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.