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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 calculation of size effects from the statistical properties that characterize the surface on a microscopic scale, for samples in which the average height-height autocorrelation function (ACF) is described either by a Gaussian or by an exponential. We also report measurements of the topography of a gold film deposited on a mica substrate using a scanning tunnelling microscope (STM) on a gold sample 70 nm thick deposited under ultrahigh vacuum on a mica substrate preheated to 300 °C. From the STM images we compute the average ACF which characterizes the surface of the film on the scale of 10 nm × 10 nm, and determine by least-squares fitting the r.m.s. amplitude and the lateral correlation length corresponding to a Gaussian and to an exponential that best represent the ACF data. Using the modified SXW (mSXW) theory and a Gaussian and an exponential representation of the ACF data, we calculate the quantum reflectivity R characterizing the interaction between the electrons and the surface, and the decrease in conductivity attributable to electron-surface scattering, for mean free paths 2.5 nm 1000 nm. We compare the predictions of the classical Fuchs-Sondheimer (FS) model for the average quantum reflectivity R = R, calculated with the mSXW model, with the predictions of the quantum theory, using both the Gaussian and the exponential representation of the ACF. We find that predicted by FS theory for R = R exceeds that predicted by the quantum mSXW theory, by an amount that increases with increasing . This discrepancy can be traced to the angular dependence of the quantum reflectivity R[cos()]. We also find that the decrease in conductivity predicted by mSXW theory for a Gaussian representation of the data is larger than that predicted for an exponential 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~1, but are different in the regions where k<1 and k>1 (k: wave vector).

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We report measurements of the temperature dependent resistivity ρ(T ) of a gold film 70 nm thick deposited on mica preheated to 300 • C in UHV, performed between 4 K and 300 K, and measurements of the surface topography of the same film performed with a scanning tunnelling microscope (STM). From the roughness measured with the STM we determine the parameters δ (r.m.s. amplitude) and ξ (lateral correlation length) corresponding to a Gaussian and to an exponential representation of the average autocorrelation function (ACF). We use the parameters δ and ξ determined via STM measurements to calculate the quantum reflectivity R, and the temperature dependence of both the bulk resistivity ρ 0 (T ) and of the increase in resistivity ρ(T ) = ρ(T ) − ρ 0 (T ) induced by electron-surface scattering on this film, according to a modified version of the theory of Sheng, Xing and Wang recently proposed (Munoz et al 1999 J. Phys.: Condens. Matter 11 L299). The resistivity ρ 0 in the absence of surface scattering predicted for a Gaussian representation of the ACF is systematically smaller than that predicted for an exponential representation of the ACF at all temperatures. The increase in resistivity ρ induced by electron-surface scattering predicted for a Gaussian representation of the average ACF data is about 25% larger than the increase in resistivity predicted for an exponential representation of the ACF data.

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