Particle Dynamics in Graphene: Collimated Beam Limit

Morandi, Omar; Barletti, Luigi

doi:10.1080/00411450.2014.942917

Cited by 8 publications

(8 citation statements)

References 17 publications

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“…A systematic way to find these relations is founded on a universal physical principle: the maximum entropy principle [6,14,27,28]. It states that, if a certain number of moments is known, then the least biased distribution functions, which can be used for evaluating the unknown moments, are those maximizing the total entropy functional under the constraint that they reproduce the known moments.…”

Section: The 3d Semiclassical Macroscopic Modelsmentioning

confidence: 99%

Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

Mascali

Romano

2017

Entropy

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Abstract:In the last two decades, the Maximum Entropy Principle (MEP) has been successfully employed to construct macroscopic models able to describe the charge and heat transport in semiconductor devices. These models are obtained, starting from the Boltzmann transport equations, for the charge and the phonon distribution functions, by taking-as macroscopic variables-suitable moments of the distributions and exploiting MEP in order to close the evolution equations for the chosen moments. Important results have also been obtained for the description of charge transport in devices made both of elemental and compound semiconductors, in cases where charge confinement is present and the carrier flow is two-or one-dimensional.

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Section: The 3d Semiclassical Macroscopic Modelsmentioning

confidence: 99%

Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

Mascali

Romano

2017

Entropy

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“…The last years have witnessed a great interest in 2D-materials for their promising applications. The most investigated one is graphene which is considered as a potential new semiconductor material for future applications in nano-electronic [1][2][3][4] and optoelectronic devices [5]. 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.…”

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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“…The diffusive and hydrodynamic descriptions of such systems are extensively treated in Refs. [4,5,6,7,8,9,10]. Here, we summarize the results contained in Refs.…”

Section: Introductionmentioning

confidence: 91%

“…which is decoupled from the continuity equation for n. As pointed out in Refs. [7,8], this equation reveals that collimated electrons in graphene have the properties of a geometricaloptics system, with "refractive index"…”

Section: Collimation Regimementioning

confidence: 99%

Hydrodynamic equations for an electron gas in graphene

Barletti

2016

J.Math.Industry

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In this paper we review, and extend to the non-isothermal case, some results concerning the application of the maximum entropy closure technique to the derivation of hydrodynamic equations for particles with spin-orbit interaction and Fermi-Dirac statistics. In the second part of the paper we treat in more details the case of electrons on a graphene sheet and investigate various asymptotic regimes. MSC: 82D37; 82A70; 76Y05

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Particle Dynamics in Graphene: Collimated Beam Limit

Cited by 8 publications

References 17 publications

Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

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

Hydrodynamic equations for an electron gas in graphene

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