The need to model the quantum effects in semiconductor devices such as resonance tunneling diodes and quantum dots has lead to an intense study of the Wigner-Poisson (WP) and Schroedinger-Poisson (SP) systems. In this work we present the mathematical analysis of several related models for these systems. These include: a time-dependent model of dissipation in (SP), a quasi-linear (SP) system, a study of the stationary (WP)-(SP) problem with a discussion of the quantum analogue of classical BGK modes and a proof of existence of eigenfunctions for (SP) with periodic boundary conditions, and an examination of the stationary Wigner equations with inflow" boundary conditions. Finally, a proposed numerical scheme for the stationary (SP) system with Boltzmann distribution functions is shown along with its corresponding Bloch equation. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/29464 |
| Date | 11 May 1998 |
| Creators | Toomire, Bruce V. |
| Contributors | Physics, Zweifel, Paul F., Ficenec, John R., Hagedorn, George A., Slawny, Joseph, Klaus, Martin, Chang, Lay Nam |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | etd.pdf |
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