Main

Following the many advances in basic science and applications of graphene, other two-dimensional materials, especially the transition-metal dichalcogenides (TMDCs), have attracted significant interest for their fascinating electrical, optical and mechanical properties1,2,3,4,5,6,7,8. Among the TMDCs, semiconducting MoS2 has been the most widely studied. It has a thickness-dependent electronic band structure3,5, reasonably high carrier mobility1,2,6,7,8,9 and demonstrates novel phenomena such as coupled spin–valley physics and the valley Hall effect10,11,12,13,14, leading to various applications including transistors1,7,15, memories16, logic circuits17,18, light-emitters19 and photodetectors20 with flexibility and transparency2,21. However, as with any two-dimensional material, the electrical and optical properties of MoS2 are strongly affected by impurities and its dielectric environment1,2,9,22, hindering the study of its intrinsic physics and limiting the design of devices based on such two-dimensional materials. In particular, the theoretical upper bound of the electron mobility of monolayer (1L) MoS2 is predicted to range from several tens to a few thousands at room temperature and exceed 105 cm2 V–1 s–1 at low temperature (T) depending on the dielectric environment, impurity density and charge carrier density23,24,25. In contrast, experimentally measured 1L MoS2 devices on SiO2 substrates have exhibited a room-temperature two-terminal field-effect mobility ranging from 0.1 to 55 cm2 V–1 s–1 (refs 1,26,27). This value increases to 15–60 cm2 V–1 s–1 with encapsulation by high-k dielectric materials1,9 due to a more effective screening of charged impurities24. Owing to the presence of large contact resistance from the metal–MoS2 Schottky barrier, however, these two-terminal measurements underestimate the true channel mobility7,28,29. Multi-terminal Hall mobility measurements8,9 still show a mobility substantially below theoretical limits, particularly at low T, with best reported values of 174 cm2 V–1 s–1 at 4 K for 1L (ref. 9) and 250 cm2 V–1 s–1 and 375 cm2 V–1 s–1 at 5 K for 1L and 2L devices, respectively (ref. 8). Typically, these thin samples exhibit a crossover to non-metallic behaviour at carrier densities below ∼1 × 1013 cm−2 (refs 8,9,30) or at smaller carrier densities by the engineering of local defect states and improved interfacial quality31. The scattering and disorder that lead to this non-metallic behaviour can arise from multiple origins, such as lattice defects, charged impurities in the substrates and surface adsorbates, and it has been difficult to identify their separate contributions1,8,9,23,30,31,32,33.

van der Waals device with tunable graphene contact

We have previously demonstrated that the encapsulation of graphene within hexagonal boron nitride (hBN) reduces scattering from substrate phonons and charged impurities, resulting in band transport behaviour that is near the ideal acoustic phonon limit at room temperature and ballistic over more than 15 µm at low T (ref. 34). These results were realized using a novel technique to create one-dimensional edge contacts to graphene exposed by plasma-etching an hBN/graphene/hBN stack. Such an approach has not yet proved effective with MoS2. However, recent reports that graphene can create a high-quality electrical contact with MoS218,35 motivated a hybrid scheme, in which the channel MoS2 and multiple graphene ‘leads’ are encapsulated in hBN and the stack is etched to form graphene–metal edge contacts. This new scheme is distinct from previous approaches in that the entire MoS2 channel is fully encapsulated and protected by hBN and we achieve multi-terminal graphene contacts without any contamination from the device fabrication process.

Figure 1a,b presents a schematic diagram and optical micrograph of a Hall bar device structure. A PDMS (polydimethylsiloxane) transfer technique2 was used to place few-layer graphene flakes around the perimeter of a MoS2 flake. These were then encapsulated between thicker hBN layers and the entire stack placed on a Si/SiO2 wafer (Supplementary Fig. 1a). The stack was then shaped into a Hall bar geometry such that the hBN-encapsulated MoS2 formed the channel. In the contact regions, the graphene overlaps the MoS2 and extends to the edge, where it is in turn contacted by metal electrodes34. Details of the fabrication process are described in the Methods and Supplementary Section 1. High-resolution scanning transmission electron microscopy (STEM) (Fig. 1c; see also Supplementary Fig. 1b for a larger clean interface area of >3 µm) confirmed that the stacking method can produce ultraclean interfaces free of the residue that can be seen when an organic polymer film is used for stacking36. We note that although ohmic contacts have also been achieved with metal–MoS2 contacts through the deposition of small-workfunction metals, vacuum annealing and electrostatic gating4,17,18, top-deposited metal electrodes are not compatible with hBN encapsulation.

