GaAs−AlxGa1−xAsdouble-barrier heterostructure phonon laser: A full quantum treatment

Abstract

The aim of this work is to describe the behavior of a device capable to generate high-frequency $(\ensuremath{\sim}\mathrm{THz})$ acoustic phonons. This device consists in a $\mathrm{GaAs}\ensuremath{-}{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ double-barrier heterostructure that, when an external bias is applied, produces a high rate of longitudinal optical (LO) phonons. These LO phonons are confined and they decay by stimulated emission of a pair of secondary longitudinal optical $(\mathrm{LO}\ifmmode \tilde{}\else \~{}\fi{})$ and transversal acoustic phonons. The last ones form an intense beam of coherent acoustic phonons. To study this effect, we start from a tight-binding Hamiltonian that takes into account the electron-phonon and phonon-phonon interactions. We calculate the electronic current through the double barrier and obtain a set of five coupled kinetic equations that describes the electron and phonon populations. The results obtained here confirm the behavior of the terahertz phonon laser, estimated by rougher treatments [S.S. Makler et al., J. Phys.: Condens. Matter $10,$ 5905 (1998).]