A resistance network representation of electrical conduction in Pt and Cu films

Abstract

The growth of ion beam sputtered (IBS) Pt and Cu films on an amorphous dielectric substrate begins with the formation of atomic clusters on the surface. The clusters grow to form islands which eventually come into contact, the intervening regions finally in-fill to form the continuous film. During this process, in which the substrate surface fractional coverage x increases over the range 0 ≤ x ≤ 1, the film resistance R f decreases from that of the substrate ( x = 0) to that of the continuous metal film ( x = 1). Computer generated images of Pt and Cu films are obtained using experimental values of the log-normal distribution function parameters describing the variation of island diameter with x. At each x an area 80 × 80 nm 2 of the Pt or Cu film is then represented by an equivalent resistance network in which 686 individual resistors represent the underlying dielectric, metallic or inter-island tunnelling conduction. Good agreement between the computed and measured R f versus x characteristics are obtained using the barrier height potential values ф Pt = 0.1 eV , ф Cu = 1.0 eV . The network model also describes the negative temperature coefficient of resistance observed in particulate films.