Two- and four-probe field-effect and Hall mobilities in transition metal dichalcogenide field-effect transistors

Abstract

We have fabricated WS₂ and MoS₂ multilayer field-effect transistors (FETs) to compare two-probe and four-probe field-effect and Hall mobility measurements. Hall mobility provides accurate information and shows the largest value, whereas field-effect mobility shows small values. The influence of contact resistance is not negligible in the two-probe field-effect mobility measurement. The current–voltage characteristics of Cr/Au (8/80 nm) contacts exhibit ohmic behavior in the WS₂ multilayer FET and non-linear behavior in the MoS₂ multilayer FET. Regardless of the electrical characteristics of the contacts, the field-effect mobility is much lower than the Hall mobility. Electrical contacts in the WS₂ or MoS₂-based FETs produce a non-discountable influence on the field-effect mobility estimation in the two-probe configuration. When the carrier concentration is not linearly dependent on gate voltage, the equivalence of field-effect and Hall mobilities does not hold. In this case, field-effect mobility provides only a rough estimate of Hall mobility.

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Introduction

Atomically thin materials with 2D structures are advantageous for basic electronic transport or optical characteristics. Moreover, they show interesting characteristics for device miniaturization, comparable with atomic thickness. Transition metal dichalcogenides (WS₂, MoS₂, etc.) have crystallographic structures with weak inter-plane van der Waal's coupling, strong in-plane covalent bonding, small inversion symmetry, and high spin–orbit coupling.¹ Compounds such as MoS₂ and WS₂ have indirect bandgaps in the range of 1–2 eV in the multilayer structure, but show direct bandgaps in single atomic layers, with the energy gap positioned at K and K′ symmetry points on the surface of the Brillouin zone. Both the maxima of valence bands and minima of conduction bands are formed because of the major contribution by Mo d-orbitals.² The highest valence bands positioned at K (K′) points split because of high spin–orbit interaction.^3–6

Field-effect transistors (FETs) formed by exfoliated transition metal dichalcogenides (TMDCs) have shown promise for low power consumption switching devices and for prospective elements of light emitting diode displays, especially when these FETs are in multilayer form.⁷ Successive studies^8,9 have been conducted on MoS₂ with thickness of about tens of atomic layers; the MoS₂ was formed through mechanical exfoliation, with SiO₂ as gate dielectrics, and exhibited rather low mobilities (10–50 cm² V⁻¹ s⁻¹). These results suggest that substrate and gate dielectrics have a non-negligible effect on the mobility of MoS₂.¹⁰ The extremely large value of mobility for graphene is nearly 140 000 cm² V⁻¹ s⁻¹;¹¹ this large value has forced researchers to find suitable ways to increase charge carrier mobilities in FETs consisting of single or multiple atomic-layered TMDCs. For example, multilayer MoS₂ transistors used Sc contacts with Al₂O₃ at 15 nm as the dielectric layer for the top-gate configuration at room temperature; these transistors were found to have mobilities as high as 700 cm² V⁻¹ s⁻¹.¹²

For TMDCs, the number of layers also plays an important role in their electrical properties, because the nature of TMDCs is highly dependent on the number of layers. As the number of layers are reduced from multilayer to monolayer, the bandgap changes from an indirect to direct one, along with an increase in bandgap and effective mass. The increase in effective mass also contributes to the reduction of mobility upon lowering the number of layers. Because compressive strain increases as the number of layers is reduced, the strain effect is another factor affecting the mobilities of thin TMDCs materials.¹³

Recently, dual-gated single-layer MoS₂ having a top-gate with HfO₂ acting as the dielectric layer, showed high field-effect mobility at about 380 cm² V⁻¹ s⁻¹.¹⁴ However, this overestimated mobility value was because of capacitive coupling associated with both top and back gates.¹⁵ The criticism of the overestimation of mobilities has been supported by many reports that show smaller mobilities when gate capacitance is measured from Hall effect investigation.^16,17 Another recent report suggested that carrier mobilities are limited by phonons in the dielectric layer, such as HfO₂. Thus, an interfacial layer should exist to absorb much of the vibrational energy.¹⁸ Investigations on single and double atomic layered MoS₂ showed Hall mobilities that increased at higher gate voltages and showed saturation between ∼250 and ∼375 cm² V⁻¹ s⁻¹ at low temperature.¹⁹ For multilayer MoS₂, the Hall mobility showed an increase from ∼175 cm² V⁻¹ s⁻¹ at a temperature of 60 K, to 311 cm² V⁻¹ s⁻¹ at 1 K, with back gate voltage of 100 V.²⁰ Although mobility has been an important factor to characterize the functionality of FET, comparisons between field-effect and Hall mobilities are scant.²¹ In particular, for field-effect mobility, the electrical contacts involved in the two-probe measurement configuration need to be examined in detail.

