A compliance/stiffness matrix formulation of general Green´s function and effective permittivity for piezoelectric multilayers

This paper presents an efficient and stable recursive compliance matrix method for analyzing wave propagation in multilayered piezoelectric media. The effective permittivity and generalized Green´s functions for a layered system, a layered system on a substrate, and a layered system between two substrates have been obtained from the elements of the total or surface compliance/stiffness matrices, which are calculated recursively, layer by layer, from the layer compliance/stiffness matrices. The method is very closely related to the transfer matrix method and retains its simplicity and efficiency, but it is numerically stable for high thickness-to-wavelength ratio. Numerical examples for wave propagation in zinc oxide (ZnO)/Diamond/silicon(Si) structures are presented using the compliance matrix formulation for effective permittivity and Green´s function.