Soft Carrier Multiplications by Hot Electrons in Graphene
  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. 
Anuj Girdhar and Jean-Pierre Leburton
cond-mat.mes-hall