Tight-Binding-Theorie für optische und magnetische Eigenschaften von Halbleitern

The subject of the first part of this thesis is the investigation of electronic and optical properties of polar and nonpolar InN/GaN quantum-dots, which was done in the framework of a cooperation with O. Marquardt and K. Schuh. The electronic properties were calculated by means of an effective-bond-orbital model (EBOM) by including the elastic properties of the nanostructure, which were provided and calculated in second-order continuum-elasticity theory by O. Marquardt. In order to solve the interacting many-body problem, K. Schuh applied a full configuration-interaction calculation and used the single-particle basis obtained by the EBOM to construct the interacting configurations. The purpose of this investigation was to study the interplay between attractive electron-hole interaction and the strong persistent intrinsic fields with piezo- and pyroelectric contributions in these nitride-heterostructures for one exciton. As a main result, the intrinsic fields were compensated by the Coulomb-interaction in the nonpolar quantum dot, thus enhancing the many-body oscillator-strength of the ground-state transition. This effect is a possible explanation for experimental findings of fast recombination rates in nonpolar nitride quantum-dots. In the second part of this thesis electronic and magnetic properties of the dilute magnetic semiconductors (DMS) Ga$_{1-x}$Mn$_{x}$As and Ga$_{1-x}$Mn$_{x}$N were studied with the goal to improve existing theoretical models describing magnetic impurities in these systems. By treating disorder effects exactly in combination with a realistic bandstructure described within the EBOM, it was shown that nonmagnetic impurity scattering terms are important to stabilize ferromagnetic order, as the effective exchange interactions are mainly ferromagnetic and agree with first-principles. The magnetic properties were examined by means of an equilibrium Green's-function theory for the disorderd Heisenberg model in Tyablikow approximation after a mapping of the exchange constants calculated earlier was done. The results for the concentration dependance of the critical temperature $T_{C}$ of Ga$_{1-x}$Mn$_{x}$As were in qualitative and quantitative agreement with existing experimental and theoretical data. Similiar studies were performed for Ga$_{1-x}$Mn$_{x}$N, but the electronic model was constructed to reproduce experimental findings of the optical conductivity, which was calculated theoretically as well. As a main result, ferromagnetic order with a low $T_{C}$ correlates with a nonvanishing AC-conductivity in the infrared spectral-region and a Fermi-level lying in the impurity-band.