Quantum Approach to Amplification of Optical Phonons in Semiconductors

Abstract

It is shown by using a quantum-mechanical treatment that, in semiconductors with some ionic character, optical phonons can be amplified via their interaction with conduction electrons. The amplification of the optical phonons occurs when the drift velocity of the conduction electrons exceeds the phase velocity of the optical phonons. Both longitudinally and transversely polarized optical phonon modes are amplified via the electron-phonon interaction when the quantum treatment given is valid. The amplification of the optical phonon modes can be viewed as a phonon maser process, with the external drift field inverting the electron population. When the drift velocity of the electrons exceeds the optical-phonon phase velocity, the number of electrons that will emit optical phonons exceeds the number that will absorb optical phonons. The result is a net gain for those optical phonon modes whose phase velocity $s=\frac{\ensuremath{\omega}}{q}$ satisfies the condition ${V}_{d}>S$.