Observation of flexural modes in FBAR resonators at MHz frequencies

Abstract

Agilent GHz FBAR resonators are fabricated as suspended membranes of piezoelectric AlN. These vibrate as plate mode resonators in a symmetric or S/sub m,n/ type mode, with the resonant frequencies controlled by the thickness of the membrane, /spl sim/1 micron for GHz frequencies. There also exists a class of anti-symmetric or A/sub 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/sub 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 /spl sim/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/sub 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 /spl sim/100. The flexural modes can be analyzed with a combined plate/drumhead theory, and the resonant frequencies f/sub 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 r/sup 2/>0.95.