Modeling of Brillouin spectrum of a quantum dot crystal

We consider a novel type of nanostructures, which consists of closely spaced 3D-regimented arrays of semiconductor quantum dots. The analogy with "real" crystals in such structure is reinforced by strong carrier and phonon spectrum modification, which leads to the formation of mini-bands. Thus, we refer to this structure as quantum dot crystal (QDC). Brillouin spectroscopy is expected to provide useful information on the phonon spectrum modification in such nanostructures. In order to help with interpretation of experimental spectra, we develop a theoretical model and carry out simulation of Brillouin spectrum of a regimented array of quantum dots. The phonon spectrum of GexSi1-x/Si QDC is found from the numerical solution of the elasticity equation for the whole structure. It is shown that our approach allows one to include the effect of the matrix, e.g., barrier material, as well as dot regimentation, and lead to solutions different from simple Lamb-type calculations.