Numerical Solutions of the Spatially Homogeneous Boltzmann Equation for Electrons in n-Doped Graphene on a Substrate

In this work, the influence of the underlying substrate on the electron distribution in graphene is evaluated by means of a numerical scheme based on the discontinuous Galerkin (DG) method for finding spatially homogeneous deterministic (non stochastic) solutions of the electron Boltzmann transport equation. A n-type density or equivalently a high value of the Fermi potential is considered; so, we neglect electron-hole scatterings. The substrate strongly affects the electron velocity and energy, on account of the additional scattering mechanisms due to the presence of the remote impurities. The main differences between graphene on a substrate and the suspended case are highlighted. Numerical results are presented and discussed. In particular, a significant reduction of the average electron velocity is observed.