The aim of this work is to simulate the charge transport in a monolayer
graphene on a substrate. This requires the inclusion of the scatterings of the charge
carriers with the impurities and the phonons of the substrate, besides the interaction
mechanisms already present in the graphene layer. As physical model, the semiclassical Boltzmann equation will be assumed. Two approaches will be used for the
simulations: a numerical scheme based on the Discontinuous Galerkin method for
finding deterministic (non stochastic) solutions and a new Direct Monte Carlo Simulation formulated in Romano et al. (J Comput Phys 302:267–284, 2015) in order to deal
in the appropriate way with the Pauli exclusion principle for degenerate Fermi gases.
A cross validation of the deterministic and stochastic solutions shows the robustness
and accuracy of both the approaches.

EB00000002619K

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• Cross validation of discontinuous Galerkin method and Monte Carlo simulations of charge transport in graphene on substrate