Thermal and Electrical Conductivities of Polycrystalline Metallic Nanofilms Based on the Kinetic Theory

A model is developed for in-plane thermal conductivity of nanostructured metallic films based on the kinetic theory, which attributes the reduced thermal conductivity to the reduced mean free path of electrons. The partially inelastic electron-surface scattering and grain-boundary impedance by quantum mechanical treatment are elaborately included. Meanwhile, the mean free path of electrons is also used to study in-plane electrical conductivity of nanofilms. Both electrical conductivity and thermal conductivity, varying with film thickness and temperature, are observed to be lower than corresponding bulk values, agreeing well with the experimental data. The grain-boundary scattering is theoretically found to dominate over surface scattering to enhance the size effect on electrical and thermal conductivities. In addition, the size effect in low temperature appears more dramatic due to larger electron Knudsen number. We further examine the Lorenz number of nanofilms and find the Wiedemann-Franz law is seriously violated. The Coulomb blockade and the neutral excitation of electron-hole pair are used to offer a more detailed picture. Excessive thermal conductivity is also evaluated resorting to concepts in granular metals to show the validity of this account.