Coulomb induced interplay of localized and reservoir carriers in semiconductor quantum dots

This thesis is about the calculation of Coulomb–scattering processes between bound states in semiconductor quantum dots and delocalized states of the surrounding reservoir. The thesis is divided into two parts. The central topic is the fundamental question, how reservoir dimensionality influences Coulomb scattering. It was discussed, that 2D scattering is more efficient than 3D scattering, due to the lower dimensionality. The results on that topic, presented in the first part, might improve the understanding of fundamental experiments like pump-probe measurements. In the second part, the influence of Coulomb scattering processes on material gain and refractive index in quantum dot devices will be investigate. This is of fundamental importance for quantum dot device simulation. The Coulomb scattering processes are treated in this thesis within the framework of a microscopic model in the limit of Born-Markov approximation. Screening effects were included in the limit of the Lindhard formula and perturbation of the reservoir wavefunctions caused by the quantum dot states are incorporated via orthogonalized plane waves. In addition, it was shown how to extend the theory for the description of weakly, spatially inhomogeneous carrier densities. In the central part of this thesis the investigation of the impact of the reservoir dimensionality Coulomb scattering rates for two system are compared. Equal quantum dots coupled to different reservoirs are assumed. The quantum dots in model system (i) are coupled to a two dimensional reservoir, for example a quantum well, whereas in model system (ii), the quantum dots are coupled to the three dimensional reservoir formed by the bulk material. The higher dimensional integrals (up to 8D), appearing in the calculation of the scattering rates, particularly in model system (ii), are evaluated efficiently via Quasi-Monte Carlo method. In the calculations presented here, the significant rates showed similar behavior concerning the carrier density dependency, although the rates differ in details. As an example, the two model systems show an opposite behavior concerning the quantum dot height. Contrary to the assumption of more efficient 2D scattering, the 2D rates have not shown to be more efficient in general. This is in agreement with experimental observations. In the second part of the presented results, the polarization dynamics are investigated to calculate gain spectra. The quantum dots under consideration, contain two energy levels and couple to a two dimensional carrier reservoir. The impact of Coulomb scattering on microscopic polarization is investigated in terms of a microscopically determined dephasing time T2. From this one can calculate the homogeneous linewidth of the quantum dot transition, which in turn can be used to calculate the gain spectra and the refractive index of the quantum dot material. The results are compared with results of the benchmark model of M. Lorke et. al. and with experimental results. It is found that the basic features like gain reduction of quantum dots and the qualitative behavior of the homogeneous broadening are nicely reproduced by the model presented here. Therefore, it improves the understanding of device limiting processes and offers a good compromise between accuracy and effort for usage in device simulation.