In the present study, we fabricated WS₂ and MoS₂ multilayer FETs to compare mobility measurement methods and examine the influence of contact resistance on mobility measurement. At room temperature, the WS₂ and MoS₂ multilayer FETs showed n-doped characteristics with on/off ratios of ∼10⁶ and ∼10⁴, respectively. Electrical properties were examined using the two-probe configuration and then compared with those by the four-probe configuration. Aside from the use of WS₂ and MoS₂ crystals as channel materials, the Cr/Au (8/80 nm) contact to channel materials is another important factor to improve FET functionality. A Schottky barrier exists between the metal contact and semiconducting channel material. Regardless of the detailed electrical characteristics of the Cr/Au (8/80 nm) contacts, the field-effect mobility obtained by the two-probe configuration was much lower than either the field-effect mobility by four-probe configuration, or the Hall mobility. The comparative measurements of the two-probe and four-probe field-effect mobilities and Hall mobility are presented to investigate the effect of metal contacts.

Experimental section

Sample preparation

Natural WS₂ and MoS₂ crystals were mechanically exfoliated on 300 nm-thick SiO₂ layers on degenerately p-doped Si substrates by using Scotch tape exfoliation. After device fabrication, all the devices in our experiment were annealed in a furnace tube at 300 °C in a flow of Ar/H₂ (97.5/2.5%) gas for 2 hours. Structural investigation, thickness measurement, and surface studies of both these materials were performed using an optical microscope, atomic force microscopy (AFM), and Raman spectroscopy, respectively. Fig. S1† shows detailed surface profiles for both WS₂ and MoS₂, which indicate multilayers. Raman spectroscopy was also performed to further verify the nature of the materials. Fig. S2† shows the detailed Raman spectra of WS₂ and MoS₂ multilayers. Laser wavelength for Raman spectroscopy was 514 nm, and power was maintained at less than 1 mW to avoid structural deformation from laser-induced heating. The size of the laser spot for Raman spectroscopy was 0.7 μm.

Device fabrication and characterization

After selecting the specified flake for investigation, photolithography was performed to obtain a large electrode pattern. Subsequently, deposition of Cr/Au (6/30 nm) was carried out using thermal evaporation. Acetone was used for the lift-off process. Electron beam lithography was applied to fabricate small-sized sources. Contacts were drained through the evaporation of Cr/Au (8/80 nm) film, using a thermal evaporation chamber with a vacuum maintained at 2 × 10⁻⁶ Torr. The electrical measurements were carried out at room temperature in a vacuum using a Keithley 2400 source-meter and Keithley 6485 picoammeter. A magnetic field of 0.6 T was used for the Hall measurement.

Results and discussion

I–V characteristics of FETs

Fig. 1a and b show WS₂ and MoS₂ optical microscopy images; both FETs (WS₂, MoS₂) displayed six contacts for voltage probes and two contacts for current injection. Only two contacts of source and drain were used for the two-probe field-effect mobility measurement, and two more contacts of voltage probes were used for the four-probe field-effect mobility measurement. Fig. 1c shows a schematic of the measurement configuration for the four-probe field-effect mobility. A bias voltage (V_app) was applied across the source and drain. V_ds was measured between two voltage probes, and the corresponding current (I_ds) was measured at the end of the drain contact. The length of the device in the four-probe field-effect mobility measurement was the distance (L) between two voltage probes, as shown in Fig. 1c. The voltage (V_ds) measured in the four-probe field-effect mobility measurement did not include the contact voltage between the metal electrode and WS₂ (or MoS₂) channel material.

