Experimental assessment of the Wiedemann-Franz law in thin metal films using thermoreflectance and electrical measurements

Abstract

Accurate thermal properties of metal thin films are essential for microelectronic thermal modeling and for interpreting thermoreflectance measurements when signals are sensitive to film thermal transport. In practice, film thermal conductivity is commonly inferred from electrical resistivity via the Wiedemann-Franz (WF) law with the Sommerfeld-Lorenz number L_0, neglecting phonon contributions and microstructure-dependent scattering. Here, we combine square-pulsed source (SPS) thermoreflectance with van der Pauw measurements to characterize thermal and electrical transport in Al, Ti, and Ta thin films prepared by thermal evaporation, e-beam evaporation, and magnetron sputtering. SPS measurements from 80 to 300 K yield the film thermal conductivity k_m and volumetric heat capacity C_m, with C_m agreeing with bulk values within +/-8%. Compared with WF-based estimates using L_0 and a modeled resistivity, \r{ho}_model (T)=\r{ho}_bulk (T)+\r{ho}_0, k_m deviates by 5-20% for Al and Ti and up to 40% for sputtered Ta at 300 K. While the smaller deviations are comparable to experimental uncertainty, the large mismatch for Ta demonstrates the limitation of applying the bulk L_0 to highly resistive metal films. Apparent Lorenz numbers L_app=k_m \r{ho}_meas/T from 150 to 300 K further reveal that deposition-induced disorder, grain-boundary scattering, and possible phase-related effects can modify the correlation between heat and charge transport in thin metal films. These results clarify the applicability of the WF law to deposited metal thin films and offer practical guidance for thermal modeling and thermoreflectance analysis.