Thermal conductivity in metallic nanostructures at high temperature: Electrons, phonons, and the Wiedemann-Franz law

TLDR

Thermal conductivity in metal nanostructures arises from both phonon and electron transport. The authors employ the Boltzmann transport equation to model thermal and electrical conductivity of 25–500 nm metal nanostructures, accounting for electron‑phonon, phonon‑phonon, phonon‑electron, grain‑boundary, and surface scattering, and they develop a modified Wiedemann–Franz law that corrects for differing electron mean‑free paths. The model reproduces measured thermal conductivities of Al, Pt, and Cu nanostructures and shows that the Wiedemann–Franz law breaks down in nanowires because of enhanced phonon transport, but a corrected law remains accurate down to sizes above the phonon mean‑free path.

Abstract

The Boltzmann transport equation is used to calculate thermal and electrical conductivity of metal nanostructures with characteristic dimensions in the 25--500 nm range, near to and above the Debye temperature. Thermal conductivity contributions from phonons and electrons are considered. The intrinsic effects of electron-phonon, phonon-phonon, and phonon-electron scattering, and grain boundary and surface interactions are addressed. Excellent agreement is found between model results and available data reporting direct measurements of thermal conductivity of nanowires, ribbons, and thin films in Al, Pt, and Cu, respectively. The Wiedemann-Franz (W-F) law and Lorenz factor are examined with decreasing size; their applicability is found to degrade in nanowires due mainly to increased relative phonon contribution. The effect of differences in the electron mean-free path for thermal gradient versus electrical field is also examined. A modified version of W-F is presented, corrected for these two factors and valid from macroscale to nanoscale provided characteristic sizes exceed the phonon mean-free path.