Ultrasonic wave propagation in multilayered piezoelectric substrates

Due to the increasing demand for higher operating frequency, lower attenuation, and stronger piezoelectricity, use of the layered structure has become necessary. Theoretical studies are carried out for ultrasonic waves propagating in the multilayered piezoelectric substrates. Each layer processes up to as low as monoclinic symmetry with various thickness and orientation. A plane acoustic wave is assumed to be incident, at varied frequency and incidence angle, from a fluid upon a multilayered substrate. Simple analytical expressions for the reflection and transmission coefficients are derived from which all propagation characteristics are identified. Such expressions contain, as a by-product, the secular equation for the propagation of free harmonic waves on the multilayered piezoelectric substrates. Solutions are obtained for the individual layers which relate the field variables at the upper layer surfaces. The response of the total system proceeds by satisfying appropriate interfacial conditions across the layers. Based on the boundary conditions, two cases, {open_quotes}shorted{close_quotes} and {open_quotes}free{close_quotes}, are derived from which a so-called piezoelectric coupling factor is calculated to show the piezoelectric efficiency. Our results are rather general and show that the phase velocity is a function of frequency, layer thickness, and orientation