Igor P. Prikhodko

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.

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.

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.

Ultra-high Q silicon gyroscopes with interchangeable rate and whole angle modes of operation

We report a new family of ultra-high Q silicon MEMS tuning fork gyroscopes demonstrating angle rate and, for the first time, rate integrating (whole angle) operation. The novel mechanical architecture eliminates low frequency in-phase modes and maximizes the Q-factors. A vacuum packaged SOI dual mass gyroscope with a 1.7 kHz operational frequency demonstrated drive- and sense- mode Q-factors of 0.31 and 0.64 million, respectively. A completely symmetric, dynamically balanced quadruple mass gyroscope with a 2.2 kHz operational frequency demonstrated identical drive- and sense-mode Q-factors of 0.45 million. Due to the stiffness and damping symmetry, the new gyroscope can be 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.

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.

North-finding with 0.004 radian precision using a silicon MEMS quadruple mass gyroscope with Q-factor of 1 million

We demonstrate north-finding capability with a measured 4 milliradian (mrad) 1-σ 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 bias instability of 0.1°/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 limit of the QMG. We also implemented self-calibration methods, including temperature compensation and discreet ±180° turning (“maytagging”) as potential alternatives to the carouseling.

Frequency modulation based angular rate sensor

We report, for the first time, a quasi-digital angular rate sensor based on mechanical frequency modulation (FM) of the input rotation rate. The new approach relies on tracking of the resonant frequencies of two ultra-high Q-factor mechanical modes of vibration in a MEMS vibratory gyroscope to produce a frequency based measurement of the input angular rate. Rate table characterization of the new FM angular rate sensor with quality factors of 1 million revealed a linear dynamic range of 2000 deg/s limited by the setup, with a fundamental performance limit in excess of 72,000 deg/s. 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-Q and wide dynamic range inertial MEMS for north-finding and tracking applications

We report high-Q and wide dynamic range MEMS gyroscopes and accelerometers for development of an IMU capable of north finding and tracking. The vacuum sealed SOI gyroscope utilizes symmetric quadruple mass architecture with measured quality factors of 1.2 million and proven sub-°/hr Allan deviation of bias. The true north detection was accomplished in conventional amplitude modulated (AM) rate mode and showed 3 milliradian measurement uncertainty. The north (azimuth) tracking necessitates a wide dynamic range, for which the same QMG transducer is switched to a frequency modulated (FM) modality. The test results for FM operation experimentally demonstrated a wide linear input rate range of 18,000 °/s and inherent self-calibration against temperature changes. Vertical alignment is possible using resonant accelerometers with a projected bias error of 5 μg and self-calibration against temperature variations, enabled by differential frequency measurements. We believe the developed low dissipation inertial MEMS with interchangeable AM/FM modalities may enable wide dynamic range IMUs for north-finding and inertial guidance applications previously limited to optical and quartz systems.