ULTRA HIGH QUALITY FACTOR AND WIDE DYNAMIC RANGE INERTIAL MEMS FOR NORTH-FINDING AND TRACKING APPLICATIONS

ULTRA HIGH QUALITY FACTOR AND WIDE DYNAMIC RANGE INERTIAL MEMS FOR NORTH-FINDING AND TRACKING APPLICATIONS Alexander A. Trusov MicroSystems Laboratory, University of California, Irvine, USA Alex.Trusov@gmail.com, http://www.alexandertrusov.com, http://mems.eng.uci.edu ABSTRACT We report high-q and wide dynamic range MEMS gyroscopes and accelerometers for development of a very compact IMU capable of North finding and tracking over dynamic environment. The vacuum packaged SOI rate sensors utilize symmetric Quadruple Mass Gyroscope (QMG) 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 measuring mode and showed 0.003 radian measurement uncertainty. The North (azimuth) tracking over dynamic environment 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 of the IMU and acceleration sensing is enabled using resonant accelerometers with 5 μg performance. The accelerometer is self-calibrated 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 systems based on optical and quartz inertial sensors. I. INTRODUCTION North-finding with 0.001 radian (1 mrad) precision and tracking of azimuth in a wide dynamic range is required for targeting, dead reckoning, and inertial guidance applications [1]. North identification is traditionally accomplished using the magnetic fi eld of the Earth. However, there are a number of spatial and temporal distortions in the magnetic field, which limit the accuracy of this method. Practical limitations of alternatives such as geodetic, celestial, and GPS-based methods make high performance gyroscopes desirable for true North seeking, or gyrocompassing. Although conventional fiber optic, ring laser, and macro-scale quartz hemispherical resonator gyroscopes can be used for precision gyrocompassing, they are not perfectly suited for man-portable and small platform applications. MEMS, in contrast, have a number of b e n e f i t s they are lightweight, low-power, batch fabricated, and are have the potential to enable very small and low cost IMU and INS technologies. Gyrocompassing typically requires better than 0.05 /hr total bias error over temperature variations Fig. 1: Photograph of a pyramid inertial measurement unit (IMU) prototype comprising MEMS quadruple mass gyroscopes and resonant accelerometers. Table 1: Comparison of the 3 main design parameters for 3 different architectures of MEMS gyroscopes (Tuning Fork Gyroscope, Disk Resonator Gyroscope, and Quad Mass Gyroscope). for repeatable measurements of the Earth s rate and 0.1 mg total bias error for vertical alignment. Several groups have reported silicon MEMS gyroscopes with sub /hr Allan deviation of bias [2-7]. However, single digit mrad North-finding and tracking over dynamic environment is still view as unattainable by MEMS technology [8]. We propose to tackle this issue using the recently developed Quadruple Mass Gyroscope (QMG) [9] and a new resonant accelerometer, with the resolution enhanced by high Q- factors and wide dynamic range provided by frequency modulated (FM) operation, which is also robust to temperature variations and shocks. Fig. 1 shows a photograph of a pyramid inertial measurement unit (IMU) prototype comprising MEMS Quadruple Mass Gyroscopes and resonant accelerometers. This review paper is based on our recent publications [6, 7, 9-14] and intends to provide a summary of the high performance inertial MEMS development at the University of California, Irvine MicroSystems Laboratory during the period from approximately 2008 to 2012. II. QUADRUPLE MASS GYROSCOPE (QMG) Ultra-high sensitivity silicon MEMS rate sensors are desired for inertial navigation and North-finding

Fig 3: Photograph of a vacuum packaged QMG used in the experiments. Insets: die before sealing of the ceramic package; glass lid wafer with getters. Fig. 4: Block diagram of QMG signal processing for rate measurements, showing drive- and sense-mode control loops. Fig. 2: SEM image of a fabricated SOI Quadruple Mass Gyroscope or QMG (die size is 8.6 8.6 mm). applications. An optimal architecture of a high resolution vibratory rate gyroscope comprises a symmetric mechanical structure with combination of very high Q-factors and decay time constant, high Coriolis coupling (angle gain), drive- and sense-mode degeneracy, and frequency tuning capability [4]. Most of these requirements