Thickness mode material constants of a supported piezoelectric film

New thick film ceramic processing techniques and microelectromechanical sys tems require material characterization of a piezoelectric film supported by a substrate. An analytical solution of the one-dimensional wave equation f or multiple layered systems driven in the thickness mode is presented. The impedance across the piezoelectric layer is derived and expressed in terms of the material properties of the two materials. This includes the open-cir cuit elastic stiffness c(33)(D), the clamped permittivity epsilon(33)(S) an d the h(33) piezoelectric constant of the piezoelectric layer and the elast ic stiffness c(s)(D) of the substrate. The properties are expressed as comp lex variables in order to account for the losses within the materials. The material parameters of the solution are extracted from experimental results using a modified Levenberg-Marquardt technique. The capabilities of this n ondestructive technique are demonstrated using experimental and simulated i mpedance spectra of lead zirconium titanate sol gel composite coatings with in the thickness range of 15-70 mu m on aluminum and on platinum electroded silicon substrates and by simulating the mass loading of a quartz thicknes s resonator. The analytical solution allows for the extension of the Instit ute of Electrical and Electronics Engineers free resonator impedance techni que to supported films and provides a method for determining the material p arameters of a piezoelectric coating. (C) 1999 American Institute of Physic s. [S0021-8979(99)03205-3].