a b s t r a c tIn this paper, the band structures of bending waves in a phononic crystal thin plate with a point defect are studied using an improved plane wave expansion method combined with the supercell technique. In particular, a phononic crystal thin plate composed of an array of circular crystalline Al 2 O 3 cylinders embedded in an epoxy matrix with a square lattice is considered in detail. Full band gaps are shown. When a point defect is introduced, the bending waves are highly localized at or near the defect, resulting in defect modes. The frequency and number of the defect modes are strongly dependent on the filling fraction of the system and the size of the point defect. The defect bands appear from the upper edge of the gap and move to the middle of the gap as the defect size is reduced. For a given defect, the frequencies of the defect bands increase as the filling fraction increases.
High-quality ZnO thin films have been grown by plasma-enhanced molecular-beam epitaxy on sapphire substrates. Free-exciton absorption and exciton-LO phonon absorption peaks are observed in the films at room temperature, indicating that the exciton states are stable even at room temperature. Three excitonic transitions associated with valence bands A, B, and C are clearly revealed in the reflectance spectrum measured at low temperatures. This result indicates that the ZnO thin films have a perfect wurtzite crystal structure. Biexciton emission is observed in the photoluminescence spectra at low temperatures, from which the biexciton binding energy is estimated to be 14.5 meV, in good agreement with previous results. Exciton-LO ͑Ex-LO͒ and exciton-2LO ͑Ex-2LO͒ photon emission peaks are observed at low temperature. The energy difference between the Ex-LO and Ex-2LO bands is about 72.5 meV, which coincides with previously reported values of the LO phonon energy for ZnO thin films.
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