can be satisfied by continuous structures such as disks or rings operated in balanced wine-glass modes. However, optimization of the performance parameters for such architectures is challenging due to the inherent coupling of the natural frequency, Q- factor, and drive-amplitude, Table 1. Frequency trimming and tuning is also quite nontrivial for solid structures as both mass and stiffness are collocated. An alternative approach investigated in this work is to use a lumped, four quadrant symmetric QMG architecture [12], Fig. 2. It comprises four symmetrically decoupled tines synchronized by anti-phase lever mechanisms, providing a unique combination of ultra-low energy dissipation due to the elimination of anchor loss and isotropy of both the resonant frequency and damping. The QMG is expected to provide ultra-high Q-factors and enable high precision rate measurements. II-A. Rate Sensitivity Analysis and Optimization The operating principle of a vibratory MEMS gyroscope is based on energy transfer between two vibratory modes. The drive-mode is continuously excited at resonance, and the sense-mode is used for rate detection. The amplitude of the sense-mode motion (y) is proportional to the rotation rate ( z ), with the angular gain factor (0 < k 1) and the driveamplitude (x): y 2Qeff k z x y, (1) where y is the resonant frequency. Here, Q eff is the gain of the sense-mode at the drive-mode frequency: Q Q 2 1 4Qy ( y eff y, (2) which reaches maximum Q y for zero mismatch ( = 0). It follows from (1) that the rate sensitivity is enhanced by maximizing the Q-factor and reducing the resonant frequency. Q-factors above 100,000 were previously realized for both continuous and lumped type MEMS gyroscopes [12, 15]. In contrast to continuous structures, lumped, mass-spring type devices operate at lower frequencies, and thus, promise superior rate sensitivity. For instance, the scale factor improves by 60 db for a 1 khz operational sensor com- ) 2

pared to a 1 MHz sensor. The trade-off between frequency and sensitivity is a limited bandwidth, which can be resolved by operating in a closed loop, or force-rebalance (FRB) mode. In addition, massspring, lumped architectures can provide high Coriolis coupling (k ~ 1) and large amplitude of motion (up to 10 microns), which also increase the rate sensitivity. Based on these considerations, we investigate a lumped design approach for high precision applications. II-B. Mechanical Design and Symmetry Mode-matched operation over a wide temperature range is desired for high-q MEMS gyroscopes. Frequency mismatch induced by fabrication imperfections is typically compensated by electrostatic tuning, which often requires high voltages and active controls. In this work, we evaluate a design-level solution, where structural symmetry of the lumped mechanical element provides identical drive and sense temperature coefficients of frequency for increased robustness to the temperature-induced drifts [13]. The recently introduced lumped Quadruple Mass Gyroscope architecture, Fig. 2, comprises four identical tines, four linear coupling flexures, and a pair of lever mechanisms for synchronization of the antiphase drive- and sense-mode motion. Momentum and torque balance in both x and y directions is expected to provide ultra-low dissipation of energy through the substrate, leading to a high resolution and equal ultrahigh Q-factors, Q x = Q y > 1 million. Symmetric lever mechanisms and flexures ensure low operational frequency (~ 2 khz), as well as the common mode rejection of input accelerations, both required for high precision rate measurements. II-C. MEMS Fabrication and Vacuum Packaging Stand-alone prototypes of the QMG were fabricated using an in-house 100 m SOI process with 5 m minimal gap size. The rate sensor was packaged using custom technology for robust vacuum sealing of the high-q gyroscopes [16], Fig. 3. First, the QMG die was attached to a ceramic 24-pin package using eutectic solder and wire bonded. The device was then sealed at sub-mtorr vacuum, preceded by the getter activation on a glass lid. II-D. Interface and Control Electronics All experiments were performed using a custom PCB connected to a FPGA-based DSP unit. The vacuum packaged sensor was mounted on a PCB with front-end electronics and installed on a 1291BR Ideal Aerosmith rate table inside the thermal chamber. Electrostatic capacitive actuation and detection