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Simulation of bipolar charge transport in graphene on h-BN

Marco Coco (Department of Mathematics and Computer Science, University of Florence, Florence, Italy)
Giovanni Nastasi (Department of Mathematics and Computer Science, University of Catania, Catania, Italy)

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering

ISSN: 0332-1649

Article publication date: 31 January 2020

Issue publication date: 20 May 2020




The purpose of this paper is to simulate charge transport in monolayer graphene on a substrate made of hexagonal boron nitride (h-BN). This choice is motivated by the fact that h-BN is one of the most promising substrates on account of the reduced degradation of the velocity due to the remote impurities.


The semiclassical Boltzmann equations for electrons in the monolayer graphene are numerically solved by an approach based on a discontinuous Galerkin (DG) method. Both the conduction and valence bands are included, and the inter-band scatterings are taken into account as well.


The importance of the inter-band 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 inter-band scatterings produces sizable variations in the average values, like the current density, at zero Fermi energy, whereas, as expected, the effect of the inter-band scattering becomes negligible by increasing the absolute value of the Fermi energy.

Research limitations/implications

The correct evaluation of the influence of the inter-band scatterings on the electronic performances is deeply important not only from a theoretical point of view but also for the applications. In particular, it will be shown that the time necessary to reach the steady state is greatly affected by the inter-band scatterings, with not negligible consequences on the switching on/off processes of realistic devices. As a limitation of the present work, the proposed approach refers to the spatially homogeneous case. For the simulation of electron devices, non-homogenous numerical solutions are required. This last case will be tackled in a forthcoming paper.


As observed in Majorana et al. (2019), the use of a Direct Simulation Monte Carlo (DSMC) approach, which properly describes the inter-band scatterings, is computationally very expensive because the valence band is highly populated and a huge number of particles is needed. Even by 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. The DG approach, used in this paper, does not suffer from the previous drawbacks and requires a reasonable computing effort.



This paper forms part of a special section “12th International Conference on Scientific Computing in Electrical Engineering (SCEE 2018)”, guest edited by Vittorio Romano.

The authors would like to thank Prof Vittorio Romano for the helpful discussions about the topics of this paper.

The authors acknowledge the support from INdAM, Progetto Giovani GNFM 2019 Modelli matematici, numerici e simulazione del trasporto di cariche e fononi nel grafene.

The author G.N. acknowledges the support from Progetto Galileo 2018 Modelli cinetici classici e quantistici e loro limiti idrodinamici: aspetti tecnici e applicativi and from Università degli Studi di Catania, Piano della Ricerca 2016/2018 Linea di intervento 2.


Coco, M. and Nastasi, G. (2020), "Simulation of bipolar charge transport in graphene on h-BN", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 39 No. 2, pp. 449-465.



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