# Optical properties of semiconductor nanostructures in magnetic field

Abstract (Summary)

In this work, the near bandgap linear optical properties of semiconductor
quantum structures under applied magnetic field are investigated. These
properties are determined mainly by a quasi-particle consisting of one electron
and one hole called exciton.
First, the exciton theory is developed starting with the one-electron Hamiltonian
in a crystal, continuing with the Luttinger and Bir-Pikus Hamiltonian,
and ending with the exciton Hamiltonian in the envelope function
approximation. Further, concentrating on the quantum well and thus assuming
strong confinement in the growth (z-) direction, the motion parallel
and perpendicular to the xy-plane is factorized leading to the well-known
single sublevel approximation. A magnetic field perpendicular to the xyplane
is applied, and a general theorem describing the behavior of the energy
eigenvalues is derived. This theorem is generally valid for any many-particle
system. Last but not least, the strain calculation within the isotropic elasticity
approach is described in detail.
Second, disorder is taken into account. After discussing its properties,
the standard ansatz of factorizing exciton relative and center-of-mass motion
is introduced. The SchrÃ¶dinger equation is solved numerically for both the
full model and the factorization with artificially generated disorder potentials
showing that the differences between them are pronounced especially
for tail states. From the physical point of view it is shown that (i) the
diamagnetic shift, i. e. energy change with magnetic field, is inversionally
proportional to the localization of the wave function, (ii) the distribution of
the diamagnetic shifts of individual exciton states exists and these shifts are
non-monotonic in energy, (iii) the average value of the diamagnetic shift increases
with energy, and (iv) absorption and consequently photoluminescence
spectra become wider with increasing magnetic field.
Furthermore, having structural information from the cross-sectional scanning
tunneling microscopy of a given sample avaible, the statistical properties
of the disorder in a real quantum well have been analyzed. This analysis enabled
the numerical generation of new lateral disorder potentials which served
as input in the simulation of exciton optical properties. In particular, temperature
dependent photoluminescence spectra and diamagnetic shift statistics,
have been compared with the experimental ones and very good agreement
has been found.
The second part of this thesis deals predominantly with highly symmetrical
structures embedded in the quantum well: namely quantum rings and
dots. First, adopting an ansatz for the wave function, the Hamiltonian matrix
is derived discussing which matrix elements are non-zero according to
the symmetry of the potential. Additionally, the expectation values of the
current and magnetization operators are evaluated. Then, concentrating on
the case of the highest (circular) symmetry, the model of zero width ring
is introduced. Within this model the close relation between the oscillatory
component of the exciton energy (exciton Aharonov-Bohm effect) and the
persistent current is revealed. Examples for different material systems follow
revealing the importance of the relation between exciton Bohr radius and
ring diameter for oscillations and persistent current to be observed. The circular
quantum dot is treated briefly. Finally, a case of the non-circular ring
is discussed and it is shown that oscillations can be observed although with
lower amplitude compared to circular case.
Finally, the exciton emission kinetics is calculated, too. The limitations
of the experimental observability of energy oscillations, photoluminescence
quenching, caused by non-zero non-radiative channels are disclosed.
Bibliographical Information:

Advisor:

School:Oberlin College

School Location:USA - Ohio

Source Type:Master's Thesis

Keywords:

ISBN:

Date of Publication: