We report a new silicon Microelectromechanical systems (MEMS) accelerometer based on differential frequency modulation (FM) with experimentally demonstrated thermal compensation over a dynamic temperature environment and $\mu g$ -level Allan deviation of bias. The sensor architecture is based on resonant frequency tracking in a vacuum packaged silicon-on-insulator (SOI) tuning fork oscillator. To address drift over temperature, the MEMS sensor die incorporates two identical tuning forks with opposing axes of sensitivity. Demodulation of the differential FM output from the two simultaneously operated oscillators eliminates common mode errors and provides an FM output with continuous thermal compensation. The first SOI prototype with quality factor of 350000 was built and characterized over a temperature range between 30 °C and 75 °C. Temperature characterization of the FM accelerometer showed less than a 0.5% scale-factor change throughout a temperature range from 30 °C to 75 °C, without any external compensation. This is enabled by an inherently differential frequency output, which cancels common-mode influences, such as those due to temperature. Allan deviation of the differential FM accelerometer revealed a bias instability of $6\,\, \mu \text{g}$ at 20 s, along with an elimination of any temperature drift due to increases in averaging time. After comparing the measured bias instability with the designed linear range of 20 g, the sensor demonstrates a wide dynamic range of 130 dB. A second design iteration of the FM accelerometer, vacuum-sealed with getter material, was created to maximize $Q$ -factor, and thereby frequency resolution. A $Q$ -factor of 2.4 million was experimentally demonstrated, with a time constant of >20 min.

High Quality Factor Resonant MEMS Accelerometer With Continuous Thermal Compensation

Reliability of MEMS: A perspective on failure mechanisms, improvement solutions and best practices at development level

In this paper, we explore the effects of electrostatic parametric amplification on a high quality factor (Q > 100 000) encapsulated disk resonator gyroscope (DRG), fabricated in 〈100〉 silicon. The DRG was operated in the n = 2 degenerate wineglass mode at 235 kHz, and electrostatically tuned so that the frequency split between the two degenerate modes was less than 100 mHz. A parametric pump at twice the resonant frequency is applied to the sense axis of the DRG, resulting in a maximum scale factor of 156.6 μV/(°/s), an 8.8× improvement over the non-amplified performance. When operated with a parametric gain of 5.4, a minimum angle random walk of 0.034°/√h and bias instability of 1.15°/h are achieved, representing an improvement by a factor of 4.3× and 1.5×, respectively.

Encapsulated high frequency (235 kHz), high-Q (100 k) disk resonator gyroscope with electrostatic parametric pump

This paper presents detailed performance status, modeling, and projections for the silicon MEMS Quadruple Mass Gyroscope (QMG) - a unique high Q, lumped mass, mode-symmetric Class II Coriolis Vibratory Gyroscope (CVG) with interchangeable whole angle, self-calibration, and force rebalance mechanizations. To support experimental work, a standalone CVG control and test suite was developed and implemented, comprising a packaged MEMS transducer, an analog buffer card, a digital control card, HRG-style real time closed loop control firmware, and a PC GUI for test control and data logging. Analysis of a QMG sealed without getter with a Q-factor of 1e3 reveals an Angle Random Walk (ARW) of 0.02 deg/rt-hr limited only by the fundamental Mechanical-Thermal Noise (MTN). Propagation of a detailed noise model to a QMG sealed with getter at a Q-factor of 1e6 (previously demonstrated) showed better than Navigation Grade ARW of 0.001 deg/rt-hr. Combination of the very low ARW with the mode-symmetry enabled self-calibration substantiates the navigation grade performance capacity of the Si-MEMS QMG.

Flat is not dead: Current and future performance of Si-MEMS Quad Mass Gyro (QMG) system

Author(s): Zotov, SA; Simon, BR; Prikhodko, IP; Trusov, AA; Shkel, AM | Abstract: This paper presents a method of dynamically balancing tuning fork microresonators, enabling maximization of quality factor Q-factor) in structures with imperfections. Nonsymmetric tuning of stiffness in a coupled 2-DOF resonator is completed through the use of the negative electrostatic spring effect. This variable stiffness is shown to be able to adjust the reaction forces of the structure at the anchors, effectively balancing any spring imperfections caused by fabrication imperfections. Balancing the structure through stiffness matching minimizes the loss of energy through the substrate and maximizes Q-factor of the device's antiphase mode. The approach is experimentally demonstrated using a vacuum packaged microelectromechanical tuning fork resonator with operational frequency of 2.2 kHz and antiphase Q-factor of 0.6 million. By electrostatically tuning the reaction force at the anchors caused by fabrication imperfections, anchor loss can be suppressed, increasing the Q-factor to above 0.8 million. The experimentally validated analytical model of substrate dissipation is confirmed to be applicable to Q-factor tuning in antiphase driven resonators and gyroscopes. © 2001-2012 IEEE.

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Quality Factor Maximization Through Dynamic Balancing of Tuning Fork Resonator

We report a new approach for improvement of the long term in-run bias stability of Coriolis vibratory gyroscopes. The approach is based on utilization of the mechanical quadrature error in gyroscopes to compensate for variation in system parameters. The proposed approach was validated by a silicon Quadruple Mass Gyroscope, with the natural frequency of 3 kHz, frequency mismatch of <;0.5 Hz, and isotropic quality factor of 950, packaged without getter. The algorithm is described and experimentally demonstrated in this paper, showing a bias stability of 0.1 deg/hr after 300 seconds, and importantly, retaining that value for over 3 hours of the integration time.

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Utilization of mechanical quadrature in silicon MEMS vibratory gyroscope to increase and expand the long term in-run bias stability

We report a new silicon MEMS accelerometer based on differential Frequency Modulation (FM) with experimentally demonstrated self-calibration against dynamic temperature environment and μg-level Allan deviation of bias. The sensor architecture is based on resonant frequency tracking in a vacuum packaged SOI tuning fork oscillator with a high Q-factor. The oscillator is instrumented with a DC voltage biased parallel plate capacitor, which couples the proof mass displacement to the effective stiffness by means of the negative electrostatic spring effect. External acceleration is detected as an FM signal. To address drift over temperature, the MEMS sensor die incorporates two identical tuning forks with opposing axes of sensitivity. Demodulation of the differential FM output from the two simultaneously operated oscillators eliminates common mode errors and provides a continuously self-calibrated FM output. An x-axis SOI prototype with a tunable scale factor was built and characterized over dynamic temperature environment, experimentally demonstrating continuous self-calibration.

/pdf/silicon-accelerometer-with-differential-frequency-modulation-4xrwpia2ax.pdf

Brenton R. Simon

Papers

High Quality Factor Resonant MEMS Accelerometer With Continuous Thermal Compensation

Flat is not dead: Current and future performance of Si-MEMS Quad Mass Gyro (QMG) system

Quality Factor Maximization Through Dynamic Balancing of Tuning Fork Resonator

Utilization of mechanical quadrature in silicon MEMS vibratory gyroscope to increase and expand the long term in-run bias stability

Silicon accelerometer with differential Frequency Modulation and continuous self-calibration