The carrier density dependence of the hot-carrier energy relaxation rate in highly photoexcited semiconductors is investigated. Results of these calculations indicate important differences between polar direct-gap and nonpolar indirect-gap materials. The critical carrier density ($N_c$) for the onset of screening in polar semiconductors is found to increase with both effective mass and phonon energy. A method for predicting trends among these materials with respect to $N_c$ is briefly described. Calculations for GaAs predict that the hot-carrier cooling rate begins to decrease at $N_c\approx 6\times {10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$. Above this density the phonon emission frequency falls rapidly. In contrast, the effects of screening in Si are shown to be negligible for $N\lesssim {10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$. In this case, a significant reduction in the energy relaxation rate does not occur until $N\sim {10}^{21}$ ${\mathrm{cm}}^{-3\mathrm{}}$.

• Received 2 September 1980

DOI:https://doi.org/10.1103/PhysRevB.23.1909