IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 43, NO. 1, JANUARY 1996 1

A Surface Micromachined Electrostatic Ultrasonic Air Transducer

Matthew I. Haller and Butrus T. Khuri-Yakub, Fellow, ZEEE

Abstruct- Airborne ultrasound has mainy applications such as, ranging, nondestructive evaluation, gas flow measurement, and acoustic microscopy. This paper investigates the generation and detection of ultrasound in air at a few MHz. Conventional plane piston lead zirconium titanate (PZT) based transducers perform poorly for this application due to the lack of proper matching layer materials. Electrostatic, or capacitive, transducers promise higher efficiency and broader bandwidth performance. The device structure in this work consists of a capacitor where one plate is a circular silicon nitride membrane coated with gold and the other is a rigid silicon substrate. By applying a voltage between the membrane and the silicon substrate, an electrostatic force is exerted on the membrane which sets it in motion, thus generating a sound wave in air. Presented here is an electrical equivalent circuit model for electrostatic transducers which is based on the early work of Mason [l]. The electrostatic transducers were designed and constructed for operation at 1.8 and 4.6 MHz. The transducers were fabricated using standard micromachining techniques. An optical interferometer was used to measure the peak displacement of the 1.8 MHz electrostatic transducer at 230 &V. A transmit-receive system was built using two electrostatic transducers. The system had a signal to noise ratio of 34 dB at a transducer separation of 1 cm. Each transducer had a 3-dB bandwidth of 20%, and a one-way insertion loss of 26 dB. There is excellent agreement betweein the measured device performance and theoretical predictions.

I. INTRODUCTION HE generation of ultrasound in air is interesting for a T variety of applications including robotics distance sensing

and imaging [2]-[6], gas flow measurements [7], in situ process monitoring [8], and acoustic microscopy [9], [lo]. For maximum resolution and sensitivity, it is desirable to operate at the highest possible frequency. The maximum frequency of operation is limited by transducer efficiency, the signal to noise ratio of the transmitter and receiver electronics, and the attenuation of sound waves in air (1.2 dB/cm at 1 MHz and increases as the square of the frequency). The interest of this research is in operating ia the 1-10 MHz frequency range. Conventional techniques to generate ultrasound at this frequency use a piezoelectric material (typically PZT) with one or more quarter wave matching layers. There is a mismatch of about 1 O5 between the impedance of the piezoelectric which is approximately 35 . lo6 kg/m2 . s andl that of air which is about 400 kg/m2 . s. This mismatch results in transducers having either narrow bandwidth or poor efficiency along with the difficulty of synthesizing the proper impedance matching layers Various attempts have been made to engineer materials

Manuscript received August 2, 1994, revised May 2, 1995 The authors are with the Edward L Ginzton Laboratory, Department of

Publisher Item Identifier S OSSS-3010(96)0035S-9. Electrical Engineering, Stanford University, Stanford, CA 94305 USA

for use as matching layers in order to improve the efficiency and bandwidth of such transducers [2], [ 111-[ 131 with limited success.

The goal of this research is to develop a technology that can generate efficient broadband ultrasound in air over a wide range of frequencies (1-10 MH;!). This technology should also be inexpensive, provide good process control, and allow for the fabrication of transducer arrays for electronic focusing and scanning. To accomplish this, the use of micromachined electrostatic actuators is proposed. Other researchers have used silicon micromachining to fabricate condenser microphones [14], pressure sensors [15]-[17], and even electrostatic ul- trasonic sources [ 181-[20]. These have typically relied on roughening the surface of a metal plate and bonding a thin metalized dielectric to the plate. The microscopic groves in the plate act as resonators and determine the frequency response of the transducer. These devicles are not easily characterized and their fabrication is more art than science.

In the work presented here, precisely controlled circular membranes are fabricated using silicon processing. Electrode separation is carefully controlleld to nanometer tolerances using thermal oxidation growth techniques. This allows repeatable manufacture and better sensitivity, as well as confirmation of theoretical models.

11. ELECTROSTATIC ACTUATION AND MEMBRANE VIBRATION

Consider a parallel plate capacitor with one fixed and one free electrode. If a voltage V is applied to the capacitor, the free electrode will experience an attractive electrostatic force of magnitude F = $ e A g , where e is the dielectric constant of the material between the plates, A is the capacitor area, V is the voltage across the capacitor, and d is the electrode spacing. Because the force depends on the square of the voltage, the second harmonic of the applied voltage will be generated. For operation at the: first harmonic, a dc bias Vbias

is applied to the capacitor along with the RF signal such that V ( t ) = Vbias + Vac cos ( w t + ($). By making the bias voltage much larger than the time varying voltage, the dominant time varying force becomes

cos (wt + 4 ) . EAVbias K c F=-- d2

A good design requires a large linear displacement due to the applied voltage so a large amount of ultrasonic energy is coupled into the air.

