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Abstract—We present the successful fabrication and finite
element analysis (FEA) validation of capacitive micromachined
ultrasonic transducers (CMUTs) targeting applications under a
wide and varying pressure range (~ 1 – 20 atm), such as
ultrasonic flow metering (UFM). In our devices each plate is in
permanent contact with the bottom of the cavity, even at zero d.c.
bias voltage condition. The fabrication is based on a direct wafer
bonding process (thick buried oxide layer process), which allows
the realization of only partially connected bottom electrodes. The
fabricated devices show measured performance in good
agreement with FEA. The results for the measured plate profiles
confirm the permanent contact and are within 3.5% of the static
FEA results. Further, in comparison to laser vibrometer
measurements, the FEA modal analysis predicts the 1st and 2nd
mode frequencies for permanent contact devices within 3% and
1.5%, respectively. In addition, the overall trends of resonant
frequency and contact radii as a function of d.c. bias voltage are
both consistent with FEA. Our results show that the fabrication
of CMUTs in permanent contact mode is feasible, and that FEA
serves as an excellent tool for predicting and designing both the
static and dynamic behavior of CMUTs operated in the
permanent contact mode.
Index Terms— Fabrication, CMUT, permanent contact mode,
wide pressure range, ultrasonic flow meter, thick BOX process.
I. INTRODUCTION
There has been an increased awareness by oil and gas
companies towards emissions monitoring and reduction for
both environmental and economical reasons [1]. There are
extreme process conditions found in flare lines, such as the
wide pressure range (~ 1–20 atm or even up to 200 atm), which
are challenging for an ultrasonic transit-time flowmeter..
For such conditions, we previously proposed a new CMUT
operational mode [2], with the CMUT plate in permanent
contact with the bottom of the cavities, even under 1 atm
pressure and zero d.c. bias voltage. The cross sectional view of
one CMUT cell (circular) is illustrated in Fig. 1(a). Our
FEA-based results showed that such operational mode
provides a more stable performance in terms of the static
operational point and resonant frequencies over a varying
pressure range. Furthermore, based on a previously introduced
thick BOX process [3], we proposed a cell structure in which
only a portion of the bottom electrode is connected to the hot
electrode [Fig. 1(b)]. The motivation for this structure is
twofold: first, the total parasitic capacitance of the device is
reduced. Second, the electric field in the insulation layer at the
contact regions and, thus, the likelihood of electrical
breakdown are reduced as well.
In this paper we report on the successful fabrication of
CMUTs having this cell structure and, in addition, we present
the characterization results, which validate our FEA for both
static and dynamic device behavior.
II. FABRICATION PROCESSES AND CHARACTERIZATION
METHODS
The fabrication is based on a thick buried oxide layer in the
substrate (thick box process; for details see [3]).
High-temperature assisted direct wafer bonding is used. The
reason why we use wafer bonding instead of sacrificial release
based fabrication techniques lies in the large cell size (radii
around 2000 µm) required for the targeted low frequencies
(100 kHz).
The fabrication starts with an SOI wafer with a 3-µm-thick
box layer [Fig. 2(a), the two cells according to Fig. 1 are
outlined]. Then the first litho step and a deep reactive ion
etching (DRIE) step define the gap height [Fig. 2(b)]. Due to
the large gap heights (10 – 30 µm), other techniques to form
the gaps, such as double oxidation [4] for accurate gap height
control and good uniformity across the wafer, cannot be used.
Then, a second litho step follows to etch the vertical
donut-shaped trenches down to the box layer to insulate
individual electrodes [Fig. 2(c)]. For cells with partially
connected electrode, an additional donut trench with smaller
diameter is etched by DRIE to define the central non-contacted
island in the bottom electrode, as required to realize the cell
structure from Fig. 1(b). The wafer is then oxidized to grow a
3-µm-thick insulation layer [Fig. 2(d)].
