CMOS-MEMS resonant pressure sensors: optimization and validation through comparative analysis

Abstract

An optimized CMOS-MEMS resonant pressure sensor with enhanced sensitivity at atmospheric pressure has been reported in this paper. The presented work reports modeling and characterization of a resonant pressure sensor, based on the variation of the quality factor with pressure. The relevant regimes of air flow have been determined by the Knudsen number (Kn), which is the ratio of the mean free path of the gas molecule to the characteristic length of the device. The sensitivity has been monitored for the resonator design from low vacuum to atmospheric levels of air pressure. This has been accomplished by reducing the characteristic length and optimization of other parameters for the device. While the existing analytical model has been adapted to simulate the squeeze film damping effectively and it is validated at higher values of air pressure, it fails to compute the structural damping mechanisms dominant in the molecular flow regime, i.e. at lower levels of air pressure. This discrepancy has been solved by finite element modeling that has incorporated both structural and film damping effects. The sensor has been designed with an optimal geometry of 140 µm x 140 µm x 8 µm having 6 x 6 perforations along the row and column of the plate respectively, for maximum Q, with an effective mass of 0.4 µg. An enhanced quality factor of 60 and reduced damping coefficient of 4.34 µNs/m have been obtained for the reported device at atmospheric pressure. The sensitivity of the manufactured device is approximately-0.09 at atmospheric pressure and increases to-0.3 at 40 kPa i.e. in the lower pressures of slip flow regime. The experimental measurements of the manufactured resonant pressure sensor have been compared with that of the analytical and finite element modeling to validate the optimization procedure. The device has been manufactured using standard 250-nm CMOS technology followed by an in-house BEOL metal-layer release through wet etching.

A Comprehensive High-Level Model for CMOS-MEMS Resonators

“…1 has been designed with an optimal geometry of 140 × 140 × 8 µm having 6 × 6 perforations along the row and column of the plate, respectively, for maximum Q, with an effective mass of 0.4 µg. An enhanced quality factor of 60 and reduced damping coefficient of 4.34 µNs/m have been obtained for the reported device at atmospheric pressure [13]- [17]. The reported capacitive pressure sensor, fabricated using IHP SG25 process, is implemented as a two aluminum layers (with a thickness of 2 μm and 3 μm) separated by a 3 μm thick tungsten via [13].…”

“…This paper presents a comprehensive guide to the modeling and simulation methodology of a CMOS-MEMS resonator in Verilog-A within Cadence framework. In Section II, a second order non-linear behavioral model, targeted to emulate the realtime behavior of a prior reported CMOS-MEMS resonator [13] is introduced. The model is written in Verilog-A and the simulations are performed within the Cadence framework, allowing co-simulation of MEMS with electronics.…”

Characterization of CMOS-MEMS Resonant Pressure Sensors

“…Here z, , ̈ are the displacement, velocity, and acceleration of the system respectively [12]. An flexural mode resonator has been analytically developed and numerically validated by FEM models in COMSOL Multiphysics in order to optimize the Q sensitivity without affecting the device capacitance [12], [13].The pressure sensor design has an effective mass of 0.4 µg with an optimal geometry of 140 µm × 140 µm × 8 µm having 6 × 6 perforations along the row and column of the plate, respectively, to achieve maximum Q while presenting an acceptable capacitance variation to the electronics [14].…”

“…In Equation (2), Kn has been used to characterize both pressure and temperature, which in turn has characterized the device performance in terms of Q, discussed in the following sub-sections. An in-detail information on the significance of the Knudsen number can be found in [13].…”

“…25 °C, and for a fixed bias voltage of 10 V. The oscillatory excitation amplitude was limited to 30 mV for all measurements to mitigate the nonlinearity effects due to excessive amplitude vibration. The device quality factor was obtained from the frequency response by aligning and validating them with the response of a second-order behavioral model using Q as one of its inputs [13], [17]. The manufactured sensor was primarily operated in the slip flow and transition flow regimes, as obtained from the Kn value.…”