Sergei A. Zotov

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.

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.

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.

Three-Dimensional Spherical Shell Resonator Gyroscope Fabricated Using Wafer-Scale Glassblowing

We report, for the first time, experimental demonstration of a 3-D spherical shell resonator microelectromechanical systems gyroscope fabricated using wafer-scale glassblowing. The gyroscope utilizes a 1-mm-diameter 10-μm-thick spherical isotropic shell surrounded by eight cofabricated satellite spheres serving as actuation and detection electrodes. To demonstrate functionality of the new device, a four-node wineglass mode at a 945-kHz frequency was utilized as the drive mode of a Coriolis vibratory gyroscope. The input rotation causes the transfer of energy from the drive mode to the sense mode, which is a complementary four-node wineglass mode oriented at a 45 ° angle. Sense-mode vibrations were capacitively detected using cofabricated 3-D metal electrodes. Experimental characterization of the spherical shell gyroscope demonstrated a wide linear range of 1000°/s, currently limited only by the experimental setup.

Foucault pendulum on a chip: angle measuring silicon MEMS gyroscope

We report detailed characterization of a vacuum sealed angle measuring silicon MEMS gyroscope. The new gyroscope utilizes completely symmetric, dynamically balanced quadruple mass architecture, which provides a unique combination of maximized quality (Q) factors and isotropy of both the resonant frequency and the damping. The vacuum sealed SOI prototype with a 2 kHz operational frequency demonstrated virtually identical X- and Y-mode Q-factors of 1.1 million. Due to the stiffness and damping symmetry, and very low dissipation, the gyroscope can be instrumented for direct angle measurements with fundamentally unlimited rotation range and bandwidth. Experimental characterization of the mode-matched gyroscope operated in whole-angle mode confirmed linear response in excess of ±450 °/s range and 100 Hz bandwidth (limited by the setup), eliminating both bandwidth and range constraints of conventional MEMS rate gyroscopes.

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.