Electronic Transport in Bilayer MoS2 Encapsulated in HfO2 - ACS

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Electronic Transport in Bilayer MoS2 Encapsulated in HfO2 Bernard R. Matis, Nelson Y. Garces, Erin R. Cleveland, Brian H. Houston, and Jeffrey W Baldwin ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b04397 • Publication Date (Web): 26 Jul 2017 Downloaded from http://pubs.acs.org on July 29, 2017

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ACS Applied Materials & Interfaces

Electronic Transport in Bilayer MoS2 Encapsulated in HfO2

Bernard R. Matis1, *, Nelson Y. Garces2, Erin R. Cleveland3, Brian H. Houston1, and Jeffrey W. Baldwin1

1

Naval Research Laboratory, Code 7130, Washington, DC 20375, United States

2

Sotera Defense Solutions, Crofton, MD 21114

3

Naval Research Laboratory, Code 6812, Washington, DC 20375, United States

*Correspondence to: [email protected]

Abstract: The exact nature of the interface between a two-dimensional crystal and its environment can have a significant impact on the electronic transport within the crystal, and can place fundamental limitations on transistor performance and long-term functionality. Twodimensional transition metal dichalcogenides are a new class of transistor channel material with electronic properties that can be tailored through dielectric engineering of the material/environmental interface. Here, we report electrical transport measurements carried out in the insulating regime of bilayer molybdenum disulphide, which has been encapsulated within a high-κ hafnium oxide dielectric. Temperature and carrier density dependent measurements show that for T < 130 K the transport is governed by resonant tunneling, and at T = 4.2 K the tunneling peak lineshape is well fitted by a Lorentzian with amplitude less than e2/h. Estimates of tunneling time give τ ~ 1.2 ps corresponding to a frequency f ~ 0.84 THz. The tunneling

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processes are observable up to T ~ 190 K (more than a factor of 6 higher than previously reported for MoS2 on SiO2) despite the onset of variable range hopping at T ~ 130 K, demonstrating the coexistence of the two transport processes within the same temperature range. At constant temperature, varying the Fermi energy allows experimental access to each transport process. The results are interpreted in terms of an increase in charge carrier screening length and a decrease in electron-phonon coupling induced by the hafnium oxide. Our results represent the first demonstration of the intermediate tunneling-hopping transport regime in a two-dimensional material. The results suggest that interface engineering may be a macroscopic tool for controlling quantum transport within such materials as well as for increasing the operating temperatures for resonant-tunneling devices derived from such materials, with applications in high-frequency electronics and logic devices.

Keywords: Molybdenum disulphide, high-κ dielectric, electronic transport, resonant tunneling, variable range hopping.

I. Introduction The transition-metal dichalcogenide (TMD) molybdenum disulfide (MoS2) has drawn considerable attention in the development of novel nanoscale devices, which include atomically thin field-effect transistors,1-5 p-n junctions,6 phototransistors,7,8 and molecular sensors.9,10 This interest is generated in part by the ability to isolate the individual layers of MoS2 that are weakly bound by van der Waals forces,11 in addition to the direct bandgap ∆ε ~ 1.8 eV for a single layer, and the indirect bandgap ∆ε ~ 1.2 eV for multilayers,12 which affords the opportunity to turn off the current within the material through an electric field effect (unseen in graphene). Electrical


