Surface roughness and size effects of thin gold films on mica

Abstract

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 \ensuremath{\sigma} 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 \ifmmode^\circ\else\textdegree\fi{}C, we compute the average autocorrelation function (ACF) that characterizes the surface of the film in the scale of $10\ifmmode\times\else\texttimes\fi{}10{\mathrm{nm}}^{2},$ and determine by least-squares fitting the parameters \ensuremath{\delta} (rms. amplitude) and \ensuremath{\xi} (lateral correlation length) corresponding to an exponential that best describes the average ACF data. Using an exponential representation of the ACF, the parameters \ensuremath{\delta} and \ensuremath{\xi} 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 ${\ensuremath{\rho}}_{0}(T)$ and of the increase in resistivity $\ensuremath{\Delta}\ensuremath{\rho}(T)=\ensuremath{\rho}(T)\ensuremath{-}{\ensuremath{\rho}}_{0}(T)$ induced by electron-surface scattering on this film. The result is that $1\ensuremath{-}\ensuremath{\sigma}/{\ensuremath{\sigma}}_{0}=1\ensuremath{-}{\ensuremath{\rho}}_{0}/\ensuremath{\rho}=\ensuremath{\Delta}\ensuremath{\rho}/\ensuremath{\rho}$ 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 \ensuremath{\Delta}\ensuremath{\rho} turns out to be weakly temperature dependent.