Terahertz conductivity of thin gold films at the metal-insulator percolation transition

Terahertz time-domain spectroscopy is used to measure the complex conductivity of nanometer-thick gold films evaporated on silicon substrates in the far-infrared spectral region from $0.2\text{to}2.7\mathrm{THz}$. With increasing film thickness a characteristic crossover from an insulating to a conducting state via a percolation transition is observed. Of particular interest is the characteristic non-Drude behavior close to the transition. Whereas effective medium theory is inconsistent with our measurements in this regime, the Drude-Smith model, a generalization of the classical Drude model which incorporates carrier localization through backscattering, provides excellent fits to the observed complex conductivity. Applying this model we observe extreme values for the carrier scattering time at the percolation threshold.