Fig. 1 Optical microscopy images of (a) multilayer (ML)-WS₂ field-effect transistor and (b) ML-MoS₂ field-effect transistor. (c) Schematic of the measurement configuration for four-probe field-effect mobility.

Two-probe current–voltage (I_ds–V_ds) characteristics for WS₂ and MoS₂ multilayer FETs were measured to examine the bias-dependent transport characteristics at different magnitudes of V_bg. Fig. 2a and b represent the I_ds–V_ds curves of WS₂ and MoS₂ multilayer FETs at room temperature. The I_ds–V_ds curve of the MoS₂ FET was nonlinear, which indicated the existence of a Schottky barrier. In contrast, the I_ds–V_ds curve of the WS₂ FET had almost linear ohmic characteristics; these results suggested that the Schottky barrier height of the WS₂ device was much lower than that of the MoS₂ FET.¹²

Fig. 2 I–V characteristics of multilayer (a) WS₂ and (b) MoS₂ FETs at various back gate voltages at room temperature.

The contact resistance for both WS₂ and MoS₂ devices is known to decrease with the application of high electrical biasing of the back gate voltage.²² According to ref. 2, the resistance of the contacts depends on V_bg because of two reasons: (i) the Schottky barrier at the metal/semiconductor boundary tuned by back gate voltage, and (ii) the electrical doping of the semiconductor. We examined the contact resistances of the WS₂ and MoS₂ FETs by using the transmission line method. The specific contact resistance (ρ_c) was estimated to be 3 kΩ μm at V_bg = 60 V for WS₂ and 13.5 kΩ μm for MoS₂, as shown in Fig. S3.† The contact resistance, which is a few kΩ in our FETs, was much lower than the resistances of WS₂ or MoS₂ multilayer films.

Field-effect mobility

Fig. 3 shows two- and four-probe transfer characteristics and the on/off ratio as a function of back gate voltage at the fixed drain–source voltage (V_ds) of 1 V. The voltage of V_ds in the two-probe configuration contains the extra voltage drop across the Schottky barrier between the metal electrode and TMDC film, whereas the voltage of V_ds in the four-probe configuration contains only the voltage drop along the TMDC channel. The on/off ratio is measured by taking the drain current (I_ds) as a function of V_bg at the fixed value of drain–source voltage V_ds of 1 V for WS₂ and MoS₂ multilayer FETs. The on/off ratio using the two-probe configuration is 9 × 10⁶ for WS₂ and 3 × 10⁴ for MoS₂, as shown in Fig. 3a and c, respectively. The on/off ratio using the four-probe configuration is 7 × 10⁵ for WS₂ and 3 × 10⁴ for the MoS₂ multilayer FETs, as shown in Fig. 3b and d, respectively. The difference in the on/off ratio of I_ds in different probe configurations is caused by the contact resistance of the devices. However, the on/off ratios do not significantly depend on the measurement configuration. We note that our devices can be used in digital logic circuits because they have on/off ratios higher than the desired criteria of ∼1 × 10⁴, which is required for devices to be used in logic applications.²³

Fig. 3 (a) Two-probe transfer characteristics of the WS₂ field-effect transistor with μ_FE = 98 cm² V⁻¹ s⁻¹. (b) Four-probe transfer characteristics of the WS₂ field-effect transistor with μ_FE = 394 cm² V⁻¹ s⁻¹. (c) Two-probe transfer characteristics of the MoS₂ field-effect transistor with μ_FE = 2.4 cm² V⁻¹ s⁻¹. (d) Four-probe transfer characteristics of the MoS₂ field-effect transistor with μ_FE = 10 cm² V⁻¹ s⁻¹.

The field-effect mobility was estimated by the relation μ_FE = (L/W)(1/C_bgV_ds)(dI_ds/dV_bg), where L and W are the length and width of the channel, respectively, and C_bg is the gate capacitance, equal to 220 aF μm⁻² for our SiO₂ substrate. The maximum values of two- and four-probe field-effect mobilities were 98 and 394 cm² V⁻¹ s⁻¹, respectively, for WS₂ FET, and the maximum values for the MoS₂ FET were 2.4 and 10 cm² V⁻¹ s⁻¹, respectively. These results are presented in Fig. 4b and d. Regardless of the devices, the four-probe field-effect mobilities were almost four times higher than the two-probe field-effect mobilities.

