Impurity effect on the line shape of the photoluminescence spectrum of modulation-doped quantum wells

The line shape of the photoluminescence spectrum is calculated for a two-dimensional model system of non-interacting particles in the presence of impurities. The photoluminescence cross section is analysed by perturbation theory within the self-consistent born approximation. The effect of a strong magnetic field on the spectrum is also investigated. The line shapes turn out to be sensitive to the nature of the scatterers especially in the high- magnetic-field limit. Experimental photoluminescence spectra thus open the possibility of distinguishing between charged impurities and neutral scatterers like surface roughness or alloy disorder. Numerical results are presented for GaAs-Ga_1-xAl_xAs modulation-doped quantum wells with short-range scattering potentials fitted to mobility data. The calculated zero-field broadening is consistent with published experimental results if charged impurity scattering is assumed.