Perturbation theory for the electric potential in a thin-film overlay acoustic surface-wave transducer

A perturbation theory for the electric potential associated with a Rayleigh wave propagating on a layered surface is presented. The case analyzed is that of a thin piezoelectric film on a nonpiezoelectric substrate. The film is regarded as perturbing the Rayleigh wave of the substrate. The velocity, stress, and electric potential within the film are approximated by power series, and the coefficients of the series are found from Poisson's equation and the mechanical equations of motion in terms of the particle displacements of the unperturbed Rayleigh wave of the substrate. The results obtained using unperturbed Rayleigh wave displacements are shown to be in good agreement with exact calculations in the thin-film limit (kh≤0.2), while the use of exact particle displacements and phase velocity are shown to yield excellent agreement out to kh≤0.9. Generalities regarding the properties of the two media that control the coupling of thin-film overlay acoustic surface-wave transducers are obtained.