Resonant Raman scattering in self-assembled quantum dots

A theoretical treatment for first-order resonant Raman scattering in self-assembled quantum dots (SAQD’s) of different materials is presented. The dots are modeled as cylindrical disks with elliptical cross section, to simulate shape and confinement anisotropies obtained from the SAQD growth conditions. Coulomb interaction between electron and hole is considered in an envelope function Hamiltonian approach and the eigenvalues and eigenfunctions are obtained by a matrix diagonalization technique. By including excitonic intermediate states in the Raman process, the scattering efficiency and cross section are calculated for long-range Fröhlich exciton-phonon interaction. The Fröhlich interaction in the SAQD is considered in an approach in which both the mechanical and electrostatic matching boundary conditions are fulfilled at the SAQD interfaces. Exciton and confined phonon selection rules are derived for Raman processes. Characteristic results for SAQD’s are presented, including InAs dots in GaAs, as well as CdSe dots in ZnSe substrates. We analyze how Raman spectroscopy would give information on carrier masses, confinement anisotropy effects, and SAQD geometry.