Surface roughness and surface-induced resistivity of gold films on mica: Influence of roughness modelling

We report measurements of the temperature dependent resistivity ρ(T) of a gold film 70 nm thick deposited on mica preheated to 300°C in UHV, performed between 4 K and 300 K, and measurements of the surface topography of the same film performed with a scanning tunnelling microscope (STM). From the roughness measured with the STM we determine the parameters δ (r.m.s. amplitude) and ξ (lateral correlation length) corresponding to a Gaussian and to an exponential representation of the average autocorrelation function (ACF). We use the parameters δ and ξ determined via STM measurements to calculate the quantum reflectivity R, and the temperature dependence of both the bulk resistivity ρ₀(T) and of the increase in resistivity Δρ(T) = ρ(T) - ρ₀(T) induced by electron-surface scattering on this film, according to a modified version of the theory of Sheng, Xing and Wang recently proposed (Munoz et al 1999 J. Phys.: Condens. Matter 11 L299). The resistivity ρ₀ in the absence of surface scattering predicted for a Gaussian representation of the ACF is systematically smaller than that predicted for an exponential representation of the ACF at all temperatures. The increase in resistivity Δρ induced by electron-surface scattering predicted for a Gaussian representation of the average ACF data is about 25% larger than the increase in resistivity predicted for an exponential representation of the ACF data.