Comparing Kinetic and MEP Model of Charge Transport in Graphene

Luca, Liliana; Mascali, Giovanni; Nastasi, Giovanni; Romano, Vittorio

doi:10.1080/23324309.2020.1822870

Cited by 4 publications

(3 citation statements)

References 37 publications

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“…The simulation has shown that the model describes qualitatively the macroscopic behavior of the charge transport and is able to differentiate the graphene ribbons from the graphene sheets. Moreover the obtained results are comparable with that ones obtained by solving numerically the Boltzmann equation [22,23,25,26] but with a remarkable reduction of the computational time.…”

Section: Discussionsupporting

confidence: 77%

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Hydrodynamical Model for Charge Transport in Graphene Nanoribbons

Camiola¹,

Nastasi²

2021

J Stat Phys

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We present a hydrodynamical model for graphene nanoribbons that takes into account the electron collisions with the lattice and with the edge of the ribbon. Moreover the bandgap due to the low dimension of the ribbon is considered. The simulation shows that the model describes qualitatively the macroscopic behavior of the charges and the results are comparable with that ones obtained by solving numerically the Boltzmann equation but with a remarkable reduction of the computational time.

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Section: Discussionsupporting

confidence: 77%

“…The comparison between linear and non-linear models can be found in [24]. A comparison between both models and numerical solutions of the kinetic equations is presented in [25].…”

Section: Closure Relationsmentioning

confidence: 99%

Hydrodynamical Model for Charge Transport in Graphene Nanoribbons

Camiola¹,

Nastasi²

2021

J Stat Phys

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“…The results are compared with the corresponding splitting algorithm, showing an excellent agreement as well as a low-cost computational effort. Future research will develop this MC methodology for the simulation of realistic devices, such as silicon nanowires according to the guidelines in [14,15] and new emerging materials such as graphene [8,10].…”

Section: Discussionmentioning

confidence: 99%

Wigner ensemble Monte Carlo simulation without splitting error of a GaAs resonant tunneling diode

Muscato

2021

J Comput Electron

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A Monte Carlo technique for the solution of the Wigner transport equation has been developed, based on the generation and annihilation of signed particles (Nedjalkov et al. in Phys Rev B 70:115319, 2004). A stochastic algorithm without time discretization error has been recently introduced (Muscato and Wagner in Kinet Relat Models 12(1):59–77, 2019). Its derivation is based on the theory of piecewise deterministic Markov processes. Numerical experiments are performed in the case of a GaAs resonant tunneling diode. Convergence of the time-splitting scheme to the no-splitting algorithm is demonstrated. The no-splitting algorithm is shown to be more efficient in terms of computational effort.

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Optimized Hydrodynamical Model for Charge Transport in Graphene

Camiola

Nastasi

Romano

et al. 2022

Mathematics in Industry

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A well known procedure to get quantum hydrodynamical models for charge transport is to resort to the Wigner equations and deduce the hierarchy of the moment equations as in the semiclassical approach. If one truncates the moment hierarchy to a finite order, the resulting set of balance equations requires some closure assumption because the number of unknowns exceed the number of equations. In the classical and semiclassical kinetic theory a sound approach to get the desired closure relations is that based on the Maximum Entropy Principle (MEP) [13] (see [20] for charge transport in semiconductors).In [9] a quantum MEP hydrodynamical model has been devised for charge transport in the parabolic band approximation by introducing quantum correction based on the equilibrium Wigner function [30]. An extension to electron moving in pristine graphene has been obtained in [29].Here we present a quantum hydrodynamical model which is valid for a general energy band considering a closure of the moment system deduced by the Wigner equation resorting to a quantum version of MEP. Explicit formulas for quantum correction at order 2 are obtained with the aid of the Moyal calculus for silicon and graphene removing the limitation that the quantum corrections are based on the equilibrium Wigner function as in [9,29]. As an application, quantum correction to the mobilities are deduced.

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Comparing Kinetic and MEP Model of Charge Transport in Graphene

Cited by 4 publications

References 37 publications

Hydrodynamical Model for Charge Transport in Graphene Nanoribbons

Hydrodynamical Model for Charge Transport in Graphene Nanoribbons

Wigner ensemble Monte Carlo simulation without splitting error of a GaAs resonant tunneling diode

Optimized Hydrodynamical Model for Charge Transport in Graphene

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