  By using Boltzmann formalism, we show that carrier multiplication by impact
ionization can take place at relatively low electric fields during electronic
transport in graphene. Because of the absence of energy gap, this effect is not
characterized by a field threshold unlike in conventional semiconductors, but
is a quadratic function of the electric field. We also show that the resulting
current is an increasing function of the electronic temperature, but decreases
with increasing carrier concentration.
