Electron scattering interaction with coupled plasmon-polar-phonon modes in degenerate semiconductors

The scattering interaction of Bloch electrons with the coupled systems of electrons and longitudinal-optical phonons in degenerate polar semiconductors is investigated. At degenerate carrier concentrations (${10}^{17}$-${10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$ in IV-VI and III-V compounds) the free-carrier plasma frequency is comparable to the LO-phonon frequency. This gives rise to electron scattering by strongly coupled plasmon-LO-phonon modes whose resonance frequencies are highly broadened in the particle-hole excitation (Landau damping) region. A generalized expression for the scattering lifetime taking these effects into account is derived in terms of a dielectric response formalism within the random-phase approximation. The factor $\mathrm{Im}\left(\frac{1}{{\epsilon }_T}\right)$ appearing in this treatment, where ${\epsilon }_T$ is the coupled-system dielectric function, modifies the bare Coulomb potential, and together they determine the effective scattering strength of the coupled modes. In the Landau-damping region the scattering strength is highly dispersive with respect to energy and momentum transfers. Calculations that illustrate these interaction effects are performed for PbTe and GaAs.