High-electric-field behavior of the metal-insulator transition in TiS₃ nanowire transistors

Beginning with graphene,¹ the creation of electronic devices from low-dimensional materials has enabled the realization of an exciting variety of rich physical phenomena.² One class of low-dimensional materials that has recently gained interest is the transition metal trichalcogenides³ (TMTs). These materials crystallize in low-symmetry classes and, thus, exhibit markedly anisotropic properties. Unlike more well-studied two-dimensional materials,² which tend to exhibit high in-plane symmetry, the reduced symmetry of TMTs endows them with quasi-one-dimensional (1D) character.⁴ The study of TMTs, thus, allows the exploration of interesting physics, including charge density wave (CDW) formation and filamentary superconductivity,^5,6 and the development of directionally selective devices and sensors.^3,7

Titanium trisulfide (TiS₃) is a TMT belonging to the low-symmetry monoclinic class⁸ (P2₁/m space group). Structurally, it is composed of trigonal prisms of Ti and S atoms that connect along the b-axis [see Fig. 1(a)] to form a linear, chain-like structure.⁶ Because of its highly anisotropic crystal structure, TiS₃ typically grows in the form of needlelike crystals in which the long axes of the crystals correspond to the b-direction of the quasi-1D TiS₃ chains.^9,10 The cleavage energies that must be overcome to break apart the material are dependent upon crystal direction; while the lowest energy corresponds to the c-axis (between the 2D layers formed by the quasi-1D TiS₃ chains), the energy for cleaving along several other directions separating the chains is only slightly larger. Consequently, exfoliation from bulk material into quasi-1D wire- and ribbon-like morphologies is energetically favored.⁹ 

Titanium trisulfide can be broadly classified as an n-type semiconductor with a bandgap^11,12 of $∼$1 eV. Two observations that have received considerable attention concern the existence of a low-temperature collective state, thought to be a CDW, in this material, and of a metal-insulator transition (MIT) near room temperature.^13–16 The presumed CDW has been studied in both bulk^17–21 and, more recently, nanoscale^22–26 samples. Several experimental results are consistent with the picture of one or more CDW states forming as the temperature is lowered below 100 K. In nanoscale materials incorporated into field-effect transistor (FET) geometries, the carrier concentration can be manipulated by gating,^10,22–24 allowing for the control of the electrical conduction in a manner similar to other nanoscale CDW materials^27,28 (such as NbSe₃ and TaS₃).

Occurring near 220 K, the MIT in TiS₃ separates a low-temperature region, in which transport is dominated by disorder and electron localization,¹⁵ from a high-temperature one that is weakly metallic and dominated by scattering from polar-optical phonons.^23,29 The critical temperature of the MIT can vary over a wide range in bulk (⁠$∼$200–300 K), and recent experiments suggest that this may be due to variations in sulfur concentration between samples, and the existence of domains with two slightly different structures into which TiS₃ can crystallize.^30,31 In nanoscale samples, the characteristics of the MIT can, moreover, be modified by tuning the carrier concentration. The cause of the MIT has been the subject of discussion for some time, with current opinion focusing on two similar interpretations. The first of these suggests that the already nominally n-type TiS₃ gradually becomes a degenerate semiconductor as the temperature is increased to the vicinity of the observed MIT.^23,32 The other scenario relates to the observation that the Hall concentration and mobility exhibit opposite dependencies on temperature, a competition that is suggested to result in a MIT at a certain temperature.^20,33

A characteristic feature of the majority of the electrical studies described above is that they have been performed in the near-equilibrium limit in which transport is probed in the presence of small electric fields (⁠$εd≤$ 10² V/cm). By contrast, far fewer studies have explored the details of high-field transport in TiS₃, with a notable exception involving a study of the mechanisms of its electrical breakdown.³⁴ In this Letter, we, therefore, systematically investigate the manner in which the MIT evolves from low to high electric fields in nanowire-based TiS₃ FETs. We observe evidence of a fixed point in the transfer curves (drain current, $Id$⁠, as a function of gate voltage, $Vg$⁠) of these devices, at a specific gate voltage (⁠$Vgc$⁠) that separates metallic and insulating regimes from one another. The fixed point corresponds to a critical density for the metal-to-insulator crossover and the value of $Vgc$ can be tuned across a wide range, by suitable control of the electric field in the FET channel (i.e., of the applied drain bias, $Vd$⁠). Under appropriate biasing, we even show that the nanowire can be configured to remain either insulating or metallic over the entire range of temperature studied (3–300 K). As such, our results provide an important demonstration of the manner in which the phase transitions of complex materials can be strongly affected under far-from equilibrium conditions.

