First-principles based analysis of thermal transport in metallic nanostructures: Size effect and Wiedemann-Franz law

Metallic nanostructures (the nanofilms and nanowires) are widely used in electronic devices, and their thermal transport properties are crucial for heat dissipation. However, there are still gaps in understanding thermal transport in metallic nanostructures, especially regarding the size effect and validity of the Wiedemann-Franz law. In this work, we perform mode-by-mode first-principles calculations combining the Boltzmann transport equation to understand thermal transport in metallic nanostructures. We take the gold (Au) and tungsten (W) nanostructures as prototypes. It is found that when the size of nanostructures is on the order of several tens of nanometers, the electronic/phonon thermal conductivity is smaller than the bulk value and decreases with size. The phonon contribution increases in nanostructures for those metals with small bulk phonon thermal conductivity (like Au), while the phonon contribution may increase or be suppressed in nanostructures for those metals with large bulk phonon thermal conductivity (like W). By assuming that the grain boundary does not induce inelastic electron-phonon scattering, the Wiedemann-Franz law works well in both Au and W nanostructures if the Lorentz ratio is estimated using electronic thermal conductivity. The Wiedemann-Franz law also works well in Au nanostructures when the Lorentz ratio is estimated by total thermal conductivity.