Transparent conducting oxide induced by liquid electrolyte gating

Significance

Highly conducting transparent oxides are widely used as electrodes in various electronic devices where optical transparency through a low-resistance electrode is needed. Here, we show that highly conducting transparent oxide films can be formed by electrolyte gating of thin films of tungsten oxide, WO₃, that are initially insulating. Optical and electronic structure measurements show that the films are transparent in the visible spectrum before gating, due to the significant electronic band gap of ∼3.0 eV. No significant change in the band gap is found on gating the films to the metallic state so that the films remain transparent in the visible spectral region. Thus electrolyte gating of insulating oxides is a means of obtaining new classes of transparent conducting electrodes.

Abstract

Optically transparent conducting materials are essential in modern technology. These materials are used as electrodes in displays, photovoltaic cells, and touchscreens; they are also used in energy-conserving windows to reflect the infrared spectrum. The most ubiquitous transparent conducting material is tin-doped indium oxide (ITO), a wide-gap oxide whose conductivity is ascribed to n-type chemical doping. Recently, it has been shown that ionic liquid gating can induce a reversible, nonvolatile metallic phase in initially insulating films of WO₃. Here, we use hard X-ray photoelectron spectroscopy and spectroscopic ellipsometry to show that the metallic phase produced by the electrolyte gating does not result from a significant change in the bandgap but rather originates from new in-gap states. These states produce strong absorption below ∼1 eV, outside the visible spectrum, consistent with the formation of a narrow electronic conduction band. Thus WO₃ is metallic but remains colorless, unlike other methods to realize tunable electrical conductivity in this material. Core-level photoemission spectra show that the gating reversibly modifies the atomic coordination of W and O atoms without a substantial change of the stoichiometry; we propose a simple model relating these structural changes to the modifications in the electronic structure. Thus we show that ionic liquid gating can tune the conductivity over orders of magnitude while maintaining transparency in the visible range, suggesting the use of ionic liquid gating for many applications.

Tungsten trioxide (WO₃) is a d⁰ transition metal oxide with an energy band gap of about 3 eV. WO₃ is a transparent insulator but has been shown to become metallic and even superconducting when doped with significant amounts of electropositive elements such as Rb (1), K (2) or Cs (3), and H (4). The optical transmittance of WO₃ can also be manipulated by the electrochemical insertion of small cations, such as H⁺ or Li⁺, which makes WO₃ extremely desirable for smart window applications (5–7). Both fundamental studies and potential applications of WO₃ require the control of charge carriers; in addition to chemical doping, this control can also be achieved by the growth of oxygen deficient structures (4, 5, 8–10). Here we investigate an alternative method for controlling the electronic properties via ionic liquid gating. Previous work on VO₂ thin films has shown that liquid electrolyte gating produces structural modifications and leads to the suppression of the metal–insulator transition (11, 12). Recent gating experiments on epitaxial WO₃ thin films indicate changes in the out-of-plane lattice parameter, concomitant with the metallization throughout the film volume (13). In the work presented here, we correlate the structural changes with modification of electronic energy bands, which result in a transparent conducting oxide, thus yielding a much more complete understanding of such gating.

The experiments were performed on 17- to 19-nm-thick epitaxial WO₃ films grown on a LaAlO₃ substrate (a = 3.86 Å) using pulsed-laser deposition; the films grow epitaxially in the (100) crystalline orientation (referenced to the monoclinic unit cell). Two samples were used, one for the photoemission and Raman measurements (17 nm) and another for the ellipsometry measurements (19 nm). The device structure is shown in Fig. 1A: source (S), drain (D), and gate (G) contacts were formed from Ru/Au. A droplet of the ionic liquid—here 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)-imide (HMIM-TFSI) (14)—covers the WO₃ channel and the S, D, and G contacts. The film was gated by applying +3 V to the G contact for a period of up to 10 h. The drain–source current (I_DS) was measured, as shown in Fig. 1B, to monitor the gating process. After gating, the liquid electrolyte was washed off with isopropanol to allow for the hard X-ray photoemission, Raman, and ellipsometry measurements. Further details of the sample preparation and gating procedure can be found in Supporting Information. The sample was measured in three states: “pristine” (“as-grown”), “gated” (after the gating procedure described above), and “ungated” (after gating the sample is exposed to air for more than 6 h, where it almost recovers the initially insulating pristine state).

Fig. 1.

