Electron–acoustic-phonon interaction and resonant Raman scattering in Ge quantum dots: Matrix and quantum confinement effects

Abstract

Calculations of the electron-acoustic phonon interaction, and Raman scattering efficiency, in matrix embedded Ge quantum dots (QDs) are presented. The work is focused on the understanding of the inelastic light scattering process excited close to resonance with the confined ${E}_{1}$ transitions. Due to the large joint density of states at the ${E}_{1}$ point, many intermediate electronic states contribute to the overall scattering efficiency. This particular situation leads to quantum interference effects between different scattering paths and has, therefore, a strong impact on the Raman line shapes and intensities. Quantum confinement of the electron and hole states is treated within the envelope wave function approximation. The QD/matrix acoustic vibrations are deduced from elasticity theory. Deformation-potential interaction between the electrons (and holes) and acoustic vibrations is assumed. The resonant Raman spectra are calculated using third order perturbation quantum theory. A Raman-Brillouin electronic density is constructed as a linear combination of the electronic states involved in the inelastic light scattering. It allows one to plot, for each excitation energy, the spatial distribution of the electronic density that gives rise to the Raman (or Brillouin) signal. It is calculated for both diagonal and off-diagonal transitions between the confined electronic states. The dependence of the spectral line shapes and intensities on homogeneous broadening of the ${E}_{1}$ transitions, QD size, surface boundary conditions is discussed in details. The calculated spectra are then compared to those measured for different QD size distributions.