A Study of Quantum Electron Dynamics in Periodic Superlattices under Electric Fields Page: 3

                                
Yuan, Daiqing, A Study of Quantum Electron Dynamics in Periodic Super-
lattices under Electric Fields. Doctor of Philosophy (Physics), May, 1996,129 pages,
14 figures, bibliography, 206 titles.
This thesis examines the quantum dynamics of electrons in periodic semicon-
ductor 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 in-
troduced, 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 evi-
dences for the existence of Wannier-Stark-Ladders are presented, and the conditions
for its experimental observability is also discussed. In Chapter 7, an analytical solu-
tion 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.