Spectral analysis on a phonon spectral function of a solid-state plasma in a doped semiconductor

•Investigated phonon spectral functions of a solid-state plasma.•Analyzed plasmon-LO phonon coupled elementary excitations.•Applied the results to conduction electron plasma in a doped GaN.•Spectral behavior of the coupled modes are heavily associated with the nonlocal and dynamic behavior of the phonon self-energy.•Identified the observable region of the coupled modes in the wavenumber and frequency space.

We report an analysis on a phonon spectral function of a solid-state plasma formed in a doped semiconductor. Real and imaginary parts of phonon propagators are evaluated including carrier screening effects within a random phase approximation, and finite-temperature spectral behavior of the phonon spectral function is examined in terms of plasmon-phonon coupled modes and quasiparticle excitation mode of the plasma. The results are applied to the case of conduction electrons in a wurtzite GaN considering carrier-phonon coupling channel via polar optical phonons. We show that the dispersion relations of the plasmon-LO phonon coupled (‘upper’ and ‘lower’) modes and the character of the additional modes via single quasiparticle excitations are heavily associated with the nonlocal and dynamic behavior of the energy shift and collisional broadening of the dressed phonon propagator of the plasma.