Resonant Raman Scattering from LO Phonons in Polar Semiconductors

Multiphonon Raman scattering from LO phonons has previously been observed in CdS in the case where the laser frequency lies near the energy gap. The combined effects of finite wave vector and resonant energy denominators are offered as the explanation for certain features of the scattering. These features include the unusual polarization properties of the single-phonon scattering and the unexpected sharpness of the two-phonon line. The effects of the Fröhlich interaction are calculated in lowest-order perturbation theory under the assumption of spherical, parabolic bands. The important part of the scattering amplitude is due to terms where the laser is resonant to interband transitions. Since the parameter $\frac{\mathrm{qv}}{{\omega }_l}$ is of order unity, the dipole approximation $q\to 0$ is not applicable. (Here $v$ is the electron velocity at that point in the zone where the laser can cause real transitions.) In the single-phonon scattering, q is the difference between the wave vectors of the incident and scattered photons, while for the double-phonon case, q is the wave vector of one of the two final-state phonons. No exciton effects are included. The temperature is taken to be zero throughout.