Surface roughness and surface-induced resistivity of gold films on mica: Application of quantitative scanning tunneling microscopy

Abstract

We report measurements of the resistivity $\ensuremath{\rho}(T)$ of a gold film 70 nm thick deposited on mica preheated to 300 \ifmmode^\circ\else\textdegree\fi{}C in UHV, performed between 4 and 300 K, and measurements of the surface topography of the same film performed with a scanning tunneling microscope (STM). From the roughness measured with the STM we determine the parameters \ensuremath{\delta} (rms amplitude) and \ensuremath{\xi} (lateral correlation length) corresponding to a Gaussian representation of the average height-height autocorrelation function (ACF). We use the parameters \ensuremath{\delta} and \ensuremath{\xi} to calculate the quantum reflectivity R and the increase in resistivity induced by electron-surface scattering on this film, according to a modified version of the theory of Sheng, Xing, and Wang (mSXW) [Munoz et al., J. Phys.: Condens. Matter 11, L299 (1999)]. The mSXW theory is able to select the appropriate scale of distance over which corrugations take place, leading to $R\ensuremath{\approx}1$ for corrugations taking place over scales of distances that are long when compared to a few Fermi wavelength ${\ensuremath{\lambda}}_{F},$ and $R<1$ for corrugations taking place over scales of distances that are comparable to ${\ensuremath{\lambda}}_{F}$ (to within an order of magnitude). The reflectivity R determined by corrugations ocurring over a scale of distances comparable to ${\ensuremath{\lambda}}_{F}$ approaches zero for a certain angle. The resistivity $\ensuremath{\rho}(T)$ of the film increases by roughly a factor of 4 between 4 and 300 K, and so does the bulk resistivity ${\ensuremath{\rho}}_{0}(T)$ predicted by mSXW theory. With the parameters \ensuremath{\delta} and \ensuremath{\xi} measured on our 70-nm film, we reproduced approximately the thickness and temperature dependence of the resistivity (between 4 and 300 K) of several gold films on mica reported by Sambles, Elsom, and Jarvis [Philos. Trans. R. Soc. London, Ser. A 304, 365 (1982)], without using any adjustable parameters. The results of this paper suggest that the relevant quantities controlling electron-surface scattering in continuous gold films of arbitrary thickness, are the parameters \ensuremath{\delta} and \ensuremath{\xi} describing the average ACF that characterizes the surface of the sample on a nanoscopic scale, in agreement with the accepted view regarding the conductivity of ultrathin films.