Mott variable-range hopping transport in a MoS2 nanoflake

The transport characteristics of a disordered, multilayered MoS2 nanoflake in the insulator regime are studied by electrical and magnetotransport measurements. The MoS2 nanoflake is exfoliated from a bulk MoS2 crystal and the conductance G and magnetoresistance are measured in a four-probe setup over a wide range of temperatures. At high temperatures, we observe that ln G exhibits a −T−1 temperature dependence and the transport in the nanoflake dominantly arises from thermal activation. At low temperatures, where the transport in the nanoflake dominantly takes place via variable-range hopping (VRH) processes, we observe that ln G exhibits a −T−1/3 temperature dependence, an evidence for the two-dimensional (2D) Mott VRH transport. Furthermore, we observe that the measured low-field magnetoresistance of the nanoflake in the insulator regime exhibits a quadratic magnetic field dependence ∼ αB2 with α ∼ T−1, fully consistent with the 2D Mott VRH transport in the nanoflake.


Temperature dependence of the electron mobility in the MoS2 nanoflake
where the channel length  23 is 650 nm and the channel width  is 400 nm.  is the unit area capacitance, which can be estimated using   =  0   , where  0 is the vacuum permittivity,  = 3.9 is the dielectric constant of SiO2, d = 300 nm is the thickness of SiO2. Figure 1 in this Supporting Information shows the extracted mobility from the measured conductance shown in Figure 1(c) of the main article.The results shown in Figure 1 manifest distinctly different temperature dependences at low and at high temperatures.In the low temperature region (the left side of the figure), the mobility decreases with decreasing temperature, which is consistent with the fact that the nanoflake is in the insulating regime at all the gate voltages considered in this work.In the high temperature region (the right side of the figure), the mobility decreases with increasing temperature, showing the characteristic influence of phonon scattering on the electron transport in the nanoflake.As discussed in the main article, in this high temperature region, the transport is predominantly carried out by the carriers which are thermally excited Electronic Supplementary Material (ESI) for RSC Advances.This journal is © The Royal Society of Chemistry 2019 to the extended states located above mobility edge.However, at these high phonons become active and phonon scattering plays a dominant role in limiting carrier transport, resulting in a characteristic dependence of the carrier mobility on temperature,  ∝  − , where constant  depends on the specific phonon scatting mechanisms.The fitting at the high temperature side of Figure 1(a) gives a value of  ≈ 1.74, which is much close to the theoretically predicted value for MoS2 optical phonon scattering in monolayer MoS2 ( ≈ 1.52) 1 and is very different from that in bulk crystals ( ≈ 2.6) 2 .The experimental results are consistent with the fact that the thickness of the MoS2 nanoflake is 10 nm in the device.

Magnetoresistance measurements with the magnetic fields applied at different angles
To show further that the transport in the MoS2 nanoflake is predominantly of 2D nature, we measure the magnetoresistance of the nanoflake device with the magnetic fields applied at different angles .The results of the measurements for the device at temperature T=6K and back gate voltage Vg=-20 V are shown in Figure 3(a).Here, as shown in the inset of Figure 3(a), the nanoflake is in the x-y plane, the transport takes place along the x direction, and the magnetic fields are applied in the y-z plane, i.e., always perpendicular to the current direction.
The magnetoresistance is defined as ∆ 23 = [() − ( = 0)]/( = 0) , where  =  23 /  , see Figure 1(a) of the main article for the measurement circuit setup.At  = 90 °, the magnetoresistance shows a positive quadratic magnetoresistance as we discussed in the main article.At  = 0 °, a weak negative magnetoresistance is observed.This weak negative magnetoresistance arises from the finite thickness nm) of the nanoflake and thus the suppression of back scattering by the top and bottom surfaces of the nanoflake by the in-plane magnetic field.However, the thickness of the nanoflake is very small, the negative magnetoresistance is small in magnitude, e.g., it is less than 3% even at the in-plane magnetic field of 8 T. Figure 3 shown in this supplementary note imply that the transport in the nanoflake is predominantly of the 2D nature, but a small 3D transport characteristic could be present which may cause some small but observable deviations from the predictions of 2D transport theory.

Figure 1 (
Figure 1(c) of the main article shows the measured channel conductance =  / 23 of the studied MoS2 nanoflake device as a function of back gate voltage Vg at different temperatures, see Figure 1(a) in the main article for the device structure and the measurement setup.The electron mobility of the nanoflake at different temperatures can be extracted from the measured conductance curves shown in Figure 1(c) of the main article using the following equation

Figure 1 . 2 .
Figure 1.Electron mobility  extracted for the MoS2 nanoflake studied in the main article as a function of temperature at different gate voltages.At low temperatures,  decreases with decreasing temperature, showing that the nanoflake is in the insulating regime at the gate voltages considered.At high temperatures,  decreases with increasing temperature as ∝ −1.74 , implying that the carrier transport is dominantly limited by optical phonon scattering in the nanoflake.

Figure 2 .
Figure 2.   plotted against T -1/4 at three representative back gate voltages.Clearly, the data in the temperature range of 6 to 80 K could not be fitted using single straight lines.
(b) shows the normalized magnetoresistance, ∆ 23 + = ∆ 23 − ∆ 23 =0 °• cos (), as a function of perpendicular component of the magnetic field   =  • sin .Here, the ∆ 23 =0 ° is the measured magnetoresistance at in-plane magnetic fields and can be acquired from Figure 3(a) at  = 0 °.It is seen that the normalized magnetoresistance is solely dependent on the perpendicular component of the applied magnetic field.Overall, the results

Figure 3 .
Figure 3. (a) Magnetoresistance measured for the nanoflake device with the magnetic fields applied at different orientations  as shown in the inset at temperature T= 6 K and at back gate voltage Vg= -20 V.A positive quadratic magnetoresistance is observed at  = 90 ° and a very weak magnetoresistance is observable at  = 0 °.(b) Normalized magnetoresistance plotted against the perpendicular component of the applied magnetic field   .Here, the normalized magnetoresistance is obtained from (a) by subtracting the in-plane contributions from the measured magnetoresistance values.