Photoluminescence in heavily doped GaAs. I. Temperature and hole-concentration dependence

The temperature and hole-concentration dependence of the photoluminescence from the $E_0$ and $E_0+{\Delta }_0$ energy gaps have been measured in $p$-type GaAs. In heavily doped GaAs the emission spectra across the $E_0$ gap can be described by taking into account band-band optical transitions with and without $\overrightarrow{k}$ conservation. The thermal shift of the band gap is the same as for pure GaAs and can be represented by the Varshni equation. The energy-gap shrinkage was measured and compared with the previously determined values of Casey and Stern. The luminescence across the $E_0+{\Delta }_0$ gap gives evidence for impurity states associated with the spin-orbit-split band. At 2.1 K this luminescence contains two peaks which are interpreted to arise from band-band and band-impurity optical recombination. The energy of these peaks does not depend on hole concentration, hence the $E_0+{\Delta }_0$ gap is not influenced by the shrinkage affecting the $E_0$ gap. The luminescence from the sample with 1.7 × ${10}^{17}$ holes ${\mathrm{cm}}^{-3\mathrm{}}$ displays at 2.1 K a series of lines corresponding to the emission of LO phonons in the energy range between the $E_0$ and $E_0+{\Delta }_0$ gaps. This observation indicates that the holes relax to the top of the valence band by hole-optical phonon scattering.