Soft carrier multiplication by hot electrons in graphene

By using the 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 an energy gap, this effect is not characterized by a field threshold but is a quadratic function of the electric field, unlike in conventional semiconductors. We also show that the resulting current is an increasing function of the electronic temperature but decreases with increasing carrier concentration.