Introduction

Molybdenum disulphide (MoS2), an n-type semiconductor1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16, shows novel properties such as superconductivity6, controllable valley polarization17,18 and metal-insulator transition3,4,5,6 (MIT). In MoS2 field-effect transistors (FETs), gate-induced charge carriers transport in a thin layer near the surface of MoS2 and are vulnerable to charge impurities and different types of disorder2,3,12,14,19,20. The presence of a high-κ dielectric material3 to monolayer MoS2 can effectively screen charge impurities and allow the observation of MIT. Based on recent transport measurements3, the phase transition behaviour of monolayer MoS2 has been attributed to transition from an insulating phase, in which disorder suppresses the electronic interactions, to a metallic phase in which strong coulomb interactions occur. However, the underlying physical mechanism and detailed MIT process need to be further clarified. Different from the studies on transport properties of MoS2, the capacitance spectroscopy14 recently applied to the characterization of MoS2 FET structures has been demonstrated as one of the most convenient and powerful method for studying the electron states in MoS2 at room temperature. At low temperatures, however, the information obtained by this technique is limited due to the large impedance near the band edge of MoS2. Different from that in graphene quantum capacitors21,22,23,24,25,26,27, the slow charge-carrier mobility in MoS2 capacitors often leads to incompletely charged states, mainly due to the localization near the band edge. The incompletely charged capacitance confuses the effect of charge traps.

In the following, we show an approach to address these problems by introducing a MoS2-based vertical metal-insulator-semiconductor-metal (MIS-M) heterostructure suitable for probing electron states using capacitance measurements. Unlike conventional FET structures14, our approach eliminates the impedance effects and can directly access the intrinsic characteristics of thin-layer MoS2 over a wide frequency (100 Hz–1 MHz) and temperature range (2–300 K). By combining capacitance and transport measurements, we show that the MIT observed in monolayer and multilayer MoS2 is consistent with the physical picture of a percolation28,29,30,31,32,33,34,35 transition model. The results of our investigation on the mechanisms of MIT and other intrinsic characteristics, such as thickness-dependent screening abilities and fast relaxation of hole carriers at the valence band, provide useful information much needed for improving the performance of the FET devices based on MoS2 monolayers and multilayers.

Results

MoS2 vertical heterostructural capacitance devices

Figure 1a,b illustrates our specially designed MIS-M capacitor device, fabricated by transferring23,36 exfoliated flakes of MoS2 and hexagonal boron nitride (BN) on a Si substrate coated with a SiO2 thin layer (300 nm). Exfoliated natural crystals of monolayer or multilayer MoS2 were first transferred onto a BN sheet, serving as an ultra-smooth and disorder-free gate dielectric37. A Ti/Au (10 nm/20 nm) local gate sits underneath the BN sheet. The critical step in achieving MIS-M structure is to have the MoS2 sheet fully covered by a top electrode (Ti/Au: 10 nm/50 nm). The equivalent circuit of this device geometry is shown in Fig. 1c. The measured capacitance Ct is the total capacitance contributed by two capacitors originating from MoS2 (CMoS) and the geometric capacitor (Cg) in serial connection, plus the residual capacitance Cp in parallel connection. Ct, shown below, is the capacitance wiping off Cp (see detailed analysis in Supplementary Figs 1–3 and Supplementary Note 1 and 2). Therefore, . With fully covered top electrodes, carriers can respond vertically instead of moving in the plane of MoS2. This unique structure directly avoids the huge lateral resistance R of MoS2 near the band edge. As a result, the measured Ct (of a 5.9-nm-thick MoS2) at 2 K (Fig. 1d) is almost independent of excitation frequencies f, which differs greatly from that obtained in conventional FET structure devices7,14. In capacitance measurement of conventional FET structures, lateral resistance R must be considered when R~1/(2πfCt). This is confirmed by our MoS2 capacitance devices with partially covered top electrodes, which show significant frequency-dependent and temperature-dependent characteristics (Supplementary Fig. 4 and Supplementary Note 3). We also achieved good Ohmic contacts between the top Ti/Au electrode and MoS2 in our devices, as evidenced by the capacitance measurements at different excitation voltages (Fig. 1e). Note that the capacitance measured at large excitation voltages (for example, at 2 V) shows deviation due to the averaging effect.