were employed along with the EAM technique for the parasitic feedthrough elimination. All control and signal processing were realized using a LabView programmable, FPGA-based HF2 unit from Zurich Instruments. Fig. 5: Experimental characterization of the packaged QMG using ring-down tests, revealing identical drive- and sense-mode Q-factors of 1.17 million (with Q/Q of 1 %). Fig. 6: Measured Q vs. temperature for a packaged QMG. The 1/T 3 dependence is attributed to the thermoelastic dissipation. Q-factors > 0.7 M were observed up to 100 C. Fig. 4 depicts drive- and sense-mode control loops used for high precision angular rate measurements. The PLL-based drive-loop sustained oscillation at resonance and provided reference for the sideband demodulations. The AGC stabilized the amplitude of drive-mode motion. Rotation was detected by demodulating the sense-mode signal. Rate was proportional to a feedback force used to null the Coriolis induced motion (FRB loop). The rate measurements were performed at a 0.2 Hz separation between driveand sense-mode frequencies. II-E. QMG Experimental Characterization The damping and frequency symmetry of the stand-alone QMG prototype with a 2 khz operational frequency was evaluated using ring-down tests in a TestEquity 107 thermal chamber. Fig. 5 shows measured time-domain amplitude decays of both mechanical modes at the room temperature. Exponential fits revealed identical drive- and sense-mode Q-factors of

the packaged QMG sensor performed under a 0.2 Hz frequency mismatch in the input angular rate range of 45 /hr, demonstrating the linearity and ability to measure rates on the order of Earth s rotation. Fig 7: Measured linear rate response in 45 /hr range. Inset: time history of a gyro output with 15 /hr increments. Fig. 8: Allan deviation of the QMG rate sensor used in this work, revealing a 0.07 / hr ARW, and a 0.22 /hr bias stability in rate measuring AM mode. 1.17 million with Q/Q variation of 1 % before tuning or compensation, confirming the complete structural symmetry. The measured Q value of 1.17 million is within 90% of the 1.3 million thermoelastic limit estimated by finite element modeling for the QMG design. The ultra-high Q-factor translates into the fundamental mechanical-thermal resolution limit of 0.01 /hr/ Hz for a mode-matched case. The temperature sensitivity of frequency and Q- factor were characterized in the range from 5 C to 100 C. Isotropic Q-factors above 0.7 million were experimentally observed up to 100 C for a packaged QMG, Fig. 6. The fit to the Q(T) data revealed 1/T 3 dependence, suggesting that the dominant energy loss mechanism is thermoelastic dissipation [17]. Frequency symmetry of the QMG design was previously evaluated in [12], and confirmed closely matched TCFs of 22.6 0.2 ppm/ C for both modes. The ultra low dissipation design and closed loop operation of the QMG are expected to provide low noise rate performance. Fig. 7 shows rate response of III. NORTH FINDING AND TRACKING The QMG transducer [9, 13] was chosen for the IMU development due to its symmetric design with low energy dissipation and isotropy of both frequency and damping. Stand- alone QMGs were fabricated using an in-house silicon-on- insulator (SOI) process with a 100 μm device layer and a 5 μm sacrificial oxide. Singulated devices were vacuum sealed using a ceramic package technology with getters, providing asub-mtorr vacuum sustainable over many years. Mechanical characterization of the packaged QMGs using ring-down tests showed drive- and sense-mode Q-factors of 1.2 million, with ΔQ/Q symmetry of 1% [11]. The high Q-factor translates into an exceptional mechanical-thermal resolution limit of 0.0001 / hr for mode-matched operation, suggesting feasibility of the sensor for gyrocompassing applications. Thermal cycling confirmed Q-factor above 0.7 million for temperatures up 100 C (with Q of 1.7 million for 20 C) [6]. The noise performance of the gyroscope used in this work was evaluated using the Allan deviation analysis. Fig. 8 shows current test results for the conventional amplitude modulated (AM) rate measuring mode [6], without temperature calibration. The QMG demonstrated angle random walk (ARW) of 0.07 / hr (4.2 /hr/ Hz), in-run bias of 0.22 /hr, and rate random walk (RRW) of 0.3 /hr/ hr (0.005 /hr Hz). Next, we demonstrate that the low level of noise the QMG allows North detection based on the Earth s rotation