Kinetic theory of parametric excitation of acoustic waves in piezoelectric semiconductors

Abstract

Using a kinetic description for electrons and the usual equation of motion for lattice displacement we have derived a general dispersion relation for acoustic waves in a piezoelectric semiconductor, in the presence of a strong high frequency electric field oscillating near the electron plasma frequency. Earlier hydrodynamic results valid for kλ_e«1 (where k is the wave number of the acoustic wave and λ_e the electron mean free path) are rederived as a special case. Fork λ_e »1, two instability branches are discovered and magnitudes of the threshold electric field required to drive the acoustic wave unstable in each case, are obtained.