(A) Photograph of device including schematic of experimental setup. The WO₃ film is outlined in green and has the lateral dimensions of 0.3 × 1.0 cm². The source (S) and drain (D) contacts are placed at either end of the channel; the contacts are 0.1 × 0.15 cm² in size. (B) The drain–source current (I_DS) versus time during gating of the device with a gate voltage (V_G) of +3 V and a drain-source voltage (V_DS) of +0.1 V.

Fig. 2 A–F shows the O 1s and W 4f core-level photoemission spectra for the pristine, gated, and ungated states of the WO₃ film. Significant changes in both the O 1s and W 4f core-level photoemission spectra are found. The binding energy was referenced to the Au E_F. To make the changes in the W 4f core-level photoemission more visible, the significant contribution of the W 5p_3/2 states are subtracted from the W 4f spectra (Fig. S1). In Fig. 2 A–C, the O 1s spectra are decomposed into two components that we label O_a and O_b. In Fig. 2 D–F, the W 4f spectra are separated in two or three components that we label W_a, W_b, and W_c.

Fig. 2.

(A–F) Photoemission spectra of the O 1s levels (A–C) and W 4f levels (D–F) for the pristine, gated, and ungated samples. The experimental data are shown as open circles and the fit to these data by solid lines. The fitted Voigt components are indicated by a, b, and c. The vertical dashed lines mark the positions of the main components of the pristine spectra. (G) Raman spectra for the pristine and gated states.

Fig. S1.

W 5p and 4f core levels.

The component O_a in the pristine state (Fig. 2A) is centered at a binding energy of 530.56 eV. In the gated (Fig. 2B) and ungated (Fig. 2C) states, this component is shifted by ∼0.10 eV to lower binding energies. The O_b component is shifted relative to the O_a component by 1.0 eV in all states. Whereas the component O_a is ascribed to the O⁻² ions in the octahedral WO₆ structure (15), O_b is consistent with oxygen atoms that have a substantially increased positive charge. The presence of such an O_b component has been previously observed in the thermal coloration of annealed WO₃ films (16) wherein it is found that the O–W bonds are weakened, and oxygen vacancies and interstitial oxygen atoms are created, resulting in a change of oxidation state of the W atoms without any substantial change in stoichiometry. Thus this component indicates the presence of nonbonded or slightly covalently bonded oxygen atoms. The intensity of this component is significantly increased in the gated state, whereas in the ungated state the component is strongly decreased, almost reaching the level found in the pristine state. The binding energies and relative intensities of the W_a, W_b, W_c, O_a, and O_b components are summarized in Tables S1 and S2 for all three states. The spectral area of the O 1s, normalized to the spectral area of the W 4p core states (Fig. S2), is the same for the pristine, gate, and ungated states within an estimated accuracy of ±3%. This comparison indicates that any variation of oxygen content during the gating process is very small, below the detection limit of the photoemission experiment.

Table S1.

Binding energies and relative spectral weights for W 4f components a, b, and c

Oxidation state	Pristine		Gated		Ungated
	Binding energy, eV	W, %	Binding energy, eV	W, %	Binding energy, eV	W, %
Subtracted 5p3/2	41.24	—	41.22	—	41.20	—
Component a	35.75	87	36.10	54	35.77	78
Component b	34.63	13	34.73	33	34.62	22
Component c	—	—	33.70	13	—	—

Dashes indicate that no significant contribution was found for this component.

Table S2.

Binding energies and relative spectral weights for O 1s components a and b

Oxidation state	Pristine		Gated		Ungated
	Binding energy, eV	W, %	Binding energy, eV	W, %	Binding energy, eV	W, %
Component a	530.56	75	530.46	40	530.46	70
Component b	531.56	25	531.46	60	531.46	30

Fig. S2.

O 1s and W 4p core levels.

The pristine and ungated W 4f spectra (Fig. 2 D and F) present two components, each split into a 5/2 and 7/2 spin–orbit doublet. The main component, W_a, originates from W atoms in a WO₆ octahedral coordination. The second component W_b, at lower binding energy, originates from atoms occupying defective WO₆ octahedra or in interstitial positions (17–19). This component is mainly ascribed to the effect of the intense hard X-ray exposure of the WO₃ film, which was estimated to reach saturation after 1 min (Fig. S3). Some contribution from oxygen vacancies in the as-grown film cannot be ruled out. After gating, the W 4f spectrum exhibits three components (Fig. 2E). An additional doublet is observed at lower binding energies (W_c). This doublet is not seen in the pristine or ungated states. In the gated state, W_a is also shifted to significantly higher binding energies by ∼0.6 eV, so we label these states W*_a. The spectral weight of W*_a decreases with respect to W_a of the pristine state: we attribute this decrease to a redistribution to the W_b and W_c components (Table S1). More interestingly, the significant shift to higher binding energies of W*_a, indicates a change of the electrostatic environment of the W atoms, which reflects a structural rearrangement. In the ungated state, this shift is reduced to ∼0.1 eV. The W_c component vanishes, as mentioned earlier, and W_b decreases. The W_a component recovers part of its initial intensity. We attribute the differences between the spectra of the pristine and ungated states to incomplete recovery due to the time limitations of the experiment.

