Dielectric Relaxation of Hopping Electrons in Reduced Rutile, TiO2

A sharp dielectric relaxation in rutile is observed at liquid-${\mathrm{He}}^4$ temperatures in the audio-frequency range in reduced specimens. A relatively narrow distribution of relaxation times is involved, distributed about ${\tau }^{*}=\tau _0^{}{}_{}{}^{*}{e}^{\frac{-Q}{\mathrm{kT}}}$, with $Q=1.0\mathrm{}\pm 0.5\times {10}^{-3\mathrm{}}$ eV and $\tau _0^{}{}_{}{}^{*}={10}^{-6\mathrm{}}$ sec. It is proposed that the relaxation is due to the hopping of an electron between normal cation sites around a complex ionic core. The change in dielectric behavior of specimens with increased trivalent impurity content suggest that the complex ionic core is an oxygen vacancy associated with an extrinsic trivalent substitional impurity.