Hydrodynamic equations for an electron gas in graphene

Barletti, Luigi

doi:10.1186/s13362-016-0023-7

Cited by 8 publications

(3 citation statements)

References 24 publications

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“…A reasonable and physically accurate model for charge transport is based on semiclassical Boltzmann equations (quantum effects have also been included in the literature, e.g. see [6,7]). Usually, the available solutions have been obtained by direct Monte Carlo simulations, e.g.…”

Section: Introductionmentioning

confidence: 99%

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

Majorana¹

2019

CICP

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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 valence 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 electronhole 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.

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Section: Introductionmentioning

confidence: 99%

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

Majorana¹

2019

CICP

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“…Note that here we are using non-dimensional chemical potentials, while the dimensional chemical potentials, that have the dimensions of a energy, are given by β −1 As 4. The normalization constant is required in order to get the the correct moments of a non-dimensional Wigner function[3].…”

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confidence: 99%

Quantum Transmission Conditions for Diffusive Transport in Graphene with Steep Potentials

Barletti¹,

Negulescu²

2018

J Stat Phys

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We present a formal derivation of a drift-diffusion model for stationary electron transport in graphene, in presence of sharp potential profiles, such as barriers and steps. Assuming the electric potential to have steep variations within a strip of vanishing width on a macroscopic scale, such strip is viewed as a quantum interface that couples the classical regions at its left and right sides. In the two classical regions, where the potential is assumed to be smooth, electron and hole transport is described in terms of semiclassical kinetic equations. The diffusive limit of the kinetic model is derived by means of a Hilbert expansion and a boundary layer analysis, and consists of drift-diffusion equations in the classical regions, coupled by quantum diffusive transmission conditions through the interface. The boundary layer analysis leads to the discussion of a four-fold Milne (half-space, half-range) transport problem.

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“…An accurate mathematical model is constituted by the semiclassical Boltzmann equations for electrons in the valence and conduction bands (quantum effects have also been included in the literature, e.g. see Barletti, 2016;Morandi and Schürrer, 2011;Luca and Romano, 2019;Muscato and Wagner, 2016, and hydrodynamical models based on the maximum entropy principle have been formulated in Luca and Romano, 2019;Camiola and Romano, 2014;Coco et al, 2015;Luca and Romano, 2018). As observed in Majorana et al (2019), the use of a Direct Simulation Monte Carlo (DSMC) approach (Romano et al, 2015;Coco et al, 2017;Majorana and Romano, 2017), 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.…”

Section: Introductionmentioning

confidence: 99%

Simulation of bipolar charge transport in graphene on h-BN

Coco

Nastasi

2020

COMPEL

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Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

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Hydrodynamic equations for an electron gas in graphene

Cited by 8 publications

References 24 publications

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

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

Quantum Transmission Conditions for Diffusive Transport in Graphene with Steep Potentials

Simulation of bipolar charge transport in graphene on h-BN

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