A self-consistent solution of the poisson and Boltzmann equations for electrons in graphene with a deterministic approach

We present the first deterministic approach for solving the Poisson and Boltzmann equations for electrons in graphene based on the expansion of the Boltzmann equation in Fourier harmonics and a Gummel iteration scheme. The approach is applied to a double-gate graphene field effect transistor considering anisotropic scattering by acoustic and optical phonons as well as remote phonons, emerging from the gate oxide. Results are presented which show the device characteristics and the feasibility of our simulator.