Introduction

Rhenium disulphide (ReS2) is a member of the family of recently rediscovered transition metal dichalcogenides (TMDCs). In contrast to the more widely studied MoS2, which preferentially crystallizes in the 2H phase1, ReS2 has a 1T′ distorted crystal structure2,3,4, which results in anisotropic optical, electrical and vibrational properties4,5,6,7. Recent Raman spectroscopy3,8 and photoluminescence measurements3 indicate that atomic layers in 1T′ ReS2, unlike those of MoS2, are decoupled from each other3, which could give rise to direct bandgap preservation from monolayers to bulk crystals. This makes ReS2 interesting not only in the monolayer but also in the bulk form for electronic and optoelectronic applications where its optical anisotropy could in principle allow the fabrication of polarization-sensitive photodetectors9,10. Field effect transistors and integrated circuits made of ReS2 have already been reported7,11,12,13,14,15, showing anisotropic electrical behaviour and mobilities of 1–30 cm2 V−1 s−1 at room temperature in a limited range of electron doping (below 1013 cm−2).

Here we use polymer electrolyte gating of mono- and multilayer ReS2 to explore a wider range of doping levels in the first ReS2 electrical double-layer transistor (EDLT)16,17,18,19,20,21,22,23 reported to date. The use of polymer electrolytes can result in charge carrier densities as high as 1015 cm−2 (ref. 24), largely exceeding doping levels that can be achieved using standard solid gates. Polymer electrolytes are however a known source of disorder. Ions from the polymer electrolyte are in direct contact with the conductive channel25 and act as charged impurities, which degrade the mobility of charge carriers25,26. We also include solid bottom gates in our devices, which allow us to modulate the charge density at low temperatures where the polymer electrolyte is frozen and to disentangle the effects of doping and electrolyte-induced disorder. The aim of this work is to explore the effects of doping and disorder on the electrical conductivity of ReS2. At high doping levels, a complete and reversible suppression of conductivity in monolayer ReS2 is observed. In multilayer flakes the effect is milder and an insulator–metal–insulator sequence is measured instead. Our band structure and transport calculations furthermore shed light on the mechanisms of conductivity suppression.

Results

Current suppression at high doping levels in monolayer ReS2

We first focus on monolayer ReS2 EDLTs. Device schematic is shown on Fig. 1a (see Methods and Supplementary Methods for the details of device fabrication and EDLT measurements). On Fig. 1b current Is as a function of polymer electrolyte voltage (VPE) is presented. Strikingly, the current falls below the instrumentation noise floor at high carrier densities after reaching a maximum. Four-probe measurements reveal that sheet conductivity G reproduces this behaviour, thus ruling out the possibility of a contact resistance effect (Supplementary Fig. 1 and Supplementary Note 1). In the main text we concentrate on devices measured using PS-PMMA-PS:[EMIM]-[TFSI] as the electrolyte. Experiments using LiClO4-based polymer electrolyte gave essentially the same result (Supplementary Fig. 2 and Supplementary Note 2). Although a strong hysteresis is present in our measurements, the initial conductivity is restored at the end of the voltage sweep, indicating that no degradation has occurred in our device. Furthermore, we swept VPE 10 times in a different device (Supplementary Fig. 3 and Supplementary Note 3), and found good current stability. The distinct behaviour of the conductivity with suppression at high carrier densities was observed in all monolayer ReS2 devices studied (six monolayer ReS2 EDLTs).

Figure 1: Room-temperature characterization of monolayer ReS2.
figure 1

(a) Schematic of the EDLT based on monolayer ReS2. (b) Current Is as a function of polymer electrolyte voltage VPE. Arrows are showing the voltage sweep direction. Conductivity is restored after full sweep.

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Since the observed effect is not related to contact resistance, electrolyte type or cycling history, we consider electrolyte-induced disorder as the possible origin of the observed conductivity suppression at high doping levels. To reveal the possible influence of polymer electrolyte on the conductivity, we perform consecutive measurements on the same device before and after deposition of the electrolyte, as a function of temperature. In addition to the polymer electrolyte, we use a back-gate stack containing a high-κ dielectric to modulate the charge density in our Hall bar devices (Fig. 2d and Supplementary Methods).

