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 [email protected], 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 Quadru- ple Mass Gyroscope (QMG) architecture with meas- ured quality factors of 1.2 million and proven sub– °/hr Allan deviation of bias. The true North detection was accomplished in conventional amplitude modu- lated (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 trans- ducer is switched to a frequency modulated (FM) mo- dality. The test results for FM operation experimen- tally demonstrated a wide linear input rate range of 18,000 °/s and inherent self-calibration against tem- perature changes. Vertical alignment of the IMU and acceleration sensing is enabled using resonant accel- erometers with 5 μg performance. The accelerometer is self-calibrated against temperature variations, ena- bled by differential frequency measurements. We be- lieve the developed low dissipation inertial MEMS with interchangeable AM/FM modalities may enable wide dynamic range IMUs for North-finding and iner- tial guidance applications previously limited to sys- tems based on optical and quartz inertial sensors. I. INTRODUCTION North-finding with 0.001 radian (1 mrad) preci- sion and tracking of azimuth in a wide dynamic range is required for targeting, dead reckoning, and inertial guidance applications [1]. North identifica- tion is traditionally accomplished using the magnetic field 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 gy- roscopes desirable for true North seeking, or gyrocompassing. Although conventional fiber optic, ring laser, and macro-scale quartz hemispherical res- onator 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 for repeatable measurements of the Earth’ s rate and 0.1 mg total bias error for vertical alignment. Sev- eral groups have reported silicon MEMS gyroscopes with sub–°/hr Allan deviation of bias [2-7]. However, single digit mrad North-finding and tracking over dy- namic 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 accel- erometer, with the resolution enhanced by high Q- factors and wide dynamic range provided by frequen- cy 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 perfor- mance 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. 1: Photograph of a pyramid inertial measure- ment unit (IMU) prototype comprising MEMS quad- ruple mass gyroscopes and resonant accelerometers. Table 1: Comparison of the 3 main design parame- ters for 3 different architectures of MEMS gyro- scopes (Tuning Fork Gyroscope, Disk Resonator Gy- roscope, and Quad Mass Gyroscope).
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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
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 accel-
erometers 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 be-
tween the full-scale linear range and the smallest de-
tectable input stimulus change. In the best case sce-
nario, 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 naviga-
tion grade) is practically impossible with conventional
MEMS sensors architectures. These fundamental limi-
tations on the dynamic range and output stability pre-
vent the use of MEMS gyroscopes and accelerometers
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. 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).
Fig. 14: Photograph of a differential FM accel-
erometer fabricated using an in-house 100 µm SOI
process. Arrows show sensitivity to acceleration and
temperature.
Fig. 15: Concept of the differential FM accelerome-ter with temperature self-calibration. Arrows show
axes of sensitivity to external acceleration and tem-
perature.
in many important applications. An alternative ap-proach to resolving these limitations is using a fre-
quency-modulated accelerometer, where induced ac-
celeration changes the resonant frequency of the de-
vice due to changes in the total effective stiffness [18,
19].
Performance of previously reported FM accel-
erometers 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 depend-ency 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 envi-
ronment changes, Fig. 14. The differential FM accel-
erometer approach relies on tracking of the resonant
frequencies of two high-Q mechanical MEMS oscilla-
tors to produce quasi-digital and decoupled FM meas-
urements of the input acceleration and temperature,
Fig. 15.
IV-A. Sensor Concept and Design
The proposed differential FM accelerometer con-
sists of two identical silicon MEMS tuning fork reso-
nators. 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 reso-
nator is dynamically balanced, eliminating dissipation
of energy due to linear and angular vibrations of the
substrate. Increase of the Q-factor up to the funda-mental thermoelastic limit improves precision, stabil-
ity, and phase noise for the anti-phase vibration. In
contrast, the in-phase vibration has a low Q-factor,
which is limited by the anchor loss [20].
Each tine includes differential lateral comb elec-
trodes for electrostatic excitation of the anti-phase
mode, differential lateral comb electrodes for capaci-
tive detection, and non-differential parallel plate ca-
pacitors for modulation of stiffness by means of the
negative electrostatic spring effect. By applying a DC
voltage bias on the parallel plates, a negative electro-
static spring is created, the stiffness of which is pro-
portional to the square of the bias voltage and inverse-
ly proportional to the cube of the capacitive gap. This makes the anti-phase natural frequency highly sensi-
tive to the gap between the fixed and moving parallel
plate electrodes. In other words, the in-phase dis-
placement 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. Be-cause the device moves only along the x-axis and is
fabricated from single crystalline silicon, a uniform
Fig. 17: Photograph of a differential FM accel-
erometer fabricated using an in-house 100 µm SOI
process.