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measurements carried out on both back-gated and dual-gated device architectures have revealed a metal-insulator transition (MIT) and have characterized the transport within the separate metal and insulator regimes.13-16 Transport within the insulating regime occurs via localized states with resonant tunneling process occurring at the lowest temperatures (T < 30 K for MoS2 on SiO2) followed by a crossover to hopping transport and thermally activated transport as T is increased.13,15 A crossover to metallic behavior occurs with high levels of induced charge carrier densities (n ≥ 1 x 1013 cm-2).13 Because of its strict two-dimensional (2D) nature, electronic transport within the MoS2 is highly affected by the local environment, and prior studies have taken advantage of this susceptibility to the surrounding environment by using dielectric engineering as a method to favorably modify overall material quality and transistor performance. Examples include the deposition of the high-κ dielectric HfO2 (dielectric constant εr = 25) on top of the MoS2 resulting in an enhanced mobility due to a modified phonon dispersion relation and screened Coulomb scattering,13 and encapsulating the MoS2 within hexagonal BN layers (εr ~ 3-4), which provides a suitable device platform for measuring intrinsic material properties and opens up the possibility of observing the quantum Hall effect within the MoS2.14 However, with much attention focused on improving charge carrier mobility, and overall device quality within the metallic transport regime, through dielectric engineering little is known about how the presence of a high-κ dielectric will affect the transport within the insulating regime. To date an adjacent layer of HfO2 has been shown to favorably modify the MoS2 transport, however fully HfO2 encapsulated MoS2 has not been investigated. Here we present electronic transport data for bilayer MoS2 that is encapsulated within atomic-layer deposition (ALD) grown HfO2. We focus on the insulating, low carrier density



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regime (n < 8.6x1012 cm-2) where the low-T transport occurs via localized states that originate from trapped charges at the MoS2/HfO2 interface. In our experiments, the conductivity, σ, is determined as a function of both T and back-gate voltage, Vg (and therefore charge carrier density n: ∝ ). Resonant tunneling processes dominate the transport for 4.2 K ≤ T ≤ 130 K and are observable for T as high as 190 K (more than a factor of 6 higher than previously reported15 for MoS2 on SiO2) despite the onset of 2D Mott variable range hopping (VRH) at T ~ 130 K, providing evidence for the intermediate tunneling-hopping transport regime. Isothermal measurements show that for 130 K ≤ T ≤ 190 K varying the Fermi energy εF permits experimental access to both resonant tunneling processes and VRH transport across the entire range of Vg used within our experiments. A transition to thermally activated transport is observed for T > 230 K.

II. Experimental Methods Our devices consist of bilayer MoS2 exfoliated on an HfO2 (5 nm – ALD, plasma grown)/SiO2 (275 nm – thermally grown)/Si (n-type, arsenic-doped) substrate followed by the deposition of Ti (10 nm)/Au (60 nm) contact electrodes defined by electron-beam lithography. Following the Ti/Au electrode deposition, a second 20 nm thick HfO2 layer is thermally grown via ALD thus encapsulating the MoS2 within the high-κ dielectric (information regarding the HfO2 growth process can be found in the Supporting Information). Three devices were tested in this study and an optical image of one of our devices can be seen in Figure 1a. All of the devices showed the same qualitative behavior, and we observe resonant tunneling for T ≥ 130 K for the two devices that were fully encapsulated within HfO2. The bilayer nature of the studied devices was chosen for several specific reasons. Theory predicts that bilayer MoS2/contact metal


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interfaces have a higher electron injection efficiency than single layer MoS2/contact metal interfaces (with a 100% predicted tunneling probability between bilayer MoS2 and titanium metal),17 which makes bilayer MoS2 more suitable for a transistor channel material than single layer MoS2 (over the same gate controllability) and more appropriate for studies of resonant tunneling. Bilayer MoS2 also affords gate controllability over the valley Hall effect, which also holds promise for valley-polarization based logic devices and information storage.18 The corresponding device architecture can be seen in Figure 1b. Figure 1c shows the Raman spectrum taken on the MoS2 flake for which data is presented before the Ti/Au contact deposition. The separation of the E (Γ) and A (Γ) peaks, which is sensitive to the number of

MoS2 layers, was found to be 20.6 cm-1; this value for the Raman peak separation is consistent with bilayer MoS2.19 All transport measurements were carried out in vacuum (pressure P ≤ 10-6 Torr) using a 2-point contact configuration (the small MoS2 flake sizes used for this study permitted only 2 contacts to be deposited) with a source-drain voltage VSD = 632 µV (DC excitation for room temperature measurements (Figure 1d) and AC excitation using a lock-in technique at a frequency f = 13.7 Hz for the temperature-dependent measurements (Figures 2-5)).



