Introduction

Two-dimensional materials are attracting considerable attention due to their unique electronic, optical and mechanical properties1. Following the success of graphene, a group of 2D materials known as the transition metal dichalcogenides (TMDs) has begun to garner attention. Among them, molybdenum disulphide (MoS2) is probably one of the most explored TMDs2,3. The sizeable (1.8 eV) direct band gap of monolayer MoS2 (ref. 4) makes it a potential material for not only digital electronics but also numerous photonic applications such as light emitter5, photodetectors6,7 and solar cells8. Excellent mechanical flexibility of MoS2 also makes it a compelling semiconducting material for flexible electronics9,10. Most existing studies and device demonstrations were performed on exfoliated MoS2 flakes11,12,13,14,15,16,17,18,19. In particular, field-effect-transistors based on monolayer MoS2 was found to exhibit high on/off ratios of ~108, steep subthreshold swing of ~70 mV dec−1 (refs 18, 20), with reported electron effective mobility ranging from 1 to 480 cm2 V−1 s−1 (refs 14, 17, 20, 21, 22, 23, 24, 25, 26) depending on the device structures, dielectric environment and processing21,27. These encouraging early reports coupled with continual engineering efforts28 present a compelling case for monolayer MoS2 as an alternative to traditional organic material or amorphous silicon for low-end applications with basic requirement of an effective mobility of >30 cm2 V−1 s−1 (ref. 20) for example, high resolution displays and photodetection6,7.

Recently, the advent of mass production technologies has enabled scalable growth of polycrystalline monolayer MoS2 by chemical vapour deposition (CVD)29,30,31,32, hence providing a commercially viable path towards MoS2 electronics at low cost33. However, the mobility of CVD MoS2 is typically much lower than its exfoliated counterpart, with reported values in the range of 5 to 22 cm2 V−1 s−1 (refs 34, 35, 36). The physical origin of the differences between CVD and exfoliated MoS2 is not clear at present; however, structural defects37 such as vacancies, dislocations, grain boundaries as well as charged interfacial states due to the dielectrics in contact14 can be responsible for the degradation in mobility. Although this problem has presented a major hurdle to the realization of wafer-scale MoS2 electronics and photonics, systematic studies of it are very few35. Very recently, the MoS2 community realized that there are technical difficulties to achieve accurate mobility extraction due to the role of contacts and fringing capacitive contributions38. Four-terminal Hall effect measurements are more accurate, but have only been demonstrated at very high carrier densities using an electrolyte gating scheme26 or at very low temperatures17. These Hall measurements were all performed on exfoliated MoS2, and will be more challenging to perform in CVD samples due to significantly larger amount of localized states, as will be discussed in this manuscript.

Here, we present a systematic methodology for characterizing electronic properties of scalable CVD MoS2, reporting also the presence of significant amounts of band tail states and their profound impact on the electrical device performance. The density distribution and dynamics of these trap states of CVD MoS2 are characterized through systematic capacitance and ac conductance measurements. Extraction of basic electronic transport quantities like the mobility edge and effective mobility is performed using four-probe current measurements. Complementary modelling allows us to draw insights into relevant device quantities such as the fractional occupation of band and trap states, band mobility and the anomalous subthreshold slope. Lastly, high-field electrical behaviour such as drain-induced barrier lowering and critical breakdown fields are examined.

Results

Characterization of monolayer CVD MoS2

Monolayer MoS2 was synthesized by CVD, using solid sulphur (S) and molybdenum oxide (MoO3) as the precursors and perylene-3,4,9,10-tetracarboxylic acid tetra-potassium salt (PTAS)39 as the seed for the CVD growth (see Methods for details). Hall-bar devices were fabricated on these CVD MoS2 monolayers. Figure 1a illustrated the schematic of the device. The top gate dielectrics are 2 nm aluminium deposited by e-beam evaporation and re-oxidized as a seed layer, followed by 30 nm HfO2 deposited by atomic layer deposition (ALD). The details of the device process are discussed in Methods. The atomic force microscopy (AFM) image and the step height profile at the boundary of a MoS2 triangular area are shown in Fig. 1b and the inset of Fig. 1b, respectively. The thickness of the MoS2 layer is measured to be about 0.8 nm, confirming its monolayer character. The Raman spectrum of the CVD MoS2 is shown in Supplementary Fig. 1. The E2g and A1g modes are at around 383 and 403 cm−1, respectively. Comparing the peak position with the spectrum obtained from the exfoliated monolayer MoS2 (ref. 40), we further verify that the MoS2 film is monolayer.

