Universal low-temperature Ohmic contacts for quantum transport in transition metal dichalcogenides

Low carrier mobility and high electrical contact resistance are two major obstacles prohibiting explorations of quantum transport in TMDCs. Here, we demonstrate an effective method to establish low-temperature Ohmic contacts in boron nitride encapsulated TMDC devices based on selective etching and conventional electron-beam evaporation of metal electrodes. This method works for most extensively studied TMDCs in recent years, including MoS2, MoSe2, WSe2, WS2, and 2H-MoTe2. Low electrical contact resistance is achieved at 2 K. All of the few-layer TMDC devices studied show excellent performance with remarkably improved field-effect mobilities ranging from 2300 cm2/V s to 16000 cm2/V s, as verified by the high carrier mobilities extracted from Hall effect measurements. Moreover, both high-mobility n-type and p-type TMDC channels can be realized by simply using appropriate contact metals. Prominent Shubnikov-de Haas oscillations have been observed and investigated in these high-quality TMDC devices.


Introduction
Experimental studies on the electrical transport properties of atomically thin semiconducting transition metal dichalcogenides (TMDCs) [1][2][3][4][5][6][7][8][9] have encountered a number of obstacles, such as high impurity, low carrier mobility, and high electrical contact resistance caused by Schottky barriers formed at the metal-TMDC interfaces [10,11]. Ohmic contacts between metals and TMDCs are difficult to achieve because of work function mismatches and Fermi level pinning effects [12]. Over the last few years, significant efforts have attempted to improve the quality of electrical contacts in metal-TMDCs, such as through using work function-matched metals [13], vacuum annealing [14], and phase engineering [15]. The quality of electrical contacts at metal-WSe2 interfaces, for example, have been gradually improved by surface doping treatment [11] and utilization of different materials with low (or tunable) work functions [10,16]. Electrical contact problems (mainly due to Schottky barriers) exist in all semiconducting TMDC devices contacted using metal electrodes particularly at cryogenic temperatures. They significantly limit the injection of charge carriers into the transport channel and thus prohibit detection of quantum transport properties in these 2D materials. Reducing the Schottky barrier at metal-TMDC interfaces is the most critical step in advancing the device transport performance of TMDCs. Recently, ultrahigh electron mobility has been achieved in MoS2 devices constructed based on graphene multi-terminal electrodes [17]. The contact resistance in these graphene-terminated devices can be largely reduced by applying a large back gate voltages, and quantum oscillations have been detected which show complicated multi-band features.
Based on our systematic investigations of electrical contacts in various TMDCs, we find 4 that cleanliness of TMDC interfaces is the critical issues in realizing high-quality Ohmic contacts and fabricating high performance devices. To eliminate the contamination/oxidation occurring on TMDC surfaces, we use a dry transfer technique in an inert environment of argon or nitrogen and protect few-layer TMDCs using ultrathin hexagonal boron nitride (h-BN) sheets [18]. Ultrathin h-BN is well-known dielectric material that provides a charge-free environment for high-quality graphene devices [19,20]. Ultrathin h-BN is also very effective in blocking charge impurities from the SiO2 substrate and hence increasing carrier mobility in TMDCs, particularly at low temperatures. To achieve high-quality Ohmic contacts, we develop Furthermore, high mobility p-type TMDCs channels are achieved using Pd contacts since Pd has a high work function and can match the valence bands of TMDCs. As an example, high quality p-type WSe2 with hole mobility of up to 8550 cm 2 /V s is demonstrated. The fabrication of high quality metal electrodes for atomically thin TMDCs demonstrated here is more practical and reliable since the contact resistance weekly depends on applied gate voltages. Remarkable improvements in contact resistance and carrier mobility allow us to observe prominent quantum phenomena, such as Shubnikov-de Haas (SdH) oscillations, in good agreement with 5 the intrinsic properties of the band structures in few-layer TMDCs.
Results and discussion To eliminate possible contamination, a polymer-free dry transfer technique recently developed for device fabrication of graphene is adopted in this study [20]. A few-layer TMDC is picked up from the SiO2/Si substrate by an ultrathin h-BN flake through van der Waals interactions.

