Surface and interface shear horizontal acoustic waves in piezoelectric superlattices

Abstract

The propagation of acoustic waves of shear horizontal polarization in infinite and semi-infinite superlattices made of two piezoelectric media is studied within a Green's function method. Localized modes induced by a free surface of the superlattice or a superlattice/substrate interface are investigated theoretically. These modes appear as well-defined peaks of the total density of states inside the minigaps of the superlattice. The spatial localization of the different modes is studied by means of the local density of states. The surface of the superlattice and the superlattice/substrate interface are considered to be either metallized or nonmetallized. We show the possibility of the existence of interface modes, which are without analogue in the case of the interface between two homogeneous media ͑the so-called Maerfeld-Tournois modes͒. We also generalize to piezoelectric superlattices a rule about the existence and number of surface states, namely when one considers two semi-infinite superlattices together obtained by the cleavage of an infinite superlattice, one always has as many localized surface modes as minigaps, for any value of the wave vector k ʈ ͑parallel to the interfaces͒. Specific applications of these results are given for CdS-ZnO superlattices with a free surface or in contact with a BeO substrate.

Existence of surface acoustic waves in one-dimensional piezoelectric phononic crystals of general anisotropy

“…According to Eqs. ( 30) and (43) 1 , the case of lowest stop band in a phononic crystal with electrically closed surface precisely fits statement (40).…”

“…On these grounds, we conclude that, given the value of k, at most four SAWs within a full stop band can occur in total in the direct and reversed phononic crystal with mechanically free electrically closed surface; (40) at most four SAWs within an upper full stop band can occur in total in the direct and reversed phononic crystals with mechanically free electrically open surface.…”

“…In particular, many studies were devoted to the wave propagation in one-dimensional (1D) phononic crystals, also termed superlattices, which consist of periodically arranged layers [35]. The most numerous results were obtained for the shear horizontally polarized SAWs considered under different settings in phononic crystals of various compositions [36][37][38][39][40][41][42][43][44][45]. The sagittally polarized twopartial and the fully coupled three-partial SAWs were also widely investigated [46][47][48][49][50][51][52][53][54].…”

Interfacial acoustic waves in one-dimensional anisotropic phononic bicrystals with a symmetric unit cell

“…The present paper is concerned with the interfacial acoustic waves (IAWs) localized at the internal boundary of 1D phononic bicrystals, which are formed from two perfectly bonded periodically layered or functionally graded semi-infinite elastic media of arbitrary anisotropy. Such waves have been considered in elastic as well as in piezoelectric structures [27][28][29][30][31][32]. The question which we would like to answer is: how many IAWs can exist in a stop band of the Floquet spectrum of a phononic bicrystal?…”

Surface acoustic waves in one-dimensional piezoelectric phononic crystals with symmetric unit cell

“…Much effort has been devoted to studying the surface acoustic waves (SAWs) in 1D elastic and piezoelectric phononic crystals. The largest amount of theoretical data was obtained for shear horizontally polarized SAWs [15][16][17][18][19][20][21][22][23]. Sagittally polarized two-partial SAWs [24][25][26][27][28][29] and fully coupled three-partial SAWs [30][31][32] were also investigated.…”