Two-component model for the resistivity and noise of tunneling metal-insulator composites

Effective-medium theory is used to examine the resistivity rho(x) and normalized 1/f noise intensity s(x)=$S_{\rho }$(x)/${\rho }^2$(x) of a model metal-insulator composite, with volume fraction x of metal, which has two distinct conduction mechanisms: (i) metallic conduction and (ii) conduction due to charge tunneling through the insulating component. The model reproduces consistently the experimental measurements of both ρ(x) and s(x) by Mantese and Webb [Phys. Rev. Lett. 55, 2212 (1985)] on Pt/${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ composites over their wide range of x including the metallic conduction threshold at $x_c$. Fitting the model parameters to ρ(x) fully determines the interpolation of the noise intensity s(x) from s(0) to s(1) in excellent agreement with experiment over the full range of x. For x>$x_c$, the electrical conduction is dominated by metallic conduction along a metallic continuum, whereas for x<$x_c$ charge tunneling between metal islands is the primary means of electrical conduction. The noise due to tunneling resistivity fluctuations dominates the composite noise intensity s(x) over nearly the entire range of x. Thus for x≥$x_c$, the dominant sources of conduction and of noise in the composite arise from completely different mechanisms.