Figure 1: Molybdenum disulphide physical properties and device structure.
figure 1

(a) Schematic of MOSFET with monolayer chemical vapour deposition (CVD) grown molybdenum disulphide (MoS2). (b) AFM image of CVD grown MoS2 on SiO2/Si substrate. The scale bar in the AFM image is 10 μm. The inset shows the step height profile of MoS2 in the AFM image.

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Density and dynamics of band tail states

At present, the reported values of the electron mobility in CVD-grown MoS2 devices34,35,36 are at least two orders of magnitude smaller than the intrinsic limit41, suggesting a high degree of disorder and scattering. An inhomogeneous potential distribution in a semiconductor leads to the smearing of the band edge and the formation of a tail of band gap state42. For example, this inhomogeneity could be the result of a random distribution of trapped charges in sulphur vacancies in MoS2 itself43 or at MoS2–dielectric (SiO2 or high-k dielectric) interfaces14. Structural defects37, for example, simple vacancies43, dislocations and grain boundaries, would also lead to localized gap states.

The electronic states in the band tail can be characterized using standard capacitance and ac conductance measurement commonly used in the study of semiconductor devices44. Here, these localized states respond like traps with different time constants τit and are electrically equivalent to an additional capacitance and resistance in parallel to the semiconductor capacitance. The gate-to-channel capacitance and resistance were measured on the Hall-bars, with high terminal on the top gate and low terminal on the source, drain and all four voltage probing leads simultaneously, as shown in Supplementary Fig. 2. The measured capacitance as a function of frequency is shown in Fig. 2a. The observed double hump feature indicates at least two types of traps with different time constants at a given gate voltage. Herein, we denote these traps by the labels ‘M’ and ‘B’, for reasons that will be made apparent below. The equivalent circuit model of the device is shown in Fig. 2b with total impedance given by:

Figure 2: Characterization of the density and dynamics of band tail states.
figure 2

(a) Capacitance as a function of frequency measured at various gate voltages. The device width is 4 μm and length is 44 μm. The symbols are the experimental results and the lines are fittings using the device model shown in (b). (b) The equivalent circuit model of the device, simplified parallel model and the measurement model in series mode. (c) Density and time constant of trap states as a function of gate voltages. The symbols are experimental results extracted from the capacitance Cms and ac conductance Gp. The lines are models, see text. (d) Extracted ac conductance over angular frequency Gp/ω as a function of frequency f at various gate voltages. (e) Parameterized model, Dn(E), describing the electronic density-of-states of both the extended and localized states. The valence density-of-state is also included in the illustration using the mirror image of conduction density-of-state. The inset illustrates the band diagram of MoS2 MOSFET. (f) Multi-frequency capacitance of MoS2 Hall-bar as a function of gate voltage. The symbols are experimental results and the lines are the modelling results.

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where ω is the angular frequency, Cs is the quantum capacitance of the MoS2, Cj is the parasitic capacitance, Cox is the oxide capacitance, rs is the series resistance, YitM and YitB are the traps’ admittance. Here YitB=[τitB/CitB+1/(iωCitB)]−1, where CitB and τitB are the capacitance and time constant of trap B. The trap capacitance CitB is related to the trap density DitB via the following: CitB=eDitB, where e is the elementary electric charge. Similar expressions apply to trap M. The measured capacitance in series mode Cms is related to the imaginary part of the total impedance Z by the following formula:

The lines in Fig. 2a are the fits using this model. We can see that the model provides an excellent fit to the experimental data. From the fitting, we can extract the density of traps and their time constant as a function of gate voltage, shown in Fig. 2c. Here, we observe that traps ‘M’ and ‘B’ are populated predominately within the ‘mid-gap’ and ‘band edge’ regions, respectively.

