Testing the Validity of Wiedemann-Franz Law Using Thermoreflectance-Based Methods in Thin Copper Films

To determine the thermal properties of thin metal films, a common approach is to measure their electrical resistivity and then calculate in-plane thermal conductivity employing the Wiedemann- Franz (WF) law and the bulk metal’s Lorenz number. However, the implementation of the WF law in calculating thermal conductivity can be refuted because of the Lorenz number deviating from its bulk value owing to thickness-dependent microstructure, inelastic electron-phonon scattering events, and/or point defect density. In this work, we address the dearth of understanding of how thermal and electrical properties of copper (Cu) films scale at nanometer dimensions via independent measurements of the thermal and electrical transport properties. We perform sheet resistance and thermoreflectance-based nanoscale thermal conductance measurements on Cu films ranging from 25 to 500 nm thick, grown by physical vapor deposition (PVD) and electroplating methods. We directly measure the in-plane thermal conductivity of the Cu thin films via time-domain thermoreflectance and steady-state thermoreflectance techniques. We find the in-plane thermal conductivity of thin films deviates at least 15% from the WF law-derived thermal conductivity. This deviation in thermal conductivity of thin films can be attributed to their columnar grain structures and more electron-phonon scattering events compared to the bulk one.