Carrier statistics in graphene at high electric field

The saturated velocity of a semiconductor is an important measure of performance. Graphene has been of interest for many applications due to its apparently high value of the saturated velocity. Recent experiments have suggested that this value is very density dependent and can even exceed the band limiting Fermi velocity. On the other hand, recent calculations have shown that the saturated velocity is largely independent of the carrier density. Here, we show that the carrier heating, due to high electric fields, can change the carrier statistics. This, and the fact that minority carriers can significantly impact the conductance may lead to erroneous conclusions about the actual total carrier density in the experimental situation.