Thin Cu film resistivity using four probe techniques: Effect of film thickness and geometrical shapes

Precise measurement of electrical sheet resistance and resistivity of metallic thin Cu films may play a significant role in temperature sensing by means of resistivity changes which can further act as a safety measure of various electronic devices during their operation. Four point probes resistivity measurement is a useful approach as it successfully excludes the contact resistance between the probes and film surface of the sample. Although, the resistivity of bulk samples at a particular temperature mostly depends on its materialistic property, however, it may significantly differ in the case of thin films, where the shape and thickness of the sample can significantly influence on it. Depending on the ratio of the film thickness to probe spacing, samples are usually classified in two segments such as (i) thick films or (ii) thin films. Accordingly, the geometric correction factors G can be related to the sample resistivity r, which has been calculated here for thin Cu films of thickness up to few 100 nm. In this study, various rectangular shapes of thin Cu films have been used to determine the shape induced geometric correction factors G. An expressions for G have been obtained as a function of film thickness t versus the probe spacing s. Using these expressions, the correction factors have been plotted separately for each cases as a function of (a) film thickness for fixed linear probe spacing and (b) probe distance from the edge of the film surface for particular thickness. Finally, we compare the experimental results of thin Cu films of various rectangular geometries with the theoretical reported results.