Resonance Raman studies inCu2O. I. The phonon-assisted1syellow excitonic absorption edge

Resonant Raman scattering in ${\mathrm{Cu}}_2$O has been studied at low temperature in the vicinity of its phonon-assisted $1s$ yellow excitonic absorption edges using a cw continuously tunable dye laser. The multiphonon Raman modes which show resonance enhancement in this region are the following: ${\Gamma }_{12}^{-}+P$ (where $P$ is an odd-parity optical phonon); $2{\Gamma }_{12}^{-}+P$ (where $P$ is an acoustic or odd-parity optical phonon); $2{\Gamma }_{12}^{-}+2\mathrm{}\mathrm{LA}$ and $4{\Gamma }_{12}^{-}$. The Raman cross sections of these modes have been calculated using perturbation theory. To explain the dispersion in the experimental cross section it was found necessary to introduce a wave-vector-dependent damping constant for the $1s$ yellow exciton. A simple model proposed earlier by Yu, Shen, Petroff, and Falicov was used to calculate this damping constant. Our result showed that the damping is predominantly due to intraband scattering via the longitudinal acoustic (LA) phonon. Good agreement was found between experiment and theory. Our results also indicate that the resonant three- and four-phonon Raman processes in ${\mathrm{Cu}}_2$O in this region involve cascading of the photoexcited $1s$ yellow exciton with emission of phonon(s). The Raman frequencies of some of the modes of ${\mathrm{Cu}}_2$O were found to depend on the incident laser frequency. The behavior of these dispersive Raman modes was found to be well explained within the above model and enabled us to determine directly the effective mass of the $1s$ exciton to be $(3.0\mathrm{}\pm 0.2)m_0$ (where $m_0$ is the free mass of the electron), as previously reported. Relative magnitudes of various $1s$ exciton-phonon interactions have also been obtained from our result.