Probing the electron states and metal-insulator transition mechanisms in molybdenum disulphide vertical heterostructures

Abstract

The metal-insulator transition is one of the remarkable electrical properties of atomically thin molybdenum disulphide. Although the theory of electron-electron interactions has been used in modelling the metal-insulator transition in molybdenum disulphide, the underlying mechanism and detailed transition process still remain largely unexplored. Here we demonstrate that the vertical metal-insulator-semiconductor heterostructures built from atomically thin molybdenum disulphide are ideal capacitor structures for probing the electron states. The vertical configuration offers the added advantage of eliminating the influence of large impedance at the band tails and allows the observation of fully excited electron states near the surface of molybdenum disulphide over a wide excitation frequency and temperature range. By combining capacitance and transport measurements, we have observed a percolation-type metal-insulator transition, driven by density inhomogeneities of electron states, in monolayer and multilayer molybdenum disulphide. In addition, the valence band of thin molybdenum disulphide layers and their intrinsic properties are accessed.

ARTICLE

Received 6 Jul 2014 | Accepted 11 Dec 2014 | Published 14 Jan 2015

Xiaolong Chen1, Zefei Wu1, Shuigang Xu1, Lin Wang2, Rui Huang1,3, Yu Han1, Weiguang Ye1, Wei Xiong1, Tianyi Han1, Gen Long1, Yang Wang1, Yuheng He1, Yuan Cai1, Ping Sheng1 & Ning Wang1

The metal-insulator transition is one of the remarkable electrical properties of atomically thin molybdenum disulphide. Although the theory of electronelectron interactions has been used in modelling the metal-insulator transition in molybdenum disulphide, the underlying mechanism and detailed transition process still remain largely unexplored. Here we demonstrate that the vertical metal-insulator-semiconductor heterostructures built from atomically thin molybdenum disulphide are ideal capacitor structures for probing the electron states. The vertical conguration offers the added advantage of eliminating the inuence of large impedance at the band tails and allows the observation of fully excited electron states near the surface of molybdenum disulphide over a wide excitation frequency and temperature range. By combining capacitance and transport measurements, we have observed a percolation-type metal-insulator transition, driven by density inhomogeneities of electron states, in monolayer and multilayer molybdenum disulphide. In addition, the valence band of thin molybdenum disulphide layers and their intrinsic properties are accessed.

DOI: 10.1038/ncomms7088

Probing the electron states and metal-insulator transition mechanisms in molybdenum disulphide vertical heterostructures

1 Department of Physics and the William Mong Institute of Nano Science and Technology, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China. 2 Department of Condensed Matter Physics, Group of Applied Physics, University of Geneva, 24 Quai Ernest Ansermet, CH1211 Geneva, Switzerland. 3 Department of Physics and Electronic Engineering, Hanshan Normal University, Chaozhou, Guangdong 521041, China. Correspondence and requests for materials should be addressed to N.W. (email: mailto:[email protected]

Web End [email protected] ).

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Molybdenum disulphide (MoS2), an n-type semiconductor116, shows novel properties such as superconductivity6, controllable valley polarization17,18

and metal-insulator transition36 (MIT). In MoS2 eld-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-k 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 claried. 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 capacitors2127, 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 Hz1 MHz) and temperature range (2300 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 percolation2835 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.

ResultsMoS2 vertical heterostructural capacitance devices. Figure 1a,b illustrates our specially designed MIS-M capacitor device, fabricated by transferring23,36 exfoliated akes 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 rst 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 13 and Supplementary Note 1 and 2). Therefore, Ct C 1MoS C 1g 1. With fully covered top

electrodes, carriers can respond vertically instead of moving in

CMoS

Cg

Cp

MoS2

BN

Vg

Bottom gate

Reference

0.216

100 Hz 1 kHz 10 kHz 100 kHz 1 MHz

Cmax

C t(F cm2)

