title: Modeling of ultrasonic wave propagation in integrated piezoelectric structures under residual stress.
abstract: The objective of this study is to understand the role of residual stress in piezoelectric layers in order to predict the performance of integrated structures. This is of particular importance in thick or thin film technology. Considering a bulk piezoelectric material, the Christoffel equation for a piezoelectric material is modified to take into account a uniform residual stress on a given cross section. A numerical study of its influence is carried out on the slowness curves and coupling coefficients of a lithium niobate material. In a second part, modified Christoffel tensor is used to calculate the dispersion curves of Lamb waves in a piezoelectric plate. The Lamb modes are found to be sensitive to the residual stress. In particular, it is shown how the behavior of the first Lamb modes is modified with residual stress. In a third part, these results are extended to a piezoelectric film laid down on a substrate in order to model the importance of these phenomena on the behavior of an integrated structure. The numerical study of guided waves in a lithium niobate plate is performed first, then the case of a lithium niobate film laid down on a silicon substrate is considered.
authors.affiliation: LUSSI-GIP Ultrasons, Université François Rabelais, FRE CNRS 2448, E.I.V.L., Rue de la Chocolaterie, 41034 Blois Cedex, France. mickael.lematre@univ-tours.fr
authors.forename: Mickaël
authors.initials: M
authors.lastname: Lematre
authors.forename: Guy
authors.initials: G
authors.lastname: Feuillard
authors.forename: Thomas
authors.initials: T
authors.lastname: Delaunay
authors.forename: Marc
authors.initials: M
authors.lastname: Lethiecq