Surface and grain boundary scattering in nanometric Cu thin films: A quantitative analysis including twin boundaries

Abstract

The relative contributions of various defects to the measured resistivity in nanocrystalline Cu were investigated, including a quantitative account of twin-boundary scattering. It has been difficult to quantitatively assess the impact twin boundary scattering has on the classical size effect of electrical resistivity, due to limitations in characterizing twin boundaries in nanocrystalline Cu. In this study, crystal orientation maps of nanocrystalline Cu films were obtained via precession-assisted electron diffraction in the transmission electron microscope. These orientation images were used to characterize grain boundaries and to measure the average grain size of a microstructure, with and without considering twin boundaries. The results of these studies indicate that the contribution from grain-boundary scattering is the dominant factor (as compared to surface scattering) leading to enhanced resistivity. The resistivity data can be well-described by the combined Fuchs–Sondheimer surface scattering model and Mayadas–Shatzkes grain-boundary scattering model using Matthiessen's rule with a surface specularity coefficient of p = 0.48 and a grain-boundary reflection coefficient of R = 0.26.