Measuring the phonon contributions to total thermal conductivity of Ruthenium and Tungsten thin films using a steady-state thermoreflectance technique

The total thermal conductivity of a metal is the sum of the electronic thermal conductivity and the phonon thermal conductivity, along with any other heat carriers if they exist. Typically we assume that phonon thermal conductivity is negligible for metals, however, this hypothesis has not been subjected to stringent experimental validation due to difficulties in measuring phonon thermal conductivity. In this work, we study the phonon and electron contribution to the thermal conductivity of ruthenium (Ru) and tungsten (W) 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 Ru films ranging from 20 to 100 nm thick and W films ranging from 20 to 30 nm thick, deposited by the physical vapor deposition (PVD) method. We obtain the electrical resistivity with the four-point probe method and then calculate in-plane thermal conductivity employing the Wiedemann-Franz (WF) law and the bulk metal's Lorenz number. We directly measure the in-plane thermal conductivity of the Ru and W thin films via steady-state thermoreflectance technique. The in-plane thermal conductivity of these thin films measured with thermoreflectance-based method is at least 15% higher than the WF law-derived thermal conductivity. This indicates the viability of thermoreflectance-based method in capturing the phonon contributions to the total thermal conductivity of metals which the sheet resistance method can not measure.