Energy trapping in extensional thin film MEMS resonators and applications to filtering at UHF frequencies

In this paper we apply the energy trapping theory to the extensional modes of 6 mm materials and particularly to piezoelectric films textured in a direction normal to the film. The 6 mm symmetries imply that the Mn\´ and Pn\´ coefficients of the Tiersten equation are equal and that energy trapping can nearly always be obtained (most often using "inverse" energy trapping with Mn\´=Pn\´<0). In this case, particular dispositions have to be taken to obtain energy trapping (in inverting of the order of the cut off frequencies of the different regions as compared to conventional energy trapping). The 6 mm symmetries imply also that resonators geometries having a revolution axis lead to more interesting properties in term of spectral purity and of electric properties (optimal character that can be demonstrated). Example of designs of filter type AlN resonators using round or annular electrodes are presented. It is observed that a wide variety of equivalent inductance can be obtained particularly in using a very interesting properties of the annular electrodes. Application of these resonators to UHF filtering is then discussed, it is observed that interesting responses and low termination impedances can be obtained using symmetrical full lattice filters "enlarged" with serial or parallel inductances.