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

Abstract

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 to 2.7 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.

Dynamics of Carrier Transport in Nanoscale Materials: Origin of Non-Drude Behavior in the Terahertz Frequency Range

“…Complex conductivity in nanostructured Au films. Open circles and triangles are the experimental data extracted from [30]. Solid lines are the conductivity predicted by the SSFTC model.…”

“…Let us examine the THz conductivity in nanostructured gold films. Open circles and triangles in Figure 7 show one of examples of the real and imaginary parts of conductivity in nanogold films [30]. Solid lines are predicted conductivity in the SSFTC model.…”

Microscopic origin of the Drude-Smith model

“…23,29,[34][35][36]39,71,73,76 Alternatively, the Drude-Smith model has also been used as an EMT in its own right and fit directly to the measured THz conductivity. [9][10][11][12][13][14][15][16][17][18][19]21,22,[25][26][27]30,31,33,38,[41][42][43][44][45]48 Each approach begins with a different physical process and leads to its own difficulties when one interprets the subsequent fits to the data. In the former case, depolarization fields are included explicitly and treated as independent from weak confinement.…”

“…76,77 Fitting these simulations enabled Nemȇc et al to provide approximate mathematical expressions for the Drude-Smith fit parameters 76 that have since been applied to experimental data to extract meaningful physical information. 15,26,27,33,38 Complementary experimental techniques are often also used to examine the structure 11,12,15,[17][18][19][20]22,23,25,26,29,31,[33][34][35][36][37][38][39][41][42][43][44]46,47,50 and carrier transport characteristics 11,12,19,23,26,43,57 in a sample to test the fidelity of the Drude-Smith fits. Nevertheless, in the absence of a tractable derivation that shows how weak carrier confinement yields the DrudeSmith formula with well-understood fit parameters, it is difficult for the Drude-Smith model to be more than a convenient expression for linking the conductivities of similar nanosystems to one another, and to Monte Carlo simulations.…”

Parallel plate waveguide with anisotropic graphene plates: Effect of electric and magnetic biases

“…27 For a 4 nm thick gold layer, the plasma frequency, x p /2p, is 280 THz, scattering time, s, is 18 fs, and the persistence of velocity, c, is À1 (Ref. 27).…”