| I present a detailed study of many-body effects associated with the interband 1s transition and intraband 1s-2 p transition in two- and three-dimensional photo-excited semiconductors. I employ a previously developed excitonic model to treat effects of exchange and phase space filling. 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 by many-body interactions, and the excitonic dynamical equations provide simple expressions for the individual contributions of screening, phase space filling and exchange.;The excitonic model correctly predicts the blue shift and bleaching of the 1s exciton resonance due to exchange and phase space filling. Free-carrier screening is found to enhance these effects by lowering the exciton binding energy. In contrast, the effects of free-carrier screening on the 1s -2p transition energy are more subtle. In the absence of free-carrier screening, exchange and phase space filling lead to a blue shift of the transition energy. However, screening decreases the 1s binding energy faster than the 2 p binding energy, which in turn decreases the transition energy. Thus, screening effects oppose exchange and phase space filling, and the overall magnitude and sign of the 1 s-2p transition energy shift depends on the free-carrier density. Specifically, for low-moderate excitation densities exchange and phase space filling 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.;The effects of exchange and phase space filling are quantified by a set of excitonic coefficients. I first calculate these coefficients analytically by omitting screening effects. In contrast, the screened coefficients 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. |
