Collective Phonon-Electron Waves and Oscillations in Piezoelectric Materials

Abstract

The behavior of collective phonon waves interacting with a drifting electron distribution under conditions of acoustic gain in piezoelectric materials is analyzed and discussed. The electrons are bunched by the phonons, and the resulting electrostatic fields become an important element in the collective-wave behavior. This results in a tendency to set up an electrostatic oscillation involving phonons as well as electrons. The oscillation frequency is the plasma frequency for electrons with mass heavily dressed by the phonons. In CdS, this frequency is about ${10}^5$ ${\sec }^{-1\mathrm{}}$. The collective wave exhibits a great deal of dispersion and is greatly amplified at frequencies near the oscillation frequency. It is believed that the spontaneous oscillations observed in piezoelectric materials at large drift velocities are the collective waves described in this analysis. The oscillations involve wavelengths which are simultaneously those of the electrostatic oscillation frequency and multiples of the length of the crystal involved.