An exactly solvable model for the graphene transistor in the quantum capacitance limit

We explore the ultimate behavior of the graphene transistor in the quantum capacitance limit. The quantum capacitance formulation allows for an exactly solvable model, and the ideal assumptions provide an upper bound on performance, including peak currents of 1 mA/mu m with mobilities as low as 2000 cm(2)/V s for channel length of 1 mu m, as well as linearly increasing transconductance not observed in conventional transistors. A negative differential resistance is predicted under certain conditions, with a maximum peak-to-valley-current ratio of 4. Finally, the effects of oxide scaling are elucidated and the oxide capacitances required for quantum capacitance limited behavior are quantified. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4739943]