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, X(-)) in quantum wells (QW's) having a low-density (n(e) < 5 x 10(10) cm(-2)) two-dimensional electron gas (2DEG) at T less than or equal to 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 n(e) is determined by the excitation intensity. At a given temperature and for every excitation intensity the photoluminescence spectrum is decomposed into a Lorentzian-shaped X(-) Line and a convoluted Lorentzian-Gaussian X line. Their intensity ratio is analyzed by assuming a thermal equilibrium distribution of X and X(-) that is determined by the chemical potential of the 2PEG. The X(-) linewidth dependence on ne is analyzed as originating from an increased X(-) dephasing rate that is caused by trion-electron (X(-)-e) scattering. We present a model of the elastic (X(-)-e) scattering and calculate its rate as a function of n(e) assuming the 2DEG screening wave vector (q(s)) to be an adjustable parameter. Although of the same order of magnitude, the fitted q(s) 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 q(s) in the low 2DEG density range studied here and T > 0, our spectroscopically extracted q(s)(n(e)) values might serve as guidelines for the required theory.