Evidence for impact ionization in vanadium dioxide

Pump-probe optical spectroscopy was used to investigate proposed charge-carrier multiplication via impact ionization in the $M_1$ insulating phase of ${\mathrm{VO}}_2$. By comparing the transient reflectivities of the film when pumped at less than and then more than twice the band-gap energy, we observed a larger ultrafast response with the higher energy pump color while the film was still transiently in the insulating phase. We additionally identified multiple time scales within the charge dynamics and analyzed how these changed when the pump and probe wavelengths were varied. This experiment provided evidence that a fast carrier multiplication process, i.e., impact ionization, acts efficiently in this prototypical strongly correlated insulator, as was recently predicted by theoretical calculations.

Figure 1

(a) An incident solar photon promotes an electron from the occupied band to the conduction band (i) with an energy greater than twice the band gap or (ii) near the band edge, creating an electron/hole pair in either case. (b) In a typical conventional insulator, the electron/hole pair dissipates its excess energy beyond the gap via phonon scattering or phonon emission and relaxes to the band edge within a time scale of the order of 0.1–1 ps. (c) In the case of a strongly correlated insulator with incident photoexcitation energy greater than twice the band gap [part (a), case (i)], the electron, the hole, or both can give up their excess energy to promote one or more electrons from the valence band to the conduction band through their interaction with the electrons of the occupied bands. (d) Auger recombination is the reverse of impact ionization.

Figure 2

(a) Resistance vs temperature curve of a ${\mathrm{VO}}_2$ film. The curve was measured while cooling and heating (arrows) showing slight hysteresis at the metal-insulator transition ($T=345$ K). Inset: Atomic force microscope image of a 100-nm ${\mathrm{VO}}_2$ film grown on a (111) ${\mathrm{SrTiO}}_3$ substrate. (b) XRD $\theta -2\theta$ scan of a ${\mathrm{VO}}_2$ film. The insets show enlarged regions around the 111 and 222 ${\mathrm{SrTiO}}_3$ peaks.

Figure 3

Normalized ${\mathrm{VO}}_2$ transient reflectivities. (a) The relative reflectivity change for the 1968-nm probe. (b) The relative reflectivity change for the 1761-nm probe. The 800-nm pump data are offset by 0.2 for clarity in both (a) and (b). Insets contain the same data as their respective panels plotted on a linear time axis.

Figure 4

${\mathrm{VO}}_2$ transient reflectivity ratios and metallic state comparison. (a) The ratios of the transient reflectivities for both sets of data in Fig. 3. (b) The normalized transient reflectivities in the metallic state. The sign of the reflectivity is inverted from the insulating phase. Inset: The 800/1466 pump ratio of the normalized data in (b). The data in (a) and (b) were smoothed using moving averages. (c) Normalized transient reflectivities in the insulating state taken at $2.6\mathrm{mJ}/{\mathrm{cm}}^2$ for the 1466-nm pump and $1.45\mathrm{mJ}/{\mathrm{cm}}^2$ for the 800-nm pump.

Figure 5

(a)–(c) The normalized transient reflectivities taken with pump energy densities of $5.0, 3.8$, and $2.6\mathrm{mJ}/{\mathrm{cm}}^2$, respectively.

Figure 6

(a)–(c) The 800/1466 ratios of the transients shown in Fig. 5, respectively. The data in (a) and (b), but not (c), were smoothed using moving averages.

Figure 7

(a) Pulse energy dependence of the reflectivity enhancement for 800/1466-nm pump comparisons. Filled circles (crosses) represent measurements when incident energy densities were the same (different) for both colors. (b) $\mathrm{\Delta }R/R$ amplitudes (1761-nm probe) occurring at long delays greater than 100 ps. The saturation level was estimated as the average of the two trends. The lines in both (a) and (b) are guides for the eyes.

Figure 8

Normalized transient reflectivities taken at $1.5\mathrm{mJ}/{\mathrm{cm}}^2$ for the 1466-nm pump and $0.85\mathrm{mJ}/{\mathrm{cm}}^2$ for the 800-nm pump. The data were smoothed using moving averages.