Excitonic analysis of many-body effects on the1s-2pintraband transition in semiconductor systems
Physical Review B
I present a detailed study of many-body eects associated with the interband 1s transition and intraband 1s-2p transition in two-and three-dimensional photo-excited semiconductors. I employ a previously developed excitonic model to treat eects of exchange and phase space lling. I extend the scope of the model to include static free-carrier screening. I also develop a factorization scheme to obtain a consistent set of excitonic dynamical equations. The exciton transition energies are renormalized
... es are renormalized by many-body interactions, and the excitonic dynamical equations provide simple expressions for the individual contributions of screening, phase space lling and exchange. The eects of exchange and phase space lling are quantied by a set of excitonic coecients. I rst calculate these coecients analytically by omitting screening eects. In contrast, the screened coecients involve multi-dimensional integrals which must be evaluated numerically. I present a detailed discussion of the numerical methods used to evaluate these integrals, which include a novel algorithm for segmenting multi-dimensional integration regions. The excitonic model correctly predicts the blue shift and bleaching of the 1s exciton resonance due to exchange and phase space lling. Free-carrier screening is found to enhance these eects by lowering the exciton binding energy. In contrast, the eects of free-carrier screening on the 1s-2p transition energy are more subtle. In the absence of free-carrier screening, exchange and phase space lling lead to a blue shift of the transition energy. However, screening decreases the 1s binding energy faster than the 2p binding energy, which in turn decreases the transition energy. Thus, screening eects oppose exchange i and phase space lling, and the overall magnitude and sign of the 1s-2p transition energy shift depends on the free-carrier density. Specically, for low-moderate excitation densities exchange and phase space lling can be dominated by screening, leading to a net red shift of the transition energy. The results for two-and three-dimensional systems are qualitatively similar, although the magnitudes of the shifts are much smaller in three dimensions. ii I would like to express my foremost gratitude to my supervisor, Prof. Marc M. Dignam, for his wise and friendly guidance during the course of my studies. Our stimulating and fruitful discussions inspired me to write this thesis. I beneted immensely from his patience and foresight, which helped me optimize the quality and scope of my work. I am thankful for the opportunity to attend a conference and present our work, and I enjoyed the time we spent together.