Charge Transport in Low Dimensional Semiconductor Structures

Camiola, Vito Dario; Mascali, Giovanni; Romano, Vittorio

doi:10.1007/978-3-030-35993-5

Cited by 21 publications

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“…The equilibrium density matrix can be obtained by employing a generalisation of the Maximum Entropy Principle (hereafter MEP) in a quantum context [ 10 , 17 , 18 ] (for the semiclassical case see [ 6 , 9 , 12 , 19 , 20 , 21 , 22 ]). According to the quantum version of MEP the equilibrium density matrix is obtained by maximising the quantum entropy

under suitable constraints on the expectation values.…”

Section: Equilibrium Density Functionmentioning

confidence: 99%

“…However, the most part of the works in the subject consider a quadratic dispersion relation for the energy. Instead, for several material like semiconductors or semimetal, e.g., graphene, other dispersion relations must be considered [ 4 , 5 , 6 , 7 ]. From the Wigner transport equation quantum hydrodynamical models have been obtained in [ 8 ] for charge transport in silicon in the case of parabolic bands, while in [ 9 ] the same has been devised for electrons moving in graphene.…”

Section: Introductionmentioning

confidence: 99%

“…A starting point is the determination of the equilibrium Wigner function. It can be obtained by using the Jaynes approach [ 6 , 10 , 11 , 12 ] of maximizing the entropy under suitable constraints on the expectation values. A crucial issue is the expression of the entropy in the quantum case.…”

Section: Introductionmentioning

confidence: 99%

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Equilibrium Wigner Function for Fermions and Bosons in the Case of a General Energy Dispersion Relation

Camiola¹,

Luca²,

Romano³

2020

Entropy

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The approach based on the Wigner function is considered as a viable model of quantum transport which allows, in analogy with the semiclassical Boltzmann equation, to restore a description in the phase-space. A crucial point is the determination of the Wigner function at the equilibrium which stems from the equilibrium density function. The latter is obtained by a constrained maximization of the entropy whose formulation in a quantum context is a controversial issue. The standard expression due to Von Neumann, although it looks a natural generalization of the classical Boltzmann one, presents two important drawbacks: it is conserved under unitary evolution time operators, and therefore cannot take into account irreversibility; it does not include neither the Bose nor the Fermi statistics. Recently a diagonal form of the quantum entropy, which incorporates also the correct statistics, has been proposed in Snoke et al. (2012) and Polkovnikov (2011). Here, by adopting such a form of entropy, with an approach based on the Bloch equation, the general condition that must be satisfied by the equilibrium Wigner function is obtained for general energy dispersion relations, both for fermions and bosons. Exact solutions are found in particular cases. They represent a modulation of the solution in the non degenerate situation.

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under suitable constraints on the expectation values.…”

Section: Equilibrium Density Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Equilibrium Wigner Function for Fermions and Bosons in the Case of a General Energy Dispersion Relation

Camiola¹,

Luca²,

Romano³

2020

Entropy

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“…Therefore, it is necessary to find out the expression of w eq . It can be obtained by using the Jaynes approach [14] of maximizing the entropy under suitable constraints on the expectation values, a crucial issue being the expression of the entropy in the quantum case. In [11,15] the standard prescription proposed by von Neumann has been adopted, which leads to a semiclassical limit represented by the Maxwell-Boltzmann distribution.…”

Section: Wigner Equation For Charge Transport In Graphenementioning

confidence: 99%

Quantum Energy-Transport and Drift-Diffusion Models for Electron Transport in Graphene An Approach by The Wigner Function

Camiola

Mascali

Romano

2021

Preprint

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The present work aims at formulating quantum energy-transport and drift- diffusion equations for charge transport in graphene from a quantum hydrodynamic model proposed in [1], obtained from the Wigner-Boltzmann equation via the mo- ment method. In analogy with the semiclassical case, we are confident that the energy- transport and drift-diffusion models have mathematical properties which allow an easier numerical treatment.

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“…Of course, a more detailed description of the electron scattering [11,20,23], more refined expressions for the mobility [24,26], a self-consistent potential model [25,26] or even quantum drift-diffusion equations [21,29,32], could be used to improve the model (see also Ref. [7] for a general reference).…”

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confidence: 99%

Mathematical modelling of charge transport in graphene heterojunctions

Barletti¹,

Nastasi²,

Negulescu³

et al. 2021

KRM

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A typical graphene heterojunction device can be divided into two classical zones, where the transport is basically diffusive, separated by a "quantum active region" (e.g., a locally gated region), where the charge carriers are scattered according to the laws of quantum mechanics. In this paper we derive a mathematical model of such a device, where the classical regions are described by drift-diffusion equations and the quantum zone is seen as an interface where suitable transmission conditions are imposed that take into account the quantum scattering process. Numerical simulations show good agreement with experimental data.

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Charge Transport in Low Dimensional Semiconductor Structures

Cited by 21 publications

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Equilibrium Wigner Function for Fermions and Bosons in the Case of a General Energy Dispersion Relation

Equilibrium Wigner Function for Fermions and Bosons in the Case of a General Energy Dispersion Relation

Quantum Energy-Transport and Drift-Diffusion Models for Electron Transport in Graphene An Approach by The Wigner Function

Mathematical modelling of charge transport in graphene heterojunctions

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