Band-gap renormalization in direct-band-gapAlxGa1−xAs

The renormalization of the fundamental band gap in direct-band-gap ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As close to the direct-to-indirect crossover composition was found to be strongly enhanced with respect to calculations based on the universal formula by Vashishta and Kalia [M. Capizzi et al., Phys. Rev. B 29, 2028 (1984)]. We remove this alleged discrepancy by a rigorous treatment if the significant side-valley populations and renormalizations, which are not directly accessible to luminescence experiments. We propose a multivalley expansion of the universal formula, which includes self-consistent calculations of the energetic position and the population of the X and L valleys, as well as the valence band. This model excellently reproduces the experimental renormalization of the fundamental band gap for various energetic constellations of the conduction-band minima, and explains the experiments of Capizzi et al.