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

We report measurements of the resistivity (Formula presented) of a gold film 70 nm thick deposited on mica preheated to 300 °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 δ (rms amplitude) and ξ (lateral correlation length) corresponding to a Gaussian representation of the average height-height autocorrelation function (ACF). We use the parameters δ and ξ 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 (Formula presented) for corrugations taking place over scales of distances that are long when compared to a few Fermi wavelength (Formula presented) and (Formula presented) for corrugations taking place over scales of distances that are comparable to (Formula presented) (to within an order of magnitude). The reflectivity R determined by corrugations ocurring over a scale of distances comparable to (Formula presented) approaches zero for a certain angle. The resistivity (Formula presented) of the film increases by roughly a factor of 4 between 4 and 300 K, and so does the bulk resistivity (Formula presented) predicted by mSXW theory. With the parameters δ and ξ 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 δ and ξ 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.