measurements. The true North orientation (as opposed to the magnetic North) is found by observing the horizontal component of the Earth s rotation vector. We implemented both maytagging and carouseling of a gyroscope on a rotary platform for North-finding. III-A. North-Finding Using Maytagging Maytagging is discrete ±180 turning of the gyroscope sensitive axis, which allows for differential azimuth detection. Following this approach, we mounted the QMG with its input axis horizontal on a rotary platform and separated the Earth s rotation rate from the sensors bias by a virtue of 0 to 180 turns. By combining the east (0 ) and west (180 ) readings of platform heading, both azimuth (North direction) and the gyroscope bias were recovered. The differential maytagging approach is effective for the constant bias. In practice, however, bias was time-varying and residues were still present in azimuth measurements, Fig. 9 inset. The detailed analysis confirmed temperature variations to be the primary drift source. Temperature self-compensation using the gyroscope frequency as an embedded thermometer resolved normal distribu-

Fig. 9: Azimuth histogram with normal distribution fit after temperature self-compensation, showing a 40 mrad error of maytagging. Inset: raw histogram. Fig. 10:. Azimuth uncertainty as a function of filtered measurements. A 3 mrad error is achieved after 150 data points. Inset: Earth s rotation measurements tion of measurement errors. The azimuth uncertainty of 100 repeated measurements was 40 mrad before filtering or averaging [7], Fig. 9. III-B. North-Finding Using Carouseling The continuous modulation of the constant Earth s rate for separation from the sensor bias is also possible as an alternative to the 2-point discrete azimuth measurement ( may- tagging ). The continuous rotation or carouseling mechanization of the platform allows identification of azimuth angle, bias and scale-factor error. Specifically, the true North was detected by rotating the QMG sensitive axis in a horizontal plane with a 1 /s rate, which modulates the Earth s constant rate with a 6 minute period, Fig. 10 inset. Every 6 minutes the azimuth was extracted from a sinusoidal fit. Probability analysis of the measurements revealed a Gaussian error model without any temperature calibration [7]. By filtering a sequence of multiple azimuth measurements, a progressively more precise azimuth was obtained (beyond the resolution of the gyroscope). The measurement uncertainty scaled Fig. 11: Schematic of the gyroscope operation based on the mechanical FM of the input angular rate. Inertial rotation causes a split between the gyroscope s two vibratory modes, producing an FM measure of the input rate. down as the square root of the number of turns, Fig. 10. The experiment achieved a 3 mrad uncertainty by averaging of 150 azimuth data points. Ongoing improvements in the gyroscope layout and electronics are projected to reduce the 3 mrad gyrocompassing time down to one minute. III-C. FM Gyroscope Operating Principle While North-finding necessitates a very low noise and narrow range sensor, North-tracking and navigation through fast motion adds the requirements for wide dynamic range and robustness. The QMG transducers address these challenges by switching between the high resolution AM and wide range FM measurement modalities [10]. The frequency modulation (FM) approach tracks the resonant frequency split between two symmetric high-q mechanical modes of vibration in the QMG transducer to produce a frequency based measurement of the input angular rate with inherent self-calibration against temperature variations, Fig. 11. The FM operation mode eliminates the gain-bandwidth and dynamic range trade-off of conventional AM gyroscopes and enables signal-to-noise ratio improvements by taking advantage of high-q transducer without limiting the measurement range and bandwidth. III-D. Wide Dynamic Range Demonstration The proposed FM gyroscope operation provides a wide input rate range, limited only by the natural frequency of a mechanical element [11]. For the experimental validation, a vacuum packaged QMG was mounted on an Ideal Aero- smith High-Speed Position and Rate Table System 1571, and characterized from 0 to 18,000 /s (50 revolutions per second). Without any compensation, the FM instrumented QMG demonstrated less than 0.2% nonlinearity throughout the entire range, Fig. 12.

