Supplementary information for
Electric field modulation of thermovoltage in single-layer MoS2
Lukas Dobusch1), Marco M. Furchi1), Andreas Pospischil1), Thomas
Mueller1), Emmerich Bertagnolli2) and Alois Lugstein2, a)
1
Institute of Photonics, TU-Wien, Gußhausstraße 27-29, A-1040 Vienna, Austria
2
Institute of Solid State Electronics, TU-Wien, Floragasse 7, A-1040 Vienna, Austria
a
Corresponding Author: alois.lugstein@tuwien.ac.at
1. Materials and characterization by optical microscopy and Raman spectroscopy
MoS2 flakes were mechanically exfoliated from natural MoS2 (SPI Supplies) onto highly doped Si
substrates with a 300nm thick SiO2 layer using wafer-dicing tape. Due to interference effects, single-layer
MoS2 can be easily identified on 300nm SiO2.1 The layer thickness of the exfoliated MoS2 flakes was
further verified by µ-Raman spectroscopy (WITec alpha300, 532nm) and AFM-techniques.2 Figure 1Sa
and 1Sb show AFM and Raman measurements of the MoS2 flake pictured on the optical micrograph in
the inset of Figure 1Sa. This optical image as well as the AFM image in Figure 1Sa clearly depicts
regions of different layer thickness, ranging from single-layer (1L) to quasi bulk (QB). Figure 1Sb shows
the corresponding Raman measurements, where the Raman shift variations of the E12g (in plane) and A1g
(out of plane) mode is used to determine the layer thickness.2 In order to avoid damage from laserheating, the laser power was kept below 100µW (~32µW @100x).
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FIG. 1S. AFM (a) and Raman (b) characterization of the MoS2 flake pictured on the micrograph in the inset, with
areas of different thickness, ranging from monolayer (1L) to quasi-bulk (QB).
2. Contact properties
The low field contact resistance RC was investigated as a function of the back gate voltage by comparing
two-point and four-point I/V measurements of the same sample within a short period of time in order to
exclude degradation effects. In doing so, the total low field sample resistance RS was taken from the
inverse gradients of the IV-characteristics between -10mV and +10mV, as indicated in Figure 2Sa. The
contact resistance RC can then be evaluated as 𝑅𝑐 =
𝑅𝑠,2𝑃𝑡 −𝑅𝑠,4𝑃𝑡
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and the MoS2 flake resistance is given by
the four-point measurement. Figure 2Sb shows the observed gate-dependent contact and MoS2 flake
resistance, respectively. Note that the contact resistance reaches values as high as the MoS 2 resistance at
negative backgate bias VBG, and thus has to be considered in further considerations.
2
FIG. 2S. (a) I/V-characteristics for two-point (blue) and four-point (red) measurements of the same sample at VBG =
20V. The sample resistance RS was evaluated as the reciprocal gradient of the I/V-curves. (b) Field modulation
dependency of the contact resistance (black triangle) and MoS2-flake resistance (red circle) of single-layer MoS2
integrated in a back gated MOSFET device.
3. Resistive heater operation and temperature measurement
Operating the resistive heater element of the test device shown in Figure 3Sa with DC voltage results in a
thermal bias between the drain and source contacts of the back gated MoS2 flake. Due to a thermally
induced differential change in the resistance of the thermometers, the obtained thermal bias is accurately
determined by four-point measurements. In doing so, the resistive thermometers were calibrated by
putting the device on a heating stage and measuring the resistance change of the thermometers using a
Keithley 4200 semiconductor analyzer. The thereof calculated linear temperature dependency of
ΔR ≈ 0.03Ω/K × ΔT is shown in the inset in Figure 3Sb. Using this calibration curve, the change in the
thermometer resistance at the drain (cold) and source (hot) side, and thus the corresponding thermal bias
ΔT can be determined as shown in Figure 3S for a stepwise increasing heater voltage VHeat.