Fig. S3.

Time dependence of HAXPES spectra using an attenuated photon flux.

Structural changes in the gated state are clearly observed in the Raman spectra measured in the pristine and gated states, as shown in Fig. 2G. In the pristine state spectrum, three peaks that are characteristic of monoclinic WO₃ are observed at ∼275, ∼715, and 802 cm⁻¹ (20, 21). Based on group theory calculations and Raman selection rules, the first is associated with the bending vibration of W in the O–W–O chain, and the second corresponds to deformation vibrations around the oxygen. The third peak is related to the asymmetric stretching modes of the W–O–W chains. After gating, the peaks around 275 and 715 cm⁻¹ are strongly suppressed, and the peak associated with the stretching mode is reduced in intensity, narrowed, and shifted to higher energies, indicating a compressive stress (22). The reduced number of Raman modes in the gated spectrum indicates an increase in symmetry of the gated structure. For instance, a symmetrization of W–O bond lengths in the film plane results in the extinction of the peak around 715 cm⁻¹, as observed in the temperature-induced phase transition from monoclinic to tetragonal structures (21). The structural transformation affects the coordination of W atoms as observed in the W 4f core level spectra. The emergence of the W_c doublet in the gated state indicates the accumulation of charge on ∼13% of W atoms (based on the intensities of the doublets, assuming the same matrix elements for all three doublets, as shown in Table S1). The shift of W_a to higher binding energies suggests an increased ionic character in the O–W*_a bonds with respect the O–W_a in the pristine condition.

Fig. 3A displays the valence band photoemission collected for the pristine, gated, and ungated states of WO₃. The valence band is mainly composed of hybridized O 2p and W 5d states, the latter being split by the crystal fields into the lower energy t_2g and higher energy e_g states (23). At the 6.5 keV photon energy of our measurements, the relative cross-sections per electron are approximately W 5d/O 2p = 150 (24), so we expect the valence spectra to be dominated by the W contributions. In the photoemission spectra, the O 2p-associated band appears below −3eV. The energy ranges are labeled in the figure according to the orbital contributions for a monoclinic WO₃ structure (25, 26); the e_g and t_2g contributions to the valence band were confirmed for the pristine condition by linear dichroism in hard X-ray photoelectron spectroscopy (HAXPES) (27) (Fig. S4). In particular, the peak near the Fermi energy (ε_F) exhibits a strong t_2g contribution. In the gated state, the valence band is broadened, which is, according to ab initio calculations, expected for structures with higher symmetries due to the increase in the dispersion (28). As can clearly be seen in Fig. 3A, we find a reduction in the magnitude of the states toward the top of the oxygen-hybridized valence band. This reduction can be interpreted as a depletion of the “nonbonding” O 2p levels (probably only weakly present in the spectra due to their low cross-section) and the 2p t_2g hybridized states that would indicate a reduction of electronic charge density (i.e., increased positive charge) around the oxygen atoms in the gated state. As shown in Fig. 3B, electrolyte gating develops a significant increase in intensity of what is a small peak near the ε_F in the pristine state. In the pristine state, we believe that this small peak mainly originates from the intense hard X-ray exposure (Fig. S3), although some contribution of oxygen vacancies in the as-grown film cannot be ruled out. The gating process produces an additional contribution in this spectral range, resulting in a strongly enhanced peak. The peak returns nearly to pristine intensity in the ungated state. Photoemission peaks in the energy range of −0.6 to −1 eV have been associated, in oxygen deficient (17) and UV-irradiated (29) WO₃, with the presence of W⁵⁺ due to the filling of 5d t_2g-like orbitals. In our spectra, this peak is centered at −0.5 eV; being located at a distance of 2.5 eV from the top of valence band, the peak resides within the band gap that is ∼3 eV.

Fig. 3.