Fig. 12: Experimental characterization of the QMG in FM mode reveals less than 0.2% nonlinearity in a wide input range of 18,000 /s. Fig. 14: Photograph of a differential FM accelerometer fabricated using an in-house 100 µm SOI process. Arrows show sensitivity to acceleration and temperature. Fig. 13: Rate characterization of the QMG in FM mode shows no drift in the response for 25 C and 70 C despite a 30% reduction in Q-factor and a 5 Hz drop of nominal frequency (without any temperature compensation). Theoretical analysis of the proposed FM rate sensor also suggests immunity against the temperatureinduced drifts by virtue of the differential frequency detection, i.e. by measuring the frequency split [10]. To experimentally investigate this concept, a vacuum packaged QMG sensor operated in FM mode was characterized on a temperature controlled Ideal Aerosmith 1291BR rate table. Without any active temperature compensation, experimental characterization of the FM instrumented QMG revealed less than 0.2% scale-factor change from 25 C to 70 C, Fig. 13. Despite a 30% reduction of the Q-factor and a 5 Hz change of the nominal frequency, the scale-factor sensitivity was less than 50 ppm/ C (limited by the experimental setup noise), demonstrating temperature robustness of the differential FM measurements. The interchangeable AM/FM operation of the QMG sensor is expected to provide wide dynamic range for North-finding and North-tracking applications. The measured 0.22 /hr bias instability of the AM mode combined with the measured ±18,000 /s linear range of the FM mode enables the dynamic range of at least 170 db. This makes a single high-q MEMS transducer fitted for demanding high precision and wide input range applications. Fig. 15: Concept of the differential FM accelerometer with temperature self-calibration. Arrows show axes of sensitivity to external acceleration and temperature. IV. SILICON ACCELEROMETER WITH DIFFERENTIAL FREQUENCY MODULATION While silicon MEMS accelerometers have proven themselves as commercially successful devices, significant challenges remain in bringing them to high performance, mission critical applications. Conventional micromachined pendulous accelerometers operate as analogue Amplitude Modulated (AM) systems, with an inherent gain-bandwidth tradeoff and dynamic range limited by the stability of capacitive pickoff electronics. These analogue devices typically show poor long term and environmental stability. Packaging requirements for the highly damped pendulous accelerometers contradict the vacuum sealing requirements of high performance MEMS gyroscopes, complicating potential single die integration. Another inherent disadvantage of conventional MEMS sensors using amplitude-modulated signals comes from the limited dynamic range, the ratio between the full-scale linear range and the smallest detectable input stimulus change. In the best case scenario, AM capacitive readout with carefully selected low-noise electronic components can only achieve a dynamic range of 10^6, with a practical limit of 10^5. This means that achieving a better than 10^6 dynamic range and 1 ppm stability (requirement of the navigation grade) is practically impossible with conventional MEMS sensors architectures. These fundamental limitations on the dynamic range and output stability prevent the use of MEMS gyroscopes and accelerometers

(a) Anti-phase mode at 2.6 khz, Q TED =O.3 million. Fig. 17: Photograph of a differential FM accelerometer fabricated using an in-house 100 µm SOI process. (b) In-phase mode at 0.9 khz. Fig. 16: Finite Element Modeling (FEM) results illustrating the (a) anti-phase and (b) in-phase vibratory modes of the FM accelerometer. in many important applications. An alternative approach to resolving these limitations is using a frequency-modulated accelerometer, where induced acceleration changes the resonant frequency of the device due to changes in the total effective stiffness [18, 19]. Performance of previously reported FM accelerometers is limited by relatively low Q-factors and temperature dependency. The main challenge to overcome in silicon MEMS accelerometers with FM operation is temperature sensitivity of the resonant frequency, caused by the strong temperature dependency of the silicon's Young's modulus. In this paper we propose a wide dynamic range, differential FM accelerometer architecture with tunable scale factor and inherent self-calibration against dynamic environment changes, Fig. 14. The differential FM accelerometer approach relies on tracking of the resonant frequencies of two high-q mechanical MEMS oscillators to produce quasi-digital and