  We develop a model for carrier generation by impact ionization in graphene,
which shows that this effect is non-negligible because of the vanishing energy
gap, even for carrier transport in moderate electric fields. Our theory is
applied to graphene field effect transistors for which we parametrize the
carrier generation rate obtained previously with the Boltzmann formalism [A.
Girdhar and J. Leburton, Appl. Phys. Lett. 99, 229903 (2011)] to include it in
a self-consistent scheme and compute the transistor I-V characteristics. Our
model shows that the drain current exhibits an "up-kick" at high drain biases,
which is consistent with recent experimental data. We also show that carrier
generation affects the electric field distribution along the transistor
channel, which in turn reduces the carrier velocity.