Fabrication of metal contacts for h-BN encapsulated TMDCs
The h-BN/TMDC flake is then transferred to a fresh h-BN flake previously exfoliated on another SiO2/Si substrate to form a h-BN/TMDC/h-BN sandwich structure. A high temperature annealing process (under H2/Ar atmosphere) is necessary to remove the small bubbles formed at the interfaces between h-BN and TMDCs. Although edge contacts can be established for our samples, the contact resistance is normally high, resulting in difficulties in detecting the intrinsic properties of TMDCs (see Supporting Information). The poor performance of the devices with edge contacts indicates that even TMDCs are encapsulated by h-BN sheets, if the contact problems are not solved, the intrinsic properties of the TMDC devices cannot be detected. By contrast, the etching process we developed (etching the top of h-BN only) can largely reduce the TMDC contact resistance. The contact areas are patterned by standard ebeam lithography techniques, and the exposed top h-BN layer is subsequently etched by O2 6 plasma at a relatively high speed. By controlling the etching duration, TMDCs can be partially exposed for metal deposition because the etching rate of TMDCs by O2 plasma is low.

Low-temperature Ohmic contacts for TMDC channel materials
To demonstrate the Ohmic contact characteristics of our TMDC devices, Ids-Vds measurements are first carried out in a two-terminal configuration at both room and cryogenic temperatures. Figures 2(a) to the band gap of the TMDCs at the contact region. Therefore, the barriers for both electron and hole injections are large but smaller than the bandgap. Therefore, the devices showed ambipolar behaviors when either Ti or Pd is used as the contact metals (see figures S13 and S14 in Supporting Information). Figure 3 shows the temperature-dependent transport characteristics of several TMDCs.

Mobility characterization for TMDC devices
The Ti contacted WSe2 device shows n-type behaviors as revealed by the increasing conductance with increasing positive gate voltages, while the Pd contacted WSe2 shows p-type behaviors. Under high gate voltages, the conductance (measured by the four-terminal configuration) dramatically increases at low temperatures. As demonstrated in a n-type WSe2 sample, at Vg=70 V, the resistance dramatically decreases from 13720 Ω (at room temperature) to 290 Ω at 1.7 K.
Our few-layer TMDC devices exhibit excellent performance at low temperatures because of their barrier-free contacts. The field-effect mobility is extracted from the linear region of the conductance curves [4]

Shubnikov-de Haas oscillations in TMDCs
Because of the reliable low-temperature Ohmic contacts and high mobilities, the SdH oscillations of the magnetoresistance (MR) can be easily detected in our TMDC devices.

Additional information
Supporting information is available.
The authors declare no competing financial interests.      Figure S1 shows the fabrication of the h-BN/TMDC/h-BN device by the dry transferring method followed by a chemical etching processes and electron beam evaporation. A WSe2 flake is used for making the device shown in Figure S1.

Ohmic contacts
Ohmic contacts have been achieved in all samples in this study. Linear Ids-Vds curves are observed at various temperatures as shown in Figure S3. To investigate the contact barriers in our devices, sample conductance is measured as a function of Vg for different excitation voltages through a four-terminal configuration (see Figure S3c). All the curves coincide to a single curve, indicating that the injection of charge carriers is independent of the excitation voltages. Thus, the electrical properties of the channel materials are truly reflected by the transport data. Similar linear Ids-Vds curves are observed in other materials as shown in Figure S4.
The barrier free contacts in our samples have been further confirmed using the Arrhenius We find that the h-BN encapsulated structure is very critical for the formation of reliable lowtemperature Ohmic contacts. Without using the bottom or top h-BN, all TMDC devices show very poor contacts, which can be found from the Ids-Vds curves obtained at room-and lowtemperatures. By applying the controlled etching process (using the same contact metals (Ti/Au)), we fabricated two kinds of devices to demonstrate the functions of h-BN: Device-A without bottom h-BN and Device-B without top h-BN. Device-A displays serious non-linear behaviors at room-and low-temperatures as shown in Figure S6, indicating the impurities induced gap states at the interface between SiO2 and TMDC, resulting in poor contacts. Device-B has a better performance, but asymmetrical Ids-Vds curves at low-temperatures, as shown in Figure S7e, indicating that a small Schottky barrier should occur at the contacts. Therefore, we believe that the clean surface realized by h-BN encapsulation plays an important role in achieving lowtemperature Ohmic contacts.   This indicates at low temperature, thermal excitation energy becomes too small to overcome the Schottky barriers, which further limit the injection of holes.

