peng jmems2014

peng jmems2014
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JMEMS Letters
A Polysilicon Microhemispherical Resonating Gyroscope
Peng Shao, Curtis L. Mayberry, Xin Gao, Vahid Tavassoli, and Farrokh Ayazi
Abstract— This letter reports, for the first time, an integrated
polysilicon microhemispherical resonating gyroscope (µHRG) with selfaligned drive, sense, and tuning electrodes, all fabricated using a single
wafer process. The polysilicon hemispherical shell is 700 nm in thickness
and 1.2 mm in diameter, resulting in a 1:3000 aspect ratio threedimensional (3-D) microstructure. The quality factor of the wineglass
mode is measured to be 8500 at 6.7 kHz with an as-fabricated frequency
mismatch of 105 Hz between the two m = 2 degenerate modes.
The modes are electrostatically matched and aligned using the tuning
electrodes with a resulting mode-matched quality factor of 11 100. Initial
characterization of the sensitivity of the µHRG shows a scale factor of
4.4 mV/º/s.
Terms— Gyroscopes,
microelectromechanical system (MEMS), mode matching, quality
factor, frequency mismatch.
Successful fabrication and operation of micro-hemispherical shell
resonators (μHSR) [1]–[4] have provided great potential for lowcost fabrication of integrated micro-hemispherical resonating gyroscopes (μHRG). Inspired by the macro-scale HRG, one of the most
successful and widely used navigational gyro designs [5], μHRGs
are aimed at low cost, high-performance microgyroscopes that offer
higher levels of integration. The state-of-the-art micro-fabrication
technologies used in MEMS inertial sensors enable miniaturization
of the conventional HRGs to chip scale μHRGs. Similar to other
MEMS axisymmetric gyroscopes, the operation is based on energy
transfer between two degenerate resonance modes caused by the
Coriolis effect. Therefore, matching the degenerate modes is essential
to maximize the rate sensitivity through quality factor amplification
of the transferred energy.
Axisymmetric structures such as ring [6], cylinder [7] and disk [8]
have been successfully used for MEMS gyroscopes. The curved
three dimensional structure of μHRGs allows low resonance frequencies (<10 kHz) at extremely small sizes compared to its planar
counterparts [9]. It also has the potential of higher mechanical quality
factor and higher degree of symmetry compared to the prior art, ring
structures [6]. Furthermore, the structure is expected to demonstrate
low stiffness, which would enable large reference vibration amplitudes with large capacitive gaps, resulting in an improved mechanical
noise floor and sensitivity. A large electrostatic tuning range will be
another outcome of the low stiffness of the μHRG structure.
Manuscript received January 7, 2014; revised May 6, 2014; accepted
May 24, 2014. This work was supported by the Defense Advanced Research
Projects Agency, Microsystems Technology Office, Microscale Rate Integrating Gyroscope Program, through Northrop Grumman, under Contract
HR0011-00-C-0032. Subject Editor A. Holmes.
P. Shao is with the Woodruff School of Mechanical Engineering,
Georgia Institute of Technology, Atlanta, GA 30332-0405 USA (e-mail:
[email protected]).
C. L. Mayberry, X. Gao, V. Tavassoli, and F. Ayazi are with the
School of Electrical and Computer Engineering, Georgia Institute of
Technology, Atlanta, GA 30332-0250 USA (e-mail: [email protected];
[email protected]; [email protected]; [email protected]).
Color versions of one or more of the figures in this letter are available
online at
Digital Object Identifier 10.1109/JMEMS.2014.2327107
Fig. 1. (a) SEM image of a fabricated polysilicon μHRG. (b) Schematic
illustration of a polysilicon μHRG with self-aligned polysilicon electrodes for
driving and sensing the device.
This letter reports, for the first time, the rate gyro operation and
characterization of a polysilicon μHRG with high quality factor
and highly symmetric structure as a potential candidate for high
performance MEMS gyroscopes. It is shown that with an open
loop operation and a quality factor that has yet to reach its full
potential, the device has strong rotation rate sensitivity. The ability
to fabricate the μHRG with a small frequency split between the
degenerate modes, and then to electrostatically tune the μHRG using
integrated electrodes to align and match the two degenerate modes
is also demonstrated. In section II the structure of the fabricated
polysilicon μHRG is briefly reviewed. The resonator characterization
is presented in section III, and then apreliminary gyro performance
characterization is given in section IV.
Fig. 1(a) shows a bird’s eye view SEM of a fabricated polysilicon
μHRG, and Fig. 1(b) illustrates schematically the cross-section of the
device. It consists of a high Q polysilicon hemispherical shell resonator surrounded by 16 polysilicon electrodes for electrical driving,
sensing and tuning. The electrodes are created by etching high aspect
ratio trenches in a silicon wafer and then refilling them with a
silicon nitride insulation layer and in-situ boron-doped polysilicon.
A hemispherical shell is then created by isotropic etching of silicon,
deposition of sacrificial and polysilicon layers and then removing the
surrounding silicon and sacrificial materials [1]. In this process, the
trenches for the electrodes and the openings for isotropic etching are
defined by the same mask, thus the electrodes and hemispherical shell
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Fig. 2. (a) Frequency response of a polysilicon µHRG, showing different
resonance modes. (b) Tuning curve of both modes, the as-fabricated frequency
mismatch between the m=2 degenerate modes is estimated to be 105 Hz by
quadratic curve fitting. The inset shows the measured frequency mismatch of
110 Hz at polarization voltage of 10V.
are self-aligned. The depth of the polysilicon electrodes is 300 μm
and is scalable to improve the efficiency of capacitive transduction
and robustness of the electrode structure during release. The gap size
between the electrodes and the hemispherical shell is 20 μm to enable
drive vibration amplitude of a few micrometers. A hole is also etched
through from the backside to allow a DC bias to be applied to the
hemispherical shell.
