity is used to ascertain the Insulator-­‐to-­‐Metal Transition Temperature (TIMT) (Fig. S5a). A metal-­‐like behaviour is observed for T>TMIT, as seen in the main text since σ ∝1 T and is further corroborated by a rapid decrease of mobility as a function of temperature µ ∝ T −1.9 (Fig. S5b). This is close to the theoretically predicted exponent of 1.7 in monolayer MoS2, which occurs due to phonon scattering. In the insulating phase for T<TMIT, it is seen that the exponent is ~0.23, which is close to the expected behaviour of µ ∝ T −1 3 in two dimensions10. Further, the conductivity in the insulating phase follows σ(T) = σ0exp[−(T0/T)1/3] in two dimensions (Fig. S5c)10,11, and matches the Mott Variable Range Hopping (M-­‐VRH) mechanism, where T0 is related to the correlation energy scale. Fiugre S5. (a) Conductivity as a function of gate voltage (high (n = 8.5×1012 cm−2 at the top) to low (n = 1.4×1012 cm−2 at the bottom) carrier concentration). As the gate voltage (carrier concentration) decreases, the insulator-­‐to-­‐metal transition temperature (TIMT) shifts to higher temperatures (indicated by the dotted arrow). (a) Temperature-­‐dependent mobility of monolayer MoS2. The mobility undergoes a rapid decrease with an exponent ~0.23 to ~1.9 crossing the metal-­‐insulator-­‐
transition temperature (TIMT). (b) Temperature-­‐dependent conductance of monolayer MoS2 in insulating phase with different gate voltages (carrier concentration). The conductance follows the relation of σ(T) = σ0exp[−(T0/T)1/3] in two dimensions, indicating the Mott Variable Range Hopping (M-­‐VRH) mechanism. xxiii References: 1. Baugher, B., Churchill, H. O. H., Yang, Y. & Jarillo-­‐herrero, P. Intrinsic Electronic Transport Properties of High Quality Monolayer and Bilayer MoS2. Nano Lett. 13, 4212–4216 (2013). 2. Najmaei, S., Liu, Z., Ajayan, P. M. & Lou, J. Thermal effects on the characteristic Raman spectrum of molybdenum disulfide (MoS2) of varying thicknesses. Appl. Phys. Lett. 100, 013106 (2012). 3. Lee, C. et al. Anomalous Lattice Vibrations of Single-­‐ and Few-­‐Layer MoS2. ACS Nano 4, 2695–
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