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| HAL: hal-00593984, version 1 |
| arXiv: 1105.3656 |
| Detailed view |  Export this paper |
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| Analysis of a diffusive effective mass model for nanowires |
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| Clément Jourdana 1, 2Nicolas Vauchelet 3, 4 |
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| (2011-05-18) |
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| We propose in this paper to derive and analyze a self-consistent model describing the diffusive transport in a nanowire. From a physical point of view, it describes the electron transport in an ultra-scaled confined structure, taking in account the interactions of charged particles with phonons. The transport direction is assumed to be large compared to the wire section and is described by a drift-diffusion equation including effective quantities computed from a Bloch problem in the crystal lattice. The electrostatic potential solves a Poisson equation where the particle density couples on each energy band a two dimensional confinement density with the monodimensional transport density given by the Boltzmann statistics. On the one hand, we study the derivation of this Nanowire Drift-Diffusion Poisson model from a kinetic level description. On the other hand, we present an existence result for this model in a bounded domain. |
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| 1: | Institut de Mathématiques de Toulouse (IMT) |
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Université Paul Sabatier [UPS] - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées (INSA) - Toulouse – CNRS : UMR5219 |
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| 2: | Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI) |
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Consiglio Nazionale Ricerche (CNR) |
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| 3: | Laboratoire Jacques-Louis Lions (LJLL) |
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CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI |
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| 4: | BANG (INRIA Rocquencourt) |
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INRIA – Laboratoire Jacques-Louis Lions |
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| Subject | : | Mathematics/Analysis of PDEs |
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| drift-diffusion system – relative entropy method – diffusive limit – Hamiltonian's spectrum. |
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| hal-00593984, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00593984 | |
| oai:hal.archives-ouvertes.fr:hal-00593984 | |
| From: Nicolas Vauchelet | |
| Submitted on: Wednesday, 18 May 2011 15:55:17 | |
| Updated on: Wednesday, 18 May 2011 22:14:45 | |
