Efficient and Accurate Modeling of the Surface Deflection of Thin Layers on Composite Substrates with Applications to Piezoelectric Parameter Measurements

The electrical and mechanical response of multilayered structures involving a piezoelectric layer and bull’s eye shaped electrodes is investigated. A boundary element method is employed based on spectral domain Green’s functions. With this method, the electric field distribution is determined first, and the local mechanical displacement in a second step. As will be shown, this allows us to exploit cylindrical symmetry for the electric surface charge distribution, but not for the vertical surface displacements. The effect of substrate bending due to in plane-stress, introduced by the piezoelectric constant d31, and the benefits of using bull’s eye electrode geometries with thick metallic backplates intended to reduce this effect are studied. A rigorous analysis and a largely simplified, but accurate approximation are compared. The application of this technique is demonstrated on a practical example for highly efficient and accurate determination of selected piezoelectric coefficients from surface topography measurements on such structures.