One phonon assisted electron Raman scattering in spherical semiconductor quantum dots

The differential cross section (DCS) for an electron Raman scattering (ERS) process in a semiconductor quantum dot (QD) of spherical geometry regarding phonon-assisted transitions, is calculated for T = 0 K. We present a complete description of the phonon modes of spherical structures embedded in another material, including a correct treatment of the mechanical and electrostatic matching condition at the surface. We consider the Frohlich interaction to illustrate the theory for a GaAs/AlAs system. Electron states are considered to be completely confined within the QD. We also assume single parabolic conduction and valence bands. The emission and excitation spectra are discussed for different scattering configurations and the selection rules for the processes are also studied. Singularities in the spectra are found and interpreted. The one-phonon-assisted ERS studied here can be used to provide direct information about the electron band structure of these systems.