Separation of terahertz and DC conductivity transitions in epitaxial vanadium dioxide films

Vanadium dioxide (VO $2$⁠) is among the most extensively studied strongly correlated electron materials, owing to its notable insulator–metal transition (IMT) occurring near room temperature (around 67  $°$C). This transition endows VO $2$ films with significant modulation effects at terahertz (THz) frequencies,^1–8 leading to the development of a wide range of THz applications, including memories,^9–11 tunable phase shifters,¹² frequency selectors,^13,14 and polarization converters,¹⁵ all based on the IMT of VO $2$ films. Despite extensive investigations, the precise physical mechanism underlying the IMT remains incompletely understood, mainly due to the concurrent structural phase transition (SPT) from the monoclinic phase to the rutile phase that accompanies the IMT. Debates persist regarding whether the transition is driven by a structurally Peierls-like mechanism,¹⁶ Mott-Hubbard mechanisms due to electronic correlations,¹⁷ or a combination of these factors.¹⁸ 

The complex interplay between Coulomb interaction and structural effects in VO $2$ films induces a percolation phenomenon—a mixture of metallic and insulating phases near the IMT.^3,19–27 Previous studies, such as those by Cocker et al.,^28,29 have reported a gradual transformation from insulating to metallic conductivity of nanogranular VO $2$ films and analyzed the influence of percolation through complex THz conductivity spectra. More recently, H.T. Stinson’s group experimentally demonstrated the coexistence of metallic and insulating domains using a home-built terahertz near-field microscope,³⁰ providing direct evidence for the percolation effect in VO $2$ films.

Typically, the effective transport properties at THz frequencies, influenced by the percolation effect, are modeled using networks of nanoparticles with varying sizes and shapes, a process often assessed through morphology characterization. For instance, Walther et al. reported on nano-structured Au thin films undergoing a transition from an insulating to a conducting state via a percolation mechanism.^31,32 However, discussing the percolation effect in epitaxial VO $2$ films, which are strained single crystals, presents challenges due to lattice distortions induced by interfacial strains or stress. These distortions result in the configuration of spatially inhomogeneous phases and even a dichotomy between the IMT and SPT.

In this study, we investigate the electronic transport properties induced by the IMT using THz time-domain spectroscopy (THz-TDS) and DC measurements, while tracking the SPT through Raman scattering spectroscopy. Our data suggest a percolation scenario across the IMT of VO $2$ films, with a notable separation between DC and THz conductivity transitions. Given that THz light interrogates the electronic response at energies close to the Fermi level, it is closely connected to DC transport. In this context, we attribute the separation between DC and THz conductivity to a weak confinement effect induced by percolation, rather than Coulomb energy effects.³⁰ Furthermore, we observe that this separation increases with increasing film thickness and improved crystallization quality. THz complex conductivity throughout IMT is fitted to the Drude–Smith model, exhibiting features of carriers confined within mesoscopic structures. These findings significantly contribute to the understanding of the IMT in epitaxial VO $2$ films and hold important implications for future applications of VO $2$-based THz devices.

Figure 1(a) depicts the experimental setup: in situ measurements of THz transmission spectra, DC conductivity, and Raman scattering spectra, aimed at analyzing the correlation between THz complex conductivity, DC conductivity, and metallic phase fraction $f m$⁠. VO $2$ films were synthesized by a polymer-assisted deposition method on a (⁠ $10 1 ¯0$⁠) Al $2$O $3$ (⁠ $m$-sapphire) substrate. The thicknesses of the films were measured in the cross-sectional SEM (scanning electron microscope) images (Fig. S1 in the supplementary material) and determined to be 35, 55, 70, and 85 nm, respectively (labeled as S35, S55, S70, and S85, respectively). The DC conductivity of VO $2$ films, measured using the four-point probe technique, exhibits a significant drop of 4-5 orders of magnitude [Fig. 1(b)], confirming the high IMT quality of all these samples.

