This paper describes the design and experimental evaluation of a silicon micro-machined resonant accelerometer (SMRA). This type of accelerometer works on the principle that a proof mass under acceleration applies force to two double-ended tuning fork (DETF) resonators, and the frequency output of two DETFs exhibits a differential shift. The dies of an SMRA are fabricated using silicon-on-insulator (SOI) processing and wafer-level vacuum packaging. This research aims to design a high-sensitivity SMRA because a high sensitivity allows for the acceleration signal to be easily demodulated by frequency counting techniques and decreases the noise level. This study applies the energy-consumed concept and the Nelder-Mead algorithm in the SMRA to address the design issues and further increase its sensitivity. Using this novel method, the sensitivity of the SMRA has been increased by 66.1%, which attributes to both the re-designed DETF and the reduced energy loss on the micro-lever. The results of both the closed-form and finite-element analyses are described and are in agreement with one another. A resonant frequency of approximately 22 kHz, a frequency sensitivity of over 250 Hz per g, a one-hour bias stability of 55 μg, a bias repeatability (1σ) of 48 μg and the bias-instability of 4.8 μg have been achieved.

In this work, the processing error including the overetching error and residual stresses in the manufacturing process of a microelectromechanical system (MEMS) resonant accelerometer is identified. The performance of the accelerometer is affected by the processing error, especially the residual stress due to the multiple temperature loads in the manufacturing process. Thus, it is essential to identify the processing error for a high-precision MEMS resonant accelerometer. The overetching error is assessed using the sensitivity of the accelerometer resonator. With the multi-step measurement of the resonator frequency variation in the packaging process, the residual stresses of the MEMS accelerometer at different stages are decomposed and identified, combined with surface morphology measurement and finite element analysis simulations. The results of the analysis demonstrate that: 1) The processing error distribution of the accelerometer at the wafer level is related to the morphology of the wafer, which is decided by the low-order main vibrating modes. 2) The residual stress is distributed from high to low from the center to the edge in the wafer. 3) The residual stress at the wafer level is the main part of the MEMS accelerometer when low-stress packaging technology is adopted at the chip level. 4) The variation of the residual stresses in the manufacturing process is a non-monotonic process. The accurate identification of the processing error provides an effective foundation for the improvement and optimization of the MEMS resonant accelerometer. [2022-0041]

Microelectromechanical system (MEMS)-based resonant accelerometers have great application potential in navigation guidance. In the present work, a systematic theoretical model of a MEMS resonant accelerometer was proposed. The coupling effect of microleverage mechanisms on the proof mass and the resonator was analyzed by the displacement coordination method for the first time. The resonant frequency of the proof mass, the natural frequency of the resonator, and the sensitivity of the accelerometer were united into one model for the structural cooperative design. The analytical model was approved by finite element simulations and verification experiments, and the relative error of key parameters was less than 13%. The analysis of the accelerometer architecture revealed that 1) joints between beams and the microleverage arm should be on the same level, 2) the geometric dimensions of the input beam and pivot beam of the microleverage should be the same, and 3) the microleverage arm width should be sufficient to ensure the rigidity. The performance of the accelerometer was also tested. The bias instability of $1 \mu \text{g}$ (Allan variance), the stability of $2.12 \mu \text{g}$ ( $1\sigma $ , 1 Hz date rate, one-hour length), and the nonlinearity of 16.3 ppm with the full range of ±20 g were achieved at room temperature.

Vibrating beam accelerometers (VBAs) have significant application potential in navigation guidance. This paper proposed a novel high-precision frequency readout method and integrated CMOS circuit implementation for VBAs. And technologies including sigma-delta modulation, up-sample and split, data synchronization and nonlinearity correction are employed in the method which is analyzed in detail in this paper. The method offers the advantages of low quantization noise, enough range, fixed output rate, and high linearity. Other force-frequency sensors could also benefit from this method but note that its noise suppression is most effective when the output rate is much smaller than the frequency under test. The method is implemented by a CMOS circuit and integrated with an oscillator circuit, which makes a full-function single-package VBA possible. Static, shock, random vibration, and centrifugal tests of the frequency readout circuit and VBA were performed. Test results show that the frequency quantization noise is less than 10 μHz/√Hz at 1 Hz, and can support 0.1 μg noise output. They also show that the vibration rectification error is lower than 0.5 mg at 8 grms, and that the 20 g full range nonlinearity is 16 ppm.

Quality factor tuning is attractive in degenerate and nondegenerate (NDE) MEMS gyros for drift suppression or shock and vibration immunity. This article proposes three resistance-based Q -factor tuning approaches without dedicated electrodes for NDE gyro. The inherent sensing capacitance is utilized as a Q -tuning mechanism for low cost, size, weight, and power (C-SWaP). Routing traces on MEMS or application-specified integrated circuit chips as well as the input impedance of charge sensitive amplifier (CSA) are utilized as damping sources. The theoretical and experimental results indicate Q -tuning utilizing the CSA's input impedance does not deteriorate the gyro's noise floor (angle random walk = 0.01°/√h, bias instability = 0.12°/h). Large-scale Q -tuning using the regulation of polarization voltage reduces the sensing Q -factor from 38 to 3 k. The gyro's settling time after shock is also reduced from 1.4 to 0.13 s after Q -tuning. Besides, a frequency-independent fine Q -tuning using tail current regulation in Opam is proposed to correct the thermal variation of the sensing Q -factor. It improves the gyro's bias drift from 1.5°/s to 0.2°/s. This work presents a low C-SWaP Q -tuning solution for high-end industrial MEMS gyro.