Alexander A. Trusov

Environmentally Robust MEMS Vibratory Gyroscopes for Automotive Applications

Automotive applications are known to impose quite harsh environmental conditions such as vibration, shock, temperature, and thermal cycling on inertial sensors. Micromachined gyroscopes are known to be especially challenging to develop and commercialize due to high sensitivity of their dynamic response to fabrication and environmental variations. Meeting performance specifications in the demanding automotive environment with low-cost and high-yield devices requires a very robust microelectromechanical systems (MEMS) sensing element. This paper reviews the design trend in structural implementations that provides inherent robustness against structural and environmental parameter variations at the sensing element level. The fundamental approach is based on obtaining a gain and phase stable region in the frequency response of the sense-mode dynamical system in order to achieve overall system robustness. Operating in the stable sense frequency region provides improved bias stability, temperature stability, and immunity to environmental and fabrication variations.

Sub-degree-per-hour silicon MEMS rate sensor with 1 million Q-factor

We report characterization of a silicon MEMS rate gyroscope with measured sub-deg/hr bias stability, enabled by the quality factor (Q) of 1.1 million. The rate sensor utilizes degenerate, dynamically balanced Quadruple Mass Gyroscope (QMG) design, which suppresses substrate energy dissipation and maximizes Q-factors. We demonstrated a 0.9°/hr in-run bias stability and a 0.06°/√hr rate noise density for the 0.1 mTorr vacuum packaged QMG with a 0.2 Hz mode-mismatch between drive- and sense-modes. This level of noise allowed detection of azimuth with 150 mrad precision, showing feasibility of a QMG for gyrocompassing.

Microscale Glass-Blown Three-Dimensional Spherical Shell Resonators

This paper introduces a new paradigm for design and batch fabrication of isotropic 3-D spherical shell resonators. The approach uses pressure and surface tension driven plastic deformation (glassblowing) on a wafer scale as a mechanism for creating inherently smooth and symmetric 3-D resonant structures. The feasibility of the new approach was demonstrated by fabrication and characterization of Pyrex glass spherical shell resonators with millimeter-scale diameter and average thickness of 10 μm . Metal electrodes cofabricated along with the shell were used to actuate the two dynamically balanced four- and six-node vibratory modes. For 1-MHz glass-blown resonators, the relative frequency mismatch Δf/f between the two degenerate four-node wineglass modes was measured as 0.63% without any trimming or tuning. For the higher order six-node wineglass modes, the relative frequency mismatch was only 0.2%, demonstrating the potential for precision manufacturing. The intrinsic manufacturing symmetry enabled by the technology may inspire new classes of high-performance 3-D MEMS for communication and inertial navigation.

Low-Dissipation Silicon Tuning Fork Gyroscopes for Rate and Whole Angle Measurements

We report a new family of ultra high- Q silicon microelectromechanical systems (MEMS) tuning fork gyroscopes demonstrating angular rate and, for the first time, rate integrating (whole angle) operation. The novel mechanical architecture maximizes the Q-factor and minimizes frequency and damping mismatches. We demonstrated the vacuum packaged SOI dual and quadruple mass gyroscopes with Q-factors of 0.64 and 0.86 million at 2 kHz operational frequency, respectively. Due to the stiffness and damping symmetry, the quadruple mass gyroscope was instrumented to measure the angle of rotation directly, eliminating the bandwidth and dynamic range limitations of conventional MEMS vibratory rate gyroscopes. The technology may enable silicon micromachined devices for inertial guidance applications previously limited to precision-machined quartz hemispherical resonator gyroscopes.

Multi-Degree of Freedom Tuning Fork Gyroscope Demonstrating Shock Rejection

This paper presents a z-axis MEMS tuning fork rate gyroscope with multi-degree of freedom (DOF) sense modes designed to provide structural robustness to environmental drifts. This concept combines the temperature robustness of multi-DOF sense modes with the common mode rejection capabilities of tuning fork architectures. The device consists of an antiphase actuated 2-DOF drive mode where each drive mass contains a 2-DOF sense mode, thus forming an overall 6-DOF mechanical system. The flat gain region of the 2-DOF sense mode provides immunity to both environmental variations and fabrication imperfections, while the anti-phase forcing of the drive mode induces an anti-phase Coriolis response allowing for the cancellation of common mode inputs such as ambient vibrations. Impulse responses were used to characterize the effect of acceleration loads on the device where a differential signal resulted in 14 dB of reduction in amplitude versus a single output.

