Modeling Hydrodynamic Charge Transport in Graphene

Graphene has exceptional electronic properties, such as zero band gap, massless carriers, and high mobility. These exotic carrier properties enable the design and development of unique graphene devices. However, traditional semiconductor solvers based on drift-diffusion equations are not capable of modeling and simulating the charge distribution and transport in graphene, accurately, to its full extent. The effects of charge inertia, viscosity, collective charge movement, contact doping, etc., cannot be accounted for by the conventional Poisson-drift-diffusion models, due to the underlying assumptions and simplifications. Therefore, this article proposes two mathematical models to analyze and simulate graphene-based devices. The first model is based on a modified nonlinear Poisson's equation, which solves for the Fermi level and charge distribution electrostatically on graphene, by considering gating and contact doping. The second proposed solver focuses on the transport of the carriers by solving a hydrodynamic model. Furthermore, this model is applied to a Tesla-valve structure, where the viscosity and collective motion of the carriers play an important role, giving rise to rectification. These two models allow us to model unique electronic properties of graphene that could be paramount for the design of future graphene devices.