Radiative recombination of excitons in semiconductors at high excitation intensities

The shape of the exciton luminescence band of the gaseous phase of free excitons in crystal Si is investigated under high level excitation. Only the exciton-exciton interaction is considered and the influence of collisions of excitons with phonons and electrons is not taken into account. The theoretical shape of the exciton luminescence band qualitatively agrees with experiment. The process of the radiative Auger-recombination of two indirect excitons without the participation of phonons is studied in Ge and Si. The expression for the frequency and temperature dependence of the probability of radiation is obtained. The band has the asymmetrical Gaussian form with the steep short-wave tail. The predicted luminescence band in Ge is shifted at the long-wavelength side from the well-known exciton luminescence bands with participation of the phonons. The selection rules for the probability amplitude of the process under consideration are obtained.