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

We report measurements of the resistivity rho(T) of a gold film 70 nm thick deposited on mica preheated to 300 degrees 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 delta (rms amplitude) and xi (lateral correlation length) corresponding to a Gaussian representation of the average height-height autocorrelation function (ACF). We use the parameters delta and 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 approximate to 1 for corrugations taking place over scales of distances that are long when compared to a few Fermi wavelength lambda(F) and R<1 for corrugations taking place over scales of distances that are comparable to lambda(F) (to within an order of magnitude). The reflectivity R determined by corrugations ocurring over a scale of distances comparable to lambda(F) approaches zero for a certain angle. The resistivity rho(T) of the film increases by roughly a factor of 4 between 4 and 300 K, and so does the bulk resistivity po(T) predicted by mSXW theory. With the parameters delta and xi measured on our 70-nm film, we reproduced approximately the thickness and temperature dependence of the resistivity (between 3 and 300 K) of several gold films on mica reported by Sambles, Elsom, and Jarvis [Philos. Trans. R. Sec. London, Ser. A 304, 365 (1982)], without using any adustable 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 delta and 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.