Plasmon-Phonon Interference in CdS

The Raman spectra of plasmons in In- and Ga-doped cadmium sulfide are shown to consist of very asymmetric peaks. A prominent interference shape is exhibited which is very similar to that manifested by anharmonic phonon interactions between two optical phonons, as in AlP${\mathrm{O}}_4$ and BaTi${\mathrm{O}}_3$. In the present case, the interaction between the heavily damped plasmon mode and one longitudinal optical phonon is due to the Coulomb interaction. The interference features of the Raman spectrum are related to the electronic (plasmon) and ionic (phonon) charge-density correlation functions, where the ionic charge is multiplied by a factor to include the nonionic (electronic) part of the light-phonon scattering amplitude. In other words, we treat the spectrum as due to interfering amplitudes for scattering into the plasmon state $〈\mathrm{PL}|$ via two channels: one direct, $〈\mathrm{PL}\left|\alpha \right|0\mathrm{}〉$; and one via an intermediate LO-phonon state coupled by the Coulomb interaction, $〈\mathrm{PL}|\mathrm{Coul}.\mathrm{}|\mathrm{LO}〉\times 〈\mathrm{LO}\left|\alpha \right|0\mathrm{}〉$. This calculation gives very good agreement with the observed line shape, and demonstrates the inadequacy of treating the spectrum in terms of the usual dielectric function. In the special case when the light-phonon scattering is purely ionic, however, our Green's-function calculation is shown to be equivalent to the dielectric-function formulation which includes both the plasmon and phonon contributions. A detailed comparison of our theory with the experimental spectrum yields an estimate of the relative contributions to the light-phonon scattering amplitude from electronic and ionic charges. For CdS, these contributions are found to be of the same order of magnitude, but opposite in sign.