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Figure 1:

Figure 1. (a) Optical image of a MoS2 device after the final HfO2 deposition. The bilayer MoS2 flake is outlined by the dotted black line. (b) Schematic of a bilayer MoS2 transistor encapsulated in ALD-grown HfO2. (c) Raman spectrum of bilayer MoS2 on the HfO2/SiO2/Si substrate prior to the Ti/Au electrode deposition. The spectrum has been normalized to the (Γ) peak. The dashed, vertical lines are guides to the eye. (d) Two-terminal drain current I as E

a function of back-gate voltage Vg at temperature T = 293 K with an applied bias voltage VSD =


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632 µV DC. The solid red line is a linear fit from which we extract the field-effect mobility. Inset: I as a function of VSD for various values of Vg.

III. Results Figure 1d shows the measured drain current, I, as a function of Vg with a 632 µV DC excitation. The device shows n-type behavior with a threshold voltage Vth ~ 0 V. From a linear fitting of the I versus Vg data (solid red line in Figure 1d) we can estimate the field-effect mobility = × where L = 1 µm and W = 2 µm are the channel length and width, respectively, VSD is the voltage excitation, and C = 1.252x10-4 Fm-2 is the total capacitance between the channel and the back gate per unit area (1 = 1 + 1

"

; " =

$% $& where εr = 3.9 and d = 275 nm for SiO2, εr = 25 and d = 5 nm for HfO2,

and εo = 8.8542x10-12 s4A2m-3kg-1 is the permittivity of free space). We find µFE ~ 14.46 cm2V1 -1

s , which is the same order of magnitude as the results obtained on dual-gated MoS2 devices

near room temperature.13 That the value of µFE is relatively low suggests other scattering mechanisms aside from the homopolar phonon mode (expected to be quenched by dielectric encapsulation)20 contribute to the charge carrier scattering such as charged impurity scattering. The devices used in this study displayed liner IV characteristics at low VSD as exemplified by the curves in the Figure 1d inset, which shows I versus VSD at varying Vg (low-temperature, linear IV curve measurements can be found in the Supporting Information). Additionally, the measured transport for T > 230 K (shown below in the Figure 4 inset where we study the temperature dependence of the device conductivity) displayed thermally activated behavior, ' ∝ ( )*∆,⁄-. /1 where kB is Boltzmann’s constant, and we find ∆ε ~ 70 meV across the entire



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range of Vg used. For a Schottky barrier with titanium contacts the expected barrier height is ~ 330 meV, considering the MoS2 electron affinity21 of ~ 4 eV and the titanium work function ~ 4.33 eV. That the value of ∆ε is an order of magnitude less than the expected Schottky barrier height and the measured IV transport in our devices is linear at high and cryogenic temperatures eliminates Schottky contact behavior within our VSD operating range. This is in agreement with other studies addressing 2-point electrical transport measurements in MoS2 devices on SiO2 substrates.15,16 Figure 2a shows the resistance R = VSD/I as a function of Vg across a wide range of T (4.2 K ≤ T ≤ 293 K) with VSD = 632 µV AC, which is well within the linear regime of transistor operation. We find insulating behavior across the entire range of Vg used in our experiments with no indication of a MIT. The R versus Vg data in Figure 2a also shows clear nonmonotonic behavior as T is decreased with local fluctuations in the data that become more distinct at lower T. The appearance of the fluctuations in Figure 2a, which indicate resonances in the device conductance at particular values of Vg, are suggestive of resonant tunneling through spatially isolated states similar to that which has been observed in single layer and trilayer MoS2 devices on SiO2 for T < 30 K.15 Figure S2 of the Supporting Information shows σ versus Vg at 4.2 K with clearly identifiable peaks and resulting negative differential conductance. The spatially isolated states are the result of trapped charges in the surrounding dielectric that modify the density of localized states and lead to charge-impurity-induced disorder within the MoS2. The observed resonances are highly reproducible and show little change in perpendicular magnetic field, B, up to 1 T as can be seen in Figure 2b. Here, we plot σ = L/RW, after having subtracted a smoothly varying background conductivity, σBG, versus Vg at T = 4.2 K and T = 4.3 K for the B = 0 T and B = 1 T data sets, respectively (information regarding σBG subtraction can be found in


