Theory of phonon sideband resonances in Raman scattering from semiconductors

A general many-body theory of phonon sidebands (replicas) of electronic transitions in semiconductors with shallow impurities is formulated. It is found that, in addition to the usual contribution to one-phonon sideband Raman amplitude due to the ordinary electron-phonon interaction term, there is another contribution which includes the effect of interaction between band electrons and electrons localized on the impurity site. The present theory, which is consistent with scattering from phonons and electronic transitions, is used to calculate the relative Raman amplitudes of $1s\to 2s$ electronic transition between the lithium acceptor states in ZnTe:Li and its LO-phonon sideband. Good agreement with experiment is obtained for electron-phonon interaction $V$, about 15 meV, and electron-electron interaction $J$, ranging between 20 and 30 meV.