Diffusive Limit of the Two-Band k⋅p Model for Semiconductors

Barletti, Luigi; Frosali, Giovanni

doi:10.1007/s10955-010-9940-9

Cited by 19 publications

(21 citation statements)

References 32 publications

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“…Note that the leading term is a matrix logarithm and that in the present, spinorial, case we cannot exclude the presence of a non-vanishing term of order h -(see e. g. Reference [7]), whereas in the scalar case we always have Log(w) = log(w)+O(h -2 ) [6]. By using the semiclassical approximation (23), the properties of the Pauli matrices and the Taylor expansion of the logarithm, it is possible to prove the following result [12].…”

Section: Form Of the Constrained Entropy Minimizermentioning

confidence: 99%

“…Quantum fluid-dynamics is a fast-developing research field in applied mathematics, especially because of its interest in nanoelectronics [4]. It has been boosted by the quantum formulation of the minimum entropy principle [5,6], whose application to spinorial system is very recent [7,8]. The strategy, generally speaking, is the following.…”

Section: Introductionmentioning

confidence: 99%

“…The strategy, generally speaking, is the following. One starts from a quantum kinetic description of the system, usually formulated in terms of Wigner functions [9], that become matrix-valued function for spinorial systems [7]. The moments of the Wigner function are the macroscopic (fluid-dynamic) quantities of interest.…”

Section: Introductionmentioning

confidence: 99%

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Quantum electronic transport in graphene: A kinetic and fluid-dynamic approach

Zamponi

Barletti

2010

Math. Meth. Appl. Sci.

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Communicated by P. M. MarianoWe derive a fluid-dynamic model for electron transport near a Dirac point in graphene. Starting from a kinetic model, based on spinorial Wigner functions, the derivation of the fluid model is based on the minimum entropy principle, which is exploited to close the moment system deduced from the Wigner equation. To this aim we make two main approximations: the usual semiclassical approximation (h -1) and a new one, namely, the 'strongly mixed state' approximation, which allow to compute the closure explicitly. Particular solutions of the fluid-dynamic equations are discussed which are of physical interest because of their connection with the Klein paradox phenomenon.

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Section: Form Of the Constrained Entropy Minimizermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum electronic transport in graphene: A kinetic and fluid-dynamic approach

Zamponi

Barletti

2010

Math. Meth. Appl. Sci.

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“…A formal proof of the following theorem makes use of the mathematical techniques adopted in similar contexts (see, e.g., Ref. [2]); however the application of these techniques to the full-spin case is far from being straightforward and a detailed proof is deferred to a forthcoming paper. Rigorous proofs also exist, but only for the simpler case of a one-dimensional system of scalar (non-spinorial) particles in an interval with periodic boundary conditions, see Refs.…”

Section: H (W) = Tr (S Log(s) − S + Hs)mentioning

confidence: 99%

Quantum drift-diffusion equations for a two-dimensional electron gas with spin-orbit interaction

Barletti¹,

Holzinger²,

Jüngel³

2020

Preprint

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Quantum drift-diffusion equations are derived for a two-dimensional electron gas with spin-orbit interaction of Rashba type. The (formal) derivation turns out to be a non-standard application of the usual mathematical tools, such as Wigner transform, Moyal product expansion and Chapman-Enskog expansion. The main peculiarity consists in the fact that a non-vanishing current is already carried by the leading-order term in the Chapman-Enskog expansion. To our knowledge, this is the first example of quantum drift-diffusion equations involving the full spin vector. Indeed, previous models were either quantum bipolar (involving only the spin projection on a given axis) or full spin but semiclassical.

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“…Generalized variants of QDD models have recently been proposed. For instance, the diffusive limit of a two band k.p model has been investigated in [4]. A multiband model with an arbitrary number of bands has been considered in [30] to describe the quantum transport in a strong force regime.…”

mentioning

confidence: 99%

A quantum Drift-Diffusion model and its use into a hybrid strategy for strongly confined nanostructures

Jourdana¹,

Pietra²

2019

Kinetic &Amp; Related Models

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In this paper we derive by an entropy minimization technique a local Quantum Drift-Diffusion (QDD) model that allows to describe with accuracy the transport of electrons in confined nanostructures. The starting point is an effective mass model, obtained by considering the crystal lattice as periodic only in the one dimensional longitudinal direction and keeping an atomistic description of the entire two dimensional cross-section. It consists of a sequence of one dimensional device dependent Schrödinger equations, one for each energy band, in which quantities retaining the effects of the confinement and of the transversal crystal structure are inserted. These quantities are incorporated into the definition of the entropy and consequently the QDD model that we obtain has a peculiar quantum correction that includes the contributions of the different energy bands. Next, in order to simulate the electron transport in a gate-all-around Carbon Nanotube Field Effect Transistor, we propose a spatial hybrid strategy coupling the QDD model in the Source/Drain regions and the Schrödinger equations in the channel. Self-consistent computations are performed coupling the hybrid transport equations with the resolution of a Poisson equation in the whole three dimensional domain.

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Diffusive Limit of the Two-Band k⋅p Model for Semiconductors

Cited by 19 publications

References 32 publications

Quantum electronic transport in graphene: A kinetic and fluid-dynamic approach

Quantum electronic transport in graphene: A kinetic and fluid-dynamic approach

Quantum drift-diffusion equations for a two-dimensional electron gas with spin-orbit interaction

A quantum Drift-Diffusion model and its use into a hybrid strategy for strongly confined nanostructures

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