Dokument

Summary:
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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