Electron-hole plasma in direct-gap ${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x$ As and $k$-selection rule

Uniformly excited electron-hole plasma under three-dimensional confinement has been studied in ${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x$ As by photoluminescence at 2 K. With this approach, a satisfactory fitting of the experimental data has been obtained over a wide range of densities and Al concentrations using a single value of density and temperature throughout the excited region. The theoretical model used is based on the preservation of $k$-selection rules with a built-in broadening in the single-particle density of states. The fitting renormalized gap closely agrees with existing many-body theories, contrary to recent claims. The possibilities of plasmon-replica contributions and of thermalization processes by recent claims. The possibilities of plasmon-replica contributions and of thermalization processes by impurity or disorder-activated scattering are discussed. A new estimate of the radiative-recombination coefficient is reported.