Surface roughness modulated resistivity in copper thin films

The surfaces of metallic thin films are never flat. The resistivity in thin films is very different from that in bulk because of the unavoidable rough surfaces. In this study, we apply a quantum-mechanical method to study the resistivity in metallic thin films. The resulting resistivity formula for metallic thin films merely involves two parameters: bulk relaxation time and surface roughness. We use the formula to fit a large number of experimental data sets for copper thin films obtained using different growing methods. With an additional tuning parameter for calibrating the film thickness, the quantum formula can provide a universal fitting to most data with a satisfactory precision, regardless of their growing methods or data source.