Fluctuation-induced tunneling conduction in disordered materials

TLDR

Disordered materials with large conducting regions separated by small insulating gaps conduct via fluctuation‑induced tunneling, where thermally activated voltage fluctuations across the gaps govern the temperature and field dependence of conductivity. The authors derive a tunneling conductivity expression that reduces to thermally activated behavior at high temperatures and elastic tunneling at low temperatures, extend it to high‑field currents, and generalize it to random networks using effective‑medium theory, then compare the predictions with experiments on carbon‑PVC composites, doped GaAs, and doped polyacetylene. The theory predicts that the temperature dependence of conductivity is governed by barrier shape, that tunneling current nonlinearity diminishes with increasing temperature, and that it accurately reproduces the nonmetallic resistivity behavior observed in doped metallic polyacetylene, with excellent agreement across all three tested systems.

Abstract

In disordered materials generally characterized by large conducting regions (or long conducting pathways) separated by small insulating barriers, it is shown that the electrical conduction can be ascribed to a novel mechanism, fluctuation-induced tunneling, in which the thermally activated voltage fluctuations across insulating gaps play an important role in determining the temperature and field dependences of the conductivity. By considering the modulating effects induced by voltage fluctuations on either an image-force corrected rectangular potential barrier or a parabolic barrier, a theoretical expression for the tunneling conductivity is derived which displays thermally activated characteristics at high temperatures but becomes identical to the temperature-independent simple elastic tunneling at low temperatures. Between the two limiting behaviors the temperature dependence of the conductivity is controlled by the shape of the tunneling barrier. An expression for the high-field tunneling current is similarly obtained. It is found that, while the tunneling current increases as a nonlinear function of the field, the degree of nonlinearity decreases as the temperature increases, indicating an effective lowering and narrowing of the barrier by voltage fluctuations. The theory is also generalized from the consideration of a single tunnel junction to a random network of tunnel junctions by the application of the effective-medium theory. The theoretical predictions are compared with the experimental results for three disordered systems: (1) carbon-polyvinylchloride composites, (2) heavily doped, closely compensated GaAs, and (3) doped polyacetylene ${(\mathrm{CH})}_{x}$ in the metallic regime. In each case excellent agreement is obtained. It is shown in particular that the nonmetallic temperature dependence of the resistivity in doped metallic ${(\mathrm{CH})}_{x}$ samples can be understood in terms of the present theory.