Figure 1: The optical and schematic images of the MoS2 MIS-M heterostructures.
figure 1

(a,b) The MoS2 flakes are fully covered by a top Ti/Au electrode. The square top electrode in a is the reference capacitor. Scale bar, 10 μm. (c) The equivalent circuit of the MoS2 capacitance devices. Total capacitance Ct measured from a 5.9-nm-thick MoS2 at 2 K at different frequencies (d) and excitation voltages (e), respectively. The measured capacitance in vertical heterostructures is almost independent of excitation frequencies, which differs greatly from that obtained in conventional FET structures (Supplementary Fig. 4). The excitation voltage used for d is 50 mV and the frequency used for e is 100 kHz.

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Characterization of the vertical MIS-M structures

The interface structure and band diagrams in the MoS2-based MIS-M devices are shown schematically in Fig. 4a–d. When the gate voltage Vg>0, electrons accumulate at the MoS2 surface (Fig. 4b). The measured capacitance approaches the geometric capacitance Cmax=Cg when Vg is sufficiently large, while under negative Vg (Fig. 4c) electrons are depleted. In this case, the measured capacitance can be described by , where εMoS and dMoS are the dielectric constant and the thickness of MoS2, respectively. This allows us to directly obtain the εMoS–dMoS relationship of MoS2. To accurately extract , the geometric capacitance Cg should be carefully treated. Here, an interlayer capacitance Cin originated from the interlayer spacing between BN and MoS2 is included in the calculation of , where CBN is the geometric capacitance of BN. This interlayer capacitance has been applied in previous studies on twisted bilayer graphene38,39,40. Here we estimate this interlayer capacitance Cin~25.3 μF cm−2 with the interlayer dielectric constant ~10ε0 and interlayer spacing ~0.35 nm38,40. The extracted εMoS with and without including the interlayer capacitance are both shown in Fig. 2.

Figure 4: The percolation transition driven by density inhomogeneity in multilayer MoS2.
figure 4

(a–d) The schematic band diagrams of metal-BN-MoS2-metal structures at flat band (a), accumulation region (b), depletion region (c) and inversion region (d). (e–j) The schematic images showing the percolation-induced MIT under different effective thicknesses of electron states (e–g) and carrier densities (h–j). The circles denote isolated carrier puddles in MoS2. (k,l) The measured total capacitance Ct (k) and effective thickness deff (l) plotted as a function of gate voltage Vg for 2–300 K. The excitation voltage and frequency used are 50 mV and 100 kHz, respectively. (m) deff plotted as a function of temperatures at different carrier densities n.

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Figure 2: Experimental data of the thickness-dependent dielectric constant of MoS2.
figure 2

The dielectric constant of MoS2 εMoS with (blue dots) and without (green dots) including interlayer capacitance is plotted as a function of thickness dMoS. εMoS increases from ~4ε0 for a monolayer to ~11ε0 for bulk MoS2. The errors originate from the measurements of sample sizes, thicknesses of MoS2 and BN, and capacitances of MoS2.

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As shown in Fig. 2, εMoS has been found to increase from ~4ε0 for a monolayer to ~11ε0 for bulk MoS2. This is in excellent agreement with theoretical predictions41,42. The small εMoS in monolayer MoS2 suggests poor dielectric screening of Coulomb interactions, indicating that strong electron–electron interactions could be achieved in clean monolayer MoS2. The largely increased mobility observed in monolayer MoS2 placed in a high-κ dielectric environment2,3,43 probably benefits from its small εMoS. In fact, the decrease in the optical phonon mode observed by a Raman spectroscopy study of few-layer and bulk MoS2 (ref. 44) is also due to the strong dielectric screening effects.

