Theory of surface-mode phonon amplification in piezoelectric semiconductor films

Amplification characteristics of surface-mode elastic waves in piezoelectric semiconductor films are investigated quantum mechanically in the microwave-frequency region, i.e., 10-100 GHz. We assume that the mediums are isotropic elastically and that a quasi-free-electron description of the conduction electrons is valid. Both the deformation-potential coupling and the piezoelectric coupling are considered to describe the electron-surface-mode-phonon interaction. Numerical examples are developed for an $n$-type GaAs epitaxial layer on a semi-insulating GaAs substrate at $T=77\mathrm{}$ K. Frequency dependence of amplifications will be discussed in comparison with those of the bulk and the surface (Rayleigh) waves.