Inelastic scattering in a doped polar semiconductor at finite temperature

We calculate, using the Born approximation, the finite-temperature scattering rate for hot electrons injected into n-type doped GaAs for various doping densities and injected-electron energies. We treat the base region as a three-dimensional coupled electron-phonon system, so that the Coulomb and Fr\"ohlich interactions with the injected electron are put on an equal footing. For moderate to high doping densities (n{}8×{}10¹⁷ cm^-3) and injection energies of E-EF{}100 meV, our results indicate that (1) the increase in the scattering rate from T=0 K to T=300 K is typically less than a factor of 2, and (2) the scattering rates decrease with increasing doping density.