Structural and electrical properties of granular metal films

Granular metal films (50–200,000 Å thick) were prepared by co-sputtering metals (Ni, Pt, Au) and insulators (SiO₂, Al₂O₃), where the volume fraction of metal, x, was varied from x = 1 to x = 0.05. The materials were characterized by electron micrography, electron and X-ray diffraction, and measurements of composition, density and electrical resistivity at electric fields ε up to 10⁶ V/cm and temperatures T in the range of 1.3 to 291 K. In the metallic regime (isolated insulator particles in a metal continuum) and in the transition regime (metal and insulator particles in a metal continuum) and in the transition regime (metal and insulator labyrinth structure) the conduction is due to percolation with a percolation threshold at x?0.5. Tunnelling measurements on superconductor-insulator-granular metal junctions reveals that the transition from the metallic regime to the dielectric regime (10–50 Å size isolated metal particles in an insulator continuum) is associated with the breaking up of a metal continuum into isolated metal particles. In the dielectric regime the temperature dependence of the low-field resistivity is given by ρL = ρo exp [2√(C/kT)], and the field dependence of the high-field, low-temperature resistivity is given by ρH = ρ∞ exp (εo/ε), where ρo, ρ∞, C, and εo are material constants. A simple theory based on the assumption that the ratio s/d (d-metal particle size and s-separation between particles) is a function only of composition yields expressions for ρ(ε, T) in excellent agreement with experiment. Furthermore, the theory predicts the experimental finding that the resistivity can be expressed in terms of a universal function of the reduced variables kT/C and ε/εo. The inter-relationship between all the important physical properties of granular metals and their structure is also discussed.