Generation of high-frequency coherent acoustic phonons in superlattices under hopping transport. I. Linear theory of phonon instability

In this work we consider the theory of high-frequency phonon generation in a weakly coupled doped semiconductor superlattice. Electric bias, applied to such a superlattice, destroys the electron minibands, creates electron states localized in the individual quantum wells, and forms population inversion between these states. An electric current occurs due to the phonon-induced interwell hops. We show that under such conditions the electric current produces a phonon instability: populations of phonon modes propagating almost collinearly with the superlattice axis increase exponentially in time. It is demonstrated that the population growth increment can be as high as several times 10⁸ s^-1, and considerably exceeds the internal phonon scattering rates. Also discussed are effects influencing the increment, such as a screening of the electron-phonon interaction and a modification of the phonon spectrum in superlattices.