Generalised Drift-Diffusion Model of Bipolar Transport in Semiconductors

Reznik, D.

doi:10.1007/978-3-7091-6619-2_61

Cited by 6 publications

(5 citation statements)

References 9 publications

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“…by collisions between electrons and so-called defect electrons. This scattering needs to be taken into account on the mesoscopic level by electron-hole collision operators in the semiconductor Boltzmann equations [55]. Then, performing the diffusion limit in the Boltzmann system for electrons and holes, drift-diffusion equations can be derived which include cross-diffusion terms arising from the interaction of the electrons and holes.…”

Section: Models Without Volume Fillingmentioning

confidence: 99%

The boundedness-by-entropy method for cross-diffusion systems

Jüngel

2015

Nonlinearity

147

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A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that the diffusion matrix may be generally neither symmetric nor positive semi-definite. The key idea of the principle is to employ a transformation of variables, determined by the entropy density, which is defined by the gradient-flow formulation. The transformation yields at the same time a positive semidefinite diffusion matrix, suitable gradient estimates as well as lower and/or upper bounds of the solutions. These bounds are a consequence of the transformation of variables and are obtained without the use of a maximum principle. Several classes of cross-diffusion systems are identified which can be solved by this technique. The systems are formally derived from continuous-time random walks on a lattice modeling, for instance, the motion of ions, cells, or fluid particles. 17 5. Proof of Theorem 4 24 6. Further results and open problems 28 Appendix A. Relations to non-equilibrium thermodynamics 32 Appendix B. Formal derivation of two-species population models 33 Appendix C. A variant of the Aubin compactness lemma 34 References 36

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Section: Models Without Volume Fillingmentioning

confidence: 99%

The boundedness-by-entropy method for cross-diffusion systems

Jüngel

2015

Nonlinearity

147

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“…This system was derived in [25,18,29]. Our derivation shows that electron-hole scattering can be understood as an independent diffusion of electrons, holes, and some pseudo-particle.…”

Section: Many Non-interacting Species and Pseudo-speciesmentioning

confidence: 98%

“…This pseudo-particle has to be taken care of, but we are not interested in its evolution. A case in point is the modeling of electron-hole scattering in semiconductor theory (see, e.g., [29]). …”

Section: Many Non-interacting Species and Pseudo-speciesmentioning

confidence: 99%

Modeling of drift-diffusion systems

Stephan

2007

Z. angew. Math. Phys.

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We derive drift-diffusion systems describing transport processes starting from free energy and equilibrium solutions by a unique method. We include several statistics, heterostructures and cross diffusion. The resulting systems of nonlinear partial differential equations conserve mass and positivity, and have a Lyapunov function (free energy). Using the inverse Hessian as mobility, non-degenerate diffusivity matrices turn out to be diagonal, or -in the case of cross diffusion -even constant. (2000). 35K55, 80A20, 82D37, 82C31, 35B50, 35G25. Mathematics Subject Classification

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“…The cross effects of E h on J e and of E e on J h in a drift-diffusion model are discussed in [10]. Moreover, we can calculate the energy flux by its very definition:…”

Section: Revised Drift-diffusion Approximation and Constitutive Lawsmentioning

confidence: 99%

A Hydrodynamical Model for Carriers and Phonons With Generation-Recombination, Including Auger Effect

Rossani¹

2015

Entropy

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The asymptotic procedure proposed allows to derive closed hydrodynamical equations from the kinetic equations of carriers and phonons (treated as a partecipating species) in a photon background. The direct generation-recombination processes are accounted for. The fluid-dynamical equations constructed for the chemical potentials of carriers, temperature, and drift velocity, are related to the extended thermodynamical (ET) ones for the chemical potentials of carriers, temperature, and drift velocity.In the drift-diffusion approximation the constitutive laws are derived and the Onsager relation recovered.

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Generalised Drift-Diffusion Model of Bipolar Transport in Semiconductors

Cited by 6 publications

References 9 publications

The boundedness-by-entropy method for cross-diffusion systems

The boundedness-by-entropy method for cross-diffusion systems

Modeling of drift-diffusion systems

A Hydrodynamical Model for Carriers and Phonons With Generation-Recombination, Including Auger Effect

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