Frequency-dependent dielectric behavior of amorphous silicon thin films

The admittance $Y=G+j\omega C$ of amorphous silicon films, produced by electron-beam evaporation, has been measured at frequencies between dc and ${10}^7$ Hz, and at temperatures between 150 and 400 K. At low frequencies the conductance $G$ was nearly independent of frequency, an exponential function of temperature, and influenced by contacts. At medium frequencies $G$ increased almost proportionally to ${\omega }^s$, with $s\simeq 0.9$. In this region $G$ was found to be contact independent and superlinearly dependent on temperature. In the high-frequency region a saturation behavior of $G$ was observed. The capacitance $C$ decreased monotonically from low to high frequencies. These measured properties have been attributed to a hopping between sites, randomly distributed in space and energy, and over the barriers separating the sites. The barrier height has been correlated to the intersite separation by assuming Coulomb-like potential wells. This model accounts both for the ${\omega }^s$ behavior and for the saturation of $G$. However, to obtain good agreement between theory and experiment it was necessary to envisage a minimum relaxation time ${\tau }_o$ not much smaller than ${10}^{-6\mathrm{}}$ sec. In contrast, ${\tau }_o$ has in previous work been interpreted to be of the order of an atomic vibrational period (∼ ${10}^{-12\mathrm{}}$ sec).