EXCITONIC MODEL FOR 2ND-ORDER RESONANT RAMAN-SCATTERING

A theoretical model for second-order resonant Raman scattering is presented. The effect of Coulomb interaction between electrons and holes is fully taken into account in the framework of the effective-mass approximation. By introducing discrete and continuous excitonic intermediate states in the Raman process, an explicit expression for the Raman scattering efficiency is given for long-range Frohlich electron-phonon interaction. The model developed can be used to evaluate Raman profiles around the resonant region. A closed-form expression for all matrix elements of the exciton-phonon interaction is obtained once the Coulomb problem for the relative electron-hole motion is separated in spherical coordinates. For the first time, to our knowledge, transitions between states from the excitonic ionization continuum for nonzero phonon wave vectors are exactly included in the calculations. The dependence of the Raman scattering efficiency on electron and hole masses is analyzed. The contribution of the different excitonic transitions to the scattering process is also studied. Finally, the model is compared to available experimental data for GaP, InP, GaAs, and GaSb. The overall agreement with the measured resonance profiles and their absolute scattering efficiencies confirms that excitonic effects are required for a satisfactory interpretation of these phenomena.