The valence band of multilayer MoS2 is also accessed by detecting the inversion layer of holes using low excitation frequencies at sufficiently high temperatures (Fig. 3a,b). However, the inversion layer is invisible when using high frequencies at low temperatures (T<100 K). This is due to the presence of the Schottky barrier between the Ti/Au contact and the valence band7. Holes must form through thermal excitations or minute current leakage into the contacts. This process often requires a long time from ~ms to seconds. In the 12-nm-thick MoS2 capacitance device, the majority of hole carriers have been relaxed around 20 kHz at 300 K, as confirmed by the phase information of the device, which is defined by Θ=arctan(G/2πfCt), where G is the conductance. As shown in Fig. 3c, the phase peaks appear at ~20 kHz for different negative gate bias voltages, indicating that the relaxation time of holes in the 12-nm-thick MoS2 device is around 50 μs. For the capacitance samples contacted by Cr/Au top electrodes (Cr has a larger work function (~4.5 eV) than that of Ti (~4.3 eV)), a short relaxation time (~5 μs) for holes has also been achieved at 300 K (Supplementary Fig. 5 and Supplementary Note 4).

Figure 3: The valence band of multilayer MoS2 accessed by capacitance measurement.
figure 3

(a) Ct measured at 300 K for different excitation frequencies. (b) Ct measured at 1 kHz for different temperatures. (c) Phase information plotted as a function of excitation frequencies at 300 K for different Vg. The phase peak around 20 kHz yields a relaxation time of hole carriers at 50 μs. (d) The quantum capacitance Cq of MoS2 plotted as a function of surface potential Vs at 300 K, which yields a band gap width of around 1.14 eV. The excitation voltage used is 100 mV. The dashed line above breaks schematically shows the expected quantum capacitance at higher Fermi energies.

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By applying the Poisson equation to model the vertical heterostructures in a quasi-quantitative manner (Supplementary Note 5), we correlated the quantum capacitance of MoS2 Cq with the surface potential Vs in our capacitance devices. Vs is extracted based on the charge conservation relation . To accurately extract Cq, the interlayer capacitance between BN and MoS2 Cin is included. Owing to the finite thickness of MoS2 (<15 nm) and the vertical configuration of the capacitance device, the MoS2 capacitance in vertical structure is a non-zero value Cs0 inside the bandgap (Supplementary Figs 6 and 7). The quantum capacitance of MoS2 Cq can be described by Cq=CMoS−Cs0 (Supplementary Fig. 8). The Cq–Vs relation is shown in Fig. 3d, yielding a band gap around 1.14 eV, which is close to the reported value of 1.2 eV45. The quantum capacitance of monolayer MoS2 is shown in Supplementary Fig. 9, which shows a smaller value compared with that in multilayer MoS2 (Supplementary Note 6). As our measurements are performed near the band edge of MoS2 and a large amount of disorders are present in MoS2, the quantum capacitance is not saturated to the predicted value 57.6 μF cm−2 (corresponding to a density of states ~3.6 × 1014 eV−1 cm−2 (refs 14, 46)) beyond the mobility edge. The dashed line above breaks in Fig. 3d schematically shows the expected quantum capacitance at higher Fermi energies.

Percolation-induced MIT in monolayer and multilayer MoS2

Similar to the MIT observed in transport measurements3,4,5,6, the capacitance data of the 5.9-nm-thick MoS2 device measured at different temperatures (Fig. 4m) show an interesting transition with a well-defined cross-over point (at Vg=5 V and corresponding to a carrier density n~6.8 × 1012 cm−2, obtained from n=Cg(Vg−Vs−VT)/e, where VT~−1 V is the threshold voltage). When Vg<5 V Ct decreases with decreasing temperature, whereas at Vg>5 V the temperature dependence of Ct is reversed. The observed cross-over point in capacitance measurements is indeed related to the MIT as its value (~6.8 × 1012 cm−2) is consistent with that measured by transport (ref. 6 and Fig. 6). More evidence is provided by capacitance measurements of monolayer MoS2 samples (Fig. 5a). In monolayer MoS2, the intersections of the capacitance curves showed obvious temperature-dependent characteristics. At temperatures below 100 K, we observed that the cross-over point was stabilized roughly at n~1.2 × 1013 cm−2, consistent with the transport results measured in monolayer MoS2 (ref. 3) with an MIT at n~1 × 1013 cm−2. Bilayer and trilayer MoS2 samples displayed similar transition phenomena with cross-over points around n~8.6 × 1012 cm−2 (Fig. 5b).