decoupled FM measurements of the input acceleration and temperature, Fig. 15. IV-A. Sensor Concept and Design The proposed differential FM accelerometer consists of two identical silicon MEMS tuning fork resonators. Each of the two resonators has two mechanical degrees of freedoms: in-phase and anti-phase motion of the coupled tines. The anti-phase mode of the resonator is dynamically balanced, eliminating dissipation of energy due to linear and angular vibrations of the substrate. Increase of the Q-factor up to the fundamental thermoelastic limit improves precision, stability, and phase noise for the anti-phase vibration. In Fig. 18: Photograph of a packaged differential FM accelerometer assembled with signal conditioning PCBs. contrast, the in-phase vibration has a low Q-factor, which is limited by the anchor loss [20]. Each tine includes differential lateral comb electrodes for electrostatic excitation of the anti-phase mode, differential lateral comb electrodes for capacitive detection, and non-differential parallel plate capacitors for modulation of stiffness by means of the negative electrostatic spring effect. By applying a DC voltage bias on the parallel plates, a negative electrostatic spring is created, the stiffness of which is proportional to the square of the bias voltage and inversely proportional to the cube of the capacitive gap. This makes the anti-phase natural frequency highly sensitive to the gap between the fixed and moving parallel plate electrodes. In other words, the in-phase displacement of the two tines modulates the resonant frequency of the anti-phase mode. Finite Element Modeling (FEM) was completed using Comsol Multiphysics to determine the vibratory modes of this device. The 2-D model of the device consists of 296,000 triangular mesh elements, the structure of which was imported from the lithography mask used to create the actual device, Fig. 16. Because the device moves only along the x-axis and is fabricated from single crystalline silicon, a uniform

Fig. 19: Measured input-output characteristic of FM accelerometer for different stiffness modulation DC voltages. Inset: scale factor vs. modulation DC voltage. Young's Modulus was used with a value of 160 GPa. The in-phase and anti-phase resonance frequency were found to be 0.9 khz and 2.6 khz, respectively. Through the suspension system design, the next mode of vibrations was pushed to 25 khz frequency to minimize cross axis sensitivity. A second FEM model was then executed to analyze the fundamental thermoelastic limit of the Q-factor. For the anti-phase mode of vibrations, a Q-factor of 0.3 million was predicted. IV-B. Self-Calibration through Differential FM The proposed temperature self-calibration approach takes advantage of the differential design, in which both oscillators have the same sensitivity to temperature but opposite sensitivity to external acceleration, Fig. 14 and 15. The dependency of frequency on temperature has a well known linear relationship for single crystalline silicon, enabling direct selfsensing of temperature. The differential FM signal processing tracks the frequency difference between the two resonant accelerometers, enabling drift free measurement of acceleration, Fig. 15. In this approach, the FM accelerometer provides a quasi-digital measurement of the input acceleration as well as direct measurement of the accelerometer temperature. The sensor becomes its own thermometer, eliminating thermal lags and hysteresis typical in compensation schemes using an external temperature sensor. V-C. FM Accelerometer Characterization The fabrication of prototype FM accelerometers was performed using an in-house, wafer-level, single mask process. Devices were fabricated using Siliconon-Insulator (SOI) wafers with a 100 μm single crystalline silicon device layer, a 5 μm buried oxide layer, and a 500 μm handle wafer, Fig. 17. After wafer fabrication and dicing, sensors were attached to a ceramic DIP-24 package, wirebonded, and vacuum sealed in-house at ~1 Torr. In future fabrication runs, accelerometers will be vacuum sealed at 0.1 mtorr using getter to enable ultra-high Q-factor operation. For testing, the packaged sensors were assembled with signal conditioning electronics, Fig. 18. Fig. 20: Measured output of two differential FM channels during dynamic temperature ramp. Bias drifts track each other, enabling self-calibration. Fig. 21: Measured differential FM output during a dynamic temperature ramp, showing self-calibration against temperature with a low drift rate of 30 µg/hr. A standard multi-point tumble test was carried out for a single tuning fork (non-differential) FM