Modeling and simulation of charge transport in graphene

Low dimensional materials are widely investigated to reduce the size of new electron devices. One of the most prominent is graphene because of its singular electronic properties, such as the very high thermal and electrical conductivity. The aim of this thesis is to present some new results on mathematical modeling and numerical simulation of charge transport in graphene. For this purpose, one of the most accurate models is the semiclassical Boltzmann equations where quantum aspects are also taken into account. Since numerical solutions of the Boltzmann equations require a high computational effort, macrosopic models have been formulated such as drift-diffusion, energy-transport or hydrodynamical. They constitute a more useful tool to design, improve and optimize new graphene based electron devices. We investigated the bipolar charge transport, improved mobility models and studied drift-diffusion equations for the simulation of Graphene Field Effect Transistors (GFET). Direct numerical simulations of the semiclassical Boltzmann equations have been performed by means of discontinuous Galerkin approach and Direct Simulation Monte Carlo method while finite difference schemes have been used for the drift-diffusion models. Finally, we presented some ongoing research about the effect of electron-electron interaction, the solutions of the semiclassical Boltzmann equations in non homogeneous cases, the inclusion of quantum effects in drift-diffusion models and the optimal control theory of charge transport in graphene.