Resonance Raman scattering by optical phonons in unstrained germanium quantum dots

The position and shape of the $E_1,E_1+{\Delta }_1$ Raman resonance depending on the size of unstrained Ge quantum dots were studied. The dots were grown in $\mathrm{Ga}\mathrm{As}∕\mathrm{Zn}\mathrm{Se}∕\mathrm{Ge}∕\mathrm{Zn}\mathrm{Se}$ structures on (111)-oriented GaAs substrates using molecular-beam epitaxy. A shift of the $E_1$ and $E_1+{\Delta }_1$ resonance energies by up to $0.3\mathrm{eV}$ was observed. The dependence of the shift on quantum dot size was shown to be well described by a cylindrical model using quantization of the bulk Ge electron-hole states that form excitons at the two-dimensional critical point of the interband density of states. A separate display of the $E_1$ and $E_1+{\Delta }_1$ resonances in the quantum dots related to transformation of the interband density of states into the δ function due to quantization of the energy spectrum was observed.