Thermal effects in monolayer graphene due to an electron flow are investigated with a direct simulation Monte Carlo (DSMC) analysis. The crystal heating is described by simulating the phonon dynamics of the several relevant branches, acoustic, optical, K and Z phonons. The contribution of each type of phonon is highlighted. In particular, it is shown that the Z phonons, although they do not enter the scattering with electrons, play a non-negligible role in the determination of the crystal temperature. The phonon distributions are evaluated by counting the emission and absorption processes during the MC simulation. The crystal temperature raise is obtained for several applied electric fields and for several positive Fermi energies. The latter produces the effect of a kind of n-doping in the graphene layer. Critical temperatures can be reached in a few tens of picoseconds posing remarkable issues regarding the cooling system in view of a possible application of graphene in semiconductor devices. Moreover, a significant influence of the lattice temperature on the characteristic curves is observed only for long times, confirming graphene rather robust as regards the electrical performance.

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