INDUCTIVE CMOS MEMS ACCELEROMETER WITH INTEGRATED

VARIABLE INDUCTORS
Yi Chiu, Hao-Chiao Hong, and Chia-Wei Lin
Department of Electrical and Computer Engineering
National Chiao Tung University, Hsin Chu, Taiwan, R.O.C.

ABSTRACT PRINCIPLE AND DESIGN

This paper reports an inductive CMOS MEMS The principle of the proposed accelerometer is shown
accelerometer with integrated variable inductors as the in Figure 1. Two differential variable inductors L1,2 = L ±
position-sensing elements. Without conventional sensing ΔL are used in two LC-tank oscillators with frequencies
comb fingers, the dependence of device characteristics on f1,2 = 1/ 2π LC1,2 (1 ± ΔL / L). The two oscillation signals
stress-induced structural deformation can be significantly
reduced. The variable inductors are used in on-chip are then mixed and filtered; the output frequency is
LC-tank oscillators. When the external acceleration f1 − f 2 = ( f 01 − f 02 ) + ( f 01 + f 02 ) × (ΔL / 2 L). (1)
deforms the inductors, the oscillation frequency variation
is proportional to the inductance change and thus the In Equation 1, the output frequency variation is
acceleration. The frequency output can be easily converted proportional to the inductance variation ΔL caused by the
to digital codes by using a counter. The integrated inductor deformation induced by the external acceleration
accelerometer was implemented by a commercial 0.18 μm a. For small deformation, ΔL is expected to be proportional
1P5M CMOS process and post-CMOS dry-etching to a. The oscillator-based frequency output can be
processes. Experimental results showed the proposed converted to a digital code with a simple counter. Thus no
accelerometer had a sensitivity of 150 kHz/g. complex analog-to-digital converter (ADC) is required.
L1=L-ΔL
INTRODUCTION
Accelerometers have been used extensively in C1 f1=f01+Δf1
automobiles, smart phones, gaming controllers, etc. In
MEMS accelerometers, the sensing structures and the
readout circuitry can be integrated by using single-chip LPF f1 - f2
SoC (system on chip), two-chip SiP (system in package),
or WLP (wafer level packaging) technology. Among C2 f2=f02 - Δf2
different packaging and integration techniques, monolithic
integration of MEMS and CMOS by using standard CMOS L2=L+ΔL
processes and post-CMOS release processes can help
enhance sensor performance and reduce fabrication cost. Figure 1: Principle of proposed inductive accelerometer
Most CMOS MEMS accelerometers employ employing LC-tank oscillators
comb-finger capacitors as the position-sensing elements
[1-4]. However, residual stress in deposited thin films and
Variable Inductors
multilayered structures often results in the curling of
The proposed accelerometer is implemented in a
suspended comb fingers and thus reduces the sensing
commercial 0.18 μm 1P5M CMOS process. The integrated
capacitance and its sensitivity. Though curled frames [1] or
variable inductors are realized by the wire winding in the
all-oxide structures [2] can be employed to reduce the
spring, as shown schematically in Figure 2. In Figure 2(a),
stress effect on sensor performance, the overlapping
the sensor is at rest and the two inductors have identical
between comb fingers is still subject to process and
shape and area so that L1 = L2 = L. When the proof mass
temperature variations. To replace the interdigited sensing
moves under the influence of an external acceleration a in
capacitors, an inductive accelerometer with variable
Figure 2(b), the two springs/inductors are deformed so that
inductors as the sensing elements is proposed and
L1 has increased area enclosed by the winding and L2 has
demonstrated in this paper. Since inductance is determined
mainly by the shape and area of the coil winding, the decreased area. Therefore, L1,2 = L ± ΔL and the two
inductance value is less sensitive to the stress-induced differential inductors have opposite change of inductance.
deformation and thus device yield and robustness can be The inductance of deformed inductors was simulated by
improved. Another advantage of the proposed device is Coventorware, as shown in Figure 3. The total length of the
that the chip size can be reduced since no area is needed to spring/inductor is 680 μm. The width of the spring/
implement comb fingers. inductor is 4 μm. Figure 3(b) shows the linear relationship
In contrast to previous inductive MEMS between the inductance and the deformation applied to the
accelerometers [5, 6], the proposed accelerometer employs inductor. The inductance sensitivity is 0.09 nH/μm.
integrated inductors implemented monolithically in the
CMOS layout. Thus no extra packaging processes such as Mass-Spring System
wire bonding [5] or wafer bonding [6] are needed after the The spring and the inductor coil shares the same
device is released. Therefore the inductance variation due physical structure composed of M1-to-M5 multilayerd
to packaging can be minimized. metal-via stacking. The proof mass has a dimension of 680