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the Supporting Information). The data presented in Figure 2b show well-isolated resonances whose amplitudes are well below the quantum unit of conductance 2e2/h where e is the fundamental unit of electric charge and h is Planck’s constant. That the resonances are robust against B-fields as high as 1 T suggests that the observed resonances are not the result of Landau level formation as has been observed in the perpendicular-to-plane transport in stacked MoS2 layers.22 Additional data sets, including low-T resistance measurements before and after encapsulation with HfO2, are shown in Figure S4 of the Supporting Information.

Figure 2:



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Figure 2. (a) Resistance R as a function of back-gate voltage Vg at varying temperature T determined by measuring the drain current I under an applied bias voltage VSD = 632 µV AC. (b) Conductivity σ with a background conductivity σBG subtracted as a function of back-gate voltage Vg at temperature T = 4.2 K and magnetic field B = 0 T, and at T = 4.3 K and B = 1 T. The slight difference in temperature (∆T ~ 100 mK) between the two data sets is due to a small heat flux generated while charging the superconducting magnet.


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The temperature dependence of the most well isolated resonance (resonance occurring at the lowest value of Vg) is shown in Figure 3 (additional data sets are shown in Figure S5 of the Supporting Information). In addition to a σ background subtraction the peaks in Figure 3 have all been shifted so that the baseline of each peak coincides with the baseline of the T = 4.2 K data set, thus allowing for a comparison of the multiple lineshapes as T is increased. Several temperature-dependent characteristics of the observed resonance are clearly identifiable: the observed resonance survives up to T = 190 K, the peak maximum shifts slightly to lower values of Vg with increasing T, and the full width at half maximum (FWHM) of the peak increases with increasing T. For resonant tunneling processes the peak lineshape is expected to be a Lorentzian centered about the resonance energy, ε*, with maximum amplitude e2/h and with the energydependent transmission coefficient given by 2*$1 = 3Γ5 Γ6 ⁄7*$ − $ ∗ 1 + *Γ5 ⁄2 + Γ6 ⁄21 ;,23-26 where η is a coefficient less than unity, and ΓL(R) is the decay width, proportional to the leak from the resonant state to the left (right) contact; the conductance, G, of a resonant tunneling particle between Fermi-liquid leads can be calculated using the Landauer formula and is related

to the transmission coefficient by < = ( ℎ >|2*$1| @, $. The dashed line in Figure 3 is a @

Lorentzian fit to the T = 4.2 K data set, which shows a good fit between experiment and theory.

Figure 3:



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Figure 3. Conductivity σ with a background conductivity σBG subtracted as a function of backgate voltage Vg at varying T for the most well isolated peak (lowest Vg) from Figure 2. The dashed line is a fit of the T = 4.2 K data set to a Lorentzian lineshape (see main text). Inset: experimentally observed full width at half maximum γ(Vg) as a function of T. The solid red line is a linear fit to the data for T ≤ 130 K.

We suspect that the peak shift in Figure 3 to lower values of Vg (indicating a realignment of energy levels associated with tunneling events), in addition to the temperature-dependent broadening of the experimentally observed FWHM, γ(Vg), is due to both thermal and inelastic effects with inelastic effects significant for T ≥ 130 K. At T = 4.2 K, ε* ~ 4.6 meV and γ(Vg) ~ 1.11 meV are both larger than kBT ~ 0.362 meV, thus permitting a measure of the intrinsic lineshape of the resonance (see the Supporting Information for calculations of ε* and γ(Vg)). For


