Deviational Monte Carlo scheme for thermal and electrical transport in metal nanostructures

The electron is the dominant heat and charge carrier in metal, yet the Monte Carlo method for thermal and electrical transport remains not fully established due to the high density and high degeneracy of electrons. In this work, we develop a deviational Monte Carlo scheme to directly solve the Boltzmann transport equation for electron transport through a simplification of the full scattering term into relaxation time approximation form automatically including the Pauli exclusion principle. It is crucial to track the occupied and unoccupied electron states above and below the Fermi energy level, respectively, for Monte Carlo simulation of electron thermal transport. Our numerical scheme not only provides a clear physical picture, but also displays a good performance in predicting the temperature distribution, electronic thermal conductivity, and electrical conductivity for in-plane and cross-plane electron transport through metallic thin films. This work will promote the fundamental understanding of electron transport at micro- and nanoscale, and also provide a ground for the investigation of electron-phonon coupling transport.