accelerometer using an Ideal Aerosmith 2102 Series Two-Axis Position and Rate Table System. The sensor was tested by measuring the change of the antiphase resonant frequency as a function of inclination angle with 10 o increments. The resonance frequency of the accelerometer was recorded for each orientation within a range from -g to g. This experiment was performed for three different tuning voltages (28, 25 and 20 V), revealing linear response to acceleration with tunable scale factors of 4.4, 2.0 and 1.2 Hz/g, respectively, Fig. 19. To evaluate the proposed self-calibration concept, a differential FM accelerometer with two tuning fork oscillators was placed into a TestEquity 107 temperature chamber. The temperature was set to 70 C for the duration of 3 hours. The temperature control was then turned off and the output signals from both tuning forks were recorded Fig. 20. Each oscillator showed an identical 500 mg drif over the temperature change. Differential FM demodulation provided automatic calibration against temperature by canceling common frequency drifts between the two sensors. As shown in Fig. 21, the drift over temperature was reduced to approximately 1 mg, currently limited by the noise performance of oscillators sealed with 1 Torr

(a) Measured resonant frequencies f1,2 as a function of the input acceleration for 30 C and 75 C. Differential frequency split f1-f2 is invariant to temperature. (b) Measured acceleration responses for 30 C and 75 C using the differential frequency split. Fig. 22: Characterization of the differential FM accelerometer at 30 C and 75 C, demonstrating selfcalibration to temperature. There is less than 0.5% response fluctuation. pressure. Testing of differential FM accelerometers sealed with getter is expected to improve the bias several orders of magnitude. Self-calibration by differential FM also applies to the scale factor. The anti-phase resonant frequencies of both tuning fork oscillators were characterized as functions of applied acceleration at two different temperatures of 30 C and 75 C, Fig. 22(a). The measured frequency split between the nominally equal modal frequencies was proportional to the input acceleration, Fig. 22(b). Without any active temperature compensation, experimental characterization of the FM accelerometer at 30 C and 75 C revealed less than 0.5 percent response fluctuation (within the accuracy of the experimental setup) despite a 4 Hz drop of the nominal frequency, Fig. 22(b). Allan deviation analysis of FM accelerometer inrun performance at constant temperature is shown in Fig. 23. For a single tuning fork (non-differential) FM accelerometer, three regimes are identified: a -1/2 slope white noise of frequency for time constants of several seconds, a zero slope flicker noise floor, and a +1 slope temperature ramp at time constants above 10 seconds. Differential FM demodulation using two Fig. 23: Measured Allan deviation for a vacuum sensor. Differential FM demodulation removes temperature ramp and achieves a 6 µg bias at 20 sec. tuning forks removes the +1 slope temperature ramp, revealing the bias instability of 6 µg at 20 s. In combination with the design linear range of 20 g, the sensor demonstrates a wide dynamic range of 130 db dynamic range. V. CONCLUSIONS We demonstrated low dissipation silicon MEMS gyroscopes and accelerometers with interchangeable AM/FM modality for wide dynamic range IMU development. The current performance results for vacuum sealed Quadruple Mass Gyroscope (QMG) showed Q-factors of 1.2 million and total bias error of 0.5 /hr over temperature variations [7]. Continuous rotation ( carouseling ) and discrete ±180 turning ( maytagging ) were implemented for true North detection, demonstrating a 3 mrad azimuth uncertainty. Once North has been identified, it can be tracked by the same transducer using FM method of detection with a proven 170 db dynamic range. Vertical alignment and acceleration sensing is enabled by the proposed resonant accelerometers, with accuracy ensured by differential frequency measurements of the acceleration. Inspired by the progress on the low dissipation inertial MEMS, we are currently developing a multiaxis MEMS based IMU with inherently quasi-digital FM operation, Fig. 24. Currently we are developing a single-die system comprising a gyroscope and two resonant accelerometers in a shared vacuum package. Due to the inherent FM nature of the system, it is expected to provide dynamic range and stability unprecedented in conventional inertial MEMS, while simultaneously reducing the power consumption of the analog-digital interface. VI. ACKNOWLEDGMENTS The author would like to thank his collaborators and colleagues at the University of California, Irvine MicroSystems Laboratory. Especially valuable contributions to this work were made by Prof. Andrei M. Shkel, Dr. Sergei A. Zotov, Dr. Gunjana Sharma, Igor P. Prikhodko, and Brenton R. Simon. The work has

