PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Electrostatically Driven Airborne Ultrasound Transducer withPerforated Backplate for Nonlinear Acoustic Applications
Takaaki KAMIGAKI1; Yuki NINOMIYA2; Hiroyuki SHINODA3
1, 2, 3

The University of Tokyo, JapanABSTRACTThis paper proposes a capacitive transducer to realize a thin airborne ultrasound phased array for nonlinear
acoustic applications. The generation of high-intensity ultrasound requires a displacement of several
micrometers of a diaphragm. Conventional capacitive transducers with parallel-plate structure have notachieved this because a thin air layer between the electrodes prevents the diaphragm from vibrating. We
have solved the problem by providing perforations at a backplate electrode. The air between the diaphragmand the perforated backplate can travel freely through the perforations when the diaphragm vibrates. We
drove the proposed transducer by controlling the amount of electrical charge stored in the diaphragm. Thisdriving method can prevent the pull-in phenomenon. In the experiment, a prototype transducer, with athickness of 334 μm, emitted 392 Pa (RMS) on the surface when driving at 51 kHz. The diaphragmvibrated with an average amplitude of 3 μm (RMS).
Keywords: Capacitive airborne ultrasound transducer, High-intensity, Perforated backplate

1. INTRODUCTION
High-intensity airborne ultrasound has a diverse range of applications, such as for parametricspeaker(1), noncontact tactile display(2–4), air flow control(5), and acoustic manipulation(6–9).
Typical devices for the above applications comprise airborne ultrasound phased arrays (AUPAs),
using commercial piezoceramic transducers. They can provide arbitrary waveforms with a hightemporal resolution by electrically controlling the phase of each transducer. Meanwhile, the existing
AUPAs have practical problems, such as their thickness and low efficiency. Solving these problems
is necessary for the expansion and practicalization of AUPA applications.
Many thin AUPAs have been developed, such as devices based on piezoelectric transducers(10),capacitive transducers(11), and thermoacoustic transducers(12). However, those piezoelectric andcapacitive transducers cannot generate high-intensity airborne ultrasound because they are generally
designed for sensing applications. The thermoacoustic transducer can generate high-intensity
airborne ultrasound, although its energy efficiency remains to be improved.
The goal of this work is to realize a thin AUPA with high intensity and high efficiency. The target
driving frequency is higher than 40 kHz, in reference to the typical piezoceramic transducers. In theprevious study, we developed a single capacitive transducer that generate s approximately 420 Pa(RMS) at the surface and achieved an electro-acoustic energy conversion efficiency of 55% at 44kHz when the DC voltage was 500 V and the amplitude of the AC voltage was 150 V(13). Thistransducer achieved the above characteristics by using a fine mesh electrode knitted with a metalthread as the backplate.
In this paper, we propose a practical structure of the capacitive transducers applicable to theAUPA. The proposed transducer adopts a parallel-plate structure with a perforated backplate. Thistransducer can be driven with a lower voltage than the mesh electrode type. We experimentally
showed that the prototype transducer generated high-intensity airborne ultrasound.

1kamigaki@hapis.k.u-tokyo.ac.jp
ninomiya@hapis.k.u-tokyo.ac.jp
3hiroyuki_shinoda@k.u-tokyo.ac.jp26363