0.210

0.204

C t(F cm2)

0.210

0.204

10 mV 30 mV 50 mV 100 mV 1 V2 V

0.198

0.192

0.198

0.192

6 4 2 0 2 4 6 8

Cmin

6 4 2 0 2 4 6 8

0.216

Vg (V)

Vg (V)

Figure 1 | The optical and schematic images of the MoS2 MIS-M heterostructures. (a,b) The MoS2 akes are fully covered by a top Ti/Au electrode. The square top electrode in a is the reference capacitor. Scale bar, 10 mm. (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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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 RB1/(2pfCt). This is conrmed by our MoS2 capacitance devices with partially covered top electrodes, which show signicant 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.

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. 4ad. When the gate voltage Vg40, electrons accumulate at the MoS2 surface (Fig. 4b). The measured capacitance approaches the geometric capacitance Cmax Cg when Vg is sufciently large, while under negative Vg

(Fig. 4c) electrons are depleted. In this case, the measured capa

citance can be described by Cmin

dMoS

eMoS

12

11

10

9

8

MoS ( 0 )

7

6

5

4

3 0 2 4 6 8 10 12

Figure 2 | Experimental data of the thickness-dependent dielectric constant of MoS2. The dielectric constant of MoS2 eMoS with (blue dots)

and without (green dots) including interlayer capacitance is plotted as a function of thickness dMoS. eMoS increases from B4e0 for a monolayer to

B11e0 for bulk MoS2. The errors originate from the measurements of sample sizes, thicknesses of MoS2 and BN, and capacitances of MoS2.

dMoS (nm)

C 1g

1 , where eMoS

and dMoS are the dielectric constant and the thickness of MoS2, respectively. This allows us to directly obtain the eMoSdMoS

relationship of MoS2. To accurately extract eMoS

dMoS C 1

min

C 1 g

, 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 Cg C 1BN C 1in 1, where CBN is the geometric capacitance of

BN. This interlayer capacitance has been applied in previous studies on twisted bilayer graphene3840. Here we estimate this interlayer capacitance CinB25.3 mF cm 2 with the interlayer dielectric constant B10e0 and interlayer spacing B0.35 nm38,40. The extracted eMoS with and without including the interlayer capacitance are both shown in Fig. 2.

As shown in Fig. 2, eMoS has been found to increase from B4e0 for a monolayer to B11e0 for bulk MoS2. This is in excellent agreement with theoretical predictions41,42. The small eMoS in monolayer MoS2 suggests poor dielectric screening of Coulomb interactions, indicating that strong electronelectron interactions could be achieved in clean monolayer MoS2. The largely increased mobility observed in monolayer MoS2 placed in a high-k dielectric environment2,3,43 probably benets from its small eMoS. In fact, the decrease in the optical phonon mode E12g 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 sufciently high temperatures (Fig. 3a,b). However, the inversion layer is invisible when using high frequencies at low temperatures (To100 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 Bms 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 conrmed by the phase information of the device, which is dened by Y arctan(G/2pfCt), where G

is the conductance. As shown in Fig. 3c, the phase peaks appear at B20 kHz for different negative gate bias voltages, indicating that

the relaxation time of holes in the 12-nm-thick MoS2 device is around 50 ms. For the capacitance samples contacted by Cr/Au top electrodes (Cr has a larger work function (B4.5 eV) than that of Ti (B4.3 eV)), a short relaxation time (B5 ms) for holes has also been achieved at 300 K (Supplementary Fig. 5 and Supplementary Note 4).

