Dedicated finite elements for electrode thin films on quartz resonators

The finite element meshes of thickness shear piezoelectric resonators must be sufficiently fine so that the mesh impedance (stiffness) itself does not interfere with the acoustic wave propagation. Since the thickness of the thin electrode film is usually much less than the resonator plate itself, the mesh for the electrodes is usually not optimal, and would usually have a poor aspect ratio, that is, the element length or width is more than twice the element thickness. Special elements for the thin electrode film are proposed, and their results are compared with accurate numerical results. Finite element models are used to demonstrate the effects of electrode boundary conditions and thickness of electrodes on the frequency-temperature curves of an AT cut plate. Results are also shown to demonstrate the efficiency of reducing the electrode to the interface of the crystal and electrode using acceptable approximations such as Guyan reduction and merging.