Figure 6: Transport results showing the percolation transition in multilayer and monolayer MoS2.
figure 6

(a,b) The MITs are clearly shown by σ measurements of a multilayer (a) and monolayer (b) MoS2 for different temperatures. The inset in b shows the optical image of a monolayer MoS2 device. (c,d) The fitting of experimental σ (orange dots) of multilayer (c) and monolayer (d) MoS2 according to the percolation conductivity σ=A(n−nc)δ (green lines). The arrows denote the positions of MITs.

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Figure 5: The percolation transition and charge traps in monolayer and trilayer MoS2.
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(a) Ct of a monolayer MoS2 measured at an excitation frequency 1 kHz and excitation voltage 50 mV for different temperatures. (b) Ct of a trilayer MoS2 measured at an excitation frequency 100 kHz. (c) Ct of a trilayer MoS2 measured for different excitation frequencies at 2 K, indicating that the charge traps are excited at low frequencies. The inset shows Ct measured at 300 K. (d) The charge-trap densities Dit as a function of Vg calculated for the monolayer and trilayer MoS2 samples. The arrows denote the transition points.

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The electronic transport of MoS2 suffers from charge impurities2,3 and short-range disorders12,14,19,20, such as ripples, dislocation and sulphur vacancies. These disorders result in the insulating transport behaviour of MoS2 in the low carrier-density region, where electrons transport through hopping between localized states (Fig. 4h) and can be well described by the variable-range-hopping model3,12,20. In the region where sufficient, large carrier densities are introduced, metal behaviour is observed3. Here we propose a percolation-type MIT in MoS2, driven by density inhomogeneity of electron states28,29,30,31,32,33,34,35 that describes the systems in which charge carriers are transported through percolating conductive channels in the disorder landscapes due to the poor screening effect at low carrier densities. When carrier density is low enough, conductive paths are efficiently blocked and MIT occurs. MoS2 has been proven to be such a disordered system, with impurity concentration ranging from 1011 to 1013 cm−2, especially for monolayer MoS2, which is more vulnerable to ripples and charge impurities2,3,12,14,19,20. Thus, the MIT in MoS2 is in line with the percolation transition theory in which disorder plays an important role. Moreover, our capacitance and transport data, shown below, provide further evidences to this effect.

The evolution of concentration and effective thickness of electron states probed by capacitance measurements can explain the observed MIT in transport measurements fairly well and provide details of the percolation transition process. The percolation transition phenomenon is illustrated in Fig. 4h–j. With increasing carrier densities n (by increasing gate voltage), the localized electron states begin to percolate with each other till a conductive channel occurs at a critical density (Fig. 4i). Further increasing carrier densities will lead to sufficient conductive channels spanning the entire system and result in metal-like transport behaviours (Fig. 4j). On the other hand, at the same carrier density, the effective thickness deff=εMoS/CMoS of electron states confined in the surface of MoS2 can be tuned by varying temperatures (Fig. 4l). Smaller deff can also be achieved at higher gate voltages where large amounts of surface charges are induced (supported by theoretical calculations in the Supplementary Note 5). As illustrated in Fig. 4e–g (assuming n remains unchanged), more conductive channels are formed at a smaller deff. The MIT should occur when deff is sufficiently small. The capacitance data of our samples (Fig. 4l,m) are similar to those obtained from transport measurements in multilayer MoS2 (showing an MIT at n=6.7 × 1012 cm−2) (ref. 6). When n<6.8 × 1012 cm−2, deff decreases with increasing temperatures. Hence, the conductivity should increase as the temperature increases. In contrast, when n>6.8 × 1012 cm−2, the increase of deff would lead to decreasing conductivity as the temperature increases. Furthermore, the increasing n and decreasing deff would also enhance the screening of disorders and electron states, and thus lead to increasing conductivity, while lowering the Coulomb interaction strength. It is noticed that the effective channel thickness is only applicable to multilayer MoS2, as monolayer MoS2 is a truly 2D system. The percolation transition in monolayer MoS2 mainly results from the tuning of concentration of electron states at different gate voltages. An alternative explanation on the transition is based on the quantum capacitance of MoS2, which is closely related to the carrier density and the effective channel thickness. A larger quantum capacitance suggests a larger density of states or a smaller effective channel thickness. Therefore, the observed gate-tuned transition from insulating to metallic region is the direct consequence of the increase of quantum capacitance with increasing gate voltages (as shown in Fig. 3d).