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the 80 K and 130 K lineshapes in Figure 3, ε* and γ(Vg) are the same order of magnitude though have become less than kBT, which suggests that thermal effects (for example, thermal broadening of the tunneling electrons spread in energy) govern the shifting of the peak resonance and FWHM broadening without significant contributions from inelastic effects (e.g. electron-phonon scattering, which is expected to dominate at higher temperatures20 and shown in our devices to be insignificant until T > 130 K: see below for the onset of VRH). With the contribution of inelastic scattering becoming relevant at ~ 130 K it is likely that the peak shift and FWHM broadening of the 190 K lineshape includes contributions from both thermal and inelastic effects. Additionally, we find γ(Vg) ∝ T (Figure 3 inset) for T ≤ 130 K (when inelastic effects are negligible), which is in agreement with resonant tunneling processes between silicon inversion layers through a non-inverted barrier in MOSFET devices.25 Also, assuming ΓR = ΓL and using the expression for a thermally broadened peak25 γ(Vg) = ΓR + ΓL we can estimate the tunneling time A = ℏ⁄Γ6 = 2ℏ⁄CD E where ħ is Planck’s constant divided by 2π, which for T = 4.2 K and

γ(Vg) = 1.11 meV gives τ ~ 1.2 ps corresponding to f ~ 0.84 THz. For T > 130 K we find that the inelastic conduction mechanism VRH is the dominant transport mechanism for Vg values that are not associated with resonant tunneling processes. Plotted in Figure 4 is σ on a logarithmic scale as a function of T -1/3 for various Vg (across the entire range of Vg used within our experiments), showing the specific region of T (130 K ≤ T ≤ F⁄G

230 K) that the 2D Mott VRH model is valid: ' ∝ ( )*/%⁄/1

where TO is a characteristic

exponent found from the fits shown in Figure 4 (the Vg dependence of TO is shown in the Figure 5 inset). We point out that the VSD value used here to obtain the data (VSD = 632 µV) is more than three orders of magnitude less than the VSD values used for other VRH studies in MoS2 devices with similar device dimensions.16 Furthermore, the VSD value used within our



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experiments is several orders of magnitude less than the values needed to induce a transition from temperature-dependent VRH conduction to electric field-dependent VRH conduction in both disordered graphene and other 2D systems.27,28 For T < 130 K, σ shows a weakened temperature dependence and the VRH model fails to describe the observed behavior of σ(T), which is due to resonant tunneling processes dominating the low-T transport. We also find that at the specific Vg values associated with resonant tunneling the VRH model failed to accurately describe the temperature dependence of σ. Thus, the data sets shown in Figures 3 and 4 demonstrate that for 130 K ≤ T ≤ 190 K both VRH and resonant tunneling transport mechanisms ℏ H

can be accessed experimentally. By varying Vg, and thus n and $ = IJ∗ ∆ where ∆Vg = Vg – Vth, and m* ~ 0.5mO is the MoS2 effective mass29 and mO is the electron mass, we can experimentally access either VRH transport or resonant tunneling transport within the specified temperature range. Additionally, within the data shown in Figure 4 is a noticeable feature occurring at T -1/3 ~ 0.2 K-1/3 corresponding to a slight decrease in σ with increasing T, which systematically appears for all Vg. The feature occurring at T -1/3 ~ 0.2 K-1/3 is a deviation from the expected behavior within the localized regime. This slight decrease in σ with increasing T occurs at the point where the transport transitions from being governed by tunneling to being governed by hopping over a finite temperature range. The slight decrease in σ is interpreted as evidence of a tunnelinghopping transition regime as the efficiency of one transport path becomes greater than the other with changing T. Such a transition has been observed in the temperature-dependent transport of solid-state electronic junctions of proteins (well-defined monolayers that contain the proton pump protein bacteriorhodopsin (bR)).30 In the case of bR, the transition region occurred across a temperature range of ~ 40K, which agrees with our observation of a concurrent tunneling-


