Violation of the Wiedemann-Franz law through reduction of thermal conductivity in gold thin films

Abstract

We present measurements of in-plane thermal and electrical conductivity in thermally evaporated gold thin-film samples ranging in thickness from $\ensuremath{\approx}20$ to $g300\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$, performed using a micromachined silicon-nitride membrane thermal isolation platform. In both $\ensuremath{\approx}300$-nm-thick films grown in a single Au deposition and a sample built up to $g300\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$ by many sequential depositions of thinner layers, we observe strong ``violations'' of the Wiedemann-Franz law that relates electrical and thermal conductivities. While electrical conductivity behaves essentially as expected, thermal conductivity first rises with growing total film thickness, and then surprisingly drops as the film becomes thicker. The sharp reduction of thermal conductivity decreases the Lorenz number $L$ for $\ensuremath{\approx}300\text{\ensuremath{-}}\mathrm{nm}$-thick samples to less than half the Sommerfeld value over the entire 78--300-K temperature range studied. Such violation near room temperature, in a metal film where electron transport should be well described by Fermi-liquid theory, is previously unreported, even in the presence of disorder introduced by grain boundaries and rough surfaces. This indicates an inelastic-scattering process that we argue, based on detailed characterization of grain size in these films, is likely driven by a combination of modified phonon density of states and structural anisotropy introduced from the strongly columnar grain structure in thicker films. This highly unusual reduction of thermal conductivity while maintaining high electrical conductivity is potentially promising for increasing thermoelectric performance of nanoscale systems.