Simulation of Bipolar Charge Transport in Graphene by Using a Discontinuous Galerkin Method

Charge transport in suspended monolayer graphene is simulated by a numerical deterministic approach,based on a discontinuous Galerkin(DG)method,for solving the semiclassical Boltzmann equation for electrons.Both the conduction and valence bands are included and the interband scatterings are taken into account.The use of a Direct Simulation Monte Carlo(DSMC)approach,which properly describes the interband scatterings,is computationally very expensive because the va-lence band is very populated and a huge number of particles is needed.Also the choice of simulating holes instead of electrons does not overcome the problem because there is a certain degree of ambiguity in the generation and recombination terms of electron-hole pairs.Often,direct solutions of the Boltzmann equations with a DSMC neglect the interband scatterings on the basis of physical arguments.The DG approach does not suffer from the previous drawbacks and requires a reasonable computing effort.In the present paper the importance of the interband scatterings is accurately evaluated for several values of the Fermi energy,addressing the issue related to the validity of neglecting the generation-recombination terms.It is found out that the inclusion of the interband scatterings produces huge variations in the average values,as the current,with zero Fermi energy while,as expected,the effect of the interband scattering becomes negligible by increasing the absolute value of the Fermi energy.

Direct Simulation of Charge Transport in Graphene Nanoribbons

Graphene nanoribbons are considered as one of the most promising ways to design electron devices where the active area is made of graphene.In fact,graphene nanoribbons present a gap between the valence and the conduction bands as in standard semiconductors such as Si or GaAs,at variancewith large area graphenewhich is gapless,a feature that hampers a good performance of graphene field effect transistors.To use graphene nanoribbons as a semiconductor,an accurate analysis of their electron properties is needed.Here,electron transport in graphene nanoribbons is investigated by solving the semiclassical Boltzmann equation with a discontinuous Galerkin method.All the electron-phonon scattering mechanisms are included.The adopted energy band structure is that devised in[1]while according to[2]the edge effects are described as an additional scattering stemming from the Berry-Mondragon model which is valid in presence of edge disorder.With this approach a spacial 1D transport problem has been solved,even if it remains two dimensional in the wavevector space.A degradation of charge velocities,and consequently of the mobilities,is found by reducing the nanoribbon width due mainly to the edge scattering.