Simulation and Analysis of a Silicon Membrane-Supported Beam–Island Diaphragm for Graphene Piezoresistive MEMS Microphones in High-SPL Acoustic Sensing

High sound pressure level (SPL) acoustic sensing requires miniaturized microphones that can operate under large acoustic loading while maintaining mechanical linearity, sufficient sensing response, and broadband audio frequency behavior. This work targets high-SPL operation and numerically investigates a graphene piezoresistive MEMS microphone based on a membrane-supported beam–island diaphragm. The proposed structure retains a continuous membrane for acoustic load bearing, while the upper beam–island topology redirects deformation-induced strain toward beam root regions where graphene piezoresistors are placed. This design is intended to increase the local strain available for piezoresistive readout without simply relying on larger global diaphragm deflection. Finite-element analysis was used to optimize the diaphragm geometry and evaluate strain enhancement, pressure response linearity, modal behavior, and harmonic response. Under the 170 dB SPL reference condition, the optimized structure increases the peak structural strain from 47.83 με in a thickness-equivalent solid diaphragm to 562.53 με, achieving an approximately 11.8-fold enhancement in local sensing strain while maintaining a highly linear pressure response (R2 > 0.9999). Additionally, the results also show that the sensor exhibits a high first natural frequency of 64.07 kHz and a small response variation of approximately 0.94 dB within the 0–20 kHz target frequency range, indicating excellent dynamic stability and high-fidelity signal transduction characteristics. To connect the structural response with piezoresistive readout, first-order electromechanical output estimation was further performed using representative graphene gauge factors, quarter-bridge readout assumptions, contact resistance correction, and Johnson-noise-limited signal-to-noise ratio estimation. A ±5% geometric tolerance check further indicates that the membrane side length is the most fabrication-sensitive parameter, while the selected design remains generally robust except for reduced linearity margin under positive membrane side-length deviation. These results demonstrate the potential of the proposed graphene-based MEMS microphone for high-SPL broadband acoustic sensing applications in harsh and high-intensity acoustic environments.