Stimulated emission of LO phonons in narrow-band-gap semiconductors

We investigate the physical effects of interband transitions induced by resonant longitudinal-optic (LO) phonons in narrow-band-gap n- and p-type ${\mathrm{Pb}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Sn}}_{\mathit{x}}$Te. With the band gap ${\mathit{E}}_{\mathit{g}}$ close to the LO-phonon energy ħ${\mathrm{\omega }}_{\mathrm{L}}$, (i) we evaluate the dielectric function that contains contributions from interband transitions induced by the LO phonons interacting with carriers, as well as by the Coulomb potential between carriers, (ii) we show that the LO-phonon and plasmon-mode mixing is strongly influenced by the interband transitions leading to a ‘‘renormalization’’ in energy of the mixed mode by ≊30%, and (iii) when the semiconductor is suitably pumped by a light wave, we find that electron-hole recombination takes place through the stimulated emission of LO phonons, and we estimate the threshold for this instability.