2. Problems in Parallel Plate Structure

Figure 1 – Typical structure of capacitive transducers.
Figure 1 shows a typical capacitive transducer driven by electrostatic force (ESF) when the AC voltage
is applied with the DC voltage. The RMS sound pressure generated from the transducer ȁ‫݌‬଴ ȁ [Pa] isdetermined by the diaphragm displacement, given by the following equation, assuming that the uniform
diaphragm oscillates with a simple harmonic motion:ȁ‫݌‬଴ ȁ ൌ ȁ݆߱ߩܿߦȁ(1)
3
where ߱ [rad/s] is the angular frequency, ߩ [kg/m ] is the air density, ܿ [m/s] is the acoustic velocity inthe air, and ߦ [m] is the average RMS displacement of the diaphragm. This equation shows that higher
frequencies decrease ߦ to obtain the same ȁ‫݌‬଴ ȁ. For example, in our measurement, ߦ is 5 μm at the 40
kHz piezoceramic transducer (T4010A1, NIPPON CERAMIC CO., LTD.) driven by a sinusoidal voltage
with 12 V amplitude, assuming ߩ = 1.2 kg/m3 and ܿ = 340 m/s. To obtain the same intensity at 80 kHz, ߦis 2.5 μm. The existing parallel-plate transducers have not achieved the above displacement due to the threefactors described below.
2.1 Discharge between Electrodes
Increasing the electric field intensity (EFI) between the diaphragm and the backplate electrodecontributes to increasing the diaphragm displacement because the ESF increases with the proportionalsquare of the EFI. The applied voltage is limited to a discharge voltage decided by the air gap D [m]and the internal pressure ‫݌‬௜௡ [Pa]. The discharge voltage in the parallel-plate structure ܸ஻ [V] isobtained by Paschen’s law, given by:‫݌ܤ‬௜௡ ‫ܦ‬ܸ஻ ൌ(2)ͳሺ‫݌ܣ‬௜௡ ‫ܦ‬ሻ െ   ቀͳ ൅ ߛቁ
where ‫ ܣ‬and ‫([ ܤ‬Pa࣭m) -1 ] are constants determined by the gas between the electrodes, and ߛ [-]is the number of electrons emitted from a cathode by ߛ-action. Figure 2(a) shows the numericalcalculation results of ܸ஻ and the EFI against D based on Eq. (2). This figure shows that the increaseof the EFI without discharge can be achieved by shortening D.
2.2 Viscosity Loss in Air Layer
The loss in the structure should be as small as possible compared with the radiated power toobtain high efficiency. The decrement of D enables a higher driving force, according to Fig. 2(a).
However, extremely shorting D in the airtight structure, as shown in Fig. 1, increases the inevitable
loss in the structure due to viscosity in the air layer. The thermal conduction loss also contributes tothe efficiency, but it is minor compared with the viscosity loss. Figure 2(b) shows our numericalcalculation result of the electro-acoustic conversion efficiency, considering the air viscosity andthermal conduction. This graph shows that increasing D contributes to higher efficiency, which is atrade-off against increasing the EFI.
2.3 Pull-in Phenomenon
The pull-in phenomenon is a well-known problem with the parallel-plate structure. Thediaphragm becomes immobile by sticking to the backplate when a predetermined voltage is applied
between the electrodes. To avoid pull-in, it is necessary to apply the voltage within the range where
the diaphragm displacement does not exceed ‫ܦ‬/3. The cause of this phenomenon is the collapse of
the force balance acting on the diaphragm, i.e., the ESF becomes larger than a restoring force due tothe diaphragm stiffness.
Capacitive transducers using the pull-in phenomenon have been proposed(14,15). These methods

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(a)

(b)

Figure 2 – Numerical calculation results of: (a) discharge voltage VB and its electric field against the air
gap D, and (b) energy efficiency of the parallel-plate structure against D.
can generate a higher sound pressure than those without pull-in, but their sound pressure is outside
the scope of the target sound pressure.

3. Proposed Transducer

Figure 3 – Cross-sectional view of a proposed structure with a perforated backplate electrode.
Figure 3 shows the proposed structure of a single transducer to solve the problems. The proposed
structure is realized by arranging periodically repeated spacers in one direction between a series of adiaphragm and a perforated backplate electrode. The air gap between the diaphragm and the backplateis set to 10 μm to secure the diaphragm displacement, assuming that the driving frequency is higherthan 40 kHz, as mentioned in Section 2. This distance supplies a high EFI. The air between thediaphragm and the backplate can travel freely through the perforations when the diaphragm vibrates.
Therefore, the proposed structure can increase the driving force with suppression of the viscosityloss.
To ensure the diaphragm displacement without the pull-in, we propose a driving method bycontrolling the charge amount. The proposed method repeats storage and dissipation in the structure
every half of the driving cycle. The stored and dissipation time is sufficiently short, compared withhalf of the driving cycle. The ESF is constant regardless of the electrode distance because the stored
electrical charge is constant. Thus, the diaphragm can be attracted towards the backplate without thepull-in. When the electrical charge is dissipated, the diaphragm lifts the outside air by diaphragm
stiffness. The push-pull circuit realizes the driving method.
Many capacitive transducers with a perforated backplate have been proposed. However, they are
not suitable for generating high-intensity ultrasound because their air gap is typically shorter than 1μm.