Alternatively, the density and time constant of the traps can be extracted from the ac conductance Gp (ref. 44). The ac conductance is obtained from the measured capacitance and resistance. The measured resistances as a function of gate voltage at various frequencies are shown in Supplementary Fig. 3. The extraction method of ac conductance are described in more detail in the Supplementary Note 1. The extracted ac conductance over angular frequency Gp/ω is plotted as function of the driving frequencies f in Fig. 2d. Since the density-of-states of type B traps is several orders of magnitude larger than that of type M in this gate bias range, we expect the former to dominate the ac conductance. The relation between Gp(ω) and the trap density DitB is given as the following (ref. 44):

from which one can deduce the DitB and the respective time constant τitB from the following simple relations44:

Here, (Gp/ω)peak is the maximum Gp(ω)/ω value and f0 is the frequency at which this maximum is obtained. Repeating the above procedure for different top gate voltages VTG allows us to extract DitB(VTG) and τitB(VTG) as shown in Fig. 2c. From Fig. 2c, we see that the density-of-states and time constant of B type traps extracted based on the capacitance and ac conductance are in good agreement.

Below, we present parameterized models for the electronic density-of-states and their time constants fitted to the experiments. We describe the electronic density-of-states of the measured distributed trap states at the band edge (that is, type B) and the extended states with two piece-wise functions as follows:

and illustrate them in Fig. 2c,e. Here, D0 is the 2D density-of-states for perfect crystalline MoS2, taken to be 3.3 × 1014 eV−1cm−2, consistent with an effective mass of 0.4m0 at the conduction band minimum at the K valley for monolayer MoS2 (ref. 45). Here we ignored contribution from the satellite valley along ΓK with energy 200 meV higher than the conduction band minimum41,46 because the carrier population is insignificant at these energies at our biasing range. Furthermore, our MoS2 devices are typically n-type doped. ϕ is the characteristic energy width of the band tail. In the limit of ϕ=0, Dn(E) becomes a step function as required for perfect 2D crystals with the conduction band edge situated at ED. ϕ′ is chosen so that the two piece-wise functions have continuous gradients at ED. Solving the electrostatics problem, to be described below, a best-fit to the experimentally extracted density-of-states yields the parameter set: α=0.33 and ϕ=100 meV. The comparison between the model Dn(VTG) and the measured band tail states DitB(VTG) is shown in Fig. 2c, and the mid-gap states DitM(VTG) is described by an error function instead. The traps’ response time is fitted to an exponential model,

and the comparison with experimental data is shown in Fig. 2c.

With the parameterized density-of-states model, we can calculate the ac capacitance and compare against experiments. The Poisson equation describing the electrostatics of the problem can be expressed as:

where ttop is the ‘effective-oxide-thickness’ for the top gate dielectric, εox is the dielectric constant of silicon oxide, Q0 is a constant that includes contributions from the fixed charges and doping in as-prepared MoS2 and so on, and Qn is the electronic charges in the smeared out conduction band and can be computed from Qn=e(E)fn(E,EF)dE where fn is the Fermi Dirac function. In solving for the self-consistent electrostatics described by using equation 8, the Fermi energy EF is taken to be the reference that is, EF=0. Once the electrostatics is determined, the admittance associated with each of the traps can then be computed via the following:

and the total capacitance can be computed employing the equivalent circuit model in Fig. 2b and using equations (1) and (2). Reasonable agreement with the measured ac capacitance is obtained as shown in Fig. 2f.

To summarize, the electronic density-of-states model described above is well-calibrated to the experimentally measured density and dynamics of the band tail states. It follows an exponentially decaying behaviour, with a significantly large energy width of ϕ=100 meV, suggesting a high degree of potential disorder and scattering. This model will be employed in the subsequent discussion to obtain other quantities of interest, such as the band mobility.

