Finite temperature inelastic scattering in a doped polar semiconductor
The authors calculate the finite temperature inelastic scattering rate for hot electrons injected into n-doped GaAs for various doping densities and injected electron energies. They use the Born approximation and treat the base region as a three-dimensional coupled electron-phonon system, so that the Coulomb and Frohlich interactions with the injected electron are put on an equal footing. As the temperature increases, the coupled electron-phonon modes broaden considerably, resulting in a rounding of the sharp emission thresholds which occur at T=0. For moderate to high doping densities (n>or approximately=8*1017 cm-3) and injection energies of E-EF>or approximately=100 meV (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.