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Entropy
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Maximum Entropy Principle and Semiconductors
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Maximum Entropy Principle and Semiconductors

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (28 February 2017) | Viewed by 15337

Special Issue Editors

Prof. Dr. Vittorio Romano

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, University of Catania, Viale A. Doria, 6, 95125 Catania, Italy
Interests: mathematical modeling and simulation of semiconductors; radiative transfer; charge and heat transport in solids
Special Issues, Collections and Topics in MDPI journals
Dr. Giovanni Mascali

E-Mail Website
Guest Editor
Dipartimento di Matematica ed Informatica, Università della Calabria, Rende, Italy
Interests: extended thermodynamics; radiative transfer; charge and heat transport in solids

Special Issue Information

Dear Colleagues,

Enhanced functional integration in modern electron devices requires an increasingly accurate modeling of charge and energy transport in semiconductors in order to describe high-field phenomena, such as hot electron propagation and heat generation. Both semi-classical and quantum hydrodynamic-like models, more general than the drift-diffusion one, have been searched for in order to cope with these requirements. One of the main problem is that of the closure of the systems of equations constituting the models. Inspired from Jaynes’ studies on Information Theory and Statistical Mechanics, an important strategy for closure is based on the Maximum Entropy Principle. This principle consists of statistically inferring the least biased distribution function on the basis of the given information. The procedure can be used for standard devices, confined structure, nanowires, quantum resonant tunneling effects, hetero-structures, and novel materials such as graphene and carbon nanotubes.

The field of semiconductor modeling is going through rapid development involving many fields of science, such as mathematics, physics, engineering, and more. We, therefore, solicit contribution to this Special Issue on “Maximum Entropy Principle and Semiconductors”.

Dr. Vittorio Romano
Dr. Giovanni Mascali
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Maximum Entropy principle
  • Semiconductors
  • Charge Transport
  • Heat transport
  • Electrons
  • Holes
  • Phonons
  • Boltzmann Equation
  • Wigner Equation

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Published Papers (3 papers)

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Research

35 pages, 2124 KiB  
Article
Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors
by Giovanni Mascali and Vittorio Romano
Entropy 2017, 19(1), 36; https://doi.org/10.3390/e19010036 - 18 Jan 2017
Cited by 28 | Viewed by 5326
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Maximum Entropy Principle and Semiconductors)
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25 pages, 566 KiB  
Article
A Hydrodynamic Model for Silicon Nanowires Based on the Maximum Entropy Principle
by Orazio Muscato and Tina Castiglione
Entropy 2016, 18(10), 368; https://doi.org/10.3390/e18100368 - 19 Oct 2016
Cited by 14 | Viewed by 4625
Abstract
Silicon nanowires (SiNW) are quasi-one-dimensional structures in which the electrons are spatially confined in two directions, and they are free to move along the axis of the wire. The spatial confinement is governed by the Schrödinger–Poisson system, which must be coupled to the [...] Read more.
Silicon nanowires (SiNW) are quasi-one-dimensional structures in which the electrons are spatially confined in two directions, and they are free to move along the axis of the wire. The spatial confinement is governed by the Schrödinger–Poisson system, which must be coupled to the transport in the free motion direction. For devices with the characteristic length of a few tens of nanometers, the transport of the electrons along the axis of the wire can be considered semiclassical, and it can be dealt with by the multi-sub-band Boltzmann transport equations (MBTE). By taking the moments of the MBTE, a hydrodynamic model has been formulated, where explicit closure relations for the fluxes and production terms (i.e., the moments on the collisional operator) are obtained by means of the maximum entropy principle of extended thermodynamics, including the scattering of electrons with phonons, impurities and surface roughness scattering. Numerical results are shown for a SiNW transistor. Full article
(This article belongs to the Special Issue Maximum Entropy Principle and Semiconductors)
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14 pages, 361 KiB  
Article
Maximum Entropy Closure of Balance Equations for Miniband Semiconductor Superlattices
by Luis L. Bonilla and Manuel Carretero
Entropy 2016, 18(7), 260; https://doi.org/10.3390/e18070260 - 14 Jul 2016
Viewed by 4521
Abstract
Charge transport in nanosized electronic systems is described by semiclassical or quantum kinetic equations that are often costly to solve numerically and difficult to reduce systematically to macroscopic balance equations for densities, currents, temperatures and other moments of macroscopic variables. The maximum entropy [...] Read more.
Charge transport in nanosized electronic systems is described by semiclassical or quantum kinetic equations that are often costly to solve numerically and difficult to reduce systematically to macroscopic balance equations for densities, currents, temperatures and other moments of macroscopic variables. The maximum entropy principle can be used to close the system of equations for the moments but its accuracy or range of validity are not always clear. In this paper, we compare numerical solutions of balance equations for nonlinear electron transport in semiconductor superlattices. The equations have been obtained from Boltzmann–Poisson kinetic equations very far from equilibrium for strong fields, either by the maximum entropy principle or by a systematic Chapman–Enskog perturbation procedure. Both approaches produce the same current-voltage characteristic curve for uniform fields. When the superlattices are DC voltage biased in a region where there are stable time periodic solutions corresponding to recycling and motion of electric field pulses, the differences between the numerical solutions produced by numerically solving both types of balance equations are smaller than the expansion parameter used in the perturbation procedure. These results and possible new research venues are discussed. Full article
(This article belongs to the Special Issue Maximum Entropy Principle and Semiconductors)
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