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  Physics Express 2014, 4: 14
  Research Article
Lattice vibrations at the intersection of embedded nanostructure and surface boundary
  R. Tigrinea,b, A. Khaterb, Y. Pennecc, B. Bourahlaa,b, R. Chadlia,b  
a Institut des Molécules et des Matériaux du Mans UMR 6283, Université du Maine, 72085 le Mans, France
b Laboratoire de Physique et Chimie Quantique, Université de Tizi-Ouzou, 15000 Tizi-Ouzou, Algérie
c Laboratoire de Structure et Propriétés de l'Etat Solide, Université de Lille I, 59655 Villeneuve d'Ascq, France

  We propose an analytical approach to investigate the vibrational dynamics at the intersection of an embedded nanostructure and boundaries of crystalline surfaces. The propagating and the evanescent modes are calculated in the bulk material and the energies of localized modes in the neighbourhood of the defect are determined. We show respectively the existence of optical localized modes and acoustical modes induced by the inhomogeneity. Also the number and features of these curves depend strongly on the parameters of a system model. The state densities are calculated by the mean of the Green functions associated with the matching method, for atomic sites that constitute a minimum representation set in the neighbourhood of the defect. The interaction between the propagating bulk modes and the localized phonons induced by the integrated nanostructure gives rise to resonances in the subband of the bulk material.
  Surface and interface; Nanostructures; Defects; Dynamical vibrations; Localized phonons; State density; Green functions  

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