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hopping regime over a 60 K temperature range. Other studies on the tunneling-hopping transition within molecules of varying length, l, up to l ~ 10 nm have demonstrated that the transition occurs near l ~ 4 nm.31 This length scale is in agreement with the length of the bR molecule (l ~ 5 nm) as well as the HfO2-modified localization length of ~ 4 nm found for our MoS2 devices (see below). Therefore, we suggest that with a higher degree of charge carrier localization due to the HfO2 encapsulation we are able to observe the persistence of resonant tunneling to higher temperatures and the intermediate-transport regime. This intermediate tunneling-hopping transport regime represents a relatively unexplored area within solid-state research, and future experiments utilizing 2D materials may use this transition as a means of studying decoherence and the quantum to classical transition. Finally, as T is increased to near room-temperature values thermally activated transport becomes the dominant transport process; this transition occurs at T -1/3 ~ 0.16 K-1/3 and the data fittings to thermally activated transport are shown in the inset to Figure 4 with which we obtain an estimate for ∆ε.

Figure 4:



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Figure 4. Conductivity σ plotted on a logarithmic scale versus T -1/3 for various values of Vg. Solid lines are linear fits to the data showing agreement with the 2D Mott VRH model for 130 K ≤ T ≤ 230 K. Inset: σ versus T -1 for various Vg (same legend as the main figure) showing a transition to thermally activated behavior for T > 230 K.

IV. Discussion The influence of charge carrier screening on the localization length within the hopping regime has been studied in order to characterize the electronic transport in few-layer MoS2 on SiO2 as well as in other 2D systems.32,33 For example, it has been demonstrated that depositing a layer of electron-beam sensitive resist (PMMA, εr ~ 3.7) onto few-layer MoS2 led to a factor of two change in the Debye screening length, λD, which resulted in a more localized trapping potential due to the change of the MoS2 dielectric environment.32 Therefore, we suggest that the


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adjacent HfO2 layers in the samples presented here modify the screening length of the MoS2 charge carriers, which affects the degree of charge carrier localization and supports the observation of resonant tunneling up to T ~ 190 K. The localization length, ξ, within the hopping regime can be estimated from fitting σ to the VRH model (shown in Figure 4), following the relation K =

L.N

-. *,O 1P

, where D(εF) ~

1.97x1014 eV-1cm-2 is the experimentally determined surface density of trapped charges at the HfO2 interface (see the Supporting Information for D(εF) estimate). We estimate ξ ~ 4 nm across the entire range of Vg, which is shown on the right vertical axis in Figure 5. This value for

ξ is the same order of magnitude (a factor of 2 less) as the localization length estimate based upon charge-carrier puddle formation in MoS2 due to extrinsic interfacial impurities within a nearby SiO2 dielectric15 while it is an order of magnitude larger than estimates based upon lattice defects.32 Thus, the low-T material performance within our devices is determined by extrinsic interfacial impurities, which is also consistent with measurements of multi-layer MoS2 encapsulated within hexagonal boron nitride.14 Furthermore, in order to estimate the screening length, the Debye wave number is replaced by the Fermi wave number kF ~ ωp/vF for the degenerate gas at lower temperatures (see the Supporting Information), where ωp is the 2D plasma frequency and vF the Fermi velocity (vF ~ 0.53x106 m/s),34 which allows us to estimate the screening length35 λF ~ 2π/kF (for λF > ξ electrons are localized while delocalization occurs when the localization length exceeds λF). Using the known expression for the 2D plasmon frequency QR *S 1 = T2US ⁄$& where εr is the dielectric constant of the surrounding environment (in this case εr = 25 for HfO2) and U = V( ⁄W∗ is the Drude weight for ordinary Schrödinger fermions36 we estimate the temperature-independent λF (left vertical axis of Figure



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5), which reaches values as high as λF ~ 118 nm for Vg corresponding to the resonance shown in Figure 3 and decreases with increasing Vg. Note that the expression used here to estimate the screening length is dimensionally equivalent to the general form of the screening length in 2D: X = $2V( ∗

Y Y

Y where Y is the density of states. The relatively large value of λF,

several orders of magnitude larger than ξ at low Vg and always greater than ξ across the entire range of Vg used, suggests a more localized trapping potential with respect to the case of MoS2 on SiO2; we note that without the presence of the HfO2 and taking εr ~ 3.9 for SiO2, λF ~ 4.37 nm at Vg = 10 V, which is the value of Vg at which λF and ξ become comparable, and λF becomes less than ξ for higher values of Vg. This would indicate a transition to a delocalized state, which is a transition unobserved within our HfO2 encapsulated MoS2 devices.


