Infrared spectroscopy and nano-imaging of the insulator-to-metal transition in vanadium dioxide

We present a detailed infrared study of the insulator-to-metal transition (IMT) in vanadium dioxide $\left({\text{VO}}_2\right)$ thin films. Conventional infrared spectroscopy was employed to investigate the IMT in the far field. Scanning near-field infrared microscopy directly revealed the percolative IMT with increasing temperature. We confirmed that the phase transition is also percolative with cooling across the IMT. We present extensive near-field infrared images of phase coexistence in the IMT regime in ${\text{VO}}_2$. We find that the coexisting insulating and metallic regions at a fixed temperature are static on the time scale of our measurements. A distinctive approach for analyzing the far-field and near-field infrared data within the Bruggeman effective medium theory was employed to extract the optical constants of the incipient metallic puddles at the onset of the IMT. We found divergent effective carrier mass in the metallic puddles that demonstrates the importance of electronic correlations to the IMT in ${\text{VO}}_2$. We employ the extended dipole model for a quantitative analysis of the observed near-field infrared amplitude contrast and compare the results with those obtained with the basic dipole model.

Figure 1

(Color online) (a) Room-temperature x-ray diffraction data for the (200)-oriented $M1{\text{-VO}}_2$ film on $\left(\overline{1}012\right)$-oriented sapphire substrate. (b) The resistance of the ${\text{VO}}_2$ film is plotted while heating and cooling across the IMT. (c) Real part of the conductivity ${\sigma }_1\left(\omega \right)$ of ${\text{VO}}_2$ plotted as a function of frequency for various representative temperatures while heating the sample through the IMT. The open circle denotes the isosbestic (equal conductivity) point for all spectra. (Inset) The temperature dependence of the real part of the dielectric function ${ϵ}_1$ in the low-frequency limit $\left(\omega =50{\text{cm}}^{-1}\right)$. (d) The optical constants of ${\text{VO}}_2$ as in (c) but with phonon contributions subtracted.

Figure 2

(Color online) Images of the near-field scattering amplitude $s_2$ (scale in relative units) over the same $4\times 4\mu {\text{m}}^2$ area obtained by s-SNIM operating at the infrared frequency $\omega =930{\text{cm}}^{-1}$. The images were obtained for various temperatures while heating ${\text{VO}}_2$ through the IMT. The metallic regions depicted in light blue (light gray) and white give higher amplitude compared to the insulating phase shown in dark blue color (dark gray).

Figure 3

(Color online) (a) The distribution of near-field amplitude $s_2$ from images in Fig. 2 for selected temperatures. Note the logarithmic scale on the vertical axis for clarity of presentation. (b) The distribution of the normalized near-field amplitude for the same temperatures as in (a). The median near-field amplitudes for the insulating phase were used for normalizing the near-field amplitude in (b). The distributions plotted in panels (a) and (b) are the number of pixels normalized such that the area under each of the histograms is unity.

Figure 4

(Color online) Optical characterization of the metallic puddles derived from experiment: (a) the real part of the optical conductivity ${\sigma }_{1a}\left(\omega \right)$, (b) the scattering rate $1/\tau \left(\omega \right)$, and (c) the optical effective mass normalized by the band value $m\ast \left(\omega \right)/m_b$ of the metallic regions of ${\text{VO}}_2$ for representative temperatures in the IMT regime. The inset in (c) shows the $\omega \to 0$ limit of the mass enhancement factor as a function of temperature (data points between $T=400$ and 550 K are from Ref. 18).

Figure 5

(Color online) Dependence of the real part of the optical conductivity ${\sigma }_{1a}\left(\omega \right)$ of the metallic puddles on the depolarization factor $q$, with $f$ fixed at 0.31 for $T=342.6\mathrm{K}$.

Figure 6

(Color online) Panels (a) and (b) display the ellipsometric coefficients $\Psi \left(\omega \right)$ and $\Delta \left(\omega \right)$, respectively, that were measured for the ${\text{VO}}_2$ film on a sapphire substrate at $T=342\text{K}$ (dashed gray curves). The thin black solid lines are the ellipsometric coefficients derived from the Bruggeman effective medium theory model as explained in Appendix . The insets show the difference between the fits and data for the respective ellipsometric coefficients.

Figure 7

(Color online) Near-field amplitude $s_2$ images (scale in relative units) obtained at $\omega =930{\text{cm}}^{-1}$ with decreasing temperature through the IMT.

Figure 8

(Color online) Near-field amplitude $s_2$ images at $\omega =930{\text{cm}}^{-1}$ at $T=342\text{K}$. Image (b) was obtained immediately after image (a).