We calculate, within a many-body theory, the inelastic-scattering rate for hot electrons injected into doped GaAs as a function of electron energy and doping density by treating Coulomb and Fr\"ohlich interactions on an equal footing. Our theory, which includes effects of quantum degeneracy, dynamical screening, plasmon-phonon mode coupling, and phonon self-energy correction, is in excellent quantitative agreement with recent experimental findings, and resolves a puzzle about why a recent observation of single-optical-phonon emission in highly doped GaAs can be quantitatively explained by unscreened theoretical results.
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Jalabert et al. (1990) studied this question.
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