Resistivity induced by a rough surface of thin gold films deposited on mica

Abstract

A central question regarding thin metallic films is how does the roughness of the film affect its electrical transport properties, when its thickness is comparable to or smaller than the electron mean free path. The drive to build ever-faster circuits generates the drive for miniaturization and VLSI, which poses a pressing need to reach full understanding of electron–rough surface scattering. We review progress in the field that has taken place over the last 5 years. From the theoretical point of view, the so-called mSXW theory [Munoz et al., J. Phys.: Condens. Matter 11 (1999) L299] was recently published. The increase in resistivity induced by electron–surface scattering is computed using Kubo's linear response theory. The conductivity of the film is determined by the spectral function characterizing the one-particle Green's function describing the electron gas confined within the film. The effect of the rough surface is to modify the self-energy of the electron gas. The conductivity of the film turns out to depend on the height–height autocorrelation function (ACF) that describes the rough surface. It can be written in a closed form if the ACF is described either by a Gaussian or by an exponential. From the experimental point of view, the tendency to use parameters provided by theory as quantities that must be fitted to describe thin-film resistivity data has been replaced by direct measurements of the surface roughness. The first measurement of the ACF of the rough surface of a 70-nm thick gold film deposited on mica was recently published [Munoz et al., Phys. Rev. B 62 (2000) 4686]. The measurement was performed with a scanning tunneling microscope (STM). Using the data recorded with the STM and the mSXW theory, we reproduced the thickness as well as the temperature dependence of the best resistivity data available for gold films on mica. Theory reproduced the data to within a few percent without adjustable parameters. We report also the first measurement of the increase in resistivity induced by electron–surface scattering in gold films deposited on mica, performed at low temperatures and high magnetic fields.