ac Conductivity of Scandium Oxide and a New Hopping Model for Conductivity

The ac conductivity of scandium-oxide thin films in the audio-frequency range at temperatures between 4 and 295 K has been measured. The frequency-dependent component of the conductivity was found to obey an equation of the form ${\sigma }_1\left(\omega \right)=A{\omega }^s$, where $\omega$ is the circular frequency and $s$ is a temperature-dependent quantity whose value is close to, but less than, unity. Interpretation of the results in terms of a single-phonon hopping theory does not yield satisfactory agreement. To account for the data a new hopping model is proposed. The conductivity is calculated for classical hopping of carriers between localization sites over potential barriers with a height distribution caused by the random spatial distribution of these sites. This model yields the ${\omega }^s$ behavior at high frequencies with the quantity ($1-s$) increasing almost linearly with temperature. In addition, it is predicted that a thermally activated dielectric-loss peak should occur for very low frequencies. It is suggested that this model may find broad application in the interpretation of ac conductivity results in amorphous materials.