Phonon optics in semiconductors: Phonon generation and electron-phonon scattering in $n$-GaAs epilayers: I. Theory

In this paper we give a theoretical account of the generation of acoustic phonons during hot carrier relaxation and recombination at donors in $n$-GaAs at liquid helium temperatures. We give explicit expressions for the effects of carrier screening on both the piezoelectric and deformation-potential scattering. The relative scattering rates are shown to depend on the propagation direction of the phonons, the electron temperature, the carrier concentration and the phonon polarization. The effects of off-axis phonon propagation and the finite aperture of the detectors used in the recent experiments of Narayanamurti, Logan, Chin, and Lax is explicitly taken into account in the calculations. The relationship of these calculations to more traditional transport measurements, such as the mobility is discussed.