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

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-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)

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500

1000

1500

2000

2500

3000

3500

4000

4500

5

10

15

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25

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5

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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

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2

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12

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-6

-4

-2

0

2

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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).

[1] C. Gulaga and B. Light, “Flare measurement ‘best practices’ to comply

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

Transactions on Ultrasonics, Ferroelectrics and Frequency Control,

vol. 52, no. 12, pp. 2185- 2198, Dec. 2005

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