Legendre polynomial modeling of composite bulk acoustic wave resonators

The Legendre polynomial method has been extended to the modeling of bulk acoustic wave (BAW) resonators. Modifications have been made to the formulation in order to account for large differences in the physical properties of adjoining layers and to take into account the electric source. A unique formalism has been obtained which allows for both harmonic and modal analyses. Resonance and antiresonance frequencies, electric input impedance, electromechanical coupling coefficients, and quality factors have been obtained for an aluminum/zinc oxide/aluminum (Al∕ZnO∕Al) BAW resonator. The results are in excellent agreement with analytical results.