Absorption spectrum of a weakly n-doped semiconductor quantum well

We calculate, as a function of temperature and conduction-band electron density, the optical absorption of a weakly n-doped, idealized semiconductor quantum well. In particular, we focus on the absorption band due to the formation of a charged exciton. We conceptualize the charged exciton as an itinerant excitation intimately linked to the dynamical response of itinerant conduction-band electrons to the appearance of the photogenerated valence-band hole. Numerical results for the absorption in the vicinity of the exciton line are presented and the spectral weights associated with, respectively, the charged exciton band and the exciton line are analyzed in detail. We find, in qualitative agreement with experimental data, that the spectral weight of the charged exciton grows with increasing conduction-band electron density and/or decreasing temperature at the expense of the exciton.