Figure 1: vdW device structure and interface characterization.
figure 1

a, Schematic of the hBN-encapsulated MoS2 multi-terminal device. The exploded view shows the individual components that constitute the heterostructure stack. Bottom: Zoom-in cross-sectional schematic of the metal–graphene–MoS2 contact region. b, Optical microscope image of a fabricated device. Graphene contact regions are outlined by dashed lines. c, Cross-sectional STEM image of the fabricated device. The zoom-in false-colour image clearly shows the ultra-sharp interfaces between different layers (graphene, 5L; MoS2, 3L; top hBN, 8 nm; bottom hBN, 19 nm).

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For this study, a series of samples with thicknesses ranging from 1 to 6 layers (1–6L) were fabricated and measured. The number of layers was identified by Raman and photoluminescence analysis (Supplementary Section 2). All samples were obtained by mechanical exfoliation except for the 1L sample, for which we used chemical vapour deposition (CVD) grown monolayer MoS2 because of the limited size of the mechanically exfoliated monolayers. The CVD-grown MoS2 single crystal has been shown to exhibit high quality (from structural, electrical and optical measurements37), although the process of transferring it from the growth substrate may introduce more contamination than is the case with mechanically exfoliated flakes.

For each sample we performed temperature-dependent two-probe measurements to examine the quality of the graphene contacts. Figure 2a presents output curves (Ids–Vds) for a 4L MoS2 device with a backgate voltage of Vbg = 80 V. The response is linear at room temperature and remains linear to low T, indicating an ohmic contact. Similar behaviour is seen for Vbg > 20 V, whereas gapped behaviour corresponding to non-ohmic contact is seen for Vbg < 20 V. This is consistent with previous studies that show a gate-tunable contact barrier between graphene and MoS2 (refs 18,35). In addition, this establishes the gate voltage range over which multi-terminal measurements can be reliably performed. Figure 2b shows the measured four-terminal resistivity ρ (log scale) of the same sample with Vbg = 20 V to 80 V (corresponding to carrier densities of ∼4.8 × 1012 to ∼6.9 × 1012 cm−2, respectively) and from room temperature to 12 K. ρ decreases with increasing Vbg, as expected for an n-type semiconductor. With decreasing temperature, ρ drops dramatically over the entire accessible range of Vbg, reaching 130 Ω at 12 K. All of the samples studied exhibited similar behaviour: n-type semiconducting behaviour and metallic temperature dependence in the gate voltage accessible to four-terminal measurements.

Figure 2: Gate-tunable and temperature-dependent graphene–MoS2 contacts.
figure 2

a, Output curves (Ids–Vds) of the hBN-encapsulated 4L MoS2 device with graphene electrodes at different temperatures. Backgate voltage Vbg was maintained at 80 V with a carrier density of 6.85 × 1012 cm−2 in MoS2. The linearity of the output curves confirms that the graphene–MoS2 contact is ohmic at all temperatures. b, Resistivity ρ of 4L MoS2 (log scale) as a function of Vbg at different temperatures. The resistivity decreases on cooling, showing metallic behaviour, reaching ∼130 Ω at 12 K. The colour legend is the same as in a (from 300 K to 12 K). c, Contact resistance RC of the same device (log scale) as a function of Vbg at different temperatures. The colour legend is the same as in a (but from 250 K to 12 K). Inset: RC as a function of temperature at different Vbg. At high Vbg the contact resistance decreases when decreasing the temperature.

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By comparing the two- and four-terminal results, the contact resistance can be determined (Supplementary Section 3). The results for the 4L MoS2 device, as shown in Fig. 2c, directly demonstrate that the contact resistance can be tuned by the backgate voltage. In fact, a small contact resistance of ∼2 kΩ µm can be reliably achieved at a large gate voltage at room temperature. This probably reflects primarily the graphene–MoS2 junction resistance, as both the graphene resistance and the graphene–metal contact resistance should be substantially less34. Below Vbg = 20 V, the contact resistance increases on cooling, indicating activated transport across a contact barrier. However, above Vbg = 20 V, the contact resistance decreases upon cooling, reaching a low-T value of ∼1 kΩ µm above Vbg = 50 V. This metallic behaviour directly demonstrates that low-resistance contacts, with no thermal activation, can be achieved at sufficiently high gate voltage. Similar behaviour was observed in all samples (Supplementary Fig. 3), with contact resistance at high Vbg ranging from ∼2 to 20 kΩ µm at room temperature and from ∼0.7 to 10 kΩ µm at low T. These values are comparable to the room-temperature values reported previously for graphene38 and metal39,40,41 contacts, but larger than the best contacts achieved by MoS2 phase engineering (0.2–0.3 kΩ µm)29. Owing to the increase in bandgap with decreasing thickness, the value of Vbg required to achieve ohmic contact is larger for thinner samples.

