Stimulated Phonon Emission by Supersonic Electrons and Collective Phonon Propagations

The emission of phonons by electrons with supersonic drift velocities is examined, and the crystal momentum transferred to a piezoelectric phonon band is determined. This momentum is transferred principally to a band of phonons which are in a cone centered about the direction of electron drift and of frequencies approximately ${10}^{10}$-${10}^{11}$ cps. This momentum-transfer process is stimulated in the sense that it amplifies any variations in the phonon momentum distribution. In particular, it will amplify a collective wave in the "phonon gas" which corresponds to a sound wave in a particle gas. The collective wave is described in terms of a local particle drift velocity and a local temperature. In a phonon gas, temperature plays the role that pressure plays in a particle gas. By the use of energy and momentum conservation equations, it is shown that such a collective wave is possible when the usual large losses are overcome. The derived gain and expected loss of the collective wave are shown to be comparable in CdS at room temperature. The current saturation observed when the electron drift velocity exceeds the sound velocity appears in the self-consistent solutions of the electron and phonon systems.