(A and B) Valence band photoemission spectra for the pristine, gated, and ungated states. (C) Optical absorption. (D) Model for the energy diagram of the gated state. The colored and hatched regions represent occupied states. Note that the states centered around −0.5 eV in the photoemission spectrum from the pristine sample likely originate from defects induced by the hard X-ray exposure (Fig. S3) and are not depicted in the model shown in D.

Fig. S4.

HAXPES of pristine WO₃(001) film grown in the same conditions as the samples reported in the main manuscript. (A) Setup. (B) Symmetry of 3d orbital with respect to the mirror plane, showing which states are excited according to the linear polarization [figure from ref. 27]. (C) Photoemission spectra.

Further insight into the nature of the states near ε_F was provided by spectroscopic ellipsometry. A second device, which was not exposed to X-rays, was used for these experiments. The low light intensity used in the ellipsometric experiments does not alter the electronic structure of the sample. The optical absorption spectra derived from ellipsometric data are shown in Fig. 3C. A clear threshold of the transition near 3 eV, observed for the gated and pristine states, corresponds to the WO₃ band gap. The intensity of the absorption for the gated state increases at low photon energies (below ∼1 eV), but the absorbance in the visible energy range remains small.

Optical transitions originating from in-gap states are routinely reported for colored WO₃ due to the creation of defects and/or insertion of ions. In those cases, they are ascribed to a polaronic transition between W⁵⁺ and W⁶⁺ atoms, where inserted electrons are localized on W⁵⁺ sites and polarize the surrounding lattice (30). The transition energy of those defects extends to the visible range and is thus responsible for the coloration. In our case, the increased optical absorption for photon energies below the visible range can be due to intraband-like transitions originating from the increased number of free carriers. The gating process weakens or breaks the W–O bonds; the free or weakly bonded oxygen acts as an electron donor to newly extended states created by the gating. A comparison with ellipsometric measurements reported on VO₂ films (31) reveals similarities in the n (refraction index) and k (extinction coefficient) wavelength dispersion curves for metallic and insulating states (Figs. S5 and S6); namely, the onset of k for long wavelengths in the metallic state [caused by intraband transitions (31)] and the stability of the optical band gap. It has been shown (32) that the electrolyte gating of VO₂ leads to an overlap between the more localized d_||-electrons [not hybridized with O 2p (33)] and the itinerant π*-band, which is shifted to lower energies. Combining the information obtained in the photoemission and optical experiments, we postulate a simplified energy diagram for the gated phase that is shown in Fig. 3D. The photoemission peak observed in Fig. 3B corresponds to filled in-gap states centered at ∼2.5 eV above the O 2p band. In a similar fashion to VO₂, we propose that the structural changes induced by the gating lead to an overlap between the created in-gap states and the π*-band (Fig. S7). The population of the itinerant states originating from the π*-band is the mechanism of the high conductivity. It is worth noting that the different charge environments observed for W atoms is an indication that charge localization due to defects is also present in this system. The small temperature dependence observed in the resistivity of the gated state (13) can be explained as a competition between localization and itinerancy of electrons (34, 35).

Fig. S5.

Wavelength dispersions of refractive index (A) and extinction coefficient (B) for VO₂ films at various temperatures between 25 and 120 °C. Solid and broken curves indicate the data obtained during the rise and drop in temperature, respectively [taken from (31) with the author’s permission].

Fig. S6.

Wavelength dispersions of refractive index (Left) and extinction coefficient (Right) for pristine, intermediate, and gated WO₃. The curves are derived from ellipsometry data collected at room temperature.

Fig. S7.

(A and B) Calculated refractive index (A) and extinction coefficient dispersion (B) using the Lorentz oscillator model with three oscillators. (C and D) Amplitude (C) and energy (D) of the Lorentz oscillators used for the simulation of pristine, intermediate, and gated dispersions. Note that the energy oscillator for j = 3 goes to 0 for the simulation of the gated state.

In conclusion, liquid electrolyte gating of a WO₃ thin film led to a more symmetric crystalline structure with no substantial change of the stoichiometry. Deep probing hard X-ray photoemission spectroscopy of core levels pointed to an inhomogeneous distribution of charge density among the W atoms and the weakening of some oxygen bonds, favoring slightly covalently bonded oxygen or trapped nonbonded oxygen atoms. We propose that the increase of spectral intensity near ε_F, as detected by photoemission, is connected to the electron transfer from weakly bonded oxygen to new in-gap states, which overlap with the bottom of the conduction band and result in metallic behavior. Intraband-like transitions from these states produce optical absorption outside of the visible range. We thus conclude that the electrolyte gated material is an inexpensive transparent conducting oxide with potential applications in displays, photovoltaics, and touchscreens.