Scattering mechanism in MoS2

To examine the quality of the hBN-encapsulated devices and determine the scattering mechanisms limiting the carrier mobility of MoS2, the Hall mobility µHall(T) was derived from ρ(T) and the carrier density n(Vbg) (obtained by Hall effect measurements, Supplementary Section 4). Figure 3a shows µHall for the 1–6L samples as a function of temperature, at carrier densities ranging from 4.0 × 1012 to 1.2 × 1013 cm−2 (Fig. 3b and Supplementary Table 1). Thinner samples were measured at the higher carrier densities required to achieve ohmic contact. For all samples, mobility increases with decreasing temperature and saturates at a constant value at low T. The low-T mobility in our devices is much higher than previously reported values and there is no sign of a metal–insulator transition as observed at similar carrier densities around 1 × 1013 cm−2 in SiO2-supported MoS2 (refs 8,9,30,32,33). This strongly suggests that extrinsic scattering and disorder (either from SiO2 or from processing with polymer resists) has been the primary source of the non-metallic behaviour in MoS2 measured to date.

Figure 3: Temperature, carrier density dependence of Hall mobility and scattering mechanism.
figure 3

a, Hall mobility of hBN-encapsulated MoS2 devices (with different numbers of layers of MoS2) as a function of temperature. To maintain ohmic contact, a finite Vbg was applied. The measured carrier densities obtained from Hall measurements for each device are listed in Supplementary Table 1. The solid fitting lines are drawn by the model described in the main text. All fitting parameters are listed in Supplementary Table 1. As a visual guide, the dashed line shows the power law μph ∼ T−γ, and fitted values of γ for each device are listed in the inset table. b, Impurity-limited mobility (μimp) as a function of the MoS2 carrier density. For comparison, previously reported values from MoS2 on SiO2 substrates (refs 8,46) are plotted. c–e, The solid lines show the theoretically calculated long-range (LR) impurity-limited mobility (c), short-range (SR) impurity-limited mobility (d) and mobility including both LR and SR based on Matthiessen's rule, 1/μ = 1/μLR + 1/μSR, as a function of carrier density for 1L to 6L MoS2 (e). Experimental data from 1L and 6L MoS2 are shown as circles (c–e).

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The measured mobility curves can be reasonably fitted to a simple functional form: 1/μ(T) = 1/μimp + 1/μph(T), where μimp is the contribution from impurity scattering and µph is the temperature-dependent contribution due to phonon scattering. In all samples, the fitted µph(T) is well described by a power law (µph ∼ T−γ) above 100 K (Supplementary Fig. 7). This behaviour is consistent with mobility limited by MoS2 optical phonons, which is theoretically predicted to have an exponent of ∼1.69 in monolayer23 and ∼2.5 in bulk42 MoS2 at T > 100 K. Although this power-law behaviour has been observed in experiments conducted by other groups8,9,30, a stronger temperature dependence was observed in our devices, with the exponent γ ranging from 1.9 to 2.5 (inset table in Fig. 3a), as opposed to 0.55–1.7 as reported previously8,9. We also note that the room-temperature mobility, which is dominated by phonon scattering in all the samples, is seen to vary from 40 to 120 cm2 V–1 s–1. At this point we can find no satisfactory explanation for this variation: there is no discernible trend with thickness and no variation in the gamma value with carrier density (Supplementary Fig. 8). Finally, we note that a deviation from the simple form µph ∼ T−γ in high-mobility samples below 100 K may indicate acoustic phonon scattering, although further study is needed to fully explore this regime.

