Thermal and electrical conductivity of approximately 100-nm permalloy, Ni, Co, Al, and Cu films and examination of the Wiedemann-Franz Law

Abstract

We present measurements of thermal and electrical conductivity of polycrystalline permalloy (Ni-Fe), aluminum, copper, cobalt, and nickel thin films with thickness $l200$ nm. A micromachined silicon-nitride membrane thermal-isolation platform allows measurements of both transport properties on a single film and an accurate probe of the Wiedemann--Franz (WF) law expected to relate the two. Through careful elimination of possible effects of surface scattering of phonons in the supporting membrane, we find excellent agreement with WF in a thin Ni-Fe film over nearly the entire temperature range from 77 to 325 K. All other materials studied here deviate somewhat from the WF prediction of electronic thermal conductivity with a Lorenz number, $L$, suppressed from the free-electron value by $10%\phantom{\rule{4.pt}{0ex}}\text{to}\phantom{\rule{4.pt}{0ex}}20%$. For Al and Cu we compare the results to predictions of the theoretical expression for the Lorenz number as a function of $T$. This comparison indicates two different types of deviation from expected behavior. In the Cu film, a higher than expected $L$ at lower $T$ indicates an additional thermal conduction mechanism, while at higher $T$ lower than expected values suggests an additional inelastic scattering mechanism for electrons. We suggest the additional low-$T\phantom{\rule{4pt}{0ex}}L$ indicates a phonon contribution to thermal conductivity and consider increased electron-phonon scattering at grain boundaries or surfaces to explain the high-$T$ reduction in $L$.