Assessment of the Constant Phonon Relaxation Time Approximation in Electron-Phonon Coupling in Graphene

The importance of the correct determination of the relaxation times, entering the electron-phonon coupling, is crucial for a proper evaluation of the rise of the crystal lattice temperature induced by a flow of electrons that undergo an external electric field. We describe the crystal heating by simulating the dynamics of all the phonon branches, i.e. acoustic, optical, K and Z phonons in a suspended monolayer graphene. At each time step the charge transport is determined by means of a direct simulation Monte Carlo procedure while the evolution of the phonon distributions is evaluated by counting the emission and absorption processes in the electron-phonon scatterings. For several applied electric fields and for several positive Fermi energies, the behaviors of the crystal lattice temperature, obtained with different models of the relaxation times, are compared and discussed. The contribution of each type of phonon is highlighted as well.