Figure 2: Monolayer ReS2 with and without the polymer electrolyte.
figure 2

(a) Sheet conductivity G extracted from four contact measurements as a function of back-gate voltage Vbg before PE deposition (left panel) and after PE deposition with different VPE applied. Colours from red to blue correspond to 300–10 (leftmost panel) and 160–10 K (the rest four panels). (b) Arrhenius plots for Ea extracted on top of conductivity dome at different values of VPE. Solid black lines correspond to linear fits to the equation . (c) Activation energy Ea, extracted from the top of the conductivity dome as a function of VPE. Error bars originate from the errors in linear fit in b. (d) Optical micrograph of a monolayer ReS2 multiterminal device used in this study. Scale bar, 10 μm long.

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The back-gate voltage Vbg dependence of the sheet conductivity G extracted from four-probe measurements for different temperatures is shown on Fig. 2a. On the left panel, the conductivity before the electrolyte deposition is shown. In the subsequent panels, G as a function of Vbg is recorded after freezing the electrolyte at a given VPE (freezing point ∼180−230 K, Supplementary Methods). Without the electrolyte, we observe a metal–insulator transition around Vbg=5.6 V and field-effect mobilities of μFE∼3 cm2 V−1 s−1, consistent with other studies of ReS2 (refs 7, 11, 14, 15). As soon as the electrolyte is deposited and VPE=0 V is applied (second panel), the overall conductivity decreases and the sample displays a purely insulating behaviour. Increasing the VPE further results in a gradual decrease of conductivity (Fig. 2a, from left to right). To quantify the changes in insulating behaviour, we tracked the conductivity dome as a distinct feature in our experiments. We fit our data in this insulating state with the thermally activated transport model , where G0 is a constant conductivity, Ea is the activation energy, kB the Boltzmann constant and T the temperature. For all values of VPE we could achieve a good fit in the range between 70 and 150 K (Fig. 2b). Figure 2c shows Ea as a function of VPE for ΔVbg=0 V, where . We can see that increasing the electrolyte voltage results in a significant increase of the activation energy (Fig. 2c). This is in contrast to band-like transport and metallic state emerging at high carrier densities in the case of solid-gated devices before electrolyte deposition. The same behaviour was observed in devices fabricated on thicker SiO2 substrates (Supplementary Fig. 4 and Supplementary Note 4).

Comparison with multilayer ReS2

Further evidence of a major role of disorder comes from our analysis of the thickness dependence. We performed similar measurements on ReS2 with thicknesses ranging from 0.75 (monolayer) to 21 nm. Figure 3a presents the room-temperature field-effect curves of ReS2 EDLTs with different thickness. For clarity, only sweeps in the reverse direction, from VPE=2.5 to −0.5 V, are shown. There is a stark contrast between the case of monolayer and thicker layers. First, monolayer EDLTs are the only devices that switch off at high doping levels, while the multilayers, although displaying a conductivity dome, remain largely conductive at VPE=2.5 V. Second, multilayer devices are systematically 4–8 times more conductive than monolayers in the ON state. Among multilayers (>2 layers (L)), device-to-device variation in doping and hysteresis are of the same order of magnitude, making these curves essentially undistinguishable. Although it is expected that monolayers are more sensitive to surface disorder, such a drastic difference was not observed between monolayer and multilayer MoS2, WSe2 or MoSe2 (Supplementary Note 5).

Figure 3: Transport in multilayer ReS2 with polymer electrolyte gating.
figure 3

(a) Sheet conductivity G as a function of VPE for ReS2 flakes of different thicknesses. (b) Insulator–metal–insulator sequence for multilayer (10 nm) ReS2 flake. Dashed lines are pointing on the regions of VPE, where transitions are occurring. (c) Hall mobility for the easy axis of trilayer ReS2 (2.2 nm thick) as a function of temperature T for different carrier densities and VPE in the metallic state. Red markers correspond to fixed carrier density n2D=1.55 × 1013 cm−2; filled, VPE=0.9 V; empty, VPE=1.6 V. Black markers, fixed carrier density n2D=1.82 × 1013 cm−2; filled, VPE=1.6 V; empty, VPE=2.1 V. Error bars originate from the uncertainty in carrier density extraction from Hall effect and conductivity measurements.

