  We investigate spectral behavior of phonon spectral functions in an
interacting multi-component hot carrier plasma. Dielectric polarization
functions are formulated so that they satisfy Dyson equations of the effective
interactions among plasma components. We find a useful sum rule giving simple
relation between plasma-species resolved dielectric functions. Spectral
analysis of various phonon spectral functions is performed considering
carrier-phonon channels of polar and nonpolar optical phonons, acoustic
deformation-potential, and piezoelectric Coulomb couplings. Effects of phonon
self-energy corrections are examined at finite temperature within a random
phase approximation extended to include the effects of dynamic screening,
plasmon--phonon coupling, and local-field corrections of the plasma species. We
provide numerical data for the case of a photo-generated electron-hole plasma
formed in a wurtzite GaN. Our result shows clear significance of the
multiplicity of the plasma species in the dielectric response and phonon
spectral functions of a multi-component plasma.
