A Hydrodynamic Model for Silicon Nanowires Based on the Maximum Entropy Principle

Muscato, Orazio; Castiglione, Tina

doi:10.3390/e18100368

Cited by 13 publications

(8 citation statements)

References 45 publications

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“…This represents a step ahead toward the simulation of quantum struc-tures such as silicon nanowire devices [22][23][24][25], where the effects of phonon scattering and heating could be included [26][27][28][29][30][31][32][33]. These topics will be the tasks of future researches.…”

Section: Discussionmentioning

confidence: 99%

A benchmark study of the Signed-particle Monte Carlo algorithm for the Wigner equation

Muscato

2017

Communications in Applied and Industrial Mathematics

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The Wigner equation represents a promising model for the simulation of electronic nanodevices, which allows the comprehension and prediction of quantum mechanical phenomena in terms of quasi-distribution functions. During these years, a Monte Carlo technique for the solution of this kinetic equation has been developed, based on the generation and annihilation of signed particles. This technique can be deeply understood in terms of the theory of pure jump processes with a general state space, producing a class of stochastic algorithms. One of these algorithms has been validated successfully by numerical experiments on a benchmark test case. Keywords:Nanostructures, Wigner transport equation, Direct simulation Monte Carlo AMS subject classification: 82D80, 82S30, 65M75The Wigner equation is a full quantum transport model able to capture the relevant physics in next generation semiconductor devices. It is well known that the pure state Wigner equation is an equivalent phase-space reformulation of the Schrödinger equation. At the same time the Wigner equation can be augmented by a Boltzmann-like collision operator accounting for the process of decoherence. However, this equation has represented a numerically daunting task and it has raised more problems than solutions. A numerical treatment of the Wigner equation can be dealt with deterministic schemes [1][2][3][4], Direct Simulation Monte Carlo [5][6][7][8], and it is often used to derive reduced transport models, such as quantum-hydrodynamic models [9][10][11][12].Among the several particle Monte Carlo methods developed during these years (see [13] for a review), we have focused in the so called Signed Monte Carlo method [14], where the Wigner potential is treated as a scat-

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Section: Discussionmentioning

confidence: 99%

A benchmark study of the Signed-particle Monte Carlo algorithm for the Wigner equation

Muscato

2017

Communications in Applied and Industrial Mathematics

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“…By exploiting the MEP, constitutive relations for the higher-order moments and the production can be obtained (see [32] for the details). In this way a physics-based hydrodynamic model is obtained, consistent with thermodynamics principles, valid in a larger neighborhood of local thermal equilibrium, and free of any tunable parameters.…”

Section: Extended Hydrodynamic Modelmentioning

confidence: 99%

Low-field electron mobility evaluation in silicon nanowire transistors using an extended hydrodynamic model

et al. 2018

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Silicon nanowires (SiNWs) are quasi-one-dimensional structures in which electrons are spatially confined in two directions and they are free to move in the orthogonal direction. The subband decomposition and the electrostatic force field are obtained by solving the Schrödinger-Poisson coupled system. The electron transport along the free direction can be tackled using a hydrodynamic model, formulated by taking the moments of the multisubband Boltzmann equation. We shall introduce an extended hydrodynamic model where closure relations for the fluxes and production terms have been obtained by means of the Maximum Entropy Principle of Extended Thermodynamics, and in which the main scattering mechanisms such as those with phonons and surface roughness have been considered. By using this model, the low-field mobility of a Gate-All-Around SiNW transistor has been evaluated.

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“…In this section, we consider the case of an ensemble of electrons (the treatment of holes would be analogous) confined along one dimension, called quasi 2Delectron gas (2DEG) [16,[18][19][20]44]. This situation arises when the length scale in one (the confined) space direction of the semiconductor device under study is of the order of de Broglie wavelength of electrons, while the nonconfined directions have a much bigger length scale.…”

Section: Two-dimensional Electron Gases: the Case Of Quantum Confinementmentioning

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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A Hydrodynamic Model for Silicon Nanowires Based on the Maximum Entropy Principle

Cited by 13 publications

References 45 publications

A benchmark study of the Signed-particle Monte Carlo algorithm for the Wigner equation

A benchmark study of the Signed-particle Monte Carlo algorithm for the Wigner equation

Low-field electron mobility evaluation in silicon nanowire transistors using an extended hydrodynamic model

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

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