The membrane is assumed to be circular in shape as shown in Fig. 1. As the membrane vibrates due to the electrostatic

0885-3010/96$05.00 0 1996 IEEE

2 IEEE TRANSACTIONS ON ULTRASONICS. FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 43, NO. 1, JANUARY 1996

L Fig. 1. Schematic of free membrane suspended above a rigid substrate

force, the gas between the membrane and the back plate is compressed. This effect can be ignored since the restoring force from the silicon nitride membrane is two orders of magnitude larger than the force from the compressed air. Following Mason's analysis [l] of a suspended membrane under tension, the equation of motion of the membrane in phasor terms (assuming e jWt time variation) can be written as

where g o is the residual stress in the membrane, t, is the membrane thickness, T is the radial position measured from the center, U is the membrane displacement as a function of r , w is the radian frequency of the drive voltage, p is the membrane density, and P is the electrostatic pressure applied to the membrane (the force phasor from (1) divided by the area)

where teff is the effective dielectric constant and deE is the effective spacing of the series combination of the membrane (silicon nitride) and air gap, E , and E , are the dielectric constants of air and silicon nitride, respectively, and t , is the air gap thickness.

The solution to (1) can be found for a circular membrane of radius a to be

This has a peak displacement at resonance when w = W O = 2 . 4 0 5 : m . Consider an array of circular membranes vibrating in unison as shown schematically in Fig. 2. The average velocity at the surface will be given by

- 2 j w a uaverage -

where a is the fraction of the surface that is a membrane. Some of the area of the capacitor will not vibrate with the applied voltage because it is mechanically clamped, thus, Q is less than one. Typically, a is on the order of 0.5 for the devices described in this paper. The effective mechanical impedance ( 2,) of the membrane, as defined by Mason [ 11, is then found to be

Fig. 2. Idealized vibration modes of 4 x 4 matrix of membranes.

_l_""__l""_"__ll"____I i~.~.....~~..."~~.~."~~~"~"~!

$:1

Fig. 3. parasitic resistances, capacitance, and acoustic losses have been accounted.

Equivalent circuit of electrostatic source for which series inductance,

Combining (3)-(3, the solution to (6) is

(7)

This equation gives the mechanical impedance of an array of circular membranes as a function of frequency and its physical properties.

111. EQUIVALENT CIRCUIT

This section describes the development of an electrical equivalent circuit of the transducer as a mechanical impedance coupled through a transformer to the electrical port [l] as shown in Fig. 3 . The force at the acoustic port can be written as

(8)

If the current is set to zero and the acoustic port is clamped (setting U' = 0), then the voltage across the transformer and the force at the acoustic port is related by the transformer ratio

(9)

F = aAP + Z,u'.

Vac = q5F = @AP. The transformer ratio is then given by

The capacitance of the active membrane elements is given by c d

(1 1) Eeff

Cd = aA-. deff

There are various parasitic losses, capacitances, inductances, and resistances that need to be included in the equivalent circuit. These arise from packaging, mechanical coupling, and resistive losses. They are taken into account as shown in

HALLER AND KHURI-YAKUB: SURFACE MICROMACHINED ELECTROSTATIC ULTRASONIC AIR TRANSDUCER

Silicon

s10,

Si,N,

Au

(0 Fig. 4. (a)-(Q Fabrication steps of the electrostatic transducer

the equivalent circuit in Fig. 3, which shows the complete equivalent circuit of the device being driven by a voltage source (V) with a source resistance (I?::). The inductor ( L ) is due to the lead interconnect wires and is typically on the order of a few pH. For the devices described in this paper, the resistor Rp is a parasitic resistor that accounts for current flowing through the packaging and is typically 25 k0. C, is the parasitic capacitance of the devicie due to the area of the transducer that is not a membrane aind is typically about 70 pF. 2, is the parasitic mechanical load impedance that represents acoustic energy not coupled to the air, typically a few hundred Rayls. This energy either propagates laterally along the surface of the silicon or is propagated into the bulk silicon or is dissipated as heat. 2, is the acoustic impedance of the air and represents the acoustic output of the device. Current flowing through 2, represents thie particle velocity of the generated acoustic wave.

This equivalent circuit is used to find the electrical impedance, the particle displacement, and the insertion loss of the device.

