## 3 Device Structure and Operation  
Hybrid MEMS resonators are configured from a novel concept to integrate capacitive and piezoelectric transduction mechanisms for activation and sensing of the target modal resonance. The main design strategy aims to achieve superior performance metrics, almost double the \(Q\)-factor value reported in literature as illustrated in Table 1, by leveraging the distinct advantages of each transduction mechanism within a single device. Specifically, hybrid resonators address the limitations of each standalone system, thereby enhancing overall device performance, including quality factor (\(Q\)), insertion loss, and motional impedance. The high \(Q\), low power consumption, and low spurious mode susceptibility of capacitive resonators could be combined with the low motional impedance and robust frequency control of piezoelectric resonators, promising more flexible frequency tuning and improved thermal stability. Hybrid resonators are typically composed of micromachined silicon resonator body structures that incorporate both capacitive and piezoelectric transducers. The design often involves a layered approach, where a piezoelectric thin film (e.g., ZnO or AlN) is deposited onto a pre-fabricated capacitive resonator body microstructure composed of silicon or another semiconductor material such as diamond, silicon carbide, or fused silica. This unique multi-layer configuration allows for the efficient coupling of mechanical and electrical energy while maximizing the resonator's performance. The piezoelectric layer is activated by electrical signals that induce mechanical strains, thereby generating an electric field across the material. On the other hand, the capacitive transducer component generates an output motional current signal by sourcing it from the changes in capacitance caused by mechanical modal vibrations. A key challenge in designing hybrid resonators is the need to integrate different material systems with distinct physical properties and processing requirements. For example, the high-temperature processes required for piezoelectric materials can affect the structural integrity of the capacitive components. To tackle this challenge, it is crucial to develop innovative and robust fabrication techniques that can effectively incorporate these materials while maintaining optimal device performance. The detailed design of hybrid MEMS resonators that seamlessly integrate capacitive and piezoelectric transduction mechanisms to enhance performance metrics such as quality factor, insertion loss, and motional impedance, and so on, is depicted in Figure 1.  
Addressing parasitic effects that arise from the close proximity of capacitive and piezoelectric transducer elements is crucial. Strategies such as optimizing electrode placement and employing advanced materials that minimize electrical crosstalk and mechanical losses were used to enhance the resonator's performance. The resonator's design, such as layer thicknesses and lateral sizes and electrode designs, are adjusted to determine its resonance frequency and electromechanical coupling coefficient directly. By employing a one side-supporting anchor with strategically designed dimensions, acoustic energy losses through the anchor have been effectively minimized. To excite wine-glass mode while reducing anchor-related losses, the supporting tethers should be placed at quasi-nodal locations where the resonator plate has no radial displacement. In this work, resonator designs with both one and two side-supporting anchors were used, among which the design with one anchor showed better performance. Single-anchor designs generally exhibit higher quality factors and reduced energy losses compared to double-side-supporting anchor designs due to less energy dissipation through the support structure [28]. The COMSOL(r) finite element eigenfrequency simulation, as shown in Figure 2, depicts the first four lateral extensional contour modes of a disk resonator.