The d⁻³ Law Describing the Thickness Dependence of the Electrical Resistivity of Rough Metal Films

Abstract

Abstract The resistivity of thin metal films with rough surfaces is higher than that of smooth films. This roughness effect is calculated assuming that the deviations of the thickness from a mean value are symmetrical. The total resistivity is found to be composed of the normal bulk resistivity, the wellknown contribution of the scattering of conduction electrons at the grain boundaries and surfaces, and an additional resistivity term due to roughness, which varies proportional to 1/d 3 . The theory is applied to polycrystalline nickel films deposited at ambient temperature under UHV conditions on glass substrates.