Surface roughness and size effects of thin gold films on mica

We report measurements of the topography of a gold film deposited on a mica substrate using scanning tunneling microscope (STM), and measurements of the conductivity {σ} of the film performed between 4 and 300 K. From images obtained with the STM running in air in the constant current mode of a gold sample 70-nm-thick deposited under UHV on a mica substrate preheated to 300 ^∘{}C, we compute the average autocorrelation function (ACF) that characterizes the surface of the film in the scale of 10×10nm², and determine by least-squares fitting the parameters {δ} (rms. amplitude) and {ξ} (lateral correlation length) corresponding to an exponential that best describes the average ACF data. Using an exponential representation of the ACF, the parameters {δ} and {ξ} determined from STM measurements, and a modified version of the theory of Sheng, Xing, and Wang recently proposed [R. C. Munoz et al., J. Phys.: Condens. Matter 11, L299 (1999)], we calculate the temperature dependence of 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. The result is that 1-σ/σ₀=1-ρ₀/ρ=Δρ/ρ amounts to about 2.6% at 300 K, and increases linearly with increasing mean free path, to about 10.5% at 4 K. The increase in resitivity {Δ}{ρ} turns out to be weakly temperature dependent.