Analytical Energy‑Based Modeling and Multi‑Objective Optimization of a Z‑Shaped MEMS Capacitive Microphone

The high cost and long turnaround time of MEMS fabrication necessitate accurate pre fabrication performance prediction. For Z shaped MEMS capacitive microphones, the lack of a complete analytical model for the suspension spring constant hinders systematic optimization and often leads to costly trial and error fabrication. This work presents a closed form energy based analytical model for Z shaped suspension arms using Castigliano’s theorem, enabling explicit derivation of the vertical spring constant and its direct link to key performance parameters. Based on this formulation, a physically grounded multi objective optimization framework is established to enhance mechanical sensitivity while satisfying resonance frequency and pull in voltage constraints. Particle swarm optimization (PSO) is employed as an efficient search strategy within the analytically defined design space. The framework allows reliable evaluation and optimization of microphone performance before fabrication, significantly reducing design uncertainty. Simulation results show that, compared with both an initial reference design and reported state of the art Z shaped MEMS microphones, the optimized structure achieves ap-proximately a threefold improvement in open circuit sensitivity while reducing the pull in voltage by nearly 30% without compromising resonance frequency constraints. The presented approach offers a systematic, fabrication oriented design pathway applicable to a wide range of MEMS microphone structures.