Design of phonon resonators based on semiconductor superlattices for the realization of phonon maser of THz-frequency range

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In this project we first considered the ABA multi-suplerlattice structures consisting of two kinds of periodic superlattices A and B. Assuming GaAs and AlAs as the constituent layers of both A and B superlattices, we have shown by numerical calculations that the resonance transmission occurs in the THz-frequency range if the layer thicknesses are chosen in 10- to 100-A range. Specifically, we found that these resonance transmissions happen at frequencies within the frequency gaps of A superlattices, where the phonon transmission is prohibited in a pure A-superlattice system. In addition we studied the frequency dependence of the phonon transmission rate in these multi-superlattice systems.Next, in order to analyze the physical reason for the resonance of phonons in the proposed systems, we developed the analytical calculation of transmission rate based on the transfer-matrix method. As a result we succeeded to derive a general formula for the resonance condition.We also examined the transmission characteristics in a system where B superlattice is replaced with a bulk layer. The resonance condition in this system is derived as a function of various parameters of constituent materials. If A (superlattice) and B (single bulk layer) are stacked alternatively, a transmission peak splits into several isolated peaks. As the number of periods (consisting of A and B structures) is increased, those transmission peaks coalesce and make a broad transmission band. We could derive phonon dispersion relation for the latter case.The phonon transmission characteristics in various multisuperlattice structures we found have opened up new possibilities for designing phonon-optics devices such as phonon filters, phonon mirrors and phonon resonators.