As described previously,¹⁰ the devices measured in this study were produced from bulk TiS₃ crystals grown by chemical vapor transport. An optical photograph of the crystals is shown in Fig. 1(b). Bulk TiS₃ produced in this manner was mechanically exfoliated onto a SiO₂/Si substrate and then processed to produce multi-electrode FETs. Exfoliation of TiS₃ in this manner tends to produce a variety of thin, nanowire, or nanoribbon structures.⁹ Here, we focus on representative results obtained in a detailed study of a nanowire FET [see Figs. 1(c) and 1(d)], whose dimensions were confirmed by atomic force microscopy [Fig. 1(e)]. Contact electrodes (Au/Cr) were fabricated on the nanowire [see Fig. 1(d)] using standard electron-beam lithography and metallization procedures. The electrode metals were chosen to establish a good Ohmic contact with the TiS₃, as we have shown previously.^23,35 Several different combinations of electrodes were tested in a two-probe geometry (defining effective channel lengths of 2.0, 5.0, and 13.5 μm), using the voltage applied to the conductive Si substrate [denoted as the gate in Fig. 1(c)] to vary carrier concentration in the channel.

In the limit of small electric fields (⁠$εd=$ 0.5 kV/cm; all field values quoted here are average values, calculated simply by dividing the applied drain voltage by the source-drain separation), as documented previously, we observe a MIT at a critical temperature $TMIT ∼$ 220 K. The features of this transition are captured in Figs. 2(a) and 2(b), the former of which plots transfer curves of the transistor at various temperatures (⁠$T$⁠). As the gate voltage is made more positive at each temperature, there is a clear trend for increasing current that is consistent with the aforementioned n-type nature of the TiS₃. Referring to the dependence of the current on temperature (at fixed gate voltage), as this is initially increased from 10 to 250 K, a monotonic increase in $Id$ is seen, indicative of an insulator (or semiconductor). At higher temperatures (250–300 K), however, the current instead starts to decrease with the increasing temperature, behavior that is consistent with a metal. This is most clearly seen at less-negative gate voltages (⁠$Vg>$−8.0 V), where the electron concentration is presumably increased to a sufficient level to support metallic conduction.

The MIT implied by the data of Fig. 2(a) is revealed more clearly in Fig. 2(b). Here, we plot the variation of conductance (⁠$Id/Vd$⁠) as a function of $T$⁠, for a section of nanowire of length 2.0 μm and at various gate voltages. The nonmonotonic character of $Id(T)$ is readily apparent at more-positive gate voltages, with a crossover from increasing to decreasing current occurring at $TMIT ∼$ 220–250 K. As noted previously,²³ the precise value of $TMIT$ is dependent upon gate voltage, shifting systematically to higher temperature when the carrier concentration is lowered at more-negative $Vg$⁠.

A common feature of systems exhibiting a phase transition is the presence of a fixed point in the conductance, which typically occurs at a specific temperature.³⁶ In the low-field data of Fig. 2(a), however, there is no clear evidence of such a critical point. This situation changes with a large source-drain field applied to the FET, as we highlight in Figs. 2(c) and 2(d). In the data of Fig. 2(c), which were obtained for a channel field $εd=$ 115 kV/cm, a very clear fixed point is now seen in the transfer curves at a critical gate voltage $Vgc=$ −14 V. For gate voltages below this, the current shows clear insulating behavior, while at larger voltages, a metallic dependence is instead found. These temperature dependent variations are captured, also, in Fig. 2(d), which shows very clearly how the critical point at $Vgc=$ −14 V represents the boundary between metallic and insulating curves.

The results of Figs. 2(c) and 2(d) indicate that application of a large electric field in the FET channel can be used to drive a MIT in TiS₃ nanowires, in contrast to Figs. 2(a) and 2(b), in which the transition is driven by temperature. In Fig. 2(e), we plot the dependence of $Vgc$ on $Vd$ and see that this parameter becomes less negative as V_d is reduced. For values of $Vd$ smaller than those plotted in the figure, the fixed point has disappeared completely. This is consistent with our observations at low field [Figs. 2(a) and 2(b)], for which $Vgc$ should essentially lie beyond the range of observation and so leading to predominantly insulating behavior at all gate voltages. Using the data of Fig. 2(e), we are able to define a phase diagram, the boundary of which separates combinations of gate and drain voltage for which the material is either metallic or insulating.

The highest electric fields reached in this study (⁠$εd$ = 115 kV/cm) are less than half the reported breakdown field (280–400 kV/cm) for similar TiS₃ nanowire FETs.³⁴ Studies of other TMTs,^37,38 graphene nanoribbons,^39,40 and MXenes^41,42 have shown that Joule heating can cause a significant increase in device conductance prior to breakdown. For TiS₃, breakdown is preceded by such a characteristic spike in conductance as well as by a degradation of the material due to the thermal generation of sulfur vacancies.³⁴ In our experiment, we observe no such increase in the conductance. In fact, at room temperature, the conductance decreases monotonically with increasing electric field. This suggests that any mechanisms related to chemical decomposition, or breakdown, of the device are not applicable to the observation of the gate-induced MIT. While it might be suggested that, even without causing breakdown, heating could still be responsible for our observations, we note that this should only make it easier for the material to transition into the metallic state. This is inconsistent with the results of Fig. 2, however, which indicate that below or above $Vgc$ the system is insulating or metallic, respectively, over the entire range of temperature studied. For this reason, we suggest that the emergence of the critical point at high drain fields cannot be attributed to Joule heating alone.