Fig. 4 (a) Carrier concentration obtained from Hall measurement of the WS₂ field-effect transistor. (b) Two- and four-probe field-effect and Hall mobilities of the WS₂ field-effect transistor as a function of back gate voltage. (c) Carrier concentration obtained from Hall measurement of the MoS₂ field-effect transistor. (d) Two- and four-probe field-effect and Hall mobilities of the MoS₂ field-effect transistor as a function of back gate voltage.

A number of WS₂ and MoS₂ FETs were made to check the reproducibility of the observation that two-probe μ_FE is always less than four-probe μ_FE. Fig. 5a and b show a comparison between the two- and four-probe μ_FE for other WS₂ and MoS₂ FETs. The small value of the two-probe μ_FE is related to the existence of Schottky barriers originating from the difference between the Fermi level of TMDCs and the work function of the metal contact. Regardless of the contact metals, the contact resistance will affect the mobility measurement of the device in two-probe configuration. In order to check this hypothesis, we performed a control experiment using WS₂ FET with Al/Au (60 nm/20 nm) contacts for two- and four-probe μ_FE measurements. Fig. 6 shows two- and four-probe μ_FE of WS₂ FET with Al/Au contacts. Two-probe μ_FE is much lower than four-probe μ_FE, which is consistent with our hypothesis made above.

Fig. 5 Two- and four-probe field-effect mobilities of (a) MoS₂ FET and (b) WS₂ FET with Cr/Au (8/80 nm) contacts as a function of back gate voltage.

Fig. 6 Two- and four-probe field-effect mobilities of WS₂ FET with Al/Au (60/20 nm) contacts as a function of back gate voltage.

Hall mobility

The field-effect mobilities were compared with the mobility obtained by Hall measurement. Hall measurement was performed to find the charge carrier density (n) and Hall mobility (μ_H) of WS₂ and MoS₂ multilayer devices. A magnetic field perpendicular to the film surface was applied; transverse or Hall resistance R_xy was measured to obtain the Hall coefficient R_H = R_xy/B, where B is the magnetic field. For all the devices, R_H was determined by a linear fitting of the slope of transverse resistance R_xy versus B, in the range of 0–0.6 T. The carrier density is measured using n = 1/(eR_H), where e is the charge on the electron. The carrier density is 9.5–12.5 ×10¹² cm⁻² for WS₂ and 9.2–12 × 10¹¹ cm⁻² for MoS₂, as shown in Fig. 4a and c, respectively. By taking n and conductivity measurements (σ = L/WR_xx) together, we can find the Hall mobility (μ_H = σ/ne) as a function of V_bg for both WS₂ and MoS₂ multilayer devices. Hall mobilities, together with two- and four-probe field-effect mobilities, are shown in Fig. 4b and d. μ_H is higher than the two-probe or four-probe field-effect mobilities. The maximum values of Hall mobilities (575 and 37 cm² V⁻¹ s⁻¹ for WS₂ and MoS₂, respectively) are comparable with previous reports, shown in Tables 1 and 2. Given that the field-effect mobility is normally taken by two-probe configuration, there is the tendency to underestimate the mobility of the channels.

Table 1 Literature review of mobility measurements of WS₂ films^a

WS2	Thickness of film	2-Probe mobility (cm^2 V^−1 s^−1)	4-Probe mobility (cm^2 V^−1 s^−1)	Hall mobility (cm^2 V^−1 s^−1)
a All the measurements were done at room temperature.
This work	Multilayer (10 nm)	98	394	575
Ref. 28	Multilayer (20–60 nm)			20–90
Ref. 29	Mono- and bi-layer (0.65–1.3 nm)	<50
Ref. 30	Monolayer to 4 layer (0.65–2.6 nm)	0.23–80
Ref. 31	Multilayer (3.55 nm)	90
Ref. 32	Monolayer (1 nm)	10
Ref. 33	Monolayer (0.8 nm)	80

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Table 2 Literature review of mobility measurements of MoS₂ films^a

