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Reply to “Comment on ‘Gate-Controlled Metal−Insulator Transition in TiS3 Nanowire Field-Effect Transistors’” Michael Randle,† Alexey Lipatov,‡ Avinash Kumar,† Peter A. Dowben,§ Alexander Sinitskii,‡ Uttam Singisetti,† and Jonathan P. Bird*,† Downloaded via 188.68.3.43 on August 30, 2019 at 03:33:07 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
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Department of Electrical Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-1900, United States ‡ Department of Chemistry, University of NebraskaLincoln, Lincoln, Nebraska 68588, United States § Department of Physics & Astronomy, Theodore Jorgensen Hall, University of NebraskaLincoln, Lincoln, Nebraska 68588, United States
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use these to argue that there is, in fact, no MIT in this material. Instead, on the basis of Hall measurements, they argue that this material remains insulating at temperatures all the way up to, and even beyond, room temperature. Within this picture, these authors attribute our observation of a nonmonotonic variation of drain current with temperature to a competition between the corresponding variations of the carrier concentration and the mobility. More specifically, they suggest that there is little physical significance to the temperature (in their notation, Tmσ) at which the drain current shows its local maximum, noting that this does not correlate to that (again, in their notation, Tmμ) at which the mobility attains its peak value. These arguments are supported with the results of Hall measurements, which also show that the concentration of free carriers decreases considerably below 70 K, a result that they suggest could reflect the increasing condensation of such carriers into the collective CDW state. To respond to Gorlova et al.,3 we begin by addressing the behavior above ∼200 K, corresponding to the presumed metallic state. In this regime, we have established that the observed variation of mobility (with temperature and gate voltage) can be well described within our microscopic model of strong polar optical phonon scattering. According to these calculations, for sufficient gate biasing,1 TiS3 may be viewed as a degenerate semiconductor over the temperature range above ∼200 K. This is indicated in our Figure 1, in which we plot the calculated variation of Fermi energy (EF, measured relative to the conduction band edge, Ec) as a function of temperature. On the same plot, we use blue shading to denote the region corresponding to degenerate transport, defined as |Ec − EF| < 3kBT. From this figure, it is clear that, for temperatures in excess of 100 K, the TiS3 remains degenerate, consistent with a metallic character. This point is further illustrated in Figure 2, in which we plot the corresponding variation of electron concentration (n), computed within our model. (We note that we are unable to determine this parameter in our experiment, due to the difficulty of making Hall measurements on
n our recent work, published in ref 1, we investigated the field-effect function of TiS3 nanowires and provided evidence of a gate-controlled metal−insulator transition (MIT) that occurred at a density-dependent temperature in the range of 200 ≲ T ≲ 250 K. The MIT was inferred from measurements of the temperature dependence of the drain current, which increased with increasing temperature (insulating behavior) up to around 200 K, before crossing over to the opposite (metallic) trend for decreasing current with further increase of temperature. For temperatures corresponding to the presumed metallic state, we showed that the electron mobility is limited primarily by scattering from polar optical phonons, whose low threshold energies (24−31 meV) allow these phonons to couple strongly to the electron system, even below room temperature. The observed variations of the (fieldeffect) mobility in this regime were captured well by our theoretical calculations, which utilized the band structure of TiS3 and an ab initio treatment of electron−phonon coupling to evaluate transport under realistic conditions. At temperatures on the insulating side of the transition, it was noted that the nanowires exhibit features that are consistent with expectations for charge-density wave (CDW) materials. These included threshold behavior in the (two- and fourterminal) current−voltage characteristics, behavior that is normally attributed to the presence of a field-dependent threshold for the onset of CDW sliding. Although this behavior was most prominent below 60 K or so, the nonlinear nature of the current−voltage characteristics persisted all the way up to the MIT transition near 200 K. Separately, measurements of the transfer curves (i.e., of the variation of channel current as a function of gate voltage) in the same temperature range revealed the presence of robust mesoscopic conductance fluctuations. These also persisted all the way up to the MIT,1 a remarkable observation and one that is in marked contrast to the much weaker fluctuations typically exhibited by metals and semiconductors. This behavior is consistent, however, with the known capacity for CDW systems to exhibit coherent mesoscopic effects over long coherence lengths, or, equivalently, up to high temperatures.2 In their Comment on our study, Gorlova et al.3 present the results of their own investigation studies of TiS3 whiskers and © 2019 American Chemical Society
Received: July 31, 2019 Published: August 27, 2019 8498
DOI: 10.1021/acsnano.9b06062 ACS Nano 2019, 13, 8498−8500
Letter to the Editor
Cite This: ACS Nano 2019, 13, 8498−8500
ACS Nano
Letter to the Editor
distinctive temperature ranges: (1) T < ∼60 K. Below this temperature, the system condenses into a fully formed CDW, consistent with which we observe a full suppression of differential conductance near zero bias (see Figure 5 of ref 1); (2) 60 < T < ∼200−220 K. As the temperature is increased over this range, normal electrons coexist increasingly with the CDW condensate, with the latter persisting in some partially formed state up to as much as 220−250 K; (3) T > ∼220 K. Here, the degenerate doping of the semiconductor endows the material with effectively “metallic” character, with a phononlimited mobility that is well described in terms of the influence of scattering from low-energy polar optical modes.1 Before concluding, we make some further remarks that are motivated by the discussion by Gorlova et al.3 These authors comment that the temperature at which the current exhibits its maximum value varies widely in their samples, from as little as 150 K to above room temperature. We find no evidence of such a large variation in our devices, in which the MIT transition appears in the aforementioned range of 200−250 K. As our experiments are performed on nanowires with a cross section much smaller than those utilized by Gorlova et al., it seems plausible that our observations may be related to the nanoscale dimensions of our structures. Indeed, we note that the field effect induces some very interesting behavior in nanoscale samples, where applied fields can have greater control over the carrier density in the system. In conclusion, the Comment of Gorlova et al.3 makes some important observations regarding the nature of temperaturedependent conduction in nanostructured TiS3. Their assertion that carriers condense into a well-formed CDW below ∼60 K and that robust fluctuations out of this state are possible at significantly higher temperatures than this appears consistent with many of the aspects of our experiment. It needs to be noted here that TiS3 differs significantly from TaS3 or NbSe3, other trichalcogenide materials that have been widely used to study CDW physics. The latter materials are metallic, and thus CDWs or 2D Peierls’ distortions are to be expected.4 Nonetheless, we disagree with the assertion3 that there is no MIT in our system and argue instead for the presence of a degenerate semiconductor in TiS3 at T > ∼220 K. In this state, the material is essentially metal-like, with a conductivity that is limited by phonon scattering and no obvious indication of localization effects. Rather, the dominant source of scattering in this regime is believed to be due to the low-energy polar optical phonons of this material.
