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Fermi-edge singularities in the optical emission of doped direct and indirect quantum wells

We study the luminescence spectrum of doped direct and indirect quantum wells. The Bethe - Salpeter equation is solved in a three-band model of parabolic wells including a static screened Coulomb interaction. In order to obtain a strong enhancement at the Fermi edge we found that it is necessary to break the symmetry of the system by shifting the electron and the hole confining parabolic potentials with respect to each other. This condition allows for a new scattering mechanism which is responsible for strong enhancements. Taking an infinite mass for the hole we found an increasing signal of the spectrum at the Fermi edge when two conditions are fulfilled: (i) the separation between the electrons and hole gravity centres is of the order of the well width; and (ii) the Fermi edge is close to the bottom of the second conduction subband. The effects of temperature and hole localization are analysed. Satisfactory agreement with recent experimental results is obtained.