The fabricated μHRG is mounted on an evaluation board and
wirebonding is performed on the polysilicon electrodes. Resonator
performance is characterized using a network analyzer (E5061B)
while the board is placed inside a vacuum chamber with ∼5 μTorr
vacuum pressure. Figure 2(a) shows the resonance peaks of the m=2,
m=3, m=4 elliptical modes, and the rocking mode for a polysilicon
μHRG with a shell thickness of 700 nm and a shell diameter of
1200 μm. The m=2, m=3 and m=4 resonances are measured to
be at 6.7 kHz, 19.1 kHz and 40.2 kHz with quality factor 8,500,
7,000, and 10,400, respectively. Fig. 2(b) shows the electrostatic
tuning curve of two degenerate m=2 modes. Polarization voltage
is applied on the hemispherical shell from 10V to 50V. By quadratic
curve fitting, the as-fabricated frequency mismatch without any tuning
effect is estimated to be 105 Hz with f/f = 1.56%. In the current
polysilicon μHRG design, the m=2 mode is selected as the working
resonance modes due to its low resonance frequency and small
frequency mismatch. The m=2 resonance mode shows a quality
factor of 8,500. The measured quality factor does not represent its
limit for a polysilicon μHRG, which is believed to be in the hundreds
of thousands. A thermoelastic damping (TED) analysis shows much
lower material dissipation (QTED ∼1 million), so there is room for
Q optimization and improvement. Current device Qs are believed to
Fig. 3. (a) Schematic illustration of the tuning electrodes and the position of
the two modes before mode matching and balancing. θ Q represents the angle
of the misalignment of the sense mode before the electrostatic alignment of
the modes. After electrostatic alignment the sense mode would be aligned
with the sense axis. (b) Rate measurement circuit architecture.
be limited by surface roughness and anchor loss. Due to the extremely
small stiffness of this structure (∼1N/m), the drive amplitude can be
as high as a few micrometers with large capacitive gaps of 20 μm.
Nonlinearity of resonance peaks can be easily observed if input
RF power exceeds −20 dBm. COMSOL multi-physics simulation
confirms that with an RF power of −24 dBm and a DC polarization
voltage of 26 V, drive vibration amplitude of 3 μm can be achieved.
The testing results demonstrate a highly symmetrical hemispherical
shell resonator with high quality factor that shows promise to be a
high performance μHRG.
Preliminary gyroscope characterization is performed on the same
polysilicon μHRG measured in the previous section. Mode matching
and balancing of the gyroscope is performed using the approach
described in [10]. As Fig. 3(a) shows, two sets of tuning electrodes
(VT1 , VT2 ) and two sets of balancing electrodes (VQ1 , VQ2 ) are
used. Tuning electrodes for the drive mode and sense mode are at
the anti-nodes of both the drive mode and sense mode, respectively.
Balancing or aligning electrodes that are at 22.5º to the drive antinodes and its equivalent position align the resonance modes with their
principal axes. Fig. 4(a) shows the two peaks as their being matched
with 27 Hz and 5 Hz frequency split, and Fig. 4(b) shows the mode
matched resonance peak with an effective quality factor of 11,100.
The mode-matched polysilicon μHRG is operated in an open loop
configuration as shown in Fig. 3(b) by exciting the drive mode
using an external sinusoidal signal at the exact resonance frequency
and an RF power of −35 dBm. The device is polarized at 40V.
The Coriolis-induced signal is then processed by a transimpedance
amplifier (TIA) with a gain of 500k and post amplification of 60 dB.
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demonstrates the transient response to a 14º/s rotation rate measured
using an oscilloscope. It shows a very clean and linear sinusoidal
output. Sensitivity is also measured by applying a rotation rate of
up to 16º/s. By linear regression, the scale factor of the polysilicon
μHRG is extracted to be 4.4 mV/(º/s). The preliminary characterization demonstrated a polysilicon microscale hemispherical resonating
gyroscope working in rate mode. This motivates further research
in improving the mechanical quality factor, decreasing the noise
level, optimizing the fabrication process, and improving the interface
This letter introduces a batch fabricated polysilicon hemispherical
resonating gyroscope that works in rate mode. The gyroscope is
operated under a mode-matched condition at 6.6 kHz with an effective
quality factor of 11,100. Open loop operation of a mode-matched
polysilicon μHRG demonstrates a sensitivity of 4.4 mV/(º/s). Further
improvement of the quality factor will make the device suitable for
operation in whole angle mode.
Fig. 4. A polysilicon μHRG with thickness of 700 nm and a diameter of
1.2 mm (a) shows the two peaks as their being matched with a 27 Hz and 5 Hz
frequency split; (b) shows mode matching at 6.6 kHz with an effective quality
factor of 11,100. Tuning and balancing are done by the polarization voltage
and four sets of tuning and balancing electrodes.
Fig. 5. Output voltage as a function of rotation rate, showing a sensitivity
of 4.4 mV/(º/s). (inset) Rate output by running rate table at 200 mHz with a
14º/s rotation rate.
After demodulation with the drive signal and low-pass filtering, the
rotation rate information can be detected. The vacuum chamber is
mounted on a rate table with a vacuum hose connected to the
pump. The rate table is programmed to run at 200 mHz with an
incremental rotation amplitude for different rotation rates. Fig. 5 inset
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