We present a phenomenological approach to the nonlinear interaction between acoustic waves and microwave electric fields in piezoelectric semiconductors. This paper is concerned specifically with the $\omega -2\mathrm{}\omega$ three-wave parametric process in which the interaction of a pump (radiation) field at frequency $2\omega$ with an acoustic wave at frequency $\omega$ generates a backward-traveling acoustic wave at frequency $\omega$. The threshold microwave field that is required for acoustic gain is found to be higher in the presence of charge carriers than in their absence. With the application of a dc electric field, however, the sound waves can be amplified at relatively low microwave-field strengths. In fact, under certain conditions a threshold field is not required. The nature of the amplification process, however, is found to be dependent upon the polarization of the microwave field and, in particular, it is sensitive to the nonlinear contributions to the current density. Furthermore, we find that in a low-mobility semiconductor, amplification can also occur when the linear electronic gain exceeds the lattice loss.

• Received 20 April 1978

DOI:https://doi.org/10.1103/PhysRevB.18.5578