This thesis examines the quantum dynamics of electrons in periodic semiconductor superlattices in the presence of electric fields, especially uniform static fields. Chapter 1 is an introduction to this vast and active field of research, with an analysis and suggested solutions to the fundamental theoretical difficulties. Chapter 2 is a detailed historical review of relevant theories, and Chapter 3 is a historical review of experiments. Chapter 4 is devoted to the time-independent quantum mechanical study of the electric-field-induced changes in the transmission properties of ballistic electrons, using the transfer matrix method. In Chapter 5, a new time-dependent quantum mechanical model free from the fundamental theoretical difficulties is introduced, with its validity tested at various limiting cases. A simplified method for calculating field-free bands of various potential models is designed. In Chapter 6, the general features of "Shifting Periodicity", a distinctive feature of this new model, is discussed, and a "Bloch-Floquet Theorem" is rigorously proven. Numerical evidences for the existence of Wannier-Stark-Ladders are presented, and the conditions for its experimental observability is also discussed. In Chapter 7, an analytical solution is found for Bloch Oscillations and Wannier-Stark-Ladders at low electric fields. In Chapter 8, a new quantum mechanical interpretation for Bloch Oscillations and Wannier-Stark-Ladders is derived from the analytical result. The extension of this work to the cases of time-dependent electric fields is also discussed.
Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc277643 |
Date | 05 1900 |
Creators | Yuan, Daiqing |
Contributors | Deering, William D., West, Bruce J., Grigolini, Paolo, Kowalski, Jacek M., Mauldin, R. Daniel |
Publisher | University of North Texas |
Source Sets | University of North Texas |
Language | English |
Detected Language | English |
Type | Thesis or Dissertation |
Format | vii, 129 leaves : ill., Text |
Rights | Public, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved., Yuan, Daiqing |
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