Next, the wafer is high-temperature assisted direct bonded to
another SOI wafer with the device layer thickness equals to the
desired plate thickness (30 – 60 µm) [Fig. 2(e)], and annealed
at 1100. Now with the CMUT cavities sealed and protected
from contamination and with strong mechanical support, the
Fabrication and model validation for CMUTs operated in permanent contact mode
Min-Chieh Ho1, Mario Kupnik2, Srikant Vaithilingam1 and Butrus T. Khuri-Yakub1
1Stanford University, CA, USA; 2Brandenburg University of Technology, Cottbus, Germany
(a) (b)
Fig. 1 shows the schematic (cross section) view of a single CMUT cell as
proposed in [2], where (a) is a cell in the permanent contact mode, i.e.
with the plate in contact with the bottom of the cavity at 1 atm and zero
d.c. bias, and (b) is a cell in the same operational mode, but with a
donut-shape, partially connected backside electrode. The central island
in the bottom electrode is floating.
wafer is ready for the backside vias etch step thru silicon
(DRIE). Again, the box oxide acts as an etching stop, and is
then opened by plasma and HF vapor etching [Fig. 2(f)].
Immediately, after the HF vapor step, a 5-µm-thick
polycrystalline silicon layer is deposited (LPCVD) with
intermediate doping iterations (1-µm + 2-µm + 2-µm) to
provide electrical connection from the wafer backside to the
bottom electrode of the CMUT cavity [Fig. 2(g)]. Then the
plate is released by 3 steps: (1) mechanically grinding down
the handle layer (~100 µm) of the plate SOI; (2) using an
isotropic etching recipe in a DRIE tool to remove the
remaining silicon; and (3) removing the box layer of the plate
SOI wafer via buffered oxide etch (BOE) solution [Fig. 2(h)].
Finally, a metallization and litho step is used, and the plate is
etched to define individual devices before the wafer is diced
(Not shown in Fig. 2).
To make sure that we obtain devices that have plates in
permanent contact with the bottom electrode, we intentionally
varied the cell radii, ranging from 1800 to 2200 um, the gap
heights, and plate thicknesses for our first fabrication run.
Notice that the permanent contact already happens during the
plate releasing step [Fig. 2(h)] after the majority of the silicon
in the handle layer is removed, resulting in the cross sectional
view as in Fig. 2(i). Fig. 3(a) also shows the wafer after all the
silicon has been removed by the isotropic etch step in the DRIE
tool. The plate deflection is visible, and a closer look reveals
the edge of the floating island in the electrode underneath the
plate. This proves that the plate is in permanent contact with
the bottom of the cavity.
Both the static & dynamic behavior for these CMUTs in
permanent contact mode were measured and simulated. By
using a Zygo white-light 3D surface profiler [Fig. 3(b)] and
Polytec optical fiber interferometer (vibrometer) at 1 atm, we
were able to validate our finite element static analysis model.
From the plate profile measurements we extracted the contact
radii for various biasing conditions. In addition, by performing
electrical impedance and displacement (optical fiber
interferometer) measurements, we were able to validate the
finite element modal analysis model as well.
The definition and notation for the partial electrode size used
in this paper are explained in Fig. 4.
III. CHARACTERIZATION RESULTS AND DISCUSSION
i. PROFILE MEASUREMENTS
The direct comparison of plate profile measurement by a
white-light 3D surface profiler (Zygo, Middlefield, CT, USA)
to our FEA based calculations [2] indicates a 3.5% difference
only [Fig. 3(b)]. Both measured and simulated curves
demonstrate a clear flat bottom in the deflection profile. Note
that the FEA curve in Fig. 3(b) has a slightly smaller contacting
region, which is caused by the stiffer boundary condition
(clamped posts) in the finite element model.
100%50%e50
100%
75%e75
(a) (b)
Fig. 4: Illustration of the definition of partial electrode size used in this
paper. Two examples are given. The electrode size is specified in terms
of radius, as a ratio of the actively connected electrode to the entire cell
radius. Therefore, the cell in (a) has a 50% electrode and is denoted as
e50, while (b) with a 75% electrode is denoted as e70.
0 1000 2000 3000 4000 5000 6000
-35
-30
-25
-20
-15
-10
-5
0
position (µm)
deflection (
µm)
FEA
Zygo
(a) (b)
Fig. 3: Photograph of a wafer after all the handle layer of the plate SOI
wafer was removed (a). We can see from the color that the box oxide is
exposed. Inset of (a) shows two cells in permanent contact, where the
edge of the floating island of the electrode underneath is visible, a clear
evidence of the permanent contact. The plate profile of a cell with 2200
µm radius, a 35.4 µm large gap, and a 30-µm-thick plate is measured by
a white light profiler (Zygo) and calculated by static FEA, as shown in
(b).