At the lowest temperature, phonon scattering is suppressed and the residual resistivity is due to dominant long-range Coulomb impurities or short-range atomic defects43,44,45, captured in the measured quantity µimp. Figure 3b shows the derived values of µimp as a function of carrier density n. For each sample, µimp increases with n, with maximum values ranging from 1,020 cm2 V–1 s–1 in the CVD monolayer to 34,000 cm2 V–1 s–1 for 6L MoS2, up to two orders of magnitude higher than previously reported values8,46 (Fig. 3b and Supplementary Table 1). These basic trends allow us to rule out scattering due to impurities or defects located within the MoS2 itself: bulk charged impurities should give rise to thickness-independent mobility, and short-range scatterers due to atomic defects should give rise to a density-independent mobility45. On the other hand, interfacial scatterers, including both Coulomb impurities and short-range defects, which are limiting scattering mechanisms in high-quality conventional two-dimensional electron gas systems (2DEGs)44, are promising candidates. Indeed, PDMS transfer, while substantially cleaner than methods involving organic polymers, can potentially introduce adsorbates to the top MoS2 surface.

To understand the effects of interfacial scattering on samples of different thickness, we modelled interfacial Coulomb and short-range scattering as a function of carrier density, for samples from 1L to 6L in thickness. For Coulomb scattering we used a model based on a perturbative approach by Stern47, from which we obtained the screened Coulomb potential used in the mobility calculation. This model has also been commonly used in the context of semiconductor devices (Supplementary Section 8). Within the model, increasing carrier density enhances screening of the interfacial Coulomb potential, which leads to improved carrier mobility, and increasing the thickness of MoS2 redistributes the charge centroid further from the interface, also resulting in enhancement of mobility. The calculated mobility is shown in Fig. 3c, assuming the same impurity concentration of 6 × 109 cm−2 (chosen to match the 6L data) located at the top MoS2 interface, for devices with different numbers of layers. Although the qualitative trend of increasing mobility with layer number and carrier density is consistent with the model, the model fails to account for the observed large thickness dependence of more than an order of magnitude between the 1L and 6L devices. Changes in the model calculations, including the effects of band structure change with increasing layer thickness, are discussed in Supplementary Section 8.

We next consider interfacial short-range scatterers with atomically localized scattering potentials, which can be modelled as delta-function potentials within the same framework as used above. Quantum lifetime measurements, as discussed later in this Article, suggest that these scatterers strongly dominate electronic transport in the 1L devices. We therefore set the interfacial short-range scattering parameter (the product of scattering potential and defect density, Supplementary Section 8) to fit the mobility of the 1L device. In this case, for the same interfacial scattering the mobility increases rapidly with sample thickness—much more than is observed experimentally.

Based on this analysis, we propose that the interfaces in our devices introduce both long-range Coulomb scattering and short-range scattering. In this case, we can calculate the total extrinsic mobility using Matthiessen's rule. The combination of long- and short-range scatterers provides better agreement with the observed layer-dependent mobility, as shown in Fig. 3e, a salient point that we will revisit again later in a quantum oscillations study. Of course, a perfect match to experiment is not expected due to sample-to-sample variations in impurity density. We also note that the long-range impurity density of 6 × 109 cm−2 is two orders of magnitude smaller than is typically obtained for graphene on SiO2, and hence accounts for the two orders of magnitude larger mobility we obtained as compared to the best reported devices8,46.

Observation of Shubnikov–de Haas oscillations in MoS2

Figure 4 presents the longitudinal (Rxx) and Hall (Rxy) resistance of the monolayer (Fig. 4a), 4L (Fig. 4b) and 6L (Fig. 4c) MoS2 samples as a function of applied magnetic field. We observe pronounced Shubnikov–de Haas (SdH) oscillations in MoS2, providing additional strong evidence of high quality and homogeneity in the heterostructure devices. In the highest-mobility (6L) sample (Fig. 4c), the onset of SdH oscillations is close to 1 T, further confirming its ultra-high mobility. Encouragingly, the high-field Hall resistance (blue curve, Rxy) begins to reveal plateau-like structures at high magnetic fields coinciding with Rxx minima. These emerging features were similarly observed in early studies of graphene samples with moderate mobility48, giving hope that fully developed quantum Hall states can be observed with further improvements in sample quality. The periodicity of the SdH oscillations can be used to estimate the carrier density, or equivalently to measure the level degeneracy g for a known density (for details see Supplementary Section 7). For the 1L samples we observe 2 < g < 4, indicating that the bands may be partially valley–spin split (the multi-band nature of the 6L sample complicates this analysis). This is consistent with the extra SdH oscillations that begin to emerge at high fields, but more detailed study is required to explore this splitting in detail.