Figure 1. Calculated variation of Fermi energy as a function of temperature for TiS3. Zero energy on the figure corresponds to the conduction band edge, and the blue shaded area denotes the region of degenerate doping (Ec − EF < 3.5kBT). EF is calculated from the density of states in our ab initio calculations and by taking into account the partial ionization of dopants at each temperature. The background dopant level was taken to be 7 × 1018 cm−3, by matching to the experimental threshold voltage. For further details, see ref 1.
Figure 2. Calculated variation of electron concentration as a function of temperature for TiS3. The concentration was determined by evaluation of the Fermi integral for all energies in the conduction band. For further details, see ref 1.
nanostructured wires.) These data suggest that, at temperatures above 175 K, n is only slightly varying (by a factor of 5), compared to the much stronger variation that would be expected for a truly intrinsic (insulating) material. Although our calculations point to the presence of a degenerate semiconductor above the MIT transition temperature, which also depends on gate voltage, this theory is unable to capture the behavior observed in experiment at lower temperatures. Whereas Figure 2 indicates a strong drop in n as the temperature is decreased below ∼100 K, this does not correlate to the significantly higher MIT transition temperature (∼200 K) seen in experiment. This is not altogether surprising as the current model of transport does not account for any possible phase transition in the material. In their Comment, Gorlova et al. use the results of Hall measurements to determine the variation of carrier concentration in TiS3, across a wide range of temperature. They present a picture of increasing condensation of carriers into a CDW, as the temperature is decreased below ∼60 K, whereas robust fluctuations in this state persist to much higher temperatures. Essentially, we are in full agreement with this picture, which we find to be consistent with our observations of both sliding-related nonlinearity in the current voltage characteristics and robust conductance fluctuations in the transfer curves. On the basis of the picture suggested by the authors, we believe that our data point to the existence of three
AUTHOR INFORMATION Corresponding Author
*Email: jbird@buffalo.edu. ORCID
Alexey Lipatov: 0000-0001-5043-1616 Peter A. Dowben: 0000-0002-2198-4710 Alexander Sinitskii: 0000-0002-8688-3451 Jonathan P. Bird: 0000-0002-6966-9007 ACKNOWLEDGMENTS This research was supported by the National Science Foundation, through Grant Nos. NSF-ECCS 1740136 and 1508541, as well as by NCORE, a wholly owned subsidiary of the Semiconductor Research Corporation (SRC). Materials characterization was supported by the U.S. Department of 8499
DOI: 10.1021/acsnano.9b06062 ACS Nano 2019, 13, 8498−8500
ACS Nano
Letter to the Editor
Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-FG02-04ER46180.
REFERENCES (1) Randle, M.; Lipatov, A.; Kumar, A.; Kwan, C.-P.; Nathawat, J.; Barut, B.; Yin, S.; He, K.; Arabchigavkani, N.; Dixit, R.; Komesu, T.; Avila, J.; Asensio, M. C.; Dowben, P. A.; Sinitskii, A.; Singisetti, U.; Bird, J. P. Gate-Controlled Metal-Insulator Transition in TiS3 Nanowire Field-Effect Transistors. ACS Nano 2019, 13, 803−811. (2) Tsubota, M.; Inagaki, K.; Matsuura, T.; Tanda, S. AharonovBohm Effect in Charge-Density Wave Loops With Inherent Temporal Current Switching. Europhys. Lett. 2012, 97, 57011. (3) Gorlova, I. G.; Pokrovskii, V. Ya.; Frolov, A. V.; Orlov, A. P. Comment on “Gate-Controlled Metal-Insulator Transition in TiS3 Nanowire Field-Effect Transistors”. ACS Nano 2019, DOI: 10.1021/ acsnano.9b04225. (4) Dowben, P. A. The Metallicity of Thin Films and Overlayers. Surf. Sci. Rep. 2000, 40, 151−247.
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DOI: 10.1021/acsnano.9b06062 ACS Nano 2019, 13, 8498−8500