IV. DEVICE FABRICATION

Devices were fabricated using a highly doped, p-type, (100) oriented, silicon wafer as a substrate. A series of oxidation, film deposition, metal evaporation, lithography, and etching

Fig. 5. diamond regions are oxide posts acting as spacers to the nitride membrane.

SEM cross section of a 25-pm period electrostatic source. The white

was performed as shown in Fig. 4(a)-(f). First, a 1-pm layer of thermal oxide was grown, followed by the deposition of a 7500-A thick layer of low stress LPCVD silicon nitride. This nitride had a measured residual stress of 280 MPa+ [21]. This value can be adjusted by varying the proportion of silane to ammonia during the deposition stage. The backside of the wafer was stripped of these layers, and a 500-A film of gold was evaporated onto both sides of the wafer. A pattern of 3- pm diameter dots on a 2-D grid with 100-pm period (other samples with 50- and 25-pm periods were also prepared) was transferred lithographically to the wafer. The gold and the nitride were etched through the holes, leaving access to the silicon dioxide, which acts as a sacrificial layer. The air gap is formed by etching the sacrificial layer in pure hydrofluoric acid during a timed etch. It was found that etching for 41 min leaves posts of silicon dioxide that serve to support the membrane without consuming much of the active area of the device. A cross section of an actual device is shown in Fig. 5.

Several devices were fabricated with periods of 100, 50, and 25 pm. The SEM of Fig. 16 is of a 25-pm period device. The 100-pm devices were found to be the most efficient at 1.8 MHz, which was the operation frequency of interest. The silicon dioxide posts provide the lateral clamping of the silicon nitride membrane. Thus, their period determines the resonant frequency of the device. Additionally, they determine the bandwidth of the membrane resonance by affecting the boundary conditions on the nitride membrane.

V. RESULTS

To test the ultrasonic performance of the device, three different measurement systems were used. The first system

4 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 43, NO. 1, JANUARY 1996

50 140

135 40 130 0

125 6 a 30 0, *.

120

115

h

i %

CD ci 2 2o m

VI '5: 10

0 2 110 -

105

-10 100 2 3 4 5 6 7

Frequency (MHz) Fig 6 Theoretical and measured electrical resistance and capacitance of 0 2 4 6 8 10 50-jim penod electrostatic transducer measured at a bias voltage of 40 V Time (usec)

Fig 7 the two-way impulse response of the acoustic system

Received signal from system shown in Fig 6 This is approximately TABLE I

VALUES USED IN EQUIVALENT CIRCUIT MODEL FOR COMPARISON WITH MEASUREMENT IN FIG 6

30 Variable Value Source t n 7500 A Measured from SEM P n 2861 kg/m3 Measured charactenstic of nitnde 9 20

E en 4 1 10-1 1 F/m Measured charactensbc of nitnde v

2 10 ?? vila, 40 V Voltage Source

0 280 MPas Measured charactenstic of nitnde v)

a 0 55 Measured from SEM 2 3 0 L 035 mH Fit to data

25 kR Fit to data 2 -10 RP CP 70 pF Measured using capacitance meter ZP 100 Rayls Fit to data Area 6 25 mm2 Size of lithographic die Rs 50 R Amplifier input impedance

U 3 26 p m Measured from SEM

2

-20 1 3 5 7 9

Time (microseconds)

was an impedance analyzer which was used to measure the input electrical impedance of the device at a bias voltage of 40 V. Fig. 5 shows the measured resistance and capacitance of a device with a hole period of 50 pm resonant at 4.6 MHz. The measuired data are compared with theory from the equivalent circuit shown in Fig. 3. Excellent agreement between measure- ment amd theory was found when the transducers parameters took on the values listed in Table I.

A traditional pitch-catch system was constructed. Ultrasonic waves were generated and received by two identical transduc- ers. The signal was detected by biasing the receive transducer with a 100-V bias and measuring the change in the current through the device using a high input impedance amplifier. In the experiment, two identical transducers with a period of 100 pm anid a resonant frequency of 1.8 MHz were used. For a spacing of about 5 mm between transmitter and receiver, and a 16-V, 100-ns electrical pulse excitation, the signal shown in Fig. 7 was received.. This is approximately the system impulse response. This system had a signal to noise ratio of 34 dB. This was measured by comparing received voltage to the rms noise signal without the acoustic signal present. The transducers were also quite efficient, demonstrated by the ability to receive a signal with a spacing of 10 cm (about 44 dB propagation loss) between transmitter and receiver.

Fig. 8. of 100-V bias and a 15-V peak-to-peak, one cycle, and 920 kHz tone burst.

