## 7 Discussion  
Hybrid RF MEMS resonators exemplify notable advancements in microelectromechanical systems by synergistically integrating capacitive and piezoelectric transduction mechanisms. This innovative design leverages the benefits of both technologies to overcome individual limitations and significantly boost overall device performance, particularly in terms of port-to-port isolation, quality factor, linearity, frequency tuning capabilities, and susceptibility to spurious modes. The hybrid resonator employs a lateral extensional contour-mode device configuration, which is instrumental for allowing the resonator to operate at multiple resonant frequencies on a single chip through lithographically defined  
Figure 11: Measured broadband frequency response of a 150 μm\(-\)radius hybrid disk resonator, with a 5 μm\(-\)thick Si device layer operating in its 4 th later extensional mode, which is actuated by the fully integrated capacitive transducer through its surrounding electrodes and detected by a piezoelectric transducer via a pair of top electrodes on top of the ZnO piezoelectric layer. Figure 10: Measured broadband frequency response of a 125 μm\(-\)radius hybrid disk resonator with a 5 μm\(-\)thick Si device layer operating in its 1 st later extensional mode, which is actuated by the fully integrated capacitive transducer through its surrounding electrodes and detected by a piezoelectric transducer via a pair of top electrodes on top of the ZnO piezoelectric layer. lateral dimensions. This capability is largely attributed to the in-plane lateral dimensions of the shared micromechanical resonator body, allowing for diverse functionality from a single fabrication run. The structural material of choice, low acoustic loss single crystalline silicon, plays a pivotal role in enhancing the linearity and quality factor of the hybrid resonators. This material is renowned for its exceptional acoustic and electrical properties that satisfy the demanding performance needs. The device's structure includes a resonator body anchored to the substrate via one or two side-supporting anchors designed to minimize acoustic energy dissipation. The strategic positioning of supporting tethers at quasi-nodal points--areas of minimal radial displacement--helps mitigate the loss of acoustic energy through the anchors. This thoughtful placement is critical for preserving the integrity and efficiency of the resonator's model mechanical vibrations, thus maintaining high-quality factor resonances essential for reliable device operation. A key enabling feature of a hybrid resonator's functionality is its layered composition, where a thin film piezoelectric transducer layer (commonly ZnO in this work) is sandwiched between two layers of metal electrodes on top of the resonator body. The top metal layer is intricately patterned to form the drive and sense electrodes, while the bottom layer acts as the ground plane. This setup utilizes the \(d_{31}\) piezoelectric coefficients effectively, allowing the resonator to be excited and detected through its contour mode resonances. Meanwhile, the inclusion of electroplated nickel electrodes surrounding the disk-shaped resonator body with a precisely defined capacitive air gap facilitates electrostatic actuation, showcasing the hybrid device's ability to harness multiple transduction mechanisms for enhanced performance. Table 1 shows the comparison between capacitive, piezoelectric, and hybrid MEMS resonators, highlighting significant differences in their performance metrics including transduction mechanism, operating frequency, bias voltage, gap size, Q-factor and motional impedance. Capacitive resonators, such as the one reported in [28] operating at 96.5 MHz with a \(Q\)-factor of 3600 and a bias voltage of 7 V, exhibit moderate performance, while another in [29] operates at a much lower frequency of 34 kHz with a high \(Q\) of 60,000, indicating low energy dissipation with a higher capacitive air gap width of 1000 nm.