3-D modeling of high-Q quartz resonators for VHF-UHF applications

This paper presents the optimized design and analysis of a new circular quartz resonator for VHF-UHF filtering applications. The resonator is designed for ease of packaging and integration with on-chip electronics using a new quartz-MEMS process that is being developed at HRL laboratories. A key feature of this design is the removal of the metal electrodes from the active regions in order to enhance the mechanical gain. As an example of this design, we have modeled a 9.8 μm thick circular plate (383-μm-diameter) with a 10-μm-thick double-sided circular resonator as the active region. The 200 μm diameter resonator has a 0.1 μm step above each face of the plate. The entire structure is composed of AT-cut quartz. This design provides a high degree of energy trapping for the fundamental thickness-shear mode at approximately 168 MHz. Around the resonator on each face of the plate is a pair of opposing 600 Å-thick annular Al electrodes. The width of the electrodes is 40 μm and a 1.5 μm gap exists between the inner edge of the electrodes and the central areas. We will present numerical results showing that this electrode arrangement provides effective acoustic coupling to the thickness shear mode of the central resonator area. A frequency sweep provides a plot of the motional impedance of the resonator and is a very effective tool for assessing the acoustic coupling between the electrodes and TS mode as function of the electrode-mesa gap. We will also demonstrate a trade-off between Au and Al electrodes for this design.