PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Design of resonant vacuum pressure sensor with CMUT for highsensitivity and linearity
Xiaoli ZHANG1; Lu YU1; Haixia YU1; Dachao LI1
1

Tianjin University, China

ABSTRACT
Vacuum pressure monitoring is mainly used for atmospheric pressure measurement and pressure
measurement inside organisms, and is widely used in aviation, meteorology and medical diagnosis. This
paper innovatively reports a vacuum pressure monitoring method using capacitive micromachined
ultrasonic transducer (CMUT) array which is a small MEMS device manufactured by wafer bonding
process. Both of the manufacturing process and detection circuits are simplified compared with those of the
traditional MEMS devices used for vacuum pressure monitoring. By detecting the change of resonant
frequency rather than capacitance of the CMUT array with varying vacuum pressure, the anti-interference
ability of vacuum pressure(less than 1atm) monitoring is improved. Simulation and experimental results are
consistent and show that the resonant frequency of the designed CMUT varies linearly with the appliedpressure ranging from 20-101kPa. The sensor achieves high detection sensitivity of 438Hz/kPa and
R-Square of 0.99335 at DC bias of 30V.
Keywords: CMUT, Resonant vacuum pressure sensor, DC bias

1. INTRODUCTION
Vacuum pressure sensors have been extensively utilized in modern aerospace field. Owing to the uniqueadvantages of micro-electromechanical processing technology, MEMS pressure sensors are popular
nowadays and mainly classified into silicon piezoresistive, silicon capacitive and silicon resonant pressure
sensors (1). For all these sensors, technical indicators such as sensitivity, linearity, and detection range
should be carefully considered.
Silicon piezoresistive pressure sensors ususally consist of pressure-sensitive resistor made on thepressure sensitive diaphragm. The pressure value is obtained by detecting change of the resistance. The
merits like feasible preparation, convenient detection and low cost make it well developed. But for the
problems such as zero and temperature drift, they are only generally suitable for the occasions with low
requirements on accuracy and long-term stability (2). In general, there exists a trade-off between sensitivity
and linearity (3). Silicon capacitive pressure sensors detect the capacitance change between the upper andlower electrodes of the sensor for the purpose of pressure detection. However, the sensitivity of capacitive
pressure sensors is limited by compressive strain and high Young’s modulus of the solid dielectric
elastomer layers (4). Although some methods has been used to increase the sensitivity, the sensitivity
decreases rapidly as the applied pressure increases and the fabrication process is complicated (5).
Silicon resonant pressure sensor, which measures external pressure by detecting the change of resonant
frequency, is a typical representative of high precision pressure sensors. Organically combining mechanicalresonance sensing technology and micro-electromechanical processing technology, silicon resonantpressure sensor not only has the advantages of high precision, good stability and quasi-digital output of
traditional mechanical resonance sensor, but also has the characteristics of small volume, low power
consumption, compatibility with integrated circuit technology, and easy to mass production (6-12).
The most common silicon resonant pressure sensor has composite structure of pressure sensitive
diaphragm and resonator, in which the resonator is fixed on the surface of pressure sensitive diaphragm.
The resonator is vacuum packaged and not easily affected by the external environment. However, thecommon complicated stress-relieving vacuum packaging, process and electrical feedthroughs to the outside
make its design and fabrication a challenging problem, hindering its widespread application (13).
1zhangxl@tju.edu.cn

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Z Li. et al (14) also used CMUT for ultra-low pressure measurement. They show that the resonant
frequency of the CMUT varies linearly with the applied pressure, and the membranes of the biased CMUTs
can produce a larger resonant frequency shift than the diaphragms with no DC bias. But they did notconduct experiments to demonstrate it.
In this paper, a CMUT array is firstly proposed for detection of high vacuum pressure and the tendencyof frequency response is quite opposite from that in ultra-low pressure scope. Firstly, the influence of DC
voltage and external pressure on the resonant frequency of CMUT was analyzed theoretically. Then finite
element model was established to conduct modal analysis of the CMUT cell to determine the structure
parameters. The vacuum bonding process was used to fabricate the CMUT device. Finally, an experimental
system was built to carry out the pressure detection experiments of the CMUT device. High detection
sensitivity of 438Hz/kPa and R-Square of 0.99335 are obtained in the pressure range of 20-101kPa. The
pressure detection range can be easily changed by changing the structural parameters of CMUT. Therefore,
CMUT devices have broad application prospects in the field of pressure detection.

2. Design
2.1 Design of CMUT Array
In this paper, a CMUT array composed of three elements was built for pressure detection, as shown in
Figure 1. The array is designed on the basis of linear relationship between the resonant frequency and theexternal pressure. All the cells in each element are connected in parallel. The outer two elements were
designed to validate the consistency of the process.

