Excitonic analysis of many-body effects on the1s-2pintraband transition in semiconductor systems

Abstract

We present a detailed study of many-body effects associated with the intraband $1s$-$2p$ transition in two- and three-dimensional photoexcited semiconductors. We employ a previously developed excitonic model to treat effects of exchange and phase space filling (PSF). In this work, we extend the model to include intraband transitions and static free-carrier screening. The exciton transition energies are renormalized by many-body interactions, and the excitonic dynamical equations provide simple expressions for the individual contributions of screening, PSF and exchange. The excitonic model correctly predicts the blue shift and bleaching of the $1s$ exciton resonance due to exchange and PSF. Free-carrier screening is found to enhance these effects by lowering the binding energy of the $1s$ exciton. In contrast, the effects of free-carrier screening on the $1s$-$2p$ transition energy are subtler. For a coherent exciton system, in the absence of free-carrier screening, exchange and PSF 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 PSF, and the overall magnitude and sign of the $1s$-$2p$ transition energy shift depends on the free-carrier density. Specifically, for low to moderate excitation densities, exchange and PSF can be dominated by screening, leading to a net redshift of the transition energy. The results for two- and three-dimensional systems are qualitatively similar, although the magnitude of the shift is much smaller in three dimensions.