The Role of Interdiffusion and Spatial Confinement in the Formation of Resonant Raman Spectra of Ge/Si(100) Heterostructures with Quantum-Dot Arrays

The phonon modes of self-assembled Ge/Si quantum dots grown by molecular-beam epitaxy in an apparatus integrated with a chamber of the scanning tunneling microscope into a single high-vacuum system are investigated using Raman spectroscopy. It is revealed that the Ge-Ge and Si-Ge vibrational modes are considerably enhanced upon excitation of excitons between the valence band $\Lambda_3$ and the conduction band $\Lambda_1$ (the E1 and E1 + $\Delta_1$ transitions). This makes it possible to observe the Raman spectrum of very small amounts of germanium, such as one layer of quantum dots with a germanium layer thickness of 10 \r{A}. The enhancement of these modes suggests a strong electron-phonon interaction of the vibrational modes with the E1 and E1 + $\Delta_1$ excitons in the quantum dot. It is demonstrated that the frequency of the Ge-Ge mode decreases by 10 cm^-1 with a decrease in the thickness of the Ge layer from 10 to 6 \r{A} due to the spatial-confinement effect. The optimum thickness of the Ge layer, for which the size dispersion of quantum dots is minimum, is determined.