Acoustoelectric interaction of surface phonons in semiconductors: Isotropic approximation

Abstract

The acoustoelectric interaction of surface phonons with conduction electrons in piezoelectric semiconductors is investigated assuming elastic isotropy. The electronic states near a semiconductor surface are properly determined taking into account the existence of the surface space-charge layer and the potential barrier associated with it. Employing the electron wave functions obtained in this manner, the acoustoelectric interaction is specified and it is applied to the study of the amplification of the surface phonons. For an $n$-type semiconductor with bulk-electron concentration of ${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$, we find that the frequency dependence of the amplification rate has two bumps in the frequency range from 1 to 10 GHz. This result will be interpreted in terms of the depth dependence of the electron wave functions and the electric potential produced by the surface phonons.