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We have performed measurements at different temperatures using a 10 nm thick flake as a representative of multilayer ReS2 (Supplementary Fig. 6 and Supplementary Note 6). On Fig. 3b we summarize our measurements on this device. Moving from the conduction band edge, the device shows weakly insulating behaviour. Around VPE=0.5 V, transition to the metallic regime occurs, which is consistent with recent measurements on multilayer ReS2 with a solid gate12. After the conductivity dome, the device undergoes a transition back to the insulating state around VPE=2.3 V.

We first examine evolution of conductivity in the metallic state around the conductivity dome. We have performed Hall effect measurements in another multilayer (three layers, 2.2 nm thickness), where we have measured simultaneously Hall mobility μHall and carrier density n2D by taking into account the anisotropy of ReS2 (Supplementary Fig. 7 and Supplementary Note 7). Carrier densities of up to 2.3 × 1013 cm−2 could be induced at high-positive VPE. We have performed three cooldowns: for charge densities left of the conductivity dome (VPE=0.9 V); near the conductivity maximum (VPE=1.6 V); and right above it (VPE=2.1 V). Cooldowns were performed at close values of VPE and we could continuously modulate the carrier density between neighbouring cooldowns by applying Vbg to the silicon substrate covered by 270 nm SiO2 (Supplementary Fig. 8b). This allowed us to measure the Hall mobility for each specific value of VPE and n2D. The striking feature of our measurements is the significant decrease of mobility at the same values of carrier density for increasing values of VPE, as shown on Fig. 3c. During the first cooldown (VPE=0.9 V), we measured metallic behaviour with Hall mobility values exceeding 200 cm2 V−1 s−1 at low temperatures (red filled markers). With VPE increasing to 1.6 V, the mobility at the same carrier density decreases by a factor of 8 (red empty markers). The same behaviour is observed while moving from the second to the third cooldown. Finally, the material becomes insulating as both the VPE and n2D are increased (Supplementary Fig. 8).

The insulating state at high carrier densities is a distinct feature of multilayer ReS2 EDLTs, in contrast to other semiconducting TMDCs16,18,27, which exhibit band-like transport (see discussion in Supplementary Note 5). On Fig. 4a, we show the dependence of the reduced activation energy w=−d(lnR)/d(lnT) (ref. 28) on temperature for the 10 nm thick flake previously discussed on Fig. 3b. We distinguish two types of behaviour. In the 96−172 K temperature range, the temperature dependence of the resistance can be fitted using the Mott variable range hopping29 behaviour R∝exp[(T0/T)1/3]. The coefficient extracted from the w−lnT dependence is 0.36 (red line on Fig. 4a), which fits well to the variable range hopping model. We find a density of states and localization length ξloc≈0.35÷0.63 nm (see also Supplementary Note 8 for effective mass calculations). At lower temperatures, w reaches saturation as a function of lnT, which is the indication of a multiphonon hopping regime. We discuss both conduction mechanisms further in Supplementary Notes 9 and 10.

Figure 4: Insulating state of multilayer ReS2 at high carrier densities.
figure 4

(a) Reduced activation energy w as a function of lnT. Red and blue dashed lines correspond to variable range hopping (VRH) and multiphonon hopping (MPH) regimes, respectively. (b) Fits for MPH (left) and VRH (right) in the corresponding range of temperatures.

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Activation and hopping regimes observed in ReS2 at high carrier densities suggest that disorder plays an important role in the observed behaviour. Aside from it, there are other possible explanation, which should be considered: phase transition due to doping, complete filling of the disentangled conduction band (see further text and Supplementary Note 8 for discussion of the ReS2 band structure) and influence of the perpendicular electric field on the band structure. These are discussed and ruled out in Supplementary Note 11.