Figure 1 – CMUT array designed for pressure detection
Each cell in Fig.1 is composed of a metalized silicon membrane and fixed bottom electrode as well as thevacuum cavity between them, which is similar to a capacitor, as shown in Fig.2. When a DC bias voltage isapplied to the top and bottom electrodes, the clamped ﬂexible membrane is deformed towards the ﬁxed
bottom electrode to reach equilibrium. When an alternating current voltage is added, a periodic vibration of
the membrane is obtained. The circular membrane is used in this paper for it greatly reduces stressconcentration.

Figure 2 – Geometry of the CMUT cell9782.2 Theory Analysis of Structure Design
The variation of external pressure can lead to a resonant frequency shift of the vibrating
membrane when the electrostatically actuated membranes are used as pressure sensors. As thepressure increases and the deflection-to-thickness ratio is higher than 0.2, the derived expressions in(15) are not valid. Therefore, the effect of electrostatic force and pressure on the resonant frequency
of CMUT membrane needs to be reconsidered.
The “soft spring effect” that the resonant frequency of the vibrating membrane decreases with theincrease of DC bias which is lower than collapse voltage has been widely studied and confirmed (16).
However, the resonant frequency of the CMUT membrane increases gradually as the externalpressure gets higher, showing stress hardening effect or “hard spring effect”.
It is interesting that hard spring effect and soft spring effect have opposite effect on the resonancefrequency. The combined influence of these two factors is furtherly researched using the FEM modelin the next section. In high pressure range, the former effect plays a leading role by reasonably design
the structural parameters.
2.3 Simulation of CMUT Parameters
To understand the behavior of CMUT, a finite element model (FEM) was created in COMSOLMultiphysics (COMSOL, Inc., Burlington, MA, USA) to represent a circular CMUT cell. The model couples
an electromechanics subdomain to the vacuum cavity and solid materials. The membrane layer (Si) is fixed at
the edges to prevent translation motion but allow for deflection, and the insulation layer is SiO2 (17).
Due to the limitation of the material, the thickness of CMUT membrane is set as 10µm. The insulation
layer, which isolates the conductive silicon substrate from the top electrode, is set to be 2um to avoid
shorting. In this paper, we proposed two structures for simulation. The dimensions of the two structures aswell as the mechanical and electrical properties (density: 𝜌, Young’s modulus: E, and Poisson’s ratio: ν,relative permittivity, 𝜀𝛾 ) of the materials used in the FEM are listed in Table 1. The simulation results ofstructure 1 and 2 for pressure detection ranging from 20kPa to 101kPa are shown in Fig. 3 and 4,
respectively.
Table 1 – Dimensions and properties of materials used in COMSOL model
Structure 1

Structure 2

radius/thickness, μm

radius/thickness, μm

Top electrode250/0.2

Membrane𝜌, kg/m3

E, GPaν𝜀𝛾

350/0.2

19300

70

0.44

--

400/10480/10

2329

130

0.18

11.7

gap

400/5

480/10

--

--

--

1

Insulation

400/2

480/2

2200

70

0.17

4.2

220

R400um-30V-simu
R400um-90V-simu
R400um-150V-simu
R400um-200V-simu

215

Frequency (kHz)

210
205
200
195
190
20

40

60

80

100

Pressure (kPa)

Figure 3 – The simulation results of structure 1 (R400µm, gap 5µm) for detection of 20-101kPa

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It can be expected that in both figures, at given pressure, the resonant frequency falls down as thevoltage increases because of the soft spring effect. In figure 3, the linearity of the curves gets worse with
the increase of DC bias because the soft spring effect gets more effective. However, in figure 4, thevariation of resonant frequency is not obvious as the DC bias gets larger for the spring softening effect issurmounted by the stress hardening effect which plays a leading role in changing the resonant frequency ofthe membrane. The resonant frequency increases linearly with the rise of pressure at a given DC bias
voltage for structure 2 which is selected for the following fabrication and experiments.
180

R480μm-30V
R480μm-90V
R480μm-150V
R480μm-200V

175

Frequency (kHz)

170
165
160
155
150
145
140
20

40

60

80

100

Pressure (kPa)

Figure 4 – The simulation results of structure 2 (R480µm, gap 10µm) for detection of 20-101kPa

3. Fabrication
The CMUT array was fabricated using Si wafer bonding process which introduces small stress, and goodcell uniformity (18). It begins with two wafers: a prime quality silicon wafer and a SOI wafer. In its simplest
form, the wafer-bonded CMUT process can be summarized as follows: The prime quality silicon wafer isthermally oxidized to a predetermined thickness (Fig. 5a), followed by a photolithography step to define thecavity shape (Fig. 5b). The silicon dioxide layer is dry etched through the photoresist pattern all the way tothe silicon, as shown in Fig. 5c. After the photoresist is removed, another layer of silicon dioxide is thermallygrown to form the insulation layer for isolating the conductive silicon substrate from the top electrode to
avoid shorting (Fig. 5d). Following RCA cleaning and surface activated, the SOI wafer and the prime wafer
are brought together in vacuum (Fig. 5e). After bonding and annealing, the handle of the SOI wafer as well as
the buried oxide layer is removed to release the membranes (Fig. 5f). Openings through the silicon andsilicon dioxide layers are deﬁned with photolithography and etched through to access the bottom silicon layer
and make the ground connection (Fig. 5g). Finally the top Au electrode was sputtered on the membranes tomake the top connection (Fig. 5h). The elements are electrically isolated by etching all the way to the oxide
layer. Wafer bonding process simpliﬁes the process, reduces the number of steps and the turn-around time,eliminates problems with membrane release, high stress, and porous ﬁlms, and increases the yield, uniformity,
and process control.

