Surface acoustic waves in one-dimensional piezoelectric-metallic phononic crystal: Effect of a cap layer

• Published in: Ultrasonics 2018-11, Vol.90, p.80-97
• Main Authors: Alami, M., El Boudouti, E.H., Djafari-Rouhani, B., El Hassouani, Y., Talbi, A.
• Format: Article
• Language: English
• Subjects: Engineering Sciences
• ISSN: 0041-624X; 1874-9968
• DOI: 10.1016/j.ultras.2018.06.010

•We give closed form expressions of the dispersion relations of surface modes induced by a piezoelectric-metallic superlattice with a cap layer.•We demonstrate a rule about the existence of surface modes in piezoelectric-metallic superlattice.•We show the existence of surface, interface and guided waves induced by the cap layer.•We discuss the behavior of the electromechanical coupling coefficient as a function of the cap layer thickness and the nature of the metallic layers inside the superlattice. We study the propagation of transverse acoustic waves associated with the surface of a semi-infinite superlattice (SL) composed of piezoelectric-metallic layers and capped with a piezoelectric layer. We present closed-form expressions for localized surface waves, the so-called Bleustein-Gulyaev (BG) waves depending on whether the cap layer is open-circuited or short-circuited. These expressions are obtained by means of the Green’s function method which enables to deduce also the densities of states. These theoretical results are illustrated by a few numerical applications to SLs made of piezoelectric layers of hexagonal symmetry belonging to the 6 mm class such as PZT4 and ZnO in contact with metallic layers such as Fe, Al, Au, Cu and boron-doped-diamond. We demonstrate a rule about the existence of surface modes when considering two complementary semi-infinite SLs obtained by the cleavage of an infinite SL along a plane parallel to the piezoelectric layers. Indeed, when the surface layers are open-circuited, one obtains one surface mode per gap, this mode is associated with one of the two complementary SLs. However, when the surface layers are short-circuited, this rule is not fulfilled and one can obtain zero, one or two modes inside each gap of the two complementary SLs depending on the position of the plane where the cleavage is produced. We show that in addition to the BG surface waves localized at the surface of the cap layer, there may exist true guided waves and pseudo-guided waves (i.e. leaky waves) induced by the cap layer either inside the gaps or inside the bands of the SL respectively. Also, we highlight the possibility of existence of interface modes between the SL and a cap layer as well as an interaction between these modes and the BG surface mode when both modes fall in the same band gaps of the SL. The strength of the interaction depends on the width of the cap layer. Finally, we show that the electromechanical coupling coefficient (ECC) is ve