Microscopic Modeling of Photoluminescence in Disordered Semiconductors
In this thesis the quantum optical properties of disordered semiconductors have been investigated. After merging together the latest results of two different fields, namely semiconductor optics and disordered semiconductors, we were able to describe the interaction of the quantized light fie...
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| Format: | Dissertation |
| Sprache: | Englisch |
| Veröffentlicht: |
Philipps-Universität Marburg
2005
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| Zusammenfassung: | In this thesis the quantum optical properties of disordered
semiconductors have been investigated. After merging together the
latest results of two different fields, namely semiconductor optics
and disordered semiconductors, we were able to describe the
interaction of the quantized light field and the disordered
semiconductor at a fully microscopical level. We have used a
one-dimensional tight-binding model. The underlying Hamiltonian
describes free electrons and photons, the Coulomb interaction and the
light--matter interaction at dipole level. Disorder is taken into
account by varying the energies of sites. The effect of
lattice vibrations (phonons) has been omitted and the microscopic
electron--electron scattering has been included by a phenomenological
damping parameter.
Absorption and photoluminescence spectra are determined by the
time evolution of the microscopic polarization and photon assisted
polarization, respectively. Thus we derived the general equation of
motion for the purely electronic and photon assisted polarization of
the disordered system. Applying the cluster expansion for these
quantities we have truncated them at single-particle level, i.e.,
Hartree--Fock level. Assuming stationary carrier populations we have
given an analytical solution for both equations of motion. The
solution of the equation of the motion of the polarization turned out
to be the famous Elliott formula of absorption and we have obtained a
similar expression for the photoluminescence spectrum, too.
Evaluating our analytical results numerically, we have investigated
the Stokes shift, the influence of direct and indirect nature and
of disorder on photoluminescence spectra, the thermodynamic relation
of absorption and luminescence and the lifetime distribution.
We have seen that the disorder induces a Stokes shift, which depends
on the temperature of the carriers and on the Coulomb interaction.
The latter does not change the presence of the Stokes shift, it only
decreases its size through enhancing the optical matrix elements for
the low-energy transitions. The temperature has turned out to be the
other essential parameter, since the Stokes shift considerably
decreases or even disappears for high temperatures.
The analysis of the direct and indirect nature has shown that disorder
obviously destroys the original electronic structure of the material and the
underlying direct or indirect nature can no longer be distinguished in
photoluminescence spectra for strong enough disorder. On the other
hand, we find it remarkable that even for relatively large disorder
the spectra still differ clearly from each other. The temperature is
important here as well, since this difference is more pronounced at
low temperature.
In the case of the thermodynamical relation between absorption and
luminescence disorder plays a crucial role. Our results have shown
that stronger disorder leads to smaller or even vanishing deviations
of the calculated luminescence from its thermodynamical value.
In our lifetime distribution study we have proved that the Coulomb
interaction does not play a significant role if a short-range disorder
potential is present. A transition from a log-normal to a power-law
distribution has also been formed as the disorder increases.
In the last Chapter of the present thesis the angular photonic
correlation has been investigated. After the derivation of the
polarization--polarization correlation function
$U_{\hbar\omega}(\Delta q)$ we have analytically shown for an
ensemble of independent two-level systems that
$U_{\hbar\omega}(\Delta q)$ carries all information on the spatial
position of emitters as well as the complete disorder potential. The
method of how to extract these data from the correlation function has
also been presented. Then the method has been extended to the general
model, where both the coupling between sites, i.e., the kinetic
energy, and the Coulomb interaction have been included. |
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| Umfang: | 105 Seiten |
| DOI: | 10.17192/z2005.0439 |