Theory of electron-hole pair excitations in semiconductor quantum dots.

Abstract

This dissertation considers one- and two-electron-hole-pair excitations in ideally spherical semiconductor quantum dots with infinite or finite confinement potentials. The optical absorption edge of the semiconductor micsrocrystallites is found to be higher than that in the corresponding bulk semiconductor. This blue shift is approximately proportional to 1/R², where R is the radius of the semiconductor microspheres. For small quantum dots with infinite confinement potential, the energies and wave-functions of quantum confined excitons and biexcitons are computed using a numerical matrix diagonalization method. Both numerical matrix digaonalization and perturbative calculations prove that the binding energy of biexcitons is strictly positive regardless of material parameters. A general formula for the optical susceptibility of quantum dots is derived, from which, optical spectra are computed. The theoretical results qualitatively agree with recent experimental observations. Some novel optical properties of quantum dots are revealed by this study, such as the existence of excited biexciton states energetically above the exciton ground state resonance and modified optical nonlinearities. Extending our numerical scheme, we compute the effects of impurities or crystal defects in a simple model. The calculation shows that charge defects or impurities have only a small influence on the optical spectra of quantum dots. The details of the quantum confinement conditions, such as the finite value of the quantum confinement potential and different electron-hole masses inside and outside the dot, are studied within the framework of the variational scheme. Finally, we extend the numerical matrix diagonalization method to investigate the valence band coupling effect in quantum dots by including the Luttinger Hamiltonian. It is found that the concept of heavy- and light-hole has to be modified to describe the hole states in semiconductor quantum dots. Also, the valence band mixing due to spin-orbit interaction changes significantly the optical selection rules and consequently influences the allowed optical excitations in quantum dots.