Excitonic Analysis of Many-Body Effects on the 1s−2p Intraband Transition in Semiconductor Systems
Parks, Andrew Marshall
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I present a detailed study of many-body effects 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 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 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. 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 2p 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 1s-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.