Surface-induced resistivity of gold films on mica: comparison between the classical and the quantum theory

We report an extension of the theory of Sheng, Xing and Wang (SXW) (Sheng L , Xing D Y and Wang Z D 1995 Phys. Rev. B 51 7325), which permits the calcu lation of size effects from the statistical properties that characterize th e surface on a microscopic scale, for samples in which the average height-h eight autocorrelation function (ACF) is described either by a Gaussian or b y an exponential. We also report measurements of the topography of a gold f ilm deposited,sited on a mica substrate using a scanning tunnelling microsc ope (STM) on a gold sample 70 nm thick deposited under ultrahigh vacuum on a mica substrate preheated to 300 degrees C. From the STM images we compute the average ACF which characterizes the surface of the film on the scale o f 10 nm x 10 nm, and determine by least-squares fitting the r.m.s. amplitud e delta and the lateral correlation length xi corresponding to a Gaussian a nd to an exponential that best represent the ACF data. Using the modified S XW (mSXW) theory and a Gaussian and an exponential representation of the AC F data, we calculate the quantum reflectivity R characterizing the interact ion between the electrons and the surface, and the decrease in conductivity her attributable to electron-surface scattering, for mean free paths 2.5 n m less than or equal to l less than or equal to 1000 nm. We compare the pre dictions of the classical Fuchs-Sondheimer (FS) model for the average quant um reflectivity R = (R), calculated with the mSXW model, with the predictio ns of the quantum theory, using both the Gaussian and the exponential repre sentation of the ACE We find that Delta sigma predicted by FS theory for R = (R) exceeds that predicted by the quantum mSXW theory, by an amount that increases with increasing l. This discrepancy can be traced to the angular dependence of the quantum reflectivity R[cos(theta)]. We also find that the decrease in conductivity Delta sigma predicted by mSXW theory for a Gaussi an representation of the data is larger than that predicted for an exponent ial representation of the same ACF data. We attribute this to the fact that the reflectivity R is determined by the Fourier transform of, the ACF, and the Gaussian and the exponential that best represent the ACF data exhibit Fourier transforms that are similar in the regions where k xi; similar to 1 , but are different in the regions where k xi < 1 and k xi > 1 (k: wave vec tor).