Thermionic and tunneling transport mechanisms in graphene field-effect transistors

We present an analytical device model for a graphene fieldeffect transistor (GFET) on a highly conducting substrate, playing the role of the back gate, with relatively short top gate which controls the source-drain current The equations of the GFET device model include the Poisson equation in the weak nonlocality approximation. Using this model, we find explicit analytical formulae for the spatial distributions of the electric potential along the channel and for the voltage dependences of the thermionic and tunneling currents.