Resistivity of thin gold films on mica induced by electron-surface scattering: Application of quantitative scanning tunneling microscopy

We report a comparison between the resistivity measured on thin gold films deposited on mica, with predictions based upon classical theories of size effects (Drude's, Sondheimer's and Calecki's), as well as predictions based upon quantum theories of electron-surface scattering (the modified theory of Sheng, Xing and Wang, the theory of Tesanovic, Jaric and Maekawa, and that of Trivedi and Aschroft). From topographic images of the surface recorded with a Scanning Tunneling Microscope, we determined the rms roughness amplitude, δ and the lateral correlation length, ξ corresponding to a Gaussian representation of the average height-height autocorrelation function, describing the roughness of each sample in the scale of length set by the Fermi wave length. Using (δ, ξ) as input data, we present a rigorous comparison between resistivity data and predictions based upon the theory of Calecki as well as quantum theoretical predictions without adjustable parameters. The resistivity was measured on gold films of different thickness evaporated onto mica substrates, between 4 K and 300 K. The resistivity data covers the range 0.1 < x(T) < 6.8, for 4 K < T < 300 K, where x(T) is the ratio between film thickness and electron mean free path in the bulk at temperature T. We experimentally identify electron-surface and electron-phonon scattering as the microscopic electron scattering mechanisms giving rise to the macroscopic resistivity. The different theories are all capable of estimating the thin film resistivity to an accuracy better than 10%; however the mean free path and the resistivity characterizing the bulk turn out to depend on film thickness. Surprisingly, only the Sondheimer theory and its quantum version, the modified theory of Sheng, Xing and Wang, predict and increase in resistivity induced by size effects that seems consistent with published galvanomagnetic phenomena also arising from electron-surface scattering measured at low temperatures.