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Figure 5:

Figure 5. (Left vertical axis) Fermi wavelength λF ~ ωp/vF where ωp is the 2D plasma frequency and vF the Fermi velocity and (right vertical axis) localization length ξ determined from VRH fits of σ versus T (linear fits in Figure 4) as a function of back-gate voltage Vg. Inset: characteristic exponent TO found from VRH fitting at different Vg.

It has been suggested that dielectric encapsulation can modify the phonon dispersion relations1,37 and the electron-phonon coupling,13 which supports the observation of VRH becoming relevant at T ~ 130 K in our samples. First principles calculations20 for monolayer MoS2, as well as transport measurements for MoS2 devices on SiO2,38 have shown that the electron mobility, µ, follows the relation ~K )[ for 100 K ≤ T ≤ 293 K (the phonon-limited temperature range where scattering from optical phonons is expected to dominate) with γ = 1.69 for single-layer MoS2 and γ = 2.6 for bulk MoS2. It has been demonstrated experimentally13 that



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capping the MoS2 with a layer of HfO2 results in a reduction of γ to the range 0.3 ≤ γ ≤ 0.78, which is well below the theoretical value expected (γ ~ 1.52) when taking into account only a quenching of the homopolar phonon mode through dielectric encapsulation,20 and provides strong evidence for a modified electron-phonon coupling.13 Although our 2-point measurements do not offer a way to measure the Hall mobility as a function of temperature, the results shown in Figure 4 indicate that inelastic processes do not become relevant until T ~ 130 K with the onset of VRH. This VRH onset temperature is ~ 30 K higher than the temperature at which scattering from optical phonons is expected to become relevant, T ~ 100 K.20 Such a higher onset temperature than that predicted by theory is in agreement with a modified electron-phonon coupling brought about by the encapsulation of the MoS2 within a high-κ dielectric. A reduced electron-phonon coupling, and therefore a higher VRH onset temperature, is also in agreement with higher operating temperatures for resonant tunneling as tunneling can persist to higher temperatures without significant contributions from inelastic thermalizing processes.

Conclusion: In conclusion, we have carried out electrical measurements within the insulating regime of bilayer MoS2 that has been encapsulated within a high-κ HfO2 dielectric. For lowtemperature resonant tunneling processes, estimates of the tunneling time give τ ~ 1.2 ps corresponding to a frequency f ~ 0.84 THz; these tunneling characteristics afford potential for high-frequency resonant tunneling applications. Our results demonstrate an intermediate transport regime where both variable range hopping and resonant tunneling processes coexist and can be accessed experimentally, which opens an avenue for studies of decoherence and the quantum to classical transition within a disordered 2D material. The results also suggest that


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such transport within a 2D material can be controlled by tailoring the material/environment interface. The ability to control quantum transport within 2D materials via dielectric engineering offers an opportunity for circumventing nanolithography techniques that are not easily scalable, such as electron-beam lithography, for observing and controlling such quantum transport.

Associated Content: Supporting Information: Includes further details on HfO2 growth procedures, measured low-temperature IV curve, conductivity background subtraction, determination of resonance energy ε*, experimentally determined full-width at half-maximum γ(Vg), and the HfO2 surface density of charge traps D(εF), additional resonant tunneling data, and a discussion on the MoS2 degenerate electron gas.

Acknowledgments: The authors gratefully acknowledge the members of the technical staff of the Institute for Nanoscience at the NRL: Dean R. St. Amand and Walter A. Spratt. B.R.M. gratefully acknowledges support through the NRL Karles Fellow program. This work was supported by the Office of Naval Research.

Author Information: *E-mail: [email protected]. Notes: The authors declare no competing financial interest.



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Table of Contents Graphic:


Electronic Transport in Bilayer MoS2 Encapsulated in HfO2 - ACS

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