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.

正确确定进入电子-声子耦合的弛豫时间的重要性，对于正确评估由经受外部电场的电子流引起的晶格温度升高至关重要。我们通过模拟所有声子支路的动力学来描述晶体的加热，即声子，光学，K和Z悬浮单层石墨烯中的声子。在每个时间步，通过直接模拟蒙特卡洛程序确定电荷传输，同时通过计算电子-声子散射中的发射和吸收过程来评估声子分布的演变。对于几个施加的电场和几个正费米能量，比较和讨论了用不同的弛豫时间模型获得的晶格温度行为。每种声子的贡献也被突出显示。