(a) (b)
(c) (d)
(e) (f)
(g) (h)
Silicon
Oxide
Poly-Si (i)
Fig. 2: The fabrication processes are illustrated from (a) to (h), while in
step (h) after the plate release, the plate will be pushed into contact with
the bottom of the cavity due to the 1 atm ambient pressure, as shown in
(i). For each figure, the left side shows a cell with a full bottom
electrode, while the right side shows one with a partially connected
bottom electrode.
ii. IMPEDANCE MEASUREMENTS
Fig. 5 shows an example of the impedance measurement
result by a impedance analyzer 4294A (Agilent Technolgies
Inc., Palo Alto, CA, USA), from which we can extract the open
and short circuit resonant freqeuencies.
We compare the short circuit resonant frequencies to the
result from a modal FEA in Fig. 6(a) for 3 devices with the
identical radius of 2000 µm, but with different electrode sizes
(e50, e75, e85, see Fig. 4). The discontinuities in the FEA data
are mesh artifacts that can be explained as follows: as the dc
bias voltage increases, the elements defined by the mesh in the
plate are pulled one by one into contact with the bottom of the
cavity, each resulting in a discontinuity in the curve. But
overall, the frequency values and trends from measurements
agree with the FEA results.
To further understand the frequency trends of devices with
different electrode sizes, the modal FEA data are plotted over a
wider d.c. bias voltage range (0 – 800 V) in Fig. 6(b). The
frequency trends can be explained by two competing
mechanisms: (1) spring softening [5], which causes the
frequency to decrease, and (2) a smaller vibrating portion of
the plate, which causes the frequency to increase as the d.c.
bias increases. For smaller partial electrode (e.g. e40 and e50)
cases, the CMUT structure above the active electrode is similar
to that of a conventional CMUT, thus the spring softening
effect dominates and the frequency decreases. For larger
partial electrode (e.g. e85), the smaller vibrating portion of the
plate dominates and the frequency increases. For the middle
cases, the curves show a combined effect of the two
mechanisms. In particular, for the e65 case, FEA static profile
analysis confirms that the dip in the frequency curve happens
when the edge of the contact region touches the boundary of
the partial electrode.
iii. DISPLACEMENT MEASUREMENTS
Fig. 7 shows an example of the displacement measurement
result by a optical fiber interferometer (Polytec, Irvine, CA,
USA) of a cell with 2200 µm radius. Again, these results
confirm the permanent contact of these CMUT devices. When
d.c. biased at 180 V, the first mode was measured at 75 kHz,
and the 100 mV a.c. peak to peak gives a maximum
displacement of 25 nm peak to peak. On the other hand, when
biased at 100 V d.c., the second mode was measured at 195.6
kHz, and the 100 mV a.c. gives a maximum displacement of ~
10 nm. When compared to the modal FEA results, the
difference in frequencies is within 3% for the first mode and
1.5% for the second mode respectively.
From the displacement measurements, we can also compute
the contact radius as illustrated in Fig. 8 (a), and the result is
compared to the static FEA calculation as shown in Fig. 8 (b).
Even though the displacement measurement is a dynamic
characterization tool and thus the contact radii under such
measurement should differ slightly from the static situation, we
still find a good agreement between the measured and the
simulated data, with the radii from dynamic displacement
0 50 100 150 200 250 30081
82
83
84
85
86
87
88
89
90
Bias voltage (V)
Frequency (kHz)
FEA e50
meas e50
FEA e75
meas e75
FEA e85
meas e85
(a)
0 100 200 300 400 500 600 700 80040
50
60
70
80
90
100
110
120
130
Bias voltage (V)
Frequency (kHz)
FEA e40
FEA e50
FEA e65
FEA e75
FEA e85
(b)
Fig. 6: Direct comparison between FEA and measurements. The
frequencies for devices with 2000 µm radius, a 28 µm gap, and a
30-µm-thick plate, but with different partial electrode sizes, as defined
in Fig. 4, are shown. In (a) the meas (measurement) data are taken from
the short circuit resonant frequencies, i.e. at the minimum of the
impedance amplitude. In both (a) & (b), the FEA data are the
(0,1)-mode frequency at zero dc bias from the modal analysis.
