Observation of flexural modes in FBAR resonators at MHz frequencies

Agilent GHz FBAR resonators are fabricated as suspended membranes of piezoelectric AlN. These vibrate as plate mode resonators in a symmetric or S_m,n type mode, with the resonant frequencies controlled by the thickness of the membrane, ∼1 micron for GHz frequencies. There also exists a class of anti-symmetric or A_m,n type flexural plate modes. Resonators operating in this mode exhibit frequencies controlled by both the lateral dimensions and the residual stress in the plate. Unlike the symmetric modes, the A_m,n modes are much harder to excite by the symmetric FBAR structure, are not easily observed at the electrical port, and occur in the MHz range for structures with lateral dimensions ∼100 microns. The imaging acoustic interferometer is a technique to visualize GHz rate vibrations in FBAR resonators, at sub-nanometer displacements. This paper describes an extension of that technique, which allows MHz rate A_m,n mode vibrations to be visualized. The first few flexural modes were observed, and will be presented as images made while operating at their respective resonant frequencies. Such modes exhibit a rich structure of nodes and phase reversals of the vertical motion. Over 21 modes were observed in the range 0.5 to 15 MHz. The Q is observed to be ∼100. The flexural modes can be analyzed with a combined plate/drumhead theory, and the resonant frequencies f_m,n are found to depend on the material properties, static film stress, and the lateral dimensions. This theory yields a regression fit to the data with a goodness of fit coefficient r²>0.95.