Fig. 18: Photograph of a packaged differential FM
accelerometer assembled with signal conditioning
PCBs.
(a) Anti-phase mode at 2.6 kHz, QTED=O.3 million.
(b) In-phase mode at 0.9 kHz.
Fig. 16: Finite Element Modeling (FEM) results il-
lustrating the (a) anti-phase and (b) in-phase vibra-
tory modes of the FM accelerometer.
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 min-
imize 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 pre-
dicted.
IV-B. Self-Calibration through Differential FM
The proposed temperature self-calibration ap-
proach takes advantage of the differential design, in
which both oscillators have the same sensitivity to
temperature but opposite sensitivity to external accel-
eration, Fig. 14 and 15. The dependency of frequency
on temperature has a well known linear relationship
for single crystalline silicon, enabling direct self-
sensing 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 ap-
proach, the FM accelerometer provides a quasi-digital
measurement of the input acceleration as well as di-
rect 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 Silicon-
on-Insulator (SOI) wafers with a 100 μm single crys-
talline silicon device layer, a 5 μm buried oxide layer,
and a 500 μm handle wafer, Fig. 17. After wafer fab-
rication and dicing, sensors were attached to a ceram-
ic DIP-24 package, wirebonded, and vacuum sealed
in-house at ~1 Torr. In future fabrication runs, accel-
erometers 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.
A standard multi-point tumble test was carried
out for a single tuning fork (non-differential) FM ac-
celerometer using an Ideal Aerosmith 2102 Series
Two-Axis Position and Rate Table System. The sen-
sor was tested by measuring the change of the anti-phase 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 per-
formed 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, respec-
tively, Fig. 19.
To evaluate the proposed self-calibration concept,
a differential FM accelerometer with two tuning fork
oscillators was placed into a TestEquity 107 tempera-ture 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 tun-
ing forks were recorded Fig. 20. Each oscillator
showed an identical 500 mg drif over the temperature
change. Differential FM demodulation provided au-
tomatic calibration against temperature by canceling
common frequency drifts between the two sensors. As
shown in Fig. 21, the drift over temperature was re-
duced to approximately 1 mg, currently limited by the
noise performance of oscillators sealed with 1 Torr
Fig. 19: Measured input-output characteristic of FM
accelerometer for different stiffness modulation DC
voltages. Inset: scale factor vs. modulation DC volt-
age.
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.
pressure. Testing of differential FM accelerometers
sealed with getter is expected to improve the bias sev-
eral 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 tem-
peratures of 30 °C and 75 °C, Fig. 22(a). The meas-
ured frequency split between the nominally equal modal frequencies was proportional to the input ac-
celeration, 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 accu-
racy of the experimental setup) despite a 4 Hz drop of
the nominal frequency, Fig. 22(b).
Allan deviation analysis of FM accelerometer in-
run 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
tuning forks removes the +1 slope temperature ramp,
revealing the bias instability of 6 µg at 20 s. In com-
bination with the design linear range of 20 g, the sen-
sor 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 de-
velopment. The current performance results for vacu-
um 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 de-
tection, 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 align-
ment and acceleration sensing is enabled by the pro-
posed resonant accelerometers, with accuracy ensured
by differential frequency measurements of the accel-
eration.
Inspired by the progress on the low dissipation
inertial MEMS, we are currently developing a multi-axis 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 ex-
pected to provide dynamic range and stability unprec-
edented in conventional inertial MEMS, while simul-
taneously reducing the power consumption of the ana-
log-digital interface.
VI. ACKNOWLEDGMENTS
The author would like to thank his collaborators
and colleagues at the University of California, Irvine
MicroSystems Laboratory. Especially valuable con-
tributions 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
(a) Measured resonant frequencies f1,2 as a function
of the input acceleration for 30 °C and 75 °C. Differ-
ential frequency split f1-f2 is invariant to tempera-
ture.
(b) Measured acceleration responses for 30 °C and
75 °C using the differential frequency split.
Fig. 22: Characterization of the differential FM ac-
celerometer at 30 °C and 75 °C, demonstrating self-
calibration to temperature. There is less than 0.5%
response fluctuation.
Fig. 23: Measured Allan deviation for a vacuum sen-
sor. Differential FM demodulation removes tempera-ture ramp and achieves a 6 µg bias at 20 sec.
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 gyro-
scopes and accelerometers were designed and charac-
terized at the MicroSystems Laboratory, University of
California, Irvine.
VII. REFERENCES
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Fig. 24: Single chip multi-axis MEMS IMU combin-
ing wide dynamic range gyroscopes and accelerome-
ters with frequency modulated operation. Total die size is 1 by 1 cm.