Primary and secondary resonance analyses of a curved microbeam for highly sensitive vacuum sensing

Microelectromechanical systems (MEMS) resonators provide compact, low-power platforms for precision sensing; however, achieving high sensitivity across a broad pressure range remains a challenge. A low-vacuum pressure sensor is introduced in this paper, based on tracking the frequency shift of the device's primary and secondary (superharmonic) resonances. The microdevice is based on a doubly clamped, highly curved microbeam resonator fabricated via the SOI-MUMPs process and operated through AC and DC electrostatic actuations. The linear and non-linear responses of the first symmetric and first anti-symmetric modes are investigated experimentally using a Laser Doppler Vibrometer (LDV) and by tuning the AC and DC electrostatic actuations. The dynamic behavior is also confirmed through a multi-physics finite-element model (FEM). Moreover, the device's secondary (superharmonic) resonance is characterized under AC and DC electrostatic actuation. Two fundamental modes, namely the antisymmetric and symmetric modes, are consistently identified at approximately 147 kHz and 173 kHz, respectively. A secondary resonance appears near 151.5 kHz, confirming nonlinear modal coupling under high AC actuation voltages. The linear and nonlinear modal coupling between the three resonance frequencies is investigated under AC and DC electrostatic actuation to identify the optimal bias values and provide high sensitivity across the 7 – 760 Torr pressure range. By tracking the frequency shift between the primary and secondary frequency differences, the microsensor exhibits ultrahigh sensitivity within the low-vacuum regime, surpassing the state of the art. More than 50 times, sensitivity magnification is demonstrated compared to those operated based on tracking the frequency shift of the primary or secondary resonance alone. At a low-vacuum pressure range (7 – 20 Torr), the microsensor achieves a sensitivity of 1.77 × 10 4 ppm/Torr with good linearity of R 2 = 0.9901. Although the present study focuses on a single-sensing application, the proposed design supports multimodal behavior, which can be further leveraged through multimodal excitation in future implementations to enable multi-sensing purposes. Hence, the demonstrated integration of geometric curvature and electrostatic actuation thus establishes a compact, low-power, and tunable framework for high-performance resonant MEMS pressure sensors.