Theoretical modelling

We have performed density functional theory calculations of the band structure of mono- and multilayer ReS2 to shed more light on the observed behaviour of electrical conductance. Figure 5a–c shows the crystal structure of monolayer ReS2 together with the calculated band structure along high symmetry directions and the integrated density of states (DOS). We find an unusual feature in the band structure—a narrow conduction band almost separated from other bands by a minimum in the DOS, as shown in Fig. 5c, right panel. This feature is present in both mono- (Fig. 5c) and multilayer ReS2 (Supplementary Fig. 9).

Figure 5: Electronic structure of monolayer ReS2 from ab initio calculations.
figure 5

(a) Ball-and-stick representation of the atomic structure of monolayer ReS2. Lattice vectors (a1,a2) and unit cell (dashed lines) are illustrated. (b) Brillouin zone and primitive vectors (b1,b2) of reciprocal lattice. (c) Energy bands calculated along high-symmetry directions connecting the vertices defined in b and k-integrated density of states (right panel). The lowest energy conductance band, as well as its contribution in the DOS are highlighted in purple. (d) Density of states modification due to addition of ions with the concentration nions=(N+−N−)/Ncells on top of conductivity channel calculated using our transport model. Colour code corresponds to the amount of ions nions. (e) Close-up view of the conduction band edge. (f) Conductivities σx and σy as a function of ionic concentration nions for directions parallel and perpendicular to the easy axis (along Re chains), respectively, calculated using the Kubo formula.

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Further on, we concentrate on the quantitative interpretation of our findings. Depending on the effective strength of the interaction between ions and electrons (holes), and the effective mass of the charge carriers, the latter may form a bound state preventing transport. Monolayer ReS2 has a narrow conduction band ≈0.4 eV wide and a large effective mass m*=0.5 me, where me is the free-electron mass (for effective masses and bulk ReS2 band structure see Supplementary Note 8). This makes ReS2 similar to organic semiconductors such as p-doped rubrene (highest occupied molecular orbital bandwidth D≈0.4 eV, hole effective mass mh*=0.6 me (ref. 30)) that shows a decrease of conductivity at high charge densities26,31,32,33, albeit without a full conductivity suppression at high charge densities like in the case of monolayer ReS2.

A fully quantum argument based on Anderson localization sheds light on this reasoning. The ionic positions at the electric double layer are to a large extent random, thus introducing a Coulomb potential that does not reproduce the periodicity of the semiconductor lattice. Assuming that one-electron states of the conduction band of ReS2 can be described by the tight-binding model, the electrolyte-induced disorder consists of a random but spatially correlated distribution of on-site energies characterized by a finite width W. Classical Anderson localization theory predicts that disorder causes full localization of the one-particle states of two-dimensional (2D) lattices, irrespective of the disorder strength W (refs 34, 35). Nevertheless, a larger amount of disorder W is generally associated with a shorter localization length ξ (refs 36, 37). Electronic transport in the presence of a localized spectrum takes place by means of hopping between localized states with a temperature dependence characteristic of an insulator. However, as Anderson localization is ultimately a consequence of destructive interference of the wave functions, phase-breaking mechanisms (for example, electron–phonon scattering) that take place over a phase conservation length Lφ≤ξ prevent the physical realization of Anderson localization.

An increase of the number of ions at the electrolyte–semiconductor interface translates into the broadening of the overall on-site energy distribution, so that the effective amount of disorder W increases. Therefore, ξ is a decreasing function of VPE. If one assumes that, at fixed temperature, Lφ does not vary considerably with doping, the condition for the onset of the metal–insulator transition is . For increasing gate voltage (VPE>, charge-carrier mobility μ(VPE) is expected to drop faster than inverse linear law, leading to a rapid decay of conductivity σ∝nμ. We stress that the narrowness of the conduction band is crucial to revealing the wave function localization, as the key quantity in Anderson localization is the adimensional disorder strength W/D (refs 36, 38). In our opinion, this phenomenon is responsible for such a peculiar behavior of monolayer ReS2 among other 2D TMDCs.

