Temperature-dependent screening and carrier-carrier scattering in heavily doped semiconductors

We present an analysis of the scattering of hot carriers by conduction electrons in heavily doped semiconductors within the random-phase approximation (RPA). Different approximations to the temperature-dependent RPA are considered: (i) the two-pole approximation developed by Rorison and Herbert, (ii) the plasmon-pole approximation, and (iii) the Lindhard dielectric function. We present a range of results for n-doped GaAs for different carrier energies, doping levels, and temperatures, and we examine the ranges of validity of the different approximations. As an extension of our theory we include, within the two-pole approximation, the coupling of optical phonons to the electron system.