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 Vs R

Vg 0

1 CtCgdVg.

To accurately extract Cq, the interlayer capacitance between BN and MoS2 Cin is included. Owing to the nite thickness of MoS2 (o15 nm) and the vertical conguration of the capacitance device, the MoS2 capacitance in vertical structure CMoS C 1t C 1g 1 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 CqVs 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 mF cm 2 (corresponding to a density of states B3.6 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 measurements36, the capacitance data of the 5.9-nm-thick MoS2 device measured at different temperatures (Fig. 4m) show an interesting transition with a well-dened cross-over point (at Vg 5 V and

corresponding to a carrier density nB6.8 1012 cm 2,

obtained from n Cg(Vg Vs VT)/e, where VTB 1 V is the

threshold voltage). When Vgo5 V Ct decreases with decreasing temperature, whereas at Vg45 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 (B6.8 1012 cm 2) is consistent with that measured by

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300 K

1 kHz 2 kHz 4 kHz

0.22

0.22

250 K

220 K

C t(F cm2)

C q(F cm2)

2)

8 kHz

200 K

10 kHz 180 K

20 kHz

0.21

0.21

Phase ()C t(F cm

150 K

0.20

30 kHz

0.20

100 K

100 kHz

2 K

1 MHz

0.19

0.19

55 3.6x10

6 0 2 4 6

4 2

Vg (V)

8 0 2 4 6

4 2

Vs (V)

6

10

Vg (V)

Vg

14 eV1 cm2

7 V

6 V

5 V

5

4.6 V 4.4 V

4.2 V 4 V

55

15

10

5

0

Mobility edge

0.9

0.6 0.3 0.0 0.3

0 0 200 400 500

300

Frequency (kHz)

100

Figure 3 | The valence band of multilayer MoS2 accessed by capacitance measurement. (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 ms. (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.

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 nB1.2 1013 cm 2, consistent

with the transport results measured in monolayer MoS2 (ref. 3) with an MIT at nB1 1013 cm 2. Bilayer and trilayer MoS2

samples displayed similar transition phenomena with cross-over points around nB8.6 1012 cm 2 (Fig. 5b).

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 sufcient, large carrier densities are introduced, metal behaviour is observed3. Here we propose a percolation-type MIT in MoS2, driven by density inhomogeneity of electron states2835 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 efciently 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. 4hj. 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 sufcient 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 eMoS/CMoS of electron

states conned 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. 4eg (assuming n remains unchanged), more conductive channels are formed at a smaller deff. The MIT should occur when deff is sufciently 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 no6.8 1012 cm 2, deff decreases with

increasing temperatures. Hence, the conductivity should increase as the temperature increases. In contrast, when n46.8 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 mono-layer 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 Cq e2 @n@EF and the effective channel thickness. A larger

quantum capacitance suggests a larger density of states or a smaller effective channel thickness. Therefore, the observed

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Vg =0 Vg >0 deff

Vg <0

BN MoS2

Vg <<0

n =0.21013 cm2

100

0.216

2 K

300 K 200 K

4

1

0.210

50 K

3

2 K

300 K

100 K

2

C t(F cm2)

50 K

150 K

250 K

0.204

100 K

200 K

d eff(nm)

0.198

150 K

250 K

0.5

0.4

0.192 0.3

6

4 2 6 0 2 4 6 8 10

n =1.01013 cm2

0 2 4 6 8

4 2

Vg (V) Vg (V) T (K)

Figure 4 | The percolation transition driven by density inhomogeneity in multilayer MoS2. (ad) The schematic band diagrams of metal-BN-MoS2-metal structures at at band (a), accumulation region (b), depletion region (c) and inversion region (d). (ej) The schematic images showing the percolation-induced MITunder different effective thicknesses of electron states (eg) and carrier densities (hj). 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 2300 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.

