A Study of Quantum Electron Dynamics in Periodic Superlattices under Electric Fields

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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 ... continued below

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vii, 129 leaves : ill.

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Yuan, Daiqing May 1996.

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This dissertation is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 27 times . More information about this dissertation can be viewed below.

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  • Yuan, Daiqing

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Description

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.

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vii, 129 leaves : ill.

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UNT Theses and Dissertations

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  • May 1996

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  • March 24, 2014, 8:07 p.m.

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  • July 31, 2015, 9:19 a.m.

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Yuan, Daiqing. A Study of Quantum Electron Dynamics in Periodic Superlattices under Electric Fields, dissertation, May 1996; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc277643/: accessed June 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .