An explicit expression for forbidden Raman scattering by one LO phonon with excitons as intermediate states is given. The theory can be applied at photon frequencies below and above the exciton energy. The matrix elements corresponding to transitions between different exciton states are calculated analytically. The different contributions to the squared Raman polarizability are compared; the most important one is found to be due to discrete-continuous transitions. It is shown in this case that the outgoing resonance in the Raman efficiency is always higher than the incoming one, a peculiarity seen experimentally in all III-V compound semiconductors. From the theoretical model a general criterion for the application of the free–electron-hole–pair theory is given in terms of the exciton Bohr radius. An analysis of the interference effect between the allowed and forbidden scattering is presented, and qualitative and quantitative differences with the free–electron-hole–pair theory are discussed. Absolute values of Raman polarizabilities are calculated and compared with recent measurements for GaP, yielding a good agreement without the use of any fit parameter.

• Received 1 March 1989

DOI:https://doi.org/10.1103/PhysRevB.40.4030