Measurement of the Frequency-Dependent Conductivity in Sapphire

Electron transport of photoexcited single-crystal sapphire ($\alpha \mathrm{\text{−}}{\mathrm{A}\mathrm{l}}_2{\mathrm{O}}_3$) is characterized by terahertz time-domain spectroscopy. The complex conductivity displays a Drude-type frequency dependence, which yields carrier scattering rates and densities. Carrier scattering is dominated by interactions with acoustical and optical phonons at low and high temperatures, respectively, and follows Matthiessen’s law over the measured temperature range of 40–350 K. The results, including low-temperature mobilities $>10000{\mathrm{c}\mathrm{m}}^2/\mathrm{V}\mathrm{s}$, are compatible with a large-polaron description of the conduction electrons.

Figure 1

Top panel: the transmitted THz electric-field waveform $E(t)$ in sapphire; Bottom panel: pump-induced change in the THz waveform $\Delta E(t)$ (dots) at room temperature and a fit to the Drude model (solid curve). The pump fluence was $3\mathrm{J}/{\mathrm{m}}^{\mathrm{2}}$ and the pump-probe time delay was 5 ps.

Figure 2

Frequency dependence of the real (${\sigma }^{\prime }$) and the imaginary part (${\sigma }^{\prime \prime }$) of the pump-induced complex conductivity (dots) of sapphire at room temperature. The solid curves represent a fit to the Drude model.

Figure 3

Temperature dependence of the scattering rate in high-purity sapphire (squares). The solid line is a fit to a transport model that includes LO-phonon and acoustic phonon scattering, as described in the text. The dashed line shows the acoustic phonon contribution. At the temperatures above that denoted by the dotted line, LO-phonon scattering dominates.