Charge transport in graphene including thermal effects

In this paper we present a hydrodynamical model for the description of the charge transport in graphene, including heating effects on the crystal lattice, and conversely the influence of crystal heating on charge transport. The state variables used for the physical system are moments of the electron, hole, and phonon occupation numbers, and their evolution equations are derived by integration from the respective Boltzmann equations. The closure of the system is obtained by means of the maximum entropy principle and all the main scattering mechanisms between charges and phonons and among phonons themselves are taken into account. Numerical simulations are presented in the case of a graphene monolayer, evaluating the influence of the optical and acoustical phonons dynamics on the current-voltage characteristics and the raise rate of the lattice temperature.