Exciton and trion spectral line shape in the presence of an electron gas in GaAs/AlAs quantum wells

We studied the photoluminescence of (e1:hh1)1S excitons (X) and negatively charged excitons (trions, (Formula presented)) in quantum wells (QW’s) having a low-density ((Formula presented)<5×(Formula presented)) two-dimensional electron gas (2DEG) at T⩽12 K. Mixed type-I-type-II GaAs/AlAs quantum wells are studied in which the 2DEG is photogenerated in the type-I QW’s and (Formula presented) is determined by the excitation intensity. At a given temperature and for every excitation intensity the photoluminescence spectrum is decomposed into a Lorentzian-shaped (Formula presented) line and a convoluted Lorentzian-Gaussian X line. Their intensity ratio is analyzed by assuming a thermal equilibrium distribution of X and (Formula presented) that is determined by the chemical potential of the 2DEG. The (Formula presented) linewidth dependence on (Formula presented) is analyzed as originating from an increased (Formula presented) dephasing rate that is caused by trion-electron ((Formula presented)-e) scattering. We present a model of the elastic ((Formula presented)-e) scattering and calculate its rate as a function of (Formula presented) assuming the 2DEG screening wave vector ((Formula presented)) to be an adjustable parameter. Although of the same order of magnitude, the fitted (Formula presented) values differ from those calculated for the ideal gas model using the Thomas-Fermi approximation. Since, to our knowledge, there is no model for calculating (Formula presented) in the low 2DEG density range studied here and T>0, our spectroscopically extracted (Formula presented)((Formula presented)) values might serve as guidelines for the required theory.