Impurity-induced resonant Raman scattering

An explicit expression for impurity-induced one-LO-phonon forbidden resonant Raman scattering in diamond and zinc-blende-type semiconductors, which includes excitonic effects, is presented. It is derived by fourth-order perturbation theory and can be applied in a photon energy range below and above the exciton energy. We have considered both neutral and ionized impurities in the exciton-impurity coupling. Discrete and continuous exciton states have been taken as virtual intermediate states in the process, and the matrix elements corresponding to different excitonic transitions have been calculated analytically. The different contributions to the squared Raman polarizability are compared; the most important ones are found to be due to discrete-discrete-discrete transitions. An analysis of the dependence of the Raman-scattering efficiency on impurity concentration, screening factor, and lifetime broadening is presented and quantitative differences with the forbidden Frölich Raman scattering by LO phonons are discussed. These results are used to calculate the absolute value of the Raman efficiency around the ${\mathit{E}}_0$ gap of AlSb and the ${\mathit{E}}_0$+${\mathrm{\Delta }}_0$ gap of GaAs. The actual role of the impurity-induced scattering in terms of the impurity concentration is clarified.