Brenton R. Simon

High Quality Factor Resonant MEMS Accelerometer With Continuous Thermal Compensation

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 μg-level Allan deviation of bias. The sensor architecture is based on resonant frequency tracking in a vacuum packaged siliconon-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 μg 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.

Silicon accelerometer with differential Frequency Modulation and continuous self-calibration

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.

Quality Factor Maximization Through Dynamic Balancing of Tuning Fork Resonator

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 devices 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.

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

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.

Anti-phase mode isolation in tuning-fork MEMS using a lever coupling design

A new coupling design is proposed and demonstrated for MEMS tuning-fork structures, which successfully isolates the anti-phase vibratory mode in both frequency and Q-factor. G-sensitivity is reduced by design through 1) creation of a high frequency separation between anti-phase and in-phase vibratory modes, 2) maximization of the in-phase resonance frequency, and 3) minimization of in-phase Q-factors. The proposed design accomplishes these goals by using a levering mechanism for coupling the proof masses, in contrast to a conventional approach via flexural spring. This structural design allows for large frequency separations between the anti-phase and in-phase vibratory modes, experimentally demonstrated up to 119% using a previously established quadruple mass gyroscope (QMG) [1]. Furthermore, due to the additional stress present within the lever coupling, in-phase Q-factors are reduced through tailored thermoelastic damping. The result is an anti-phase resonance separated in Q-factor and fQ product by over two orders of magnitude, compared to the in-phase mode. This is shown in comparison to an identical device with a spring coupling, demonstrated with a 25% frequency separation and one order of magnitude separation in both Q-factor and fQ product.

Flat Is Not Dead: Current and Future Performance of Si-MEMS Quad Mass Gyro (QMG) System

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.

Intrinsic stress of eutectic Au/Sn die attachment and effect on mode-matched MEMS gyroscopes

We report on the intrinsic stress imparted to MEMS gyroscopes and the effects on frequency mismatch due to high-temperature die attachment processes, such as eutectic Au/Sn solder. The resonant frequencies of a number of symmetric MEMS gyroscopes are characterized before and after die attachment, along with X-ray imaging to observe the random solder reflow that occurred during attachment. Frequency shift is observed and compared to the die attachment area, with an 87 percent correlation to the length of the solder reflow. A model of the phenomena is presented with less than 0.1 percent agreement to the experimental results, indicating an optimal die attachment for the minimization of stress-induced frequency changes.

Force rebalance, whole angle, and self-calibration mechanization of silicon MEMS quad mass gyro

This paper reports experimental demonstration and characterization of the MEMS Quadruple Mass Gyroscope (QMG) operated in three distinct mechanizations, namely force rebalance, whole angle, and virtual carouseling self-calibration. The three runtime interchangeable control modes are implemented using a custom standalone electronics suite running control firmware with a separate computer GVI for experiment control and data logging. The results of this work demonstrate that the Coriolis Vibratory Gyroscope (CVG) Class II theoretical framework developed by D.D. Lynch is directly applicable to MEMS devices and establishes a path for potentially groundbreaking improvement of their long term stability in support of inertial navigation through self-calibration. While the simple fabrication and outstanding measured characteristics of the QMG (Q>106, Δf<;0.2 Hz, τ>170 s, Δ(1/τ)<;10-4Hz) make it an ideal MEMS Class II CVG, a wide variety of other planar and 3-D mode-symmetric MEMS gyroscope resonators can leverage the developed approach, hardware, software, and analysis tools.

Mode ordering in tuning fork structures with negative structural coupling for mitigation of common-mode g-sensitivity

This paper reports a method of mode ordering in tuning fork structures, effectively inducing a negative coupling stiffness between the resonant proof masses. The coupling mechanism selectively stiffens the undesirable in-phase resonance mode and softens the desirable out-of-phase resonance, thus widening the frequency separation between the desirable and undesirable modes of vibration in tuning fork structures. In gyroscopes, the approach leads to improved robustness to fabrication imperfections and immunity to environmental vibrations, while at the same time enhancing the scale factor and reducing the noise. Advantages of the method are illustrated on a Quadruple Mass Gyroscope (QMG) architecture, which was previously reported. It is experimentally demonstrated that the common-mode g-sensitivity can be reduced by over 20 times with design modifications resulting in mode re-ordering.

Electrostatic Stabilization of Thermal Variation in Quality Factor using Anchor Loss Modulation

We report an ultra-low energy dissipation silicon MEMS tuning fork resonator with a Q-factor of over 2 million at 570 Hz, with the ability of Q-factor stabilization throughout a temperature range of over 100 °C. This stabilization approach relies on the controlling of energy dissipation through regulating the stiffness misbalance of the tuning fork resonator. Without Q-factor regulation, the resonator demonstrates a Q-factor with a 25% drift from 2.14 million to 2.67 million, over a temperature range from -40 °C to +60 °C. With implementation of the proposed stabilization method, the experimental characterization reveals a stable Q-factor of 2.14 million within 0.3% (+1σ) variation for an identical temperature range (-40 °C to +60 °C).