Excitons in one-phonon resonant Raman scattering: Deformation-potential interaction

A theory of one-phonon resonant Raman scattering in diamond and zinc-blende-type semiconductors which includes excitonic effects has been developed. The theory can be applied at frequencies below and above the band gap. We have considered the deformation-potential interaction for the electron–one-phonon coupling, and discrete and continuous exciton states have been taken as intermediate states in the process. The interband transitions between different valence bands (heavy and light holes and split-off bands) included in the calculation of the Raman tensor are characterized by excitonic states with different Bohr radii. General analytical expressions of the matrix elements corresponding to different transitions between excitonic states (discrete-discrete, discrete-continuous, and continuous-continuous) are reported as a function of the Bohr-radius ratio. A simplified expression of the Raman tensor obtained under the assumption of the same Bohr radii for both excitonic transitions is given. These results are used to calculate the absolute value of the Raman efficiency in the $E_0$ and $E_0$+${\Delta }_0$ absorption edge of III-V compound semiconductors. Comparison with the electron-hole uncorrelated theory and with the corresponding experimental data recently reported for GaP, GaAs, and InP explains these spectra and emphasizes the decisive role of excitons in the one-phonon resonant Raman scattering.