Interplay of out-of-equilibrium phonons and self-heating under high field transport conditions in graphene

The interaction between out-of-equilibrium phonons and Joule heating in the static electron transport properties of monolayer graphene supported on $\text{Si}{\text{O}}_2$ is investigated. An ensemble Monte Carlo electronic transport engine with a self-consistent out-of-equilibrium phonon population is coupled to a thermal resistive model describing the heat dissipation, so experimental velocity-field curves are successfully reproduced for samples 7 μm wide and 4 μm long. The separate effect of self-heating and hot phonons is analyzed in depth, showing that neglecting the hot phonon effect yields to an overestimation of the lattice temperature and drift velocity. In particular, the lowest energy surface polar phonon mode is found to present a strong coupling between both effects, which need to be considered together in a consistent manner to correctly describe the heating of graphene samples at high fields. (paper)