THOMAS-FERMI AND POISSON MODELING OF GATE ELECTROSTATICS IN GRAPHENE NANORIBBON

We describe a simple graphene nanoribbon and bottom gate system and present numerical algorithms for solving Poisson's and Thomas-Fermi equations for electrons in the graphene nanoribbon. The Poisson's equation is solved using finite difference and finite element methods. Using the Poisson and Thomas-Fermi equations we calculate an electrostatic potential and surface electron density in the graphene nanoribbon. Finally, the Poisson-Thomas-Fermi model for the graphene nanoribbon is compared to a tight-binding Hartree model. The results show a good correspondence with the tight-binding model. The developed solver of the Poisson's equation can be used in the future calculations of more complex graphene and gate systems.