A drift-diffusion model for charge transport in GFETs with a proper modeling of the electrostatic potential

The absence of a gap in pristine graphene is considered as hampering the possibility to realize an efficient field effect transistor (hereafter GFET). Nevertheless, in (Nastasi and Romano in Commun. Nonlinear Sci. Numer. Simul. 87:105300, 2020; Nastasi and Romano in IEEE Trans. Electron. Devices 68:4729–4734, 2021) a peculiar geometry has been proposed which seems to realize a robust GFET, at least according to the simulation results. One crucial aspect is the shape of the electrostatic potential. In (Nastasi and Romano in Commun. Nonlinear Sci. Numer. Simul. 87:105300, 2020; Nastasi and Romano in IEEE Trans. Electron. Devices 68:4729–4734, 2021) the electrostatic potential is simulated by distributing the charge in a volume surrounding the graphene sheet. In this work, we want to test the robustness of the GFET model proposed in (Nastasi and Romano in IEEE Trans Electron Devices 68:4729–4734, 2021). For this purpose we solve the Poisson equation by modeling the charge distribution in a different way, considering the graphene layer as a charge discontinuity surface and imposing the continuity of the electric displacement field. The two approaches give comparable results and furnish a further confirmation that the GFET in (Nastasi and Romano in IEEE Trans Electron Devices 68:4729–4734, 2021) does not stem from a spurious discretization of the Poisson equation for the electrostatic potential.