Abstract
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.
Highlights
Theoretical and computational models [23,24,25,26] have shown that the physical properties of percolating systems deal with scaling laws which are sensitive only to dimensionality
When D = 2R, clusters start to interconnect and form a conductive pathway over the macroscopic sample area. This corresponds to the percolation threshold [36] for which, in the case of gold, 3.5 × 1011 clusters cm−2 composed of approximately (1.25 ± 0.21) × 105 atoms impinge on each other according to this model while only 6% of the gold atoms on the surface of the clusters
Hövel et al [29, 30], showed that in a set of granular Au thin films, the zero crossing of ε1(0) occurred at the metal-to-dielectric transition at a thickness of 6.7 nm which was slightly larger than the critical thickness of 6.4 nm
Summary
Theoretical and computational models [23,24,25,26] have shown that the physical properties of percolating systems deal with scaling laws which are sensitive only to dimensionality. In the dielectric regime, it has been recently shown [5] that Jonscher’s universal power law (JUPL) [22] holds for the ac conductance, but a complete description of the electronic transport in granular metals has yet to be reported.
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