The universality of the ac electrical transport in granular metals has been scarcely studied and the actual mechanisms involved in the scaling laws are not well understood. Previous works have reported on the scaling of capacitance and dielectric loss at different temperatures in Co-ZrO₂ granular metals. However, the characteristic frequency used to scale the conductivity spectra has not been discussed, yet. This report provides unambiguous evidence of the universal relaxation behavior of Pd-ZrO₂ granular thin films over wide frequency (11 Hz–2 MHz) and temperature ranges (40–180 K) by means of Impedance Spectroscopy. The frequency dependence of the imaginary parts of both the impedance Z″ and electrical modulus M″ exhibit respective peaks at frequencies ω_max that follow a thermal activation law, ω_max ∝ exp(T^1/2). Moreover, the real part of electrical conductivity σ′ follows the Jonscher’s universal power law, while the onset of the conductivity dispersion also corresponds to ω_max. Interestingly enough, ω_max can be used as the scaling parameter for Z″, M″ and σ′, such that the corresponding spectra collapse onto single master curves. All in all, these facts show that the Time-Temperature Superposition Principle holds for the ac conductance of granular metals, in which both electron tunneling and capacitive paths among particles compete, exhibiting a well-characterized universal behavior.

The ac response in the dielectric regime of thin films consisting of Pd nanoparticles embedded in a ZrO ₂ insulating matrix, fabricated by co-sputtering, was obtained from impedance spectroscopy measurements (11 Hz–2 MHz) in the temperature range 30–290 K. The response was fitted to an equivalent circuit model whose parameters were evaluated assuming that, as a consequence of the bimodal size distribution of the Pd particles, two mechanisms appear. At low frequencies, a first element similar to a parallel RC circuit dominates the response, due to two competing paths. One of them is associated with thermally-activated tunneling conductance among most of the smallest Pd particles (size ~ 2 nm), which make up the dc tunneling backbone of the sample. The other one is related to the conductance associated with the capacitive paths among larger Pd particles (size > 5 nm). At low temperature and intermediate frequencies (~1 kHz), a shortcut process between the larger particles connects regions initially isolated from the backbone at low frequencies. These regions, populated by some additional smaller particles located around two bigger particles, were isolated because the bigger particles separation is too large for the tunneling current. Once connected to the backbone, current may also flow through them by means of the so-called thermally-activated assisted tunneling resistive paths, yielding the second element of the equivalent circuit (a parallel RLC element). At high temperature, the thermal energy shifts the onset of the shortcut process high frequencies and, thus, only the first element is observed. Considering these results, controlling the particle size distribution could be helpful to tune up the frequency at which tunneling conductance dominates the ac response of these granular metals.

We report on the electronic and optical properties of ultrathin granular films. We demonstrate that the static dielectric constant increases with thickness in the dielectric regime and diverges at the critical thickness, as predicted by classical percolation theory. However, for thicker samples, the dc conductivity does not obey scaling laws due to the presence of tunneling conduction. In this region the dielectric constant is positive, and the electronic transport is not metallic but can be described by Jonscher’s universal power law, even though there is a Drude-like response indicating the presence of free charge carriers. Only for thicker films when the dielectric constant becomes negative is there metallic conduction.

Discontinuous multilayer (DML) thin films, which consist of nano-granular metals (NGMs) embedded in a dielectric matrix, have attracted significant interest as engineered plasmonic metamaterials. In this study, a systematic layer-by-layer deposition of three-dimensional sub-wavelength periodic plasmonic DML structures via the radio frequency sputtering of a composite target has been reported. The overall optical response of the DML films composed of Au–Al ₂ O ₃ NGM homogenous layers, which are periodically sandwiched between two amorphous Al ₂ O ₃ layers, are studied using reflection spectroscopic ellipsometry and transmission spectroscopy techniques. By applying the analytical optical approaches based on multiple Gaussian oscillators, ambient DML sub-wavelength structures have been successfully modeled. As a result, the effects of the size and shape of the Au nanoparticles as well as of the surrounding and interfacial media on their localized surface plasmon resonance (LSPR) are elucidated, and the related films thickness and effective optical constants are determined. Interestingly, during the examination of resonance frequencies and dielectric functions, the obtained DML structures exhibit unusual characteristics that are different from those of their NGM constituents due to the electromagnetic interactions of the NGM layers with the LSPR, which represent metamaterial features.