For the thermovoltage-measurements, the heaters were operated at a bias of VHEAT = 3V, corresponding
to a heating power of approximately 180mW and leading to thermal biases between 2K and 6K,
depending on the respective device geometry. The thermal bias could thereby be measured with an
accuracy of ±0.34K.
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FIG. 3S. (a) SEM image of the device with resistive thermometers at the cold (blue) and hot (red) side enabling the
determination of the thermal bias ΔT between source and drain due to resistive heating. (b) Differential change of
the thermometer resistance and temperature at source (hot side) and drain (cold side), respectively, as a function of
VHEAT. The inset shows the linear character of the resistive Au-thermometers as a function of temperature.
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4. Determination of the Thermovoltage
The thermovoltage was evaluated according to an approach published by Roddaro et al.3 Therefore, the
I/V characteristics of backgated MoS2 flakes were recorded for different gate voltages by sweeping the
source-drain voltage between -10mV and +10mV with and without thermal bias, respectively. The
isothermal measurement serves for calibration in order to eliminate measurement offsets (compare Figure
4S, blue dashed line). The shift of the thermally biased IV-curves along the VDS–axis, evaluated at
IDS = 0A, with respect to the isothermal measurement, can then be attributed to the thermoelectric voltage
VTE.
Since most devices are equipped with two heater structures, control measurements were made in order
to exclude the influence of leakage currents. By reversing the temperature gradient, the I/V-characteristics
are supposed to shift towards the opposite direction, as shown in figure 4S. Further, changing the heater
supply from +3V to -3V has no influence. The different gradients of the I/V curves in figure 4S for the
thermal biased (red lines) and isothermal (blue dashed line) cases are attributable to the negative
temperature coefficient of semiconductors and superimposed degradation effects. All measurements were
performed using an HP4156B semiconductor analyzer and a Keihtley 6430 sub-fA sourcemeter at
ambient condition.
FIG. 4S. I/V-characteristics at VBG = -20V for isothermal conditions (blue dashed line) and with a thermal bias (red
solid lines) due to heating close to the source (Heater1) or drain ( Heater2), respectively. The thermal bias for this
particular device was ΔT = 3.8K
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5. Photoconductivity
The influence of photoconductivity on the MoS2 resistivity is shown in Figure 5S. This long-time fourpoint measurement was performed in a dark box straight after annekaling. In doing so, the dark box was
closed at the beginning of the measurement and opened again for 15 minutes after 45.5 hours. During this
short illumination the resistivity decreased almost to the initial value and increased steadily after closing
the dark box again due to the decay of the photoconductivity. Thereby, the difference in the resistivity
under illumination can be attributed to a superimposed degradation effect.
FIG. 5S. Long-time four-point measurement at VDS = 2V and VBG = 0V performed in a dark box, indicating the
influence of photoconductivity on the MoS2 resistivity. The dark box was closed at the beginning of the measurement
and opened again for about 15 minutes after 45.5 hours.
6. Influence of adsorbates on MoS2 FET functionality
In order to investigate the influence of adsorbates, transfer characteristics of a single-layer MoS2 FET
were measured at air and after introducing the device into vacuum, in order to intentionally remove
surface adsorbates. After evacuation to a base pressure of 10-7 mbar for 12 hours, the ON state current
increased by more than one order of magnitude, the threshold voltage shifted towards negative VBG and
the hysteresis decreased, as shown in Figure 6S.
The significant broadened hysteresis for the FET device measured at air might be a consequence of the
slow dynamics of surface states and traps induced by the adsorbates, leading to a time dependent
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screening of the gate.4 Further, the observed shift of the threshold voltage indicates that the adsorbates
from ambient air partly compensate the intrinsic n-type behaviour and are thus acting as p-dopants for
MoS2. This confirms the discussion in the main text, concerning degradation effects due to adsorbates
from ambient air.
FIG. 6S. Transfer characteristics recorded by sweeping the backgate voltage forward and reverse as indicated by
the arrows of a backgated MoS2 FET measured at air (dashed red line) and in vacuum (solid blue line),).
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References (Supplementary Information)
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