Figure 5 – Detailed view of the manufacture process of the CMUT array
The finished bare CMUT chip is glued on a specially designed printed circuit board (PCB), and the top
and bottom electrodes of the CMUT device are wire bonded to the corresponding pads on PCB, as shown in
Fig. 6a, the partial enlarged detail of the CMUT array is shown in Fig.6b. The gold color represents the gold
electrode on the membrane. A cross-section view of a single cell of the CMUT array is shown in Fig.6c.

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Figure 6 – (a) The photo of the CMUT array, (b) partial enlarged detail of the CMUT array,(c) a cross-section view of the CMUT cell.

4. Experiments
4.1 Pressure Detection System
After the top and bottom electrodes of the CMUT device are wire bonded to the corresponding pads on the
PCB, a vacuum pressure detection system was built to perform measurements at elevated pressure. Figure 7
shows the schematic view of the experimental setup.

Figure 7 – Schematic view of the experimental setup
During the experiment, a vacuum pump is used to extract air from the chamber to provide vacuum
pressure. The wires are inserted into the chamber through a plug. One ends of the wires are connected to the
top and bottom electrodes of the CMUT device placed in the vacuum chamber, and the other ends areconnected to the two ports of the impedance analyzer fixture. The output of DC source is connected to theimpedance analyzer fixture which provides DC bias voltage to CMUT. At each DC bias, measurements wereconducted by the impedance analyzer HP 4294 (Agilent Technolgies Inc., Palo Alto, CA, USA) to obtainelectrical impedance curves of the CMUT device at various pressures. The measured data and curves can berecorded by the personal computer connected to the impedance analyzer.
4.2 Experiment Results and Discussion
The measured resonant frequency curves of the fabricated CMUT array are shown in Fig. 8. The linear fit
was conducted for each curve at DC biases of 30V, 90V, 150V, 200V, respectively. Then the results weresummarized in Table 2. High sensitivity and linearity were achieved, and the sensitivity at 30V can reach as
high as 438Hz/kPa. According to the R-Square value of the curves under different DC biases, the981

improvement of linearity is not obvious when the DC bias is increased from 30V to 200V. So 30V is preferredsince low voltage is more convenient and safe. The experimental curve shows a good agreement with the
FEM result as shown in Fig. 9. The FEM underestimates the magnitude of the resonant frequency for theinternal stress of the CMUT membrane induced during the fabrication.
185

exp-30V
exp-90V
exp-150V
exp-200V

180

Frequency(kHz)

175
170
165
160
155
150
145
20

40

60

80

100

Pressure (kPa)

Figure 8 – The resonant frequency variation of the CMUT array
under pressures of 20kPa-101kPa at different voltages

Table 2 – Sensitivity and linearity of pressure curves of cells 2 under different DC bias
DC bias, V

Slope, Hz/kPa

R-square30

438.14

0.9933590

434.530.9942150

429.37

0.99607200

412.420.99829185

sim-30V
exp-30V

180

Frequency(kHz)

175
170
165
160
155
150
145
140
20

40

60

80

100

Pressure (kPa)

Figure 9 – Comparison of experiment and simulation results of
the resonant frequency variation at 30V, 20kPa-101kPa

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5. CONCLUSIONS
A novel method of vacuum pressure monitoring using CMUT is proposed in this paper. The array isdesigned on the basis of linear relationship between the resonant frequency and the external pressure ranging
from 20 kPa-101 kPa. The tendency of frequency shift here is quite different from that in micro-pressure
detecting process. With the rise of DC bias, the sensitivity gets lower while the linearity gets higher. The
finite element model and the experimental results show a strong agreement. The sensor achieves highdetection sensitivity of 438Hz/kPa and R-Square of 0.99335 at DC bias of 30V. The CMUT has simple
processing technology, approvable consistency and high yield. It can be used for detection of other pressure
ranges only by altering the structure parameters. Integrated circuit will be used to realize portable andminiaturized detection in the future. Therefore, CMUT array has broad application prospects in the field ofpressure measurement.

ACKNOWLEDGEMENTS
This work was supported by the National Key Research and Development Program of China(No.2017YFA0205103), the National Natural Science Foundation of China (No.81571766) and the 111
Project of China (No.B07014).

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