Acoustoelectric Effects with Hypersonic Waves of Large Amplitude

The classical treatment of acoustoelectric interactions in piezoelectric semiconductors is extended into the range where the amplitude of the potential wave ${\phi }_0$ is not small compared with $\frac{\mathrm{kT}}{e}$. It is assumed that the wavelength is short compared with the Debye length so that the effect of the electronic space charge may be neglected. It is shown that when $e{\phi }_0>2\mathrm{kT}$ an electric field in the direction of sound propagation may cause an instability in the electron current owing to the change in electron temperature with field. The conditions for such an instability are derived in terms of the electron energy relaxation time $\tau$ and an effective diffusion time for the electrons $\frac{{\lambda }^2}{4\pi D}$.