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 concentration3032. In our MoS2 samples, the transition density was in the range 10121013 cm 2 due to the presence of large amounts of impurities. Moreover, the transition density in monolayer MoS2 (B1 1013 cm 2) was larger than that

observed in multilayer MoS2 (B6 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 s, at different temperatures, similar to previous reports36. The MIT occurs at nB6 1012 cm 2 for multilayer

MoS2 and nB1.1 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

sAn ncd 1 where A is a constant of proportionality and d 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, d is expected to be 4/3 and a cross-over point (Be2/h) above the percolation threshold density is suggested at nite temperatures30,31. Based on the percolation model, we t our

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0.41

0.245

2 K

60 K

C t(F cm2)

C t(F cm2)

180 K

250 K

200 K

C t(F cm2)

0.238

0.40

220 K

300 K

2 Trilayer

0.39

300 K

0.231

2 K

0.38

0.228

0.224

4

3

2 1

0 1 2 3

8 0 2 4 6

4 2

6

6

Vg (V)

Vg (V)

0.245 1 kHz

1 MHz

6

0.246

C(F cm)

0.238

D it(1012eV1cm2)

5

Monolayer

0.231

0.240

4

0.224

3

6

4 2

0 2 4 6

0.234

V (V)

100 Hz

1 kHz 100 kHz 1 MHz

1

0

8 0 2 4 6

4 2

6

8 0 2 4 6

4 2

Vg (V) Vg (V)

Figure 5 | The percolation transition and charge traps in monolayer and trilayer MoS2. (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.

0

75

150 2 K

200 K

125

60 2 K

300 K

80 K 110 K

250 K

100

150 K

45

(S)

(S)

75

(S)

230 K

30

50

25

15

0

2 4 6

0 0 8

6 10 12

2

4

Vg (V) Vg (V)

75

150

100

50

(S)

50

25

0

0 4 8

6 10

n (1012 cm2)

12

4 5 6

n (1012 cm2)

7 8 9

Figure 6 | Transport results showing the percolation transition in multilayer and monolayer MoS2. (a,b) The MITs are clearly shown by s 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 tting of experimental s (orange dots) of multilayer (c) and monolayer (d) MoS2 according to the percolation conductivity s A(n nc)d (green lines).

The arrows denote the positions of MITs.

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 dB1.7 and ncB3.2 1012 cm 2

in multilayer MoS2 and dB1.8 and ncB3.8 1012 cm 2 in

monolayer MoS2. The obtained percolation exponents are consistent with experimental values d 1.41.7 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 sufciently low. The percolation transition model can be applied only near the transition point at low temperatures. In the metallic region with

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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 tting curves at low carrier densities is due to enhanced hopping conductivity and quantum tunnelling at nite temperatures.

DiscussionOne alternative scenario besides the percolation transition model is the phase transition theory for a metallic phase (stabilized by ee interactions) and an insulating phase (disorder prevails over ee 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 inuence 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 hetero-structures built from 2D materials.

Methods

Sample preparation. Monolayer and multilayer MoS2 akes were exfoliated from MoS2 crystals (from 2D semiconductors) by the micromechanical cleavage technique. MoS2 and BN akes were placed on the surface of a glass slide coated with Polydimethylsiloxane/Methyl methacrylate as described for graphene-BN device fabrication36. Next, these thin akes 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 akes 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 B0.1 fF in a cryogenic system (2300 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.

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Acknowledgements

We are grateful for fruitful discussions with Professor Z.Q. Zhang from HKUST. Financial support from the Research Grants Council of Hong Kong (Project Numbers HKU9/CRF/13G, 604112, HKUST9/CRF/08, N_HKUST613/12 and HKUST-SRFI) and technical support of the Raith-HKUST Nanotechnology Laboratory for the electron-beam lithography facility at MCPF (Project Number SEG_HKUST08) are hereby acknowledged.

Author contributions

X.C. is the main contributor, who initiated and conducted most experiments including sample fabrication, data collection and analyses. N.W. is the principle investigator and coordinator of this project. X.C., N.W. and P.S. provided the physical interpretation and wrote the manuscript. The remaining authors provided technical assistance in sample preparation, data collection/analyses and experimental setup.

Additional information

Supplementary Information accompanies this paper at http://www.nature.com/naturecommunications

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Competing nancial interests: The authors declare no competing nancial interests.

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

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