The epitaxial growth of VO $2$ films has been demonstrated by high-resolution x-ray diffraction (XRD) patterns. In the $θ$–2 $θ$ scan [Fig. 1(c)], a single VO $2$ diffraction peak is observed at 65.10 $°$⁠, 65.08 $°$⁠, 65.06 $°$⁠, and 65.07 $°$ for S35, S55, S70, and S85, respectively. This peak is assigned to the (⁠ $4 ¯02$⁠) diffraction of $M$1-VO $2$⁠, indicating VO $2$(⁠ $4 ¯02$⁠) $∥$ (⁠ $10 1 ¯0$⁠)Al $2$O $3$ in the growth direction (detailed epitaxial relationship in Sec. S2 of the supplementary material). Consequently, a compressive strain is exerted along the $a R$ axis of the M1 phase, which aligns with the V–V chains. The compressive strain values are $−$0.434%, $−$0.407%, $−$0.380%, and $−$0.3932% for S35, S55, S70, and S85, respectively. This compressive strain softens the Coulomb energy and enhances the electrical conductivity at the M1 phase near 35 $°$⁠.³³ As the film thickness increases, the softening of the Coulomb energy weakens due to decreased compressive strain along the $a R$ axis. Consequently, the DC conductivity near 35  $°$C decreases with increasing film thickness. Rocking curve measurements of VO $2$ (⁠ $4 ¯02$⁠) diffraction were performed to evaluate the crystallinity of epitaxial films (Fig. S2 in the supplementary material). The full width at half maximum (FWHM) values of the rocking curves are 0.758 $°$⁠, 0.603 $°$⁠, 0.623 $°$⁠, and 0.582 $°$ for S35, S55, S70, and S85, respectively. The narrowed FWHM with increasing thickness is the signature of improved crystallinity and decreased defect density.

Accompanied with the IMT, VO $2$ undergoes SPT from a monoclinic lattice to a rutile lattice. Consequently, the percolation scenario in VO $2$ films can be characterized through Raman scattering, which provides insights into the phase fraction of the M1 phase and the rutile phase.^34–36 H. A. Dürr’s group has demonstrated a similar scenario of a strained (⁠ $−402$⁠)-oriented VO $2$ epitaxial film on the TiO $2$ substrate. Their research demonstrates no separation between IMT and SPT during the heating process.³³ Therefore, it is possible to evaluate the metallic phase fraction by considering the M1 phase fraction. A continuous-wave laser with a wavelength of 532 nm was employed, and the laser power was attenuated to 1.25 mW to minimize the photo-thermal effect. Experimental results demonstrate that the localized temperature increase induced by laser annealing remained negligible (Sec. S3 in the supplementary material).

The temperature-dependent Raman spectra of S85 is shown in Fig. 3(a) as an example. At room temperature (20  $°$C), the pure $M$1 (insulating) phase of VO $2$ is identified by the eight Raman-active phonon modes at 143, 195, 223, 260, 308, 389, 498, and 613 cm $− 1$⁠.^34,35 With increasing temperature, these Raman spectra maintain unchanged, until metallic VO $2$ domains begin to nucleate. As a consequence, in the spectra measured at 60  $°$C and 62  $°$C (blue and green lines), the Raman peaks of the insulating VO $2$ phase decreased to a certain extent. As S85 is heated to 80  $°$C, the Raman spectra (red line) are characterized by a featureless luminescence, indicating the VO $2$ film fully transformed into the metallic phase. Note that the photon energy (2.3 eV) of the laser source (532 nm) is well above the plasma frequency (⁠ $∼1.8$ eV) of metallic VO $2$ and is in a spectral region that the optical properties of metallic and insulating VO $2$ are nearly identical.³⁵ Therefore, the strength of the incident laser and outgoing Raman scattering will not be influenced by the varied optical properties across the IMT.

The strong peak at around 195 cm $− 1$ (⁠ $ω V - V$⁠) in Fig. 3(a) originates from the characteristic V–V dimers of insulating VO $2$³⁶ and is carefully observed to evaluate the volume fraction (⁠ $f i$ and $f m$⁠) of insulator and metallic phases. As shown in Fig. 3(b), the Raman scattering of $ω V - V$ in S35 and S85 gradually weakens as the sample is heated. The slight red shift observed on the $ω V - V$ wave number is induced by the thermal phonon softening. In this way, setting $f i=1$ and $f m=0$ for the VO $2$ film at 20 $°$C, the $f i$ of the inhomogeneous VO $2$ film at $T$ can be evaluated by the relative intensity (⁠ $I V - V(T)$⁠) of the remained $ω V - V$ scattering, i.e., $f i= I V - V(T)/ I V - V(20 ° C)$⁠, and $f m=1− f i$⁠.

In Figs. 4(a) and 4(b), real-component and imaginary-component conductivity changes for VO $2$ films (S35, S55, S70, and S85) at DC and THz frequencies are plotted against $f m$⁠. Dashed lines highlight the critical thresholds (⁠ $f c$⁠) of a conductivity transition, determined by identifying extreme points of their respective differential functions. While DC conductivity reflects long-range carrier transport, THz conductivity reflects localized electron transport. The distance (⁠ $L f$⁠) traveled by charge carriers during a single period of THz pulse is described by $L f= D / f$ (⁠ $D$ represents the diffusion coefficient), typically in nanometers for VO $2$ films.^28,29 This discrepancy in electron conduction between THz and DC suggests that long-range carrier transport is not necessary for effective conductivity at THz frequencies, resulting in the lower $f c$ at THz frequency compared to DC. Of note, a clear negative relationship between film thickness and $f c$ at THz frequencies emerges. For instance, at 0.3 THz, $f c$ values are 0.67, 0.48, 0.26, and 0.15 for S35, S55, S70, and S85, respectively. Similarly, at 1.0 THz, $f c$ values are 0.56, 0.42, 0.18, and 0.12 for S35, S55, S70, and S85, respectively. In the case of the thicker film (S85), a significant reduction in $f c$ to 0.12 at 1.0 THz was observed. Moreover, it is evident that $σ 2$ at 1.0 THz becomes less negative as film thickness increases. This phenomenon demonstrates released carrier confinement at 1.0 THz in thicker films.

