Effects of acoustic anisotropy and screening on the energy relaxation of hot electrons in heterojunctions and quantum wells

In this paper we present theoretical calculations of the angle and mode dependence of the phonon emission by hot two-dimensional electrons in gallium arsenide. We compare them with experimental results of heat-pulse studies of the acoustic-phonon emission in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterojunctions and GaAs quantum wells. It is shown that the ratio of the strengths of the longitudinal- and transverse-acoustic modes is correctly predicted only by a theoretical model that properly includes the effects of acoustic anisotropy on the electron-phonon matrix elements, screening, and the form of the confining potential. As a result of this work, we are finally able to account for why longitudinal phonon emission from a heterojunction is not seen in heat-pulse experiments despite the fact that earlier theories predicted that it should be the dominant mode.