MoS2	Thickness of film	2-Probe mobility (cm^2 V^−1 s^−1)	4-Probe mobility (cm^2 V^−1 s^−1)	Hall mobility (cm^2 V^−1 s^−1)
a All the measurements were done at room temperature.
This work	Multilayer (14 nm)	2.4	10	37
Ref. 20	Multilayer (5–6 nm)			24
Ref. 22	Multilayer (20 layers)	91	306.5
Ref. 10	Multilayer (15–90 nm)		30–60
Ref. 8	Multilayer (5.7–77 nm)	1.6–42
Ref. 9	Multilayer (35 nm)		40
Ref. 34	Bilayer (1.3 nm)	5–15
Ref. 35	Multilayer (4.5 nm)	25.7
Ref. 36	Bilayer (1.3 nm)	17
Ref. 37	Monolayer (0.9 nm)	6

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Carrier mobilities are limited because of intrinsic characteristics²⁴ and substrate phonons. The presence of charge traps and non-regularity at the interface between TMDC (WS₂ and MoS₂) crystals and SiO₂ limits carrier mobility. Recently, low contact resistance and enhancement of field-effect mobility were achieved by applying a thin layer of polymer electrolyte consisting of poly(ethylene oxide) (PEO) and lithium perchlorate (LiClO₄) on top of the device, which was due to the neutralization of the uncorrelated charged impurities on the MoS₂ channel or substrate by the counter ions in the PE.²⁵ Therefore, it is important to consider the substrate effect on the device performance. Aside from WS₂ and MoS₂ crystals as channel materials, the electrical contact to channel materials is another important factor that affects FET functionality. A Schottky barrier exists between metal contact and semiconducting channel material; this barrier causes two-probe field-effect mobility to be far lower than Hall mobility. A number of strategies have been implemented to overcome this Schottky barrier problem. Different metal contacts, such as Au,²⁶ Mo,²⁷ and Ni,¹² have been used to decrease the Schottky barrier. Some reports have shown reasonable results, but contact resistance is still a major hindrance for devices used in a wide range of FETs.

Four-probe field-effect mobility is obtained from the transfer characteristics; the gate capacitance (C_bg) plays an important role in determining the magnitude of mobility. Given that both four-probe field-effect mobility (μ_FE) and Hall mobility (μ_H) exclude contact resistance, their magnitudes should be more or less the same. However, μ_H is much higher than μ_FE for our WS₂ and MoS₂ FETs; these results differ from a previous report on WSe₂ FETs, where μ_H and two-probe μ_FE showed comparable magnitudes.²¹ Pradhan et al., extensively studied Hall and two-probe field-effect mobilities in multilayer WSe₂ FETs. They found a linear dependence of carrier concentration as a function of V_bg from Hall measurement and could extract effective gate capacitances to estimate μ_FE. However, the situation is different in our experiments. The carrier concentration (n) has no linear dependence on V_bg, as illustrated in Fig. 4a and c. This will cause discrepancy between μ_H and μ_FE. Furthermore, non-metallic materials, such as WS₂ and MoS₂ in our experiment, do not follow the relation, , which holds for metallic channels on oxide gate insulators. In such a case as our devices, μ_FE gives merely a rough estimate of μ_H, which is obtained using Hall measurement of n at a given V_bg.

Conclusion

In summary, we have compared two- and four-probe field-effects and Hall mobilities for WS₂ and MoS₂ FETs at room temperature. Cr/Au (8/80 nm) contacts show ohmic behavior in WS₂ multilayer FET, but nonlinear behavior in MoS₂ multilayer FET. Regardless of the electrical characteristics of contacts, field-effect mobility obtained by the two-probe configuration is much lower than both four-probe field-effect mobility and Hall mobility. Electrical contacts in the WS₂ or MoS₂-based FETs have a non-discountable influence on the field-effect mobility estimation in the two-probe configuration. When carrier concentration has a nonlinear dependence on V_bg, the equivalence of field-effect and Hall mobilities does not hold, and field-effect mobility provides only a rough estimate of Hall mobility.

Acknowledgements

This study was supported by the Nano-Material Technology Development Program (2012M3A7B4049888) through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning. This research was also supported by the Priority Research Center Program (2010-0020207) and the Basic Science Research Program (2013R1A1A2061396) through NRF funded by the Ministry of Education.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra14638d

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