High-Range Angular Rate Sensor Based on Mechanical Frequency Modulation

We report, for the first time, an angular rate sensor based on mechanical frequency modulation (FM) of the input rotation rate. This approach tracks the resonant frequency split between two X - Y symmetric high-Q mechanical modes of vibration in a microelectromechanical systems Coriolis vibratory gyroscope to produce a frequency-based measurement of the input angular rate. The system is enabled by a combination of a MEMS vibratory high-Q gyroscope and a new signal processing scheme which takes advantage of a previously ignored gyroscope dynamic effect. A real-time implementation of the quasi-digital angular rate sensor was realized using two digital phase-locked loops and experimentally verified using a silicon MEMS quadruple mass gyroscope (QMG). Structural characterization of a vacuum- packaged QMG showed Q factors on the order of one million over a wide temperature range from -40 °C to +100°C with a relative x/y mismatch of Q of 1 %. Temperature characterization of the FM rate sensor exhibited less than 0.2% variation of the angular rate response between 25°C and 70 °C environments, enabled by the self-calibrating differential frequency detection. High-speed rate table characterization of the FM angular rate sensor demonstrated a linear range of 18 000 deg/s (50 r/s, limited by the setup) with a dynamic range of 128 dB. Interchangeable operation of the QMG transducer in conventional amplitude- modulated and new FM regimes provides a 156-dB dynamic range.

What is MEMS Gyrocompassing? Comparative Analysis of Maytagging and Carouseling

North-finding based on micromachined gyroscopes is an attractive possibility. This paper analyzes north-finding methods and demonstrates a measured 4 mrad standard deviation azimuth uncertainty using an in-house developed vibratory silicon MEMS quadruple mass gyroscope (QMG). We instrumented a vacuum packaged QMG with isotropic Q-factor of 1.2 million and Allan deviation bias instability of 0.2 °/hr for azimuth detection by measuring the earths rotation. Continuous rotation (“carouseling”) produced azimuth datapoints with uncertainty diminishing as the square root of the number of turns. Integration of 100 datapoints with normally distributed errors reduced uncertainty to 4 mrad, beyond the noise of current QMG instrumentation. We also implemented self-calibration methods, including in-situ temperature sensing and discrete ±180° turning (“maytagging” or two-point gyrocompassing) as potential alternatives to carouseling. While both mechanizations produced similar azimuth uncertainty, we conclude that carouseling is more advantageous as it is robust to bias, scale-factor, and temperature drifts, although it requires a rotary platform providing continuous rotation. Maytagging, on the other hand, can be implemented using a simple turn table, but requires calibration due to temperature-induced drifts.

Effects of Operational Frequency Scaling in Multi-Degree of Freedom MEMS Gyroscopes

This paper analyzes the design tradeoffs associated with increasing the operational frequency of single-axis microelectromechanical systems (MEMS) gyroscopes with multi-degree of freedom (DOF) sense modes. Previously, a z-axis multi-DOF gyroscope (1-DOF drive, 2-DOF sense) was shown to be robust to thermal variations using a prototype with a subkilohertz operational frequency; automotive applications, however, require higher frequencies of operation to suppress the effect of ambient vibrations. To study scaling effects on the multi-DOF concept, design equations were obtained in terms of operational frequency. These revealed a constraint on system parameters that introduces two scaling methods that dictate a tradeoff between gain, die size, and sense capacitance. Second generation multi-DOF gyroscopes were designed and fabricated resulting in 0.7-, 3.1-, and 5.1-kHz devices with smaller sense mode resonant frequency spacings than previously achievable. Experimental rate characterization resulted in scale factors of 14.2, 5.08, and 2.34 mu V/deg /s, respectively, confirming the predicted scaling effects while also demonstrating the feasibility of increased frequency multi-DOF gyroscopes.

Achieving Sub-Hz Frequency Symmetry in Micro-Glassblown Wineglass Resonators

We demonstrate, for the first time, sub-1 Hz frequency symmetry in micro-glassblown wineglass resonators with integrated electrode structures. A new fabrication process based on deep glass dry etching was developed to fabricate micro-wineglasses with self-aligned stem structures and integrated electrodes. The wineglass modes were identified by electrostatic excitation and mapping the velocity of motion along the perimeter using laser Doppler interferometry. A frequency split (Δf) of 0.15 and 0.2 Hz was demonstrated for n=2 and n=3 wineglass modes, respectively. To verify the repeatability of the results, a total of five devices were tested, three out of five devices showed . Frequency split stayed below 1 Hz for dc bias voltages up to 100 V, confirming that the low frequency split is attributed to high structural symmetry and not to capacitive tuning. High structural symmetry and atomically smooth surfaces (0.23 nm Sa) of the resonators may enable new classes of high performance 3-D MEMS devices, such as rate-integrating MEMS gyroscopes.

Folded MEMS Pyramid Inertial Measurement Unit

This paper reports a new approach for design and fabrication of chip-level inertial measurement units (IMUs). The method utilizes a 3-D foldable silicon-on-insulator (SOI) backbone with in-situ fabricated high-aspect-ratio sensors. A planar multisensor unit was fabricated and subsequently folded in a pyramidal shape, forming a compact IMU. Inertial characterization of the sensors integrated on the IMU pyramid was performed at atmospheric pressure. Structural rigidity and sensor axis alignment stability of the folded IMUs have been characterized under various environmental conditions, including vibration, thermal loading, thermal shock, and constant acceleration. The maximum angular misalignment due to variation in environmental conditions between IMU pyramid sidewalls was shown to be less than 4 and 0.2 mrad for epoxy and solder reinforced structures, respectively. Vibration testing revealed no resonances up to 10 kHz in the assembled 3-D structures. Our results confirm feasibility of the fabrication approach.