978-1-5090-1973-1/16/$31.00 ©2016 IEEE 974 MEMS 2016, Shanghai, CHINA, 24-28 January 2016
μm × 460 μm × 8.8 μm. The mass-spring system was LC-tank Oscillator
designed with a mechanical resonance frequency of 2 kHz. The on-chip readout circuit is monolithically integrated
Figure 4 shows the simulation of the in-plane translational with the sensor. Figure 5(a) shows the schematic of the
modal shape with a resonance frequency of 2.1 kHz. From LC-tank oscillator in which L = 1.13 nH and C = 4.6 pF.
the resonance frequency, the inductance sensitivity can be The capacitance C includes the effect of all parasitic
calculated to be 4.3×10-3 (ΔL/L)/g. capacitance. The nominal LC oscillation frequency of the
oscillator itself is 2.2 GHz in the post-layout simulation.
anchor spring inductor winding
The mixer shown in Figure 1 is realized by a Gilbert cell
whose schematic is shown in Figure 5(b). The two
differential oscillation signals are fed into the mixer input
L1 = L L2 = L V1n/V1p and V2n/V2p through two differential buffer circuits.
proof
mass The two differential buffers also set up different bias
voltages at the mixer input pairs M1/M2 and M3/M6 (also
M4/M5) for correct mixer operation. It is noteworthy that
(a) the different bias voltages on the outputs of the two
differential buffers make their input capacitance different.
L1 = L2 = The different input capacitance is used as different loading
L+ΔL L-ΔL for the two oscillators to set up the frequency offset
proof between the two oscillation frequencies f01 and f02 in
mass Equation 1. R1/C1 and R2/C2 are low-pass filters to filter
out the high-frequency component f10 + f02 ≈ 4.4 GHz after
mixing. A differential-to-single-end amplifier follows the
(b) mixer to generate a rail-to-rail frequency output.
Figure 2: Schematic layout showing inductor wiring, (a) at
rest, (b) under external acceleration FABRICATIION AND MEASUREMENT
After the standard CMOS process, the sensor
anchor1 structures were released in a dry-etching post-process [7]
current in
current out
M4 M3

anchor2 C
ǻx
L
ID2 ID1
(a)
M2 M1
1.55
Inductance (nH)

1.35
MB
1.15

0.95 (a)
0.75
-2 -1 -4 0 -3 1 2 3 4
Deformation Δx (μm)
(b) C1 R1 R2 C2

Figure 3: Inductance simulation, (a) solid model, (b)

Von Vop
inductance vs. deformation
V2p M3 M4 M5 M6
V2n
IDM3 IDM4 IDM5 IDM6

V1n M1 M2 V1p

IDM1 IDM2
Mb IDMb

(b)
Figure 4: Finite element simulation of resonance mode Figure 5: Schematic of (a) LC-tank oscillator, (b) Gilbert
and frequency cell

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with the top metal layer as the etching mask. First, deterioration. Figure 8(c) shows the power spectrum of the
anisotropic reactive ion etching (RIE) was employed to digitized output of the counter. Various noise and
etch the oxide layers and define the movable structure. harmonics can be identified. The noise floor has a 1/f
Then XeF2 isotropic silicon etching was employed to shape, consistent with the observation in Figure 7(b). The
remove the silicon substrate and release the structure. performance comparison between the proposed device and
Figure 6 is the optical micrograph of a device after release. prior publications designed and fabricated with similar
processes is shown in Table 1.
Electrical Measurement
The oscillation outputs of a sensor before release were CONCLUSION
measured by using an Agilent MSO 9404A oscilloscope An inductive CMOS MEMS accelerometer with
and an Agilent E4440A spectrum analyzer. Phase noise integrated variable inductors as the position-sensing
was measured by using an Agilent E5052B signal source elements was proposed and demonstrated. The device was
analyzer. Figure 7(a) is the waveform of an oscillator designed and implemented in a commercial 0.18 μm 1P5M
output. The frequency is about 2.7 GHz, close to the value
in simulation. Figure 7(b) shows the phase noise of the
oscillator. The slope is approximately -30 dBc/decade from
1 kHz to 10 MHz frequency offset, indicating the dominant
circuit noise is the flicker (1/f) noise. Figure 7(c) shows
final output waveform of the sensor. The intrinsic 50 mV/div

frequency offset f 01 − f 02 is around 34 MHz.

.
Acceleration Test
The sensor was first mounted on a rotation table in the
1 ns/div
static ± 1g test. The output frequency was converted to a
digital code by using a Standford Research Systems
SR-620 counter. Figure 8(a) shows the output frequency
variation as a function of rotation angle. From data fitting,
the output sensitivity is about 1 MHz/g. In dynamic
vibration tests, the sensor was excited by a shaker with (a)
various amplitude and frequency. A reference commercial
accelerometer was used to calibrate the vibration level.
Figure 8(b) shows the frequency output in a ±2g and 50 Hz
vibration test. The output frequency has an intrinsic offset
f 01 − f 02 of about 87 MHz and a sensitivity of 150 kHz/g. 1 kHz:
10 kHz:
-29.1 dBc/Hz
-63.6 dBc/Hz
It is noted that the intrinsic frequency offset (center 100 kHz:
1 MHz:
-90.4 dBc/Hz
-114.2 dBc/Hz
frequency of mixer output) f 01 − f 02 in Figures 7(c) and 8(b) 10 MHz: -132.0 dBc/Hz

are different. The sensitivity obtained in static and dynamic

tests are also different. These differences can be attributed
to potential variation in measurement environments
(calibration, temperature, humidity, etc.) and device