One possibility regarding the emergence of the critical point at high fields is that it may signal the emergence of some novel CDW state. Previously, the possible connection between the MIT and CDW formation was excluded for bulk TiS₃, based on x-ray diffraction measurements that did not reveal any distortion of the crystal structure near $TMIT.$^13,18 While the usual MIT associated with low-field transport is, therefore, likely not related to a CDW phase transition, the field-induced MIT analyzed here may plausibly be connected to such a transition. In the transition-metal oxide VO₂, for example, it is noteworthy that the interplay of electric-field and temperature can dynamically induce a phase transition.⁴³ The microscopic origin of this phase transition and a related MIT remains the subject of debate, however.⁴⁴ In many materials, charge ordering is important, leading to unconventional density waves that are not accompanied by a lattice distortion.^45–47 Given that electron correlations may also be important in TiS₃, the possibility of an unconventional density wave forming seems worth exploring.

At temperatures below $TMIT$⁠, especially below 100 K, the analysis of transport may be complicated by the coexistence of localization¹⁵ and the increasing condensation of electrons into a CDW state.²⁷ In nanoscale samples, with dimensions comparable to the CDW coherence length, low-dimensional fluctuations of the CDW that can allow an incipient CDW transition can be seen over a wider temperature range than in bulk.^5,48,49 In this context, we find evidence of low-field thresholding of the conductance that is typically associated with CDW systems,²⁷ over the entire range of temperature up to $TMIT$⁠. This behavior is demonstrated in the main panel of Fig. 3 in which we show the variation of conductance as a function of electric-field strength at various temperatures ranging from 3 to 200 K. The key feature here is the presence of a range of (low) electric field over which the conductance remains relatively constant; this behavior represents a typical signature of CDW systems and corresponds to the pinned condition prior to the onset of CDW sliding.²⁷ At 3 K, the threshold field required to overcome the pinning is $>$ 1 kV/cm, significantly higher than expected for bulk materials but consistent with reports for nanoscale CDW materials near the limit of 1D conduction.^49,50 The threshold field generated in the channel by the drain bias increases systematically with the increasing temperature, reaching a maximum of $∼$ 7 kV/cm near $TMIT$ before becoming undiscernible at even higher temperatures (not shown here). Such behavior is the opposite of what one might expect for a thermally driven phase transition in which the applied electric field is viewed as generating the Joule heat needed to trigger the MIT. In such a scenario, the threshold field for increasing conductance should likely decrease with the increasing temperature, opposite to the trend shown in Fig. 3. In the inset to Fig. 3, we show that the threshold source-drain field for CDW conduction is dependent upon gate voltage, growing increasingly larger as the carrier concentration in the wire is reduced by making $Vg$ more negative. While this dependence on $Vg$ is the opposite of that reported recently for nanoscale TiS₃ devices,²⁶ it is interestingly similar to that found in older studies of NbSe₃.^27,28

In conclusion, we have investigated the MIT in nanoscale TiS₃ FETs and characterized its evolution from low to high (channel) electric fields. At low-fields, the MIT manifests itself as a transition with respect to temperature (⁠$TMIT ∼$ 220 K), separating a low-temperature insulating region from a high-temperature one that is weakly metallic. In the presence of strong, drain-bias induced, fields, on the other hand, a fixed point emerges in the temperature-dependent transfer curves. The critical gate voltage (⁠$Vgc$⁠) that defines this fixed point evolves systematically with the drain bias (field), allowing us to map out a phase diagram that identifies specific combinations of $Vg$ and $Vd$ that yield either a metallic or an insulating state. Dependent upon the choice of the gate voltage, which tunes the carrier concentration in the nanowire, the existence of the field-induced MIT allows the TiS₃ to be either insulating or metallic, over the entire range of temperature of interest. The possible connection of this strongly nonequilibrium state to some form of CDW would appear to be worthy of further investigation.

Work at Buffalo was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering (No. DE-FG02-04ER46180) and the National Science Foundation (No. NSF-ECCS 1740136) and nCORE, a wholly owned subsidiary of the Semiconductor Research Corporation (SRC), through the Center on Antiferromagnetic Magneto-electric Memory and Logic (tasks 2760.001 and 2760.002). The device fabrication at UNL was performed using the facilities of the Nebraska Nanoscale Facility: National Nanotechnology Coordinated Infrastructure, which is supported by the NSF (No. ECCS-1542182) and the Nebraska Research Initiative.