Experimental Procedures

In the present study, Raman measurements were performed in a confocal microscope using a LabRam HR800 equipped with a 2,400 l/mm grating. The 325-nm line of a He–Cd laser was used as the optical source. Filters with attenuation up to 10³ were used to reduce the laser power to prevent sample damage. Ellipsometry measurements were done using a Woollam M-2000 T-Solar in a range from 0.7 to 5 eV. HAXPES was performed at beamline 12XU at SPring-8 in Hyogo, Japan, using an excitation energy of ∼6.5 keV. All measurements were carried out at room temperature. Further details of the thin-film growth and characterization are given in ref. 13.

The BE is referenced to the kinetic energy of photoelectrons from the Fermi edge (ε_F) of gold. The experimental spectra were normalized by area, and the core levels were fit by Voigt peaks using CasaXPS [Farley Casaxps Version N 2.3.16 (2011); Casa Software Ltd.; www.casaxps.com].

Each component in Fig. 2 D–F represents the doublet (f_5/2, f_7/2), for which we consider fixed values of spin–orbit splitting (2.15 eV) and integrated intensity ratio between the f_7/2 and f_5/2 peak (4/3). The vertical dashed lines in Fig. 2 A–F indicate the binding energy position of the main components of the pristine O 1s and W 4f spectra, O_a and W_a, respectively.

Sample Preparation, Device Fabrication, and Gating Procedure

Epitaxial WO₃ films were prepared by pulsed laser deposition from a polycrystalline WO₃ target using a laser with an energy density per pulse of ∼0.7 J cm^–2, a repetition rate of 4 Hz, and a target-substrate distance of ∼7.1 cm. A molecular oxygen pressure of 0.2 millibars was used during deposition and sample cool down. The WO₃ films were grown on single-crystalline LaAlO₃ (100) substrates (supplied by Crystec GmbH) at deposition temperatures of 750 °C. Crystallinity, uniformity, smoothness, and high resistivity confirm the high quality of the samples. Further details can be found in ref. 13.

For the ionic liquid gating experiments, devices with channel sizes of about 6 × 2 mm² were fabricated from the WO₃ films using shadow masks: insulating layers of 80-nm-thick amorphous alumina and 70-nm-thick SiO_x were deposited to define the channel area and to separate the WO₃ channel from the lateral gate electrode. Source, drain, and gate electrodes, composed of 5 nm Ru/65 nm Au, were grown onto the WO₃ films by ion-beam sputter deposition.

Electrolyte gating was performed under vacuum using water-free HMIM-TFSI (Merck Millipore). The liquid was deposited on the sample using a syringe. To remove any water contamination in the liquid electrolyte, the sample was held under vacuum for ∼8 h before the gating procedure. The film was gated for about 10–15 h. The process was monitored by measuring the I_DS current, as shown in Fig. 1B. Two samples were used, one for the photoemission and Raman measurements and another for the ellipsometry measurements. The gating procedure was identical, and after gating, the liquid electrolyte was washed with alcohol (in air). The sample for the photoemission measurements was immediately transferred to the measurement chamber (under vacuum) after cleaning. The total time the sample was exposed to air in this process was less than 3 min. The Raman and ellipsometry measurements were performed in air; the resistance of the sample was monitored to ensure the sample remained in the gated state. Details of the measurement steps, approximate duration, and measured resistance are given below for the Raman and ellipsometry measurements. The samples indeed remained gated longer in vacuum or in a glovebox; however, the Raman and ellipsometry experimental setups did not allow for such apparatus.

Raman Measurements.

• i)Pristine sample resistance (R) on handheld ohmmeter, >200 MΩ.
• ii)After 16 h gating in vacuum, R ∼1 kΩ.
• iii)Sample removed from vacuum, washed, and dried, 8 min, R ∼3 kΩ.
• iv)Raman measurements, 30–40 min, R ∼5–50 kΩ.
• v)One-week exposure to air R >200 MΩ.

Ellipsometry Measurements.

• i)Pristine sample resistance, R >200 MΩ.
• ii)After 16 h gating in vacuum, R ∼1 kΩ.
• iii)Sample removed from vacuum, washed, and dried, 15 min, R ∼8 kΩ.
• iv)Ellipsometry measurements, <10 min, R ∼8 kΩ.
• v)Exposure to air for ungated measurement, 3 h, R ∼5 MΩ.

Electronic Transport of Pristine, Gated, and Ungated WO₃

Details of the electronic transport can be found in ref. 13.