Figure 4: Observation of Shubnikov–de Haas oscillations in an hBN-encapsulated MoS2 device.
figure 4

a, Longitudinal resistance Rxx (red curve) and Hall resistance Rxy (blue curve) of an hBN-encapsulated CVD 1L MoS2 device as a function of magnetic field B measured at 0.3 K and with a carrier density of 9.7 × 1012 cm−2. Inset: Oscillation amplitude (black curve) as a function of 1/B after subtraction of the magnetoresistance background. The quantum scattering time extracted from the fitted Dingle plot (red dashed line) is 176 fs. b, Rxx (red curve) and Rxy (blue curve) of the hBN-encapsulated 4L MoS2 device as a function of B. Hall measurements were conducted at 0.3 K and at a carrier density of 4.9 × 1012 cm−2. c, Rxx (red curve) and Rxy (blue curve) of an hBN-encapsulated 6L MoS2 device as a function of B. Hall measurements were conducted at 3 K and with a carrier density of 5.3 × 1012 cm−2.

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The quantum scattering time τq, which is limited by both small- and large-angle scattering (which destroys quantized cyclotron orbits), can be estimated from the magnetic field corresponding to the onset of SdH oscillations, following the relation μq = eτq/m* ≈ 1/Bq (ref. 49), where e is the electron charge and m* is the effective mass obtained from ab initio band structure calculations50. This yields quantum mobilities for 1L, 4L and 6L MoS2 of ∼1,400, ∼3,100 and ∼10,000 cm2 V–1 s–1, respectively. A more accurate estimate of τq in MoS2 can be obtained using a Dingle plot (Supplementary Fig. 9), a well-established method in conventional 2DEGs (for details see Supplementary Section 6). The inset of Fig. 4a shows the SdH oscillations of 1L MoS2 after subtraction of a magnetoresistance background, as function of 1/B. The red dashed line is the fitted envelope, from which we estimate a quantum scattering time of τq = 176 fs. We show the values of τq obtained using both methods (oscillation onset and Dingle plots) in Supplementary Fig. 9c. The ratio of transport to quantum scattering time can provide additional evidence of the dominant scattering sources. In our samples, a ratio near 1 in 1L devices indicates predominantly short-range scattering, and an increase in τt/τq with increasing thickness indicates a crossover to long-range scattering. This trend is consistent with our previous physical picture of low-T electronic transport dominated by a mix of short- and long-range interfacial impurities.

Conclusion

We have demonstrated a van der Waals heterostructure device platform in which an atomically thin MoS2 layer is encapsulated by hBN and contacted by graphene. The van der Waals heterostructure provides a standard device platform that enables us to measure the intrinsic electrical transport of two-dimensional materials and achieve high-mobility two-dimensional devices in which to study their unique transport properties and novel quantum physics. By forming robust and tunable electrical contacts and dramatically reducing the interfacial impurities, intrinsic electron–phonon scattering can be observed at high T, and substantially improved mobility can be achieved at low T. This has enabled the first observation of SdH oscillations in MoS2. Modelling and quantum lifetime analysis suggest that a combination of short- and long-range interfacial scattering limits the low-T mobility, indicating that further improvements should be possible.

Methods

Device fabrication

The hBN/MoS2/graphene/hBN stacks were fabricated using the ‘PDMS transfer’2 technique on 285 nm SiO2/Si substrates. The transfer techniques are described in detail in Supplementary Section 1. The stacks were then shaped to the desired Hall bar structure through electron-beam patterning and reactive ion etching (RIE) with a mixture of CHF3 and O2. Finally, metal leads were patterned by electron-beam lithography and subsequent deposition of metals (Cr 1 nm/Pd 20 nm/Au 50 nm). The metal leads make edge-contact to the graphene electrodes, as reported previously34.

TEM sample preparation

For high-resolution imaging we fabricated a cross-sectional TEM lift-out sample from the finished encapsulated devices, using an FEI Strata 400 dual-beam focused ion beam device. STEM imaging was carried out with an FEI Tecnai F-20 STEM operated at 200 kV, with a 9.6 mrad convergence semi-angle and high-angle annular dark-field detector. False colouring was added by hand.

Electrical measurements and magneto-transport measurements

Two-terminal transport characteristics were measured by applying a d.c. bias (Keithley 2400) to the source and gate electrodes and measuring the drain current using a current amplifier (DL 1211). For four-terminal measurements, a standard lock-in amplifier (SR830) was used to measure the voltage drop across the channel with constant current bias. Magneto-transport measurements were performed in a Physical Property Measurement System (PPMS; Fig. 4c) and a He3 cryostat at the National High Magnetic Field Laboratory (NHMFL) (Fig. 4a,b).