Electrical conduction in ultra thin metal films I. Theoretical

Abstract
A theory is developed to account for the transport of charge in ultra thin, aggregated metal films, using quantum mechanical electron tunnelling, and thermionic emission theories. The current density in the film is expressed as a direct function of the structure of the film, the electrical properties of the substrate, the applied voltage and the temperature. It is shown that for a typical aggregated metal film conduction is by electron tunnelling, and that the tunnelling path is through the substrate. The trap hopping model of conduction on an active substrate is re-examined and limits are established for each of the mechanisms. It is shown that the activation energy associated with conduction in very thin films is due to the interaction of Coulombic fields surrounding small, discrete, metal particles. Four types of film structures are analysed, depending on whether the particles and the gaps between them are large or small. For small particles and small gaps the basic mechanism of conduction is an activated quantum mechanical tunnelling; for large gaps conduction in the substrate dominates, whereas for large particles with small gaps a simple, unactivated, tunnelling process is dominant.