Mobility edge

The concept of a ‘mobility edge’ has greatly facilitated our understanding of electronic transport in a disordered system47. The mobility edge is a boundary located in the band tail, in which states above it are extended states with band transport, while those below it are localized states that conduct via thermally assisted mechanisms such as Mott variable range hopping (VRH)48,49,50 or an Arrhenius-type activated behaviour51. Four-point variable temperature measurements were performed on our devices from 4.4 to 400 K as shown in Fig. 3a. We found that neither the VRH nor the Arrhenius model can individually describe the data satisfactorily over the whole temperature range. It is very likely that a combination of both transport mechanisms might be operating here. For example, the VRH usually dominates for localized states deep in the band tail, while the Arrhenius-type activated behaviour is more likely for shallow localized states.

Figure 3: Temperature dependence of conductance and activation energy.
figure 3

(a) Four-point conductance as a function of gate voltage measured at various temperatures from 4.4 to 400 K on a MoS2 Hall-bar. (b) Conductance as a function of reverse of temperature 1/T at various gate voltages. The inset shows the activation energy at various gate voltages fitted to the Arrhenius-activated energy model. The symbols are experimental results extracted from the conductance; the solid line gives the modeling results. (c) The calculated band carriers as a function of gate voltage at various temperatures.

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The conductance versus the inverse of temperature (1/T) is shown in Fig. 3b, showing the exponential decrease with 1/T over the intermediate temperature range, where the conductance G can be described by:

where Ea is the activation energy, kB is the Boltzmann constant and G0 is a fitting parameter. This allows us to extract the activation energy Ea=EM−EF. The measured Ea (versus VTG) is compared with the model (see Fig. 3c inset), which allows us to determine the location of the mobility edge in the energy band picture. We found that in our devices EM is ≈0.01 eV above ED, as illustrated in Fig. 2e. We also noticed a departure from activated behaviour at lower temperature or bias, indicating the possible onset of an additional transport mechanism such as VRH. The extracted activation energy in the inset of Fig. 3b suggests that, in most of our gate biases, the Fermi level does not exceed the mobility edge energy. However, at large VTG that is, VTG>2V , the Fermi energy is within tens of meV from the mobility edge. Hence, one can expect an appreciable fraction of extended states occupation due to thermal smearing. The calculated band carrier densities as a function of gate voltage at various temperatures are shown in Fig. 3c.

Transport coefficients

The ‘effective mobility’, or sometimes referred to as the ‘drift mobility’, is a commonly used transport coefficient in semiconductors52. It is defined as the ratio of the measured conductivity to the total charge density that is, μeff=σ/Qtotal. The total charge density Qtotal is typically estimated from Cox(Vg−VT), where Cox is the oxide capacitance, Vg is the gate voltage and VT is the threshold voltage. We extract Cox from the measured capacitance at strong accumulation. Figure 4a shows the effective mobility as a function of gate voltage at different temperatures. The effective mobility is <10 cm2 V−1 s−1 over the range of temperature and applied bias in our experiments. Contact resistance is eliminated in our measurement that employs a four-probe scheme. The measured effective mobility is significantly lower than the phonon-limited intrinsic mobility in monolayer MoS2, predicted to be over 400 cm2 V−1 s−1 (ref. 41), and the highest measured mobility of ~200 cm2 V−1 s−1 in exfoliated MoS2 devices20. However, it is consistent with results on similar CVD-grown MoS2 devices that report mobilities in the range of 5 to 25 cm2 V−1 s−1 (ref. 35). The significantly lower mobility for CVD-grown MoS2 is, to a large part, due to the presence of traps.

Figure 4: Effective mobility and band mobility.
figure 4

(a) Effective mobility as a function of gate voltage measured at various temperatures in MoS2 Hall-bar. (b) Effective mobility and the corresponding band mobility as a function of temperature at VTG=4V. The mobility limited by MoS2 phonons scattering based on theoretical calculations41 are also plotted for comparison.

