Equivalent circuit modeling of the ac response of Pd-ZrO2 granular metal thin films using impedance spectroscopy

The ac response in the dielectric regime of thin films consisting of Pd nanoparticles embedded in a ZrO2 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 similar to 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 (similar to 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.