The percolation transition also suggests an increasing transition density at the cross-over point with increasing impurity concentration30,31,32. In our MoS2 samples, the transition density was in the range 1012–1013 cm−2 due to the presence of large amounts of impurities. Moreover, the transition density in monolayer MoS2 (~1 × 1013 cm−2) was larger than that observed in multilayer MoS2 (~6 × 1012 cm−2), which agreed with the prediction of percolation theory as monolayer MoS2 was more vulnerable to disorders. This was further evidenced by extracting charge trap densities, Dit, of MoS2 from capacitance measurements (a trilayer sample shown in Fig. 5c). The presence of impurities or disorder may cause charge-trapping effects in MoS2 capacitance devices, particularly at low temperatures. The charge traps can be fully excited only at relatively low frequencies (for example, 100 Hz). The density of the charge traps can then be estimated by measuring the difference in capacitance at low and high frequencies, that is, Dit=(CMoS(low_f)–CMoS(high_f))/e. The trap densities in our monolayer and trilayer MoS2 samples were in the order of 1012 eV−1 cm−2 (Fig. 5d). The trap densities in monolayer MoS2 were apparently large, suggesting that monolayer MoS2 is more sensitive to disorder. In fact, the trap densities in our samples were underestimated because of the limitation of the excitation frequency ranges. At relatively high temperatures (inset of Fig. 5c), the charge traps were easily excited and the capacitances measured at low and high frequency show no difference.

The percolation-induced MIT in MoS2 is further supported by transport data at low temperatures. The MITs of multilayer (Fig. 6a) and monolayer (Fig. 6b) MoS2 are clearly shown by the conductivity σ, at different temperatures, similar to previous reports3,4,5,6. The MIT occurs at n~6 × 1012 cm−2 for multilayer MoS2 and n~1.1 × 1012 cm−2 for monolayer MoS2, consistent with the capacitance data. The mobilities of the monolayer and multilayer MoS2 samples measured at 2 K are around 90 and 250 cm2 V−1 s−1, respectively (Supplementary Fig. 10 and Supplementary Note 7). To gain further insight into the transition behaviour, we applied the percolation model of conductivity31,32,35 near the percolation threshold density nc, which is described by

where A is a constant of proportionality and δ is the percolation exponent. Below the threshold density nc, the 2D electron gas broke up into isolated puddles of carriers, with no conducting channels crossing the whole sample. The conductivity showed insulating behaviour and eventually vanished at T=0 K. In 2D systems, δ is expected to be 4/3 and a cross-over point (~e2/h) above the percolation threshold density is suggested at finite temperatures30,31. Based on the percolation model, we fit our experimental data of multilayer (Fig. 6c) and monolayer (Fig. 6d) MoS2 samples at 2 K. The experimental results show excellent agreement with theoretical predictions near the transition point. The extracted parameters are δ~1.7 and nc~3.2 × 1012 cm−2 in multilayer MoS2 and δ~1.8 and nc~3.8 × 1012 cm−2 in monolayer MoS2. The obtained percolation exponents are consistent with experimental values δ=1.4–1.7 found in other 2D systems, such as GaAs/AlGaAs heterostructures31,32. The obtained percolation threshold density nc is lower than the value of MIT cross-over point (mobility edge) because of thermal activation of localized electron states. nc would approach the mobility edge when temperature is sufficiently low. The percolation transition model can be applied only near the transition point at low temperatures. In the metallic region with higher carrier densities, the conductivity would show a linear increase with gate voltages where the conductivity is mainly limited by the linearly screened charge impurity scattering31. The slight deviation between experimental data and fitting curves at low carrier densities is due to enhanced hopping conductivity and quantum tunnelling at finite temperatures.