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The total charge density includes both the free and trapped charges: Qtotal=e(nloc+nband) where nloc and nband refer to the density of occupied states below and above the mobility edge, respectively. Another commonly used transport coefficient in a disordered system is the ‘band mobility’53,54. It is defined as the ratio of the measured conductivity to the density of occupied states above the mobility edge (that is, extended states):

In general, the density of the extended states is difficult to measure, since the large amount of localized states would result in large noise-to-signal ratio the in the Hall measurement. Up to now, the Hall effect has only been observed in exfoliated MoS2 with very high carrier density induced by an electrolyte gating scheme26 or at very low temperatures17.

Previously, we obtained Dn(E) in conjunction with EM in the energy band picture. Solving the electrostatics in conjunction with the above information would allow us to estimate the fraction of localized and extended states. Figure 3c plots the computed nband(VTG) at different temperatures. The result indicates that nband only accounts for <25% of ntotal. Only at high temperature or bias, nband can exceed 25% that is, T>300 K and VTG>2V. The comparison between the extracted band mobility and measured effective mobility is shown in Fig. 4b. The band mobility is several times higher than the effective mobility, but still significantly lower than the phonon-limited mobility as predicted in ref. 41. This mobility degradation may involve many sources of scattering. For example, structural defects in CVD MoS2 layer and grain boundaries can induce short-range scattering. Surface polar phonon either in the high-k dielectrics (HfO2 and AlOx) or in the SiO2 substrate underneath can also play a role. However, the significant trap population measured here suggests that Coulomb scattering due to trapped charges is the likely limiting factor for the electron mobility. Because of the parabolic band structure of MoS2, the energy averaged scattering time due to Coulomb scattering should increase proportionally to temperature55 μkBT. This is also consistent with the observed trend in Fig. 4b for temperature below 300 K. Above this temperature phonon scattering takes over.

Subthreshold swing

In an ideal semiconductor, the subthreshold swing is given by52: S=kBTIn(10)(1+CD/Cox), where CD is the depletion capacitance. The subthreshold swing increases linearly with temperature, since the carrier density increases exponentially with temperature nexp. In our device, we observed that the subthreshold swing is ≈200 mV dec−1 and nearly independent of temperature, as shown in Fig. 3a. Similar observations were made on MoS2 flakes11. This departure from the ideal behaviour can be understood by recalling that the band tail is distributed in energy, that is, exp, with an energy width that is significantly larger than the thermal energy that is, φ>>kBT. Indeed, the calculated subthreshold behaviour confirms that temperature does not have a significant effect, as shown in Fig. 3c. Hence, the observed temperature-independent subthreshold swing reinforced our earlier conclusions on the existence of band tail states.

Drain-induced barrier lowering

The electrostatic integrity of an electronic device upon downscaling is often quantified by evaluating the amount of drain-induced barrier lowering (DIBL)56. This measures the reduction in threshold voltage due to the applied drain bias. A common approach used to suppress DIBL involves reducing the channel thickness, since the minimum channel length needed to preserve the long channel behaviour is typically ~4–5 times the electrostatic scaling length λ= for a planar device structure57,58, where εs and εox are the dielectric constants of the semiconductor and the gate oxide, and ts and tox are the thicknesses of the semiconductor and gate oxide, respectively. In this regard, thinner silicon has been pursued by using SOI (silicon-on-insulator) and ETSOI (extremely thin silicon-on-insulator). However, the mobility degrades markedly as the thickness is scaled down due to surface roughness59,60. Atomically thin 2D semiconducting material such as MoS2 and WSe2 are promising candidates in this regard. The typical DC performances of MoS2 MOSFETs with various channel lengths are shown in Supplementary Fig. 4. Figure 5a shows the DIBL of CVD MoS2 MOSFET with variable channel lengths from 4 μm to 32 nm. Despite the thick dielectric used in our MOSFETs, (~34 nm HfO2/ AlOx stack for the long channel devices, ~60 nm HfO2/ AlOx for the short channel devices, limited by the bulging of gate dielectrics on the source/drain side wall), a clear upturn of DIBL is only observed at a channel length of 32 nm. Extrapolating to a device with a 3 nm HfO2 gate insulator would predict a limiting channel length feature of ~7 nm. Theoretically, for a MOSFET with monolayer MoS2 (channel thickness: ~0.8 nm, dielectric constant: 6.8~7.1 ε0, where ε0 is the vacuum permittivity61) and 1 nm equivalent oxide thickness (EOT), the electrostatic scaling length λ is only about 1.2 nm. These considerations suggest that MoS2 could be a very promising material for scaled, high-density electronics.

