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https://hdl.handle.net/2142/18886
Description
Title
Theoretical and numerical study of nanostructures
Author(s)
Pevzner, Vadim B.
Issue Date
1992
Doctoral Committee Chair(s)
Hess, Karl
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
theoretical physics
numerical techniques
nanostructures
electron propagation
semiconductors
nanometer-scale physics
phase coherence
electron wave function
Path Decomposition Expansion method (NPDX)
Language
en
Abstract
"The methods presented in this thesis were developed to study the electron propagation
in nanostructures with special emphasis on semiconducting materials. The essence
of nanometer-scale physics is in the phase coherence of an electron wave function over
a length scale that is comparable to the size of the structure itself. In order to study
the electron transport in these nanostructures we have developed numerical Path Decomposition
Expansion method (NPDX). Many different techniques have been used in
the study of mesoscopic systems with complex geometry including transmission matrix
methods, mode matching, and tight binding Green's function techniques such as the one
used by Sols et al. in the study of the quantum modulated transistor. NPDX, however,
permits the study of mesoscopic structures where other techniques are either not applicable
or numerically prohibitive due to the geometric complexity. In addition, the nature
of NPDX algorithm permits investigation of various geometries without modifications to
the algorithm itself or any significant effect on the size of the computation. The transmission
(reflection) coefficients calculated with the use of NPDX can then be related
to the electric conductance via Landauer's formula. We have investigated a number of
structures where other methods are applicable and we have found a good agreement with
NPDX. We have also investigated the effects of dissipation on electron transport in
these structures. Two models of dissipation are presented. These involve localized (onsite)
and extended phonons linearlyt coupled to the electron. The coupling is localized
to the ""cavity"" region only. Due to the resonant nature of electron scattering, the greatest
influence of dissipation on the scattering of electron is presumably inside the cavity
region. Thus, the essential features of dissipative effects should be well captured by such
spatially confined phonon models. The main advantage of the localized phonon model is
that it can be solved exactly. While the extended phonon model, although it can only
be solved perturbatively, is a more realistic model of dissipation. Both models exhibit
significant changes in the calculated transmission probabilities due to dissipation. In addition,
in the localized phonon model, the ""effective"" cavity size as seen by the electron
is modified by the dephasing nature of electron-coupling. Thus the effects of dissipation
play an important role on the electron transport in nanostructures and on their practical
applications.
tThe choice of linear coupling was made only for the sake of simplicity."
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