Discussion

One alternative scenario besides the percolation transition model is the phase transition theory for a metallic phase (stabilized by e–e interactions) and an insulating phase (disorder prevails over e–e interactions), which are separated by a quantum critical point3,47. This theory shows the existence of the quantum critical point where the density of states of the underlying collective modes is divergent at the transition point. The transport data obtained from MoS2 cannot provide more information for distinguishing these divergent collective modes. In contrast, the capacitance measurement is able to probe the global behaviour of these divergent collective modes, which would lead to a divergent quantum capacitance at the transition point22,25,47. In our capacitance experiments, however, the divergent quantum capacitance was not observed around the transition point. The capacitance data seems to be more inclined to the density inhomogeneity induced by disorder, which dominates the properties at the MIT transition point, as the Coulomb interactions of electrons could be suppressed by a large amount of disorder existing in MoS2. Based on our transport and capacitance data, the percolation transition model is more consistent with the MIT phenomena in MoS2.

The vertical MIS heterostructures built from atomically thin MoS2 are ideal capacitor structures for probing the electron states and intrinsic properties of MoS2. According to the analyses of experimental data obtained by electrical transport measurement and capacitance spectroscopy, we believe that the percolation-type MIT (driven by density inhomogeneities of electron states) is the dominating mechanism of the MIT in both monolayer and multilayer MoS2. The vertical heterostructures offer the added advantages of eliminating the influence of large impedance at the band tails and accessing intrinsic characteristics such as thickness-dependence dielectric constant and band gap variation in atomically thin MoS2. The present study also provides a new approach to characterizing the intrinsic properties of other atomically thin-layered materials and interface states of heterostructures built from 2D materials.

Methods

Sample preparation

Monolayer and multilayer MoS2 flakes were exfoliated from MoS2 crystals (from 2D semiconductors) by the micromechanical cleavage technique. MoS2 and BN flakes were placed on the surface of a glass slide coated with Polydimethylsiloxane/Methyl methacrylate as described for graphene-BN device fabrication36. Next, these thin flakes were transferred onto a local Ti/Au (10 nm/20 nm) gate. The top electrodes were patterned using standard electron-beam lithography. Two types of top electrodes, Ti/Au (10 nm/50 nm) and Cr/Au (2 nm/50 nm), were fabricated through electron-beam evaporation. The dielectric constant of the BN sheet is measured by calibrating an internal reference capacitor that sits near the MoS2 capacitance device (Fig. 1a). The thicknesses of MoS2 and BN flakes were measured by an atomic force microscope (Veeco-Innova).

Capacitance and transport measurements

Capacitance measurements were carried out using an HP Precision 4284A LCR Meter with a sensitivity of ~0.1 fF in a cryogenic system (2–300 K). All wires in the measurement circuits were shielded and the p-Si substrates were also grounded to minimize residual capacitance. The residual capacitance in the measurement setup is at the order of 1 fF (see Supplementary Fig. 3). Transport measurements were performed in the same cryogenic system using lock-in techniques.

Additional information

How to cite this article: Chen, X. et al. Probing the electron states and metal-insulator transition mechanisms in molybdenum disulphide vertical heterostructures. Nat. Commun. 6:6088 doi: 10.1038/ncomms7088 (2015).