Electrical resistivity of Cu and Nb thin films

The electrical resistivity and temperature coefficient of resistivity (TCR) of Cu and Nb thin films have been measured over a range of layer thicknesses between 5.6 nm and 1106 nm. The structure of the films has been characterized using transmission electron microscopy (TEM) and x-ray diffraction. The experimental results have been compared with the semi-classical theory of thin-film resistivity due to Dimmich. The grain boundary reflectivity, R , has been found to vary with grain size in the Nb films. Dimmich's theoretical expression for the TCR does not match experiment, but by adapting the theoretical treatment a satisfactory fit has been obtained. The semi-classical expression predicts a negative TCR for certain thin-film and multilayer systems without the need to appeal to localization or correlation.