Figures 5(a)–5(c) display the complex conductivity spectra for S35, S55, and S85 in the vicinity of $f c$⁠. The conductivity spectra for S70, showing a similar signature to S85, are presented in Fig. S4 of the supplementary material. The presence of a real conductivity that increases with frequency and a negative imaginary conductivity shown in Fig. 5 is a characteristic signature of non-Drude behavior and has been assigned to a carrier confinement effect due to the inhomogeneous phase transition of the VO $2$ film.^28,31,39,40 In more detail, for the thinner film S35, $σ 1$ is continuously suppressed until $f m$ reaches 0.62, at which point a non-zero $σ 1$ at 1.0 THz becomes evident. Simultaneously, $σ 2$ of S35 remains negative, with its magnitude increasing with frequency. Such results indicate that a carrier confinement effect persists in S35 throughout the IMT. Comparatively, for S55, the critical $f m$ for non-zero $σ 1$ shifts to a lower value, accompanied by a less negative $σ 2$⁠. In the case of S85 in Fig. 5(c), we observe the lowest $f c$ for non-zero $σ 1$⁠, and $σ 2$ is near zero throughout the phase transition. The $σ ~(f)$ spectrum of S85 exhibits a feature close to free Drude scattering, indicating a significantly weakened carrier confinement effect.

Utilizing the Drude–Smith model, we have elucidated the variation in the carrier confinement effect among different films. As shown in Fig. 6(a), the parameter $c 1$ displays different trends among different films. To clarify, the phase transition process can be divided into three stages:

• Below the 2D percolation threshold (⁠ $f m<0.5$⁠), $c 1$ remains close to $−$1.0 in the thinner epitaxial film (S35). Conversely, in the thicker epitaxial film (S85), $c 1$ becomes less negative and stabilizes around $−$0.5. This observation highlights a notable difference in the carrier confinement effect among films with different thicknesses when $f m<0.5$⁠.

• Above and near the percolation threshold (⁠ $0.5< f m<0.9$⁠), $c 1$ in all samples shifts to less negative values. This aligns with the notion that the filling of channels between isolated metallic domains leads to the formation of randomly connected metal networks, releasing the confinement effect.

• In fully metallized films (⁠ $0.9< f m<1.0$⁠), carrier confinement still persists, possibly due to back-scattering on crystallite boundaries.

In summary, we investigated the relationship between THz conductivity, DC conductivity, and f_m of epitaxial VO₂ films across the IMT. Our findings reveal a separation between THz and DC conductivity transitions as $f m$ is heated from 0 to 1. This separation increases with film thickness and crystallite quality, and is attributed to changes in carrier confinement effects as analyzed through complex conductivity spectra. For a thinner film (S35), we observed a significant capacitive response (zero $σ 1$ and negative $σ 2$⁠) until $f m$ reaches the critical threshold of 0.62, indicating greatly conductivity suppression due to the confinement effect. With increasing film thickness, the $f c$ of VO $2$ films shifts to lower $f m$ values (⁠ $f m=0.12$⁠), and the $σ 2$ component becomes less negative, indicating a release of a carrier confinement effect. Overall, our results highlight the influence of a mesoscopic carrier confinement effect on the conductivity transition of the VO $2$ film at THz frequencies and demonstrate the potential for manipulating THz properties through a percolation effect.

Please refer to the supplementary material for comprehensive experimental details on film thickness measurements, XRD analysis for epitaxial growth characterization, and findings indicating the negligible thermal effect of the incident laser in in situ Raman scattering measurements.

This work was supported in part by the Natural Science Foundation of China under Grant Nos. 52272138, 61825102, U21A20460, and 52021001.

The authors have no conflicts to disclose.

Chang Lu: Conceptualization (equal); Data curation (equal); Writing – original draft (equal). Min Gao: Funding acquisition (equal); Writing – review & editing (equal). Junxiao Liu: Investigation (equal). Yantong Lu: Investigation (equal). Tianlong Wen: Investigation (equal). Yuan Lin: Funding acquisition (equal); Investigation (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.