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, ${\mathit{X}}^{\mathrm{-}}$) in quantum wells (QW’s) having a low-density (${\mathit{n}}_{\mathit{e}}$<5×${10}^{10}$ ${\mathrm{cm}}^{\mathrm{-}2}$) 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 ${\mathit{n}}_{\mathit{e}}$ is determined by the excitation intensity. At a given temperature and for every excitation intensity the photoluminescence spectrum is decomposed into a Lorentzian-shaped ${\mathit{X}}^{\mathrm{-}}$ line and a convoluted Lorentzian-Gaussian X line. Their intensity ratio is analyzed by assuming a thermal equilibrium distribution of X and ${\mathit{X}}^{\mathrm{-}}$ that is determined by the chemical potential of the 2DEG. The ${\mathit{X}}^{\mathrm{-}}$ linewidth dependence on ${\mathit{n}}_{\mathit{e}}$ is analyzed as originating from an increased ${\mathit{X}}^{\mathrm{-}}$ dephasing rate that is caused by trion-electron (${\mathit{X}}^{\mathrm{-}}$-e) scattering. We present a model of the elastic (${\mathit{X}}^{\mathrm{-}}$-e) scattering and calculate its rate as a function of ${\mathit{n}}_{\mathit{e}}$ assuming the 2DEG screening wave vector (${\mathit{q}}_{\mathit{s}}$) to be an adjustable parameter. Although of the same order of magnitude, the fitted ${\mathit{q}}_{\mathit{s}}$ 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 ${\mathit{q}}_{\mathit{s}}$ in the low 2DEG density range studied here and T>0, our spectroscopically extracted ${\mathit{q}}_{\mathit{s}}$(${\mathit{n}}_{\mathit{e}}$) values might serve as guidelines for the required theory. © 1996 The American Physical Society.