  Hot carriers in a doped graphene under dc electric field is described taking
into account the intraband energy relaxation due to acoustic phonon scattering
and the interband generation-recombination transitions caused by thermal
radiation. The consideration is performed for the case when the intercarrier
scattering effectively establishes the quasiequilibrium electron-hole
distributions, with effective temperature and concentrations of carriers. The
concentration and energy balance equations are solved taking into account an
interplay between weak energy relaxation and generation-recombination
processes. The nonlinear conductivity is calculated for the momentum relaxation
caused by the elastic scattering. The current-voltage characteristics, and the
transition between bipolar and monopolar regimes of conductivity are obtained
and analyzed, for different temperatures and gate voltages.