Low-temperature contact resistance
The contact resistance can be estimated by = 2 − 4 , where 2 is two-terminal resistance, 4 is the four-terminal resistance, and are the total and inner channel lengths, 10 respectively. as a function of gate voltages at T=2 K are plotted in Figure S8 for different materials. The unit length contact resistance can be calculated as /2, considering the source and drain contributions. The results are summarized in Table 1.

Carrier density and gate capacitance determined by Hall effects
We use Hall effect data to determine the Hall mobility, density of charge carriers and gate capacitance. Figure S10a shows that the transverse Hall resistance of the device at different . is linearly dependent on the magnetic field . The Hall coefficient H is extracted from 11 the slope. Then the carrier density is calculated according to 2 = 1/ H and the Hall mobility is obtained by H = / . The variation of 2 as a function of is shown in Figure S10b. The data can be fitted by 2 = 0 + / , whose slope yields = 1.14 × 10 −8 F/cm 2 . This gate capacitance is used to calculate the field-effect mobility. Figure S11 illustrates that the Hall mobility is dependent on the carrier density. The density dependence of the Hall mobility is due to the long-range Coulomb impurities in the samples.
Increasing the carrier density enhances the screening of Coulomb potential, which results in an increase of the Hall mobility. The carrier density dependence of the Hall mobility leads to that the measured H is smaller than F . Because when we substitute σ = ne H and n = ( − ℎ )/e into the definition of field-effect mobility = ( / )/ , we will find = H + H / . Therefore, will be larger than H when H / > 0.

Stability of h-BN encapsulated TMDC devices
The h-BN encapsulated devices can maintain their high performance after a long time storing in air. Figure S12 shows the mobility of a WSe2 device is still over 8000 cm 2 /V s after 4 months.
The slight shift of the threshold voltage may be due to the influence of the impurity levels in SiO2.
13 Figure S12: The changes of the electrical transport characteristics of a WSe2 sample after storing in air for 4 months.

Transport behaviors of few-layer WSe2 prepared on SiO2/Si substrates
We have studied the transport behaviors of few-layer WSe2 exfoliated on SiO2/Si substrates.
Two kinds of metal contacts, Ti/Au and Pd/Au have been used for comparison. As shown in Figure S13 and S14, both contacts show poor performance since large Schottky barriers formed at the interfaces between the electrodes and WSe2. It is difficult to measure the conductance by four-terminal configurations or at low temperatures due to the large contact resistances. Figure   S13 and S14 show the characteristics of Pd   excellent electrical performance, the same fabrication did not produce satisfactory results for h-BN encapsulated few-layer WSe2. To achieve the edge contacts, 4 sccm O2 and 40 sccm CHF3 were used. The inset in Figure S15 shows the Hall bar pattern after the etching process. Two kinds of electrodes, Ti/Au and Pd/Au have been tested as edge contacts. Although the edge contact does work, the performance are not good enough. As shown in Figure S15, the hole mobility obtained using Pd/Au edge contacts was about 5 cm 2 /V s. For Ti/Au edge contacts ( Figure S16), we obtained the electron mobility of about 6.4 cm 2 /V s at = 0.5 V.

Thickness determination by atomic force microscopy
We use AFM to identify the thickness of TMDC samples. The thickness of single layer WSe2 is about 0.7 nm. Figure S17 shows AFM data for the 5L and 8L WSe2 samples.

Raman characterization of controlled area etching
To identify the influence of controlled area etching on sample quality, we used Raman spectroscopy to examine the sample. The optical image of the sample is shown in Figure S20.

Performance summary of h-BN encapsulated TMDC devices
* Limited by the sample size, four-terminal device was fabricated for 2L WSe2 sample. Therefore, the Hall mobility for this device was absent.

Angular dependence of the SdH oscillations
The dimensionality of the electronic states can be identified by measuring the angular dependence of the SdH oscillations. Figure S6 shows the magneto-resistance plotted as a function of magnetic fields at different tilt angles θ (between the normal axis of the substrate and B fields). By plotting the derivative dR/dB as a function of (Bcosθ) −

SdH oscillations in few-layer MoSe2
Figure S22: SdH oscillations in a n-type few-layer MoSe2 sample. Some data were plotted by subtracting a given value for clarity. -30