Comparing Kinetic and MEP Model of Charge Transport in Graphene

Abstract

Graphene has attracted the attention of several researchers because of its peculiar features. In particular, the study of charge transport in graphene is challenging for future electron devices. Usually, the physical description of electron flow in graphene given by the semiclassical Boltzmann equation is considered to be a good one. However, due to the computational complexity, its use in simulation tools is not practical and, as already done for traditional semiconductors such as Si or GaAs, simpler models are warranted. Here we will assess the validity of a class of hydrodynamical models based on the maximum entropy principle (MEP), by comparing, in the case of suspended monolayer graphene, the direct solution of the semiclassical Boltzmann equation for electrons, obtained by employing a discontinuous Galerkin approach, with the MEP distribution function. A reasonable agreement is observed.

Keywords:

• Graphene
• charge transport
• discontinuous Galerkin method
• Maximum Entropy Principle

AMS CLASSIFICATION:

• 82D37
• 82C70
• 65M60
• 82C80

Acknowledgments

The authors acknowledge the support from INdAM, Progetto Giovani GNFM 2019 “Modelli matematici, numerici e simulazione del trasporto di cariche e fononi nel grafene” and from Università degli Studi di Catania, “Piano della Ricerca 2020/2022 Linea di intervento 2 QICT”.

Notes

1 This amounts to consider a wave function envelope with Dirac point wave-vectors.