## 1 Introduction  
Radio frequency micro-electro-mechanical systems (RF MEMS) are a transformative technology that has emerged as a key area of research while benefiting from foundry processes. Integrating mechanical and electrical functionalities at a microscopic scale has led to substantial advancements in commercial and military telecommunications, radar, and electronic warfare systems [1]. RF MEMS resonators play a crucial role in various devices such as oscillators, filters, and frequency synthesizers in RF front ends, where their mechanical vibrations maintain frequency accuracy while ensuring signal integrity in communication systems [2]. Recent advancements in RF piezoelectric arrays have shown that mechanically coupling several identical resonators into an array can effectively reduce the overall motional resistance, despite the trade-off of increased resistance due to reduced transduction areas [3]. Integrating MEMS resonators in consumer electronics and specialized military communication systems has enabled significant device miniaturization and performance enhancement, thus leading to ubiquitous, compact, and high-performance devices essential in our increasingly connected world [4]. The advancements in foundry microfabrication have facilitated the volume manufacturing of devices that perform reliably under varied environmental conditions [5; 6]. Capacitively transduced MEMS resonators have been highly valued for their impressive quality factor (\(Q\)), particularly within the very high frequency (VHF) and ultra-high frequency (UHF) ranges [7]. They operate based on changes in capacitance due to mechanical vibrations in the desired acoustic mode when an electric field aligned with modal vibration is applied, thus enabling them to stabilize resonance frequencies with remarkable timing accuracy. Moreover, the direct integration of capacitively transduced resonators with complementary metal oxide semiconductor (CMOS) transistor circuit technology enhances the microsystem's compactness and functionality. However, capacitive MEMS resonators encounter significant challenges, such as high motional impedance, which complicates their employment with standard 50 \(\Omega\) RF systems, leading to increased insertion losses [8]. Techniques such as reducing the capacitive transducer air gap all the way down to ~13 nm have been employed to mitigate these issues, although this has caused some problems regarding the force balance of the resonator when a DC bias voltage is applied [9]. On the other hand, piezoelectric RF MEMS resonators, utilizing materials like zinc oxide (ZnO) and aluminum nitride (AlN), are pivotal due to their superb energy conversion efficiency that leads to high electromechanical coupling coefficient [10]. Recent studies have demonstrated that RF piezoelectric arrays, particularly those integrating multiple resonators, effectively reduce motional resistance by leveraging mechanical coupling, which significantly lowers insertion loss and boosts energy conversion efficiency [11]. Furthermore, advances in materials like periodically poled lithium niobate and contour-mode aluminum nitride, along with optimized electrode designs, have significantly improved the quality and performance of piezoelectric resonators across a broad frequency range [12]. With strong electromechanical coupling coefficients, these materials enable piezoelectric resonators to operate with lower motional impedance and improved insertion loss characteristics as compared to their capacitive counterparts. Meanwhile, piezoelectric resonators encounter their own challenges, such as thermal budget constraints set by post-CMOS fabrication processes, often necessitating high processing temperatures incompatible with integrated circuit technologies. Also, resonators with piezoelectric transducers are often more susceptible to excitation of spurious modes, which has imposed significant challenges and device-specific solutions [13; 14; 15].