To investigate qualitatively the discussed phenomenon, we consider the following model of electronic transport. We describe the lowest conduction band of ReS2, highlighted in Fig. 5c, with a tight-binding model on a rectangular lattice, with x and y directions corresponding to the parallel and perpendicular directions relative to the easy axis (along Re chains). Monovalent point charges (for example, Li+) are placed at a distance Δz=20 Å from the plane of the rectangular lattice. To guarantee the total charge neutrality of the ionic gate-semiconductor interface, the ionic concentration nions must be equal to the electron concentration n2D. The electrical conductivity has been calculated by means of the Kubo formula39,40 assuming linear response to the applied electric field. Further details could be found in Supplementary Note 12.

The calculated DOS shown in Fig. 5d is characterized by long tails on increasing nions. These tails indicate the presence of localized states induced by electrostatic disorder. Moreover, nions determines the chemical potential μ of the electrons, which shifts further into the conduction band on the increase of doping. The transport behaviour as a function of nions is ultimately determined by the interplay between the increasingly localized states of the spectrum and the position of the chemical potential within the conduction band. The conductivity σ calculated along x and y directions is shown in Fig. 5e. Here a pronounced dome in the conductivity followed by its full suppression at high carrier densities is observed. The ionic concentration, that is, the carrier density associated with the peak of the dome, is n*ions=0.06÷0.08 ions per unit cell. We observe a very good agreement with measured carrier densities extracted from the Hall effect data (Supplementary Fig. 8a). The anisotropy calculated in the region of the dome, σy/σx=0.6 also agrees well with our experimental data. Above certain ionic concentrations the curves along the two directions merge and become undistinguishable. This isotropic regime at high carrier densities could be clearly seen in the experimentally measured two-probe conductivity curves (Supplementary Fig. 10). We ascribe this feature to the onset of full localization in the states in the energy region around the chemical potential, that is, those states responsible for transport. Therefore, localization eliminates any preferential direction for transport.

Theoretical intuition suggests how the behaviour of conductivity must change in multilayer ReS2. First, classical scaling theory of Anderson localization in d=2+ɛ (ɛ>0) dimensions predicts that extended states do not disappear entirely, but in the energy spectrum they are separated from localized states by so-called mobility edges. Second, the injection of electrons itself into the conduction band of ReS2 results in a rapid screening of the Coulomb potential in the bulk of the sample, which is less affected by electrostatic disorder (Supplementary Fig. 11), thus preserving the charge-carrier mobility. These arguments point towards a scenario where the multilayer ReS2 conductivity is less influenced by disorder than in the case of the monolayer.

Discussion

In conclusion, we have realized the first transport study of ReS2 EDLT with thicknesses ranging from 1 (0.75 nm) to ∼30 layers (21 nm). We demonstrate that ionic disorder leads to an unusual OFF state at high carrier densities in the case of monolayers. In the case of multilayers, an insulator–metal–insulator sequence, as well as a quenching of Hall mobility with increasing VPE were observed. The highly doped state of multilayer ReS2 is characterized by a hopping mechanisms with small localization length. Owing to the unique band structure with a narrow low-energy conduction band ReS2 stands apart from other TMDCs, where such modulation of conductivity at high carrier densities was not observed. Our transport model quantitatively explains our findings.

Methods

Device fabrication

Flakes of mono- and multilayer ReS2 were obtained from bulk crystals, which were cleaved using an adhesive tape and transferred onto a degenerately doped n++ Si chip covered by 270 nm SiO2. Contacts were fabricated using standard e-beam lithography, followed by evaporation of Pd/Au contacts and liftoff in acetone. Selected devices were also patterned with a second e-beam step and subsequently etched in O2/SF6 plasma. Another series of devices was fabricated by transferring monolayer flakes on top of local back gates (Cr/Au) covered with 30 nm HfO2 deposited using atomic layer deposition.

Data availability

The data that support the findings of this study are available from the corresponding author on request.

Additional information

How to cite this article: Ovchinnikov, D. et al. Disorder engineering and conductivity dome in ReS2 with electrolyte gating. Nat. Commun. 7:12391 doi: 10.1038/ncomms12391 (2016).