Fig. 24: Single chip multi-axis MEMS IMU combining wide dynamic range gyroscopes and accelerometers with frequency modulated operation. Total die size is 1 by 1 cm. been supported by various grants from NSF, NSWCDD, DARPA, and SPAWAR. The author would also like to acknowledge valuable assistance from several exceptional vendors, including Dr. Flavio Heer and Stephan Senn of Zurich Instruments, Heather Florence of SAES Getters, Zappella Pierino and David Muhs of SST International. The gyroscopes and accelerometers were designed and characterized at the MicroSystems Laboratory, University of California, Irvine. VII. REFERENCES [1] A. Shkel, Microtechnology comes of age, GPS World, pp. 43 50, 2011. [2] B. Johnson, E. Cabuz, H. French, and R. Supino, Development of a MEMS gyroscope for Northfinding applications, in Proc. ION Position, Location and Navigation Symposium, may 2010, pp. 168 170. [3] W. Geiger et al., MEMS IMU for AHRS applications, in Proc. ION Position, Location and Navigation Symposium, May 2008, pp. 225 231. [4] K. Shcheglov, DRG a high performance MEMS gyro, in Joint Precision Azimuth Sensing Symposium, Las Vegas, NV, Aug. 2 4, 2010. [5] M. Zaman, A. Sharma, Z. Hao, and F. Ayazi, A modematched silicon yaw tuning-fork gyroscope with sub degree-per-hour Allan deviation bias instability, Journal of Microelectromechanical Systems, vol. 17, no. 6, pp. 1526 1536, dec. 2008. [6] I. Prikhodko, S. Zotov, A. Trusov, and A. Shkel, Subdegree-per-hour silicon MEMS rate sensor with 1 million Q-factor, in Proc. 16th International Conference on Solid- State Sensors, Actuators and Microsystems (TRANSDUC- ERS 11), June 2011, pp. 2809 2812. [7] I. Prikhodko, A. Trusov, and A. Shkel, North-finding with 0.004 radian precision using a silicon MEMS quadruple mass gyroscope with Q-factor of 1 million, in Proc. IEEE Int. Conf. Micro-Electro-Mechanical Systems 2012, Paris, France, Jan. 29 Feb. 2, 2012, pp. 164 167. [8] F. Ayazi, Multi-DOF inertial MEMS: From gaming to dead reckoning, in Proc. 16th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANS- DUCERS 11), June 2011, pp. 2805 2808. [9] A. Trusov, I. Prikhodko, S. Zotov, and A. Shkel, Lowdissipation silicon tuning fork gyroscopes for rate and whole angle measurements, Sensors Journal, IEEE, vol. 11, no. 11, pp. 2763 2770, nov. 2011. [10] S. Zotov, I. Prikhodko, A. Trusov, and A. Shkel, Frequency modulation based angular rate sensor, in Proc. IEEE Int. Conf. Micro-Electro- Mechanical Systems, Cancun, Mexico, Jan. 23 27, 2011, pp. 577 580. [11] S. Zotov, A. Trusov, and A. Shkel, Demonstration of a wide dynamic range angular rate sensor based on frequency modulation, in Proc. IEEE Sensors 2011 Conf., Oct. 2011, pp. 149 152. [12] A. Trusov et al., Ultra-high Q silicon gyroscopes with interchangeable rate and whole angle nodes of operation, Proc. IEEE Sensors 2010, pp. 864-867. [13] A. Trusov et al., Micromachined tuning fork gyroscopes with ultra-high sensitivity and shock rejection, US Patent 8,322,213. [14] S. Zotov, A. Trusov, A. Shkel, "High-range angular rate sensor based on mechanical frequency modulation," IEEE/ASME JMEMS, vol. 21, no. 2, April 2012, pp. 398-405. [15] H. Johari et al., High frequency XYZ-axis single-disk silicon gyroscope, Proc. IEEE MEMS 2008, 856-859. [16] A. Schofield et al. Versatile sub-mtorr vacuum packaging for the experimental study of resonant MEMS, Proc. IEEE MEMS 2010, pp. 516-519. [17] B. Kim et al., Temperature dependence of quality factor in MEMS resonators, IEEE/ASME JMEMS, vol.17, no.3, pp. 755-766, 2008. [18] R. Hopkins, et al., "The silicon oscillating accelerometer: a high-performance MEMS accelerometer for precision navigation and strategic guidance applications," ION NTM 2005, 24-26 January 2005, San Diego, CA, pp. 970-979. [19] S. Sung, G. Lee, T. Kang. "Development and test of MEMS accelerometer with self-sustained oscillation loop," Sensors and Actuators A, 109, 2003. [20] A. Trusov, A. Schofield, A. Shkel, "A substrate energy dissipation mechanism in in-phase and anti-phase micromachined z-axis vibratory gyroscopes," IOP JMM, vol. 18, pp. 095016(10), September 2008. [21] A. Seshia, R.Howe, S. Montague, "An integrated microelectromechanical resonant output gyroscope," Proc. MEMS'02, 2002, pp. 722-726. [22] C. Comi et al.,"a High Sensitivity Uniaxial resonant accelerometer," Proc. IEEE MEMS 2010, PP-260-263.