4. Experiments
4.1 Prototype Transducers
Figure 4 shows the prototype transducer by laminating the diaphragm on a stainless structure. Thediaphragm was a 4.4-μm-thick aramid film (Mictron, TORAY INDUSTRIES, INC.) deposited with
30-nm-thick platinum. The stainless structure comprises three stainless steel plates of different
thicknesses (SHIN-EI SANGYO CO., LTD). The top and bottom layers were spacers, and their6365

(a)(b)Figure 4 – (a) Photograph of a prototype transducer; (b) Cross-sectional view of the prototypetransducer.
thicknesses were 10 μm and 300 μm, respectively. The spacer width was 150 μm with the interval tothe next spacer was 850 μm. The middle layer was a 20-μm-thick perforated backplate. Thebackplate had repeated rectangular openings of 80 μm × 500 μm. We selected the dimensions after
theoretical consideration in reference to (16, 17) because they contribute to the air viscosity loss.
The total movable area of the diaphragm was 10.1 mm × 10.5 mm. We minimized the peripheralarea where the diaphragm and stainless structure overlap out of the movable area. Furthermore, wecovered the peripheral area by placing a 1-mm-thick acrylic plate with a 10.1 mm × 10.5 mm
aperture on the prototype surface so that sound waves from the peripheral area do not affect themeasurement sound pressure. We inserted a 12.5-μm-thick insulating film (Kapton 50EN, DU
PONT-TORAY INDUSTRIES, INC.) between the diaphragm and the stainless structure to prevent
discharge.
We fabricated two kinds of transducers to obtain the contribution of the diaphragm stiffness to thegenerated sound pressure. One type is the diaphragm with applied external tension in one direction.
The other type is the diaphragm without external tension. The value of the external tension was notquantified because the tension was applied by the author’s hand. We fabricated two transducers ofeach type.
4.2 Experimental Results
We measured the generated sound pressure within the applied voltage range where no discharge
occurs. A standard microphone (4138-A015, Bruel&Kjaer) was set 20 cm above the transducer andthe sound pressure was obtained by an oscilloscope (DCS-1074B, TEXIO CORPORATION)
connected to the microphone through an amplifier (NEXUS Conditioning Amplifier, Bruel&Kjaer).
We confirmed that interference is negligible by measuring the sound pressure fluctuations when themicrophone was moved from the original position. The push-pull circuit was used to drive theprototype transducer. The storage and dissipation time was one-eighth of the driving cycle.
First, we obtained the frequency characteristics of each transducer. The applied voltage for thetransducer was 100 V when the diaphragm was at the initial gap. Figure 5 shows the frequency
characteristics of the four prototype transducers. The RMS sound pressure ȁ‫݌‬ȁ observed at 20 cm
above each prototype transducer was calculated by Fourier transformation. The result shows a peakat 51 kHz when the diaphragm was with applied external tension, and the peaks around 86 kHz exist
regardless of the external tension.
Next, we obtained the contribution of the applied voltage to the generated sound pressure at thepeak frequency of both types (V2 in Fig. 5), i.e., 60 kHz and 88 kHz in the case without the externaltension, and 51 kHz and 86 kHz in the case with the external tension. The experimental setup was
the same as the first experiment. The applied voltage was from 50 V to 300 V when the diaphragm
was at the initial gap. Figure 6(a) shows the RMS sound pressure ȁ‫݌‬ȁ observed at 20 cm above each
prototype transducer and Fig. 6(b) shows the calculated RMS sound pressure at the prototype surfaceȁ‫݌‬଴ ȁ, following the theoretical relationship between the device surface pressure and pressure in theair (18). The maximum ȁ‫݌‬଴ ȁ was 392 Pa at 51 kHz when the maximum voltage was applied to thetransducer. In this time, the average displacement of the diaphragm was approximately 3 μm, as
calculated using Eq. (1).

6366Figure 5 – Frequency characteristic of each prototype transducer. The sound pressure was obtained at 20cm.

(a)

(b)

Figure 6 – Applied voltage contribution to generated sound pressure. (a) Sound pressure obtained at 20cm, (b) sound pressure at prototype surface.
4.3

Discussion
In the first experiment, the peaks occur at around 86 kHz regardless of the external tension state.
It is assumed this is due to the resonance of the perforated backplate. We analyzed the resonant
frequency of the backplate supported by the spacers, using ANSYS 19.1(ANSYS Inc.), andconfirmed that the resonant frequency was 83 kHz. In the second experiment, the generated soundpressure at 51 kHz increased proportional to the approximate square of the applied voltage according
to the principle, whereas the other did not increase according to the principle. This reason is not
obvious, and the dynamic mechanism in the large-amplitude operation is still unclear.

5. Conclusions
In this paper, we proposed a practical capacitive transducer for AUPA. The proposed transducer,
with a perforated backplate, enhanced the ESF with the suppression of the viscosity loss. The
transducer emits airborne ultrasound by controlling the amount of electrical charge accumulated in thediaphragm. In the experiment, we obtained 392 Pa (RMS) at 51 kHz. In the future, we will measure
the electro-acoustic energy efficiency and clarify the mechanism.

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ACKNOWLEDGEMENTS
This research was supported by JSPS KAKENHI Grant Number JP16H06303 and JST CREST
JPMJCR18A2.

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