Core Level Photoelectron Spectroscopy

Fig. S1 shows the W 5p and 4f core levels for the pristine and gated states. The excitation energy used in these experiments results in a relatively large photoelectron cross-section for the W 5p states (shown in gray). The fitting of the 5p core levels was performed simultaneously with the W components (main text). We considered a fixed spin–orbit energy split and ratio between p_3/2 and p_1/2 areas. The binding energies for W 4f and O 1s are listed in Tables S1 and S2, respectively.

Fig. S2 shows the O 1s and W 4p core levels. The spectral area of the O 1s peak normalized by the spectral areas of the W 4p peak is the same for all states—pristine, gated, and ungated—indicating that the gating procedure does not produce a significant change in oxygen content.

Exposure of WO₃ to Hard X-Ray (6 keV).

The exposure of WO₃ to hard X-rays during the HAXPES measurement induces changes in the core level spectra and produces a peak near the Fermi energy. Different from reports on UV exposure, these changes reach saturation after a short time, which indicates a fast decay of the induced defects.

In the reported experiment, the photon flux was about 10¹³ photons per second. At this high flux, the saturation occurs in a very short time; that is, the saturation time is of order of the energy scan time (about 1 min) and no time dependence could be detected. In a second experiment [Deutsches Elektronen-Synchrotron (DESY) at beamline P09], we measured the WO₃ photoemission using an attenuated photon flux (∼10⁷–10⁸ photons per second). In this condition, we were able to measure the time evolution of the spectra as shown in the Fig. S3.

Confirmation That the d-States Contribute to the Valence Band.

The valence band (Fig. S4) shows strong dependence on the light polarization (s- and p-linearly polarized light). The band indicates that d orbitals with distinct symmetries (odd and even with respect to the scattering plane) are mixed with the 2p states forming the valence band. The peak near E_f has a very strong contribution of W 3d t_2g.

Complex Refractive Index Derived from Ellipsometric Spectroscopy.

We found similarities between the complex refractive index (N) dispersion during the insulator–metal transition in VO₂ (31) and the electrolyte gating of WO₃.

Fig. S5 shows the changes of the refractive index n and the extinction coefficient k dispersions in VO₂ for increasing/decreasing temperatures. Fig. S6 shows n and k dispersion in WO₃ for three states: pristine, gated, and “intermediate,” which is the gated sample exposed to air for nearly 4 h. In the intermediate state, the sample is partially ungated.

Kakiuchida et al. (31) used the Lorentz oscillator model, using three oscillators, to describe the wavelength dispersion of N in VO₂ according to the equation:

$${(n\left(\lambda \right)+ik\left(\lambda \right))}^2={\mathit{ϵ}}_{\infty }+{\displaystyle \sum }_{j=1}^3\frac{A{m}_j}{E_j^2-{(hc/\lambda )}^2-iB{r}_j(hc/\lambda )},$$

where the parameters E_j, Am_j, and Br_j are energy, amplitude, and damping coefficient of the oscillator j, respectively. ${\mathit{ϵ}}_{\infty }$ is the dielectric constant at $\lambda \to \infty$. That work showed that the energy of one of the oscillators (E₂) goes to 0 during the insulator–metal transition. The authors ascribed it to the transition energy between the V 3d levels, whose separation is decreased due to the lowering of empty-3d states and the π*-band in the rutile phase. When E₂ = 0, the contribution to the formula is equivalent to the metallic Drude model, representing the overlap of the bands at the Fermi energy.

Given the resemblance in behavior of VO₂ and WO₃ refractive index dispersions, we use the same approach to describe our data. Fig. S7 A and B shows the calculated curves. The oscillator parameters are shown in Fig. S7 C and D. The damping coefficient and dielectric constant were fixed: Br₁ = 0.8 eV, Br₂ = Br₃ = 0.6 eV, and ${\mathit{ϵ}}_{\infty }=3.$

The oscillator j = 1 represents the main transition from the 2p band to the conduction band, whereas j = 2 and j = 3 are associated with the in-gap states created during the gating process, as suggested by the increase of Am₂ and Am₃ (Fig. S7C) from the pristine to the gated state. The decrease of E₃ to 0 in the gated state (Fig. S7D) can be interpreted as caused by regions where the energy lowering of the π*-band leads to an overlap with the in-gap states. As a very simple model, the Lorentz approach with three oscillators cannot precisely fit the experimental data; however, the approach describes qualitatively the behavior of the optical properties through the gating process, which supports our conclusions.