Line shapes of intersubband and excitonic recombination in quantum wells: Influence of final-state interaction, statistical broadening, and momentum conservation

A realistic and comprehensive theory of line shapes for spontaneous recombination of two-dimensional carriers in quantum-well (QW) structures is developed. Starting from the line shape for intersubband recombination, which takes into account the QW density of states and the thermal carrier distribution function, the impact of momentum (non)conservation on the luminescence line shape is considered. Then Lorentzian broadening due to the finite lifetime of the final states and Gaussian broadening due to statistical fluctuations of quantum-well eigenenergies characteristic, e.g., of interface roughness is incorporated. The effects of Coulomb interaction of the charge carriers at low densities are considered quantitatively, including both excitonic bound states and excitonic enhancement above the two-dimensional band gap. For a case study, GaAs QW luminescence line shapes are investigated. The line-shape evaluation definitely proves that recombination is excitonic at any temperature up to 300 K in contradiction to previous assumptions of some other authors. At low temperatures all lines consist, on a first view, of unresolved doublets which are very close in energy. The high-energy component is identified as the free-electron--heavy-hole exciton. Momentum is not found and does not need to be conserved in the free-exciton recombination process at low temperatures. At high temperatures, momentum conservation is found to be reestablished: Momentum conservation is understood to depend on the relative amplitude of interface-roughness-induced lateral potential fluctuations as compared to the thermal energy of the excitons.