Figure 5: Device properties at high electrical fields.
figure 5

(a) Drain-induced barrier lowering (DIBL) of MOSFET with CVD MoS2 at various channel lengths. The inset shows the SEM image of the 32 and 80 nm channel length devices. (b) Critical electric field of CVD MoS2 and graphene. The upper inset shows the measurement configuration. The lower inset shows the lateral breakdown voltage as a function of channel length for MOSFET with CVD MoS2.

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Breakdown electric fields

The large band gap of MoS2 implies the possibility of device operation at higher voltages or electric fields. Figure 5b shows the critical breakdown fields of graphene and CVD MoS2 MOSFETs devices. The measurement setup is shown on the upper-left inset of Fig. 5b. The channel-length dependence of breakdown voltage of MoS2 MOSFETs is shown in the lower-right inset of Fig. 5b. The critical field can be extracted from the slope of the breakdown voltage versus channel length. Here we extracted the breakdown field from MoS2 transistors with channel lengths of 80 and 285 nm. (More details about the breakdown test results of MoS2 transistors and graphene transistors are shown in the Supplementary Figs 5 and 6, and Supplementary Notes 2 and 3.) The measured breakdown field of CVD MoS2 is about five times larger than that of graphene and significantly larger than that of SOI with 100 nm silicon thickness62. In this regard, MoS2 can also be a very promising platform for power devices.

Discussion

We have systematically studied the electronic transport properties of CVD MoS2 devices. We report the observation of a significant amount of electronic trap states through capacitance and ac conductance measurements and their impact on the low-field electronic properties of MoS2 devices. In particular, the measured effective mobility significantly underestimates the band mobility. An anomalous subthreshold behaviour, with distinctive temperature insensitivity, is also accounted for by the presence of these band tail states. We also studied the high-field electronic properties of MoS2 devices and demonstrated the possibility to aggressively scale them down and their high breakdown electric fields. These attractive device attributes present a compelling case for wafer-scale monolayer MoS2 as alternative to organic and other thin film materials for flexible electronics and photonics, including high resolution displays, photo-detection, logic electronics, power devices with solar energy collecting and so on. From the fundamental material stand point, understanding of the microscopic origin of these band tail states is critical for further improvement of the material’s electronic properties.

Methods

Fabrication

Large-scale monolayer MoS2 was synthesized at 650 C by APCVD using perylene-3,4,9,10-tetracarboxylic acid tetra-potassium salt (PTAS) as the seed on SiO2/Si substrate39. Sulphur powder and molybdenum oxide (MoO3) were used as the precursors for the synthesis. The SiO2 thickness was 300 nm. In the Hall-bar and transistor devices, the source/drain contact metal stack consisted of Ti/Au/Ti (5/15/5 nm). The MoS2 channel was patterned using electron beam lithography and oxygen plasma etching. The top gate dielectric comprised an AlOx/HfO2 stack. The AlOx was formed by electron beam evaporation of 2 nm of aluminum metal followed by its natural oxidization in air for a few hours. The 30 nm thick HfO2 layer was formed using atomic layer deposition (ALD) at 170 degrees. The top gate electrode was Ti/Au (5/40 nm).

Characterization

The capacitances were measured using Agilent B1500 Semiconductor Device Analyzer produced by Agilent technology. The temperature dependence of conductance was measured using cryogenic probestation produced in Lake Shore Cryotronics, Inc. The Raman spectrum was taken using Labram Aramis produced by Horiba Jobin Yvon. Scanning electron microscopy was measured using Leo 1560 produced by Carl Zeiss.

Additional information

How to cite this article: Zhu, W. et al. Electronic transport and device prospects of monolayer molybdenum disulphide grown by chemical vapour deposition. Nat. Commun. 5:3087 doi: 10.1038/ncomms4087 (2014).