(b)
spring/inductor

(a) (b) 50 mV/div

OSC2
mixer

proof mass 20 ms/div

(c)
OSC1
(d)
(c)
Figure 6: Optical micrographs of a released device, (a)
overall view, (b) spring/inductor and proof mass, (c) Figure 7: Oscillator output, (a) waveform before mixing,
spring, (d) after wire bonding (b) phase noise before mixing, (c) waveform after mixing

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 data fit CMOS process and post-CMOS dry-etching processes.
1.5 Experimental results showed the proposed accelerometer
Frequency variation (MHz)
had an intrinsic frequency offset of 87 MHz and sensitivity
1.0
of 150 kHz/g. The dominant noise at sensor output was the
0.5 flicker (1/f noise). The device performance was
comparable to the other devices fabricated by similar
0.0 processes.
-0.5
-1.0 ACKNOWLEDGEMENTS
The project was supported in part by the Ministry of
-1.5 Science and Technology, Taiwan, R.O.C. (NSC
0 100 200 300 400 101-2221-E-009-171, NSC 102-2221-E-009-191 and
Angle (deg) MOST 103-2221-E-009-218). The authors were grateful
(a) for the use of facilities at the Chip Implementation Center,
the National Center for High-performance Computing, the
data fit National Nano Device Laboratory, and the National Chiao
87.4
Tung University Nano Facility Center, Taiwan, R.O.C..
Output frequency (MHz)

The authors appreciate the assistance of Mr. Fu-Hwei

87.2 Hong of Solistron Electronics in the CMOS tapeout.

87.0 REFERENCES
[1] J. Wu, G. K. Fedder, and L. R. Carley, ȾA low-noise
86.8 low-offset capacitive sensing amplifier for a
50-μg/√Hz monolithic CMOS MEMS
86.6 accelerometer,ȿ IEEE J. Solid-State Circuits, 39 (5),
0.66 0.68 0.70 0.72 0.74 722-730, 2004.
Time (sec) [2] Y.-C. Liu, M.-H. Tsai, and W. Fang, “Pure oxide
(b) structure for temperature stabilization and
performance enhancement of CMOS-MEMS
20 accelerometer,” Proc. IEEE MEMS 2012, Paris,
10 2nd harmonic France, 2012, 591-594.
3rd harmonic [3] S.-S. Tan, C.-Y. Liu, L.-K. Yeh, Y.-H. Chiu, M. S. Lu,
0
PSD (dBg/bin)

60Hz 4th harmonic

-10 K.Y.J. Hsu, “An integrated low-noise sensing circuit
180Hz with efficient bias stabilization for CMOS MEMS
-20
capacitive accelerometers,” IEEE Trans. Circuits and
-30 Systems I- Regular Papers, 58 (11), 2661-2672, 2011.
-40 [4] Y. Chiu, H.-C. Hong, and P.-C. Wu, “Development
-50 and characterization of a CMOS-MEMS
-60 accelerometer with differential LC-tank oscillators,”
10 15 0 520 25 J. Microelectromech. Syst., 22 (6), 1285-1295, 2013.
Frequency (Hz)
[5] Y.-T. Liao, W. J. Biederman, and B. P. Otis, “A fully
(c) integrated CMOS accelerometer using bondwire
Figure 8: (a) Static rotation table testing of sensor at ±1 g inertial sensing,” IEEE Sensors J., 11 (1), 114-122,
input, (b) dynamic testing at ±2g, 50 Hz input, (c) power 2011.
spectrum of digitized sensor output at ±2g, 50 Hz input [6] E. Abbaspour-Sani, R.-S. Huang, C. Y. Kwok, “A
novel electromagnetic accelerometer,” IEEE Electr.
Device Lett., 15 (8), 272-273, 1994.
Table 1: Performance comparison
[7] S.-H. Tseng, Y.-J. Hung, Y.-Z. Juang, and M. S.-C.
[2] [4] [7] this work
Lu, “A 5.8-GHz VCO with CMOS-compatible
Device Acc1 Acc1 VCO Acc1 MEMS inductors,” Sens. Actuators A, Phys., 139
Technology 0.35μm 0.18μm 0.18μm 0.18μm (1-2), 187-193, 2007.
2P4M 1P6M 1P6M 1P5M
Resonance 12.9 7 - 2 CONTACT
frequency kHz kHz kHz
* Yi Chiu, tel: +886-3-5731838; yichiu@mail.nctu.edu.tw
Sensitivity 7.6 3.6 - 150
mV/g MHz/g kHz/g
Oscillator - 1.9 5.8 2.7
frequency GHz GHz GHz
Phase noise - -115 -117 -114
@ 1 MHz dBc/Hz dBc/Hz dBc/Hz
1
accelerometer

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