Modélisation mathématique et numérique du transport de gaz quantique dans des situations de fort confinement

Abstract : This thesis lies in the field of mathematics applied to nanoelectronic devices. It raises the question of knowing how to mathematically and numerically simulate the transport of electrons that are confined in some space directions. At the scale of nanoelectronic devices, quantum effects due to the transport of electrons can no longer be ignored and the usual classical description has to be replaced by a quantum analysis. The study of such quantum tranports require solving Schrödinger-Poisson systems, which is a costly numerical task. The thesis is therefore based on a strong anisotropic confinement analysis of the quatum transport in such devices in order to obtain low-dimensional asymptotic models. The most important mathematical difficulty here lies in the fast oscillations that are due to the strong confinement. They are dealt with thanks to long time averaging procedures. In this prospect, the thesis presents different cases of confinement. Indeed, two different asymptotic models are presented in order to model the transport of electrons in a fine slab, and a specific asymptotic model is obtained in the case of a quantum gas that is confined along a plane and subject to a strong uniform magnetic field. Finally, we present a mathematical asymptotic model and numerical results for the transport of an electron gas in a nanowire. The numerical methods at hand here are also based on the idea of reducing the problem dimensions and, in that view, we make great use of subband decompostion methods.
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Submitted on : Thursday, December 10, 2009 - 1:32:24 PM
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Fanny Delebecque. Modélisation mathématique et numérique du transport de gaz quantique dans des situations de fort confinement. Mathématiques [math]. Université Rennes 1, 2009. Français. ⟨tel-00440334⟩

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