## 1 Introduction
Various bonding techniques are employed, including fusion bonding, anodic bonding, and eutectic bonding, with selection dependent on specific application requirements and processing constraints [18]. While eutectic bonding techniques, particularly Au-Sn systems, offer established reliability and low-temperature processing capabilities, they present significant challenges for precision filter applications. The Au-Sn eutectic composition (Au 80-Sn 20%) with its 280 \({}^{\circ}\)C melting point requires precise pressure and temperature control to prevent material flow that can contaminate bonding chambers and compromise interface flatness [17; 18]. This issue becomes particularly critical for microwave interdigital filters requiring precise pattern maintenance and dimensional accuracy. Au-Au thermocompression bonding has emerged as a superior alternative for RF MEMS applications, offering distinct advantages including superior electrical conductivity through pure gold-to-gold interfaces that minimize contact resistance critical for maintaining low insertion loss across wide bandwidths. Unlike eutectic systems, Au-Au bonding eliminates additional material systems that might introduce electromagnetic interference or thermal expansion mismatches. When properly executed, Au-Au bonds achieve tensile strengths exceeding 200 MPa, providing robust mechanical protection for sensitive filter structures [19]. However, Au-Au bonding presents unique challenges for wideband filter implementations. The complex geometries typical of wideband resonator structures demand alignment precision below \(\pm\)10 \(\upmu\)m during bonding operations. Surface roughness requirements are exceptionally stringent (Ra \(<\) 10 nm) to ensure intimate contact across bonding interfaces [19]. Most critically, larger bonding areas improve mechanical strength but may introduce parasitic capacitances that degrade RF performance across the filter's operating bandwidth, creating a fundamental trade-off between electrical performance and mechanical reliability. This study addresses these challenges by focusing on resonator width optimization, a critical design parameter chosen for its direct and simultaneous impact on both mechanical reliability and RF performance. The width fundamentally defines the bonding interface area, which is critical for mechanical strength, while also governing the electromagnetic properties of the filter. This allows for a targeted investigation into the trade-offs between these two essential aspects of device design. To achieve this, we systematically evaluate three distinct resonator width configurations chosen to represent key points in the design space: 0% (L1), which serves as a microstrip-like baseline with minimal resonator bonding; 100% (L3), representing the ideal case with a maximized and symmetric bonding interface; and 60% (L2), an intermediate, asymmetric case to study the effects of partial matching. This approach provides a clear comparison of how different bonding strategies influence overall device performance and robustness. This research provides three key contributions: understanding misalignment effects on RF performance during actual processing, quantifying differences between theoretical filter design and post-processing results, and determining how bonding area influences Q-factor and bonding quality relationships. The findings establish fundamental design principles for next-generation wideband MEMS filters, particularly for emerging applications in 5G/6G communications, automotive radar systems, and advanced military electronics where both exceptional performance and long-term reliability are critical requirements. By optimizing the resonator width relationship between cap and bottom wafers, this work demonstrates a practical approach to achieving enhanced RF performance and improved mechanical reliability simultaneously in wideband MEMS filter designs.