40 60 80 100 120 140
20
40
60
80
Amplitude (k Ω)
Frequency (kHz)
40 60 80 100 120 140-100
-80
-60
-40
-20
Phase (degree)
Frequency (kHz)
30V
60V
90V
120V
150V
180V
200V
Fig. 5: Electrical impedance measurement results for a cell with a
radius of 2000 µm and 85% (e85) electrode at different d.c. bias
voltages.
measurement being smaller than the static FEA result, which is
expected.
IV. CONCLUSION
The fabrication of CMUTs with the plate in permanent
contact with the bottom of the cavity is feasible. The direct
wafer bonding allows the large cell size required by the
airborne applications, while the processes based on a thick
buried oxide layer allows the realization of a partially
connected bottom electrode.
The characterization results demonstrate that our FEA
model predicts the behavior of our CMUTs in the permanent
contact mode very well, in both static and dynamic situations.
The model has not been validated at pressures higher than
1 atm, yet with the results presented in this paper, we are
confident that the model will predict the device behavior at
higher pressure as well.
Finally, since our targeted flowmeter application generally
requires the transducer to work in the pitch-catch configuration,
we will characterize our devices in a pitch-catch measurement
in the near future.
ACKNOWLEDGMENT
This research is funded by Fluenta Inc., Norway. The
authors also thank Kristian Eckhoff and Dag Sigmund
Johansen for many discussions on flare gas metering.
REFERENCES
0 1000 2000 3000 4000 5000
-10
-5
0
5
10
distance (µm)
displacement (nm)
(a)
0 100 200 300 400 500 600 700 800200
300
400
500
600
700
800
900
1000
DC bias (V)
Contact radius (
µm)
Contact radius comparison
measurement
FEA
(b)
Fig. 8: (a) the cross-sectional view from the displacement measurement
from Fig. 7(b). The contact radius is computed from the length of the
central none-moving part; (b) shows the contact radii calculated from
the profile of the static FEA result, and compares them to the values
obtained from the displacement measurement.
x (µm)
y (
µm)
Displacement (nmpp)
1000 2000 3000 4000
500
1000
1500
2000
2500
3000
3500
4000
4500
5
10
15
20
25
0 1000 2000 3000 4000 5000
-10
-5
0
5
10
distance (µm)
displacement (nm)
(a) (b)
x (µm)
y (
µm)
Displacement (nmpp)
1000 2000 3000 4000
500
1000
1500
2000
2500
3000
3500
4000
4500
1
2
3
4
5
6
7
8
9
10
11
12
0 1000 2000 3000 4000 5000
-6
-4
-2
0
2
4
6
distance (µm)
displacement (nm)
(c) (d)
Fig. 7 shows the displacement measurement by Polytec optical fiber
interferometer for a cell with 2200 µm radius, 75% electrode, 34 µm
gap, and 30 µm thick plate. Result for the first mode at 75 kHz was
measured with 180 V d.c. bias, 100 mV peak to peak a.c., and is shown
as a 2D contour in (a) and a cross-sectional view (displacement at
different time) in (b). The second mode at 195.6 kHz was measured
with 100 V d.c. bias, 100 mV peak to peak a.c., and is shown in (c) &
(d).
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with national & provincial regulations,” from CB Engineering Ltd., 2005.
[2] M.-C. Ho, M. Kupnik, and B. T. Khuri-Yakub, “FEA of CMUTs suitable
for wide gas pressure range applications,” in Proc. IEEE Ultrasonics
Symposium, pp. 1234-1237, 2010.
[3] M. Kupnik, S. Vaithilingam, K. Torashima, I. O. Wygant, and B. T.
Khuri-Yakub, “CMUT fabrication based on a thick buried oxide layer,” in
Proc. IEEE Ultrasonics Symposium, pp. 547-550, 2010.
[4] K. K. Park, H. J. Lee, M. Kupnik, and B. T. Khuri-Yakub, “Fabrication of
capacitive micromachined ultrasonic transducers via local oxidation and
direct wafer bonding,” IEEE/ASME Journal of Microelectromechanical
Systems, vol. 20, no. 1, pp. 95-102, 2011.
[5] G. G. Yaralioglu, S. A. Ergun, and B. T. Khuri-Yakub, "Finite-element
analysis of capacitive micromachined ultrasonic transducers," IEEE
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vol. 52, no. 12, pp. 2185- 2198, Dec. 2005
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