A Semicontinuous Formulation of the Bloch--Boltzmann--Peierls Equations

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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“…. , 3ν, whose time evolution is determined by the Boltzmann-Bloch-Peierls (BBP) system (see [24] and references therein)…”

Section: The 3d Semiclassical Macroscopic Modelsmentioning

confidence: 99%

“…The collision operators which appear in the Boltzmann-Peierls equations for phonons, relative to their interactions with carriers, read [24] C p…”

Section: The 3d Semiclassical Macroscopic Modelsmentioning

confidence: 99%

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

Mascali

Romano

2017

Entropy

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“…To obtain semicontinuous versions of the BBP equations, the considered dispersion relations must meet the following conditions (Auer, Schürrer, and Koller 2004). Concerning electrons and acoustic phonons, the moduli of the wave vectors must be unique functions of the energies E and e for given direction unit vectors V k ¼ k/jkj and V q ¼ q/jqj, i.e.,…”

Section: Requirementsmentioning

confidence: 99%

“…For such sets of energies and wave vectors, we provide the semicontinuous BBP equations (Auer, Schürrer, and Koller 2004) …”

Section: Semicontinuous Bbp Equationsmentioning

confidence: 99%

“…Taking also the non-equilibrium behavior of the phonons into account leads to a system of coupled Boltzmann equations for electrons and phonons, the so-called Bloch-Boltzmann-Peierls (BBP) equations (Ziman 1960;Rossani 2002). Lately, we have presented a semicontinuous version of the BBP equations (Auer, Schürrer, and Koller 2004). The derived model equations prove to describe accurately the far-form-equilibrium kinetics of coupled electron-phonon systems and provide an alternative solution to the popular Ensemble Monte Carlo methods (Jacoboni and Reggiani 1983).…”

Section: Introductionmentioning

confidence: 99%

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Semicontinuous Kinetic Theory of the Relaxation of Electrons in GaAs

Auer

Schürrer

2004

Transport Theory and Statistical Physics

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This paper presents a semicontinuous version of the Bloch-BoltzmannPeierls equations describing the kinetics of a coupled electron-phonon system in polar semiconductors. The model equations are specialized to the case of spherically symmetric dispersion relations and transition rates. Detailed numerical studies of the relaxation process of an electron gas interacting with polar-optical and acoustic phonons are performed. The results are compared with calculations carried out on the level of quasi-hydrodynamic transport models concerning the phonon system.

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