Received signal from system shown in Fig. 6 with a drive voltage

The transducers were observed to have a flat frequency response below resonance. Fig. 8 shows the received signal when the dnve signal was a single cycle sinusoid at 920 kHz (where the spectrum of Fig. 7 was flat). This signal is very compact and demonstrates the broadband operation of the device.

The third system used to measure the performance of the transducer was an optical interferometer capable of detecting subangstrom displacements. This system measured the dis- placement at one point on the surface of the membrane. Fig. 9 shows the measured displacement near one of the etch holes in the 100-pm period device compared with the theoretically predicted displacement using the equivalent circuit shown in Fig. 3. Excellent agreement between theory and experiment is observed. The measured peak displacement is 230 &V, which corresponds to an average membrane displacement of 126 &V. The maximum RF drive voltage used was 16 Vpp, which resulted in approximately 3000 of displacement at resonance. It is important to note the large displacement away from resonance, over a wide frequency range. Below 1 MHz, the displacement is relatively flat at approximately 30 &V.

HALLER AND KHURI-YAKUB: SURFACE MICROMACHINED ELECTROSTATIC ULTRASONIC AIR TRANSDUCER 5

300

I00

10 0.5 0.9 1.3 1.7 2.1 2.5

Frequency (MHz)

Fig 9. Theoretical and optical interferometer measured peak displacements of 100-pm penod device with 100-V bias

1 1.5 2 2.5 Frequency (MH[z)

Fig. 10. Theoretical and acoustically measured one-way insertion loss of 100-pm period device with 100 V bias.

This enables the devices to operate below resonance with reasonable efficiency and excellent band width.

The insertion loss of the transduceir was calculated by comparing the generated acoustic pow er to the maximum power that the source can provide through its source resistance. The measured one-way insertion loss of a 1.8-MHz transducer is compared to theory in Fig. 10. Again, excellent agreement between measurement and theory is observed. The measured insertion loss of the device is 26 dB and the 3-dB bandwidth is approximately 20%.

The performance was compared between the electrostatic transducer and a reference piezoelectric transducer made from PZT-5H with a single quarter-wave matching layer of low impedance (IO6 kg/m2. s) rubber (GE RTV-615). This trans- ducer was a focused 1-MHz circular transducer with a diameter of 1.2 cm and an F number of three, terminated with a 50- L? load. The measured peak displacement of the piezoelectric transducer was 100 h V . The measured one-way insertion loss was 20 dB with a 3-dB bandwidth of 4%.

The radiation pattern of the devices was investigated using the pitch-catch system while scanning ithe receive transducer in one dimension. The transducer separation was 1 cm which corresponds to the far field for the individual membrane

Piston Theory -20

-25 ,: -30

-4 -3 -2 -1 0 1 2 3 4 Position (mm)

Fig. 11. Measured beam profile compared with piston theory. The measnre- ment was performed using the system in Fig. 6 with a transducer separation of 1 cm.

elements and the near field (S == 0.5) for the active transducer area. The measured data shown in Fig. 11 are compared to what one would predict from a piston transducer with an active area of 2.5 mm x 2.5 mm. Excellent agreement between theory and experiment is seen indicating that the array acts as standard piston transducer at a sufficiently (> 1 mm) large distance from the membrane elements.

The breakdown voltage of the devices was measured to be 120 V across the 1-pm air gap. This large breakdown voltage allows the device to operate at large bias voltages, improving its output power. The breakdown voltage could be increased by using a gas with a larger breakdown voltage or with a vacuum if the holes are sealed. The strain of the membrane was less than loF5, and there was no observed fatigue in the silicon nitride membrane.

VI. CONCLUSIONS Silicon micromachining techniques provide unrivaled

process control, making it possible to fabricate capacitance transducers with an electrode spacing of 1 pm or less. This allows efficient generation of high frequency ultrasound in air. A one-way insertion loss of 26 dB and a 3-dB bandwidth of 20% was measured as cornpared to 20-dB insertion loss and 4% bandwidth for a reference piezoelectric transducer. Using two identical transducers, one used as a transmitter and the other used as a receiver, the signal to noise ratio was measured to be 34 dB. Using an optical interferometer, a peak displacement of 230 AN wa- measured at 1.8 MHz. Since these devices are fabricated using standard silicon processing, integrated electronics and transducers can be made. Switch electronics, focusing, and scanning electronics could be used to fabricate monolithic imaging systems.

One typical problem with micromachined structures is their tendency to become contaminated when left open to the air. Water vapor, dust particles, and other airborne contaminants get into the small spaces and prevent the devices from working. Since the devices described in this paper have very small (-3 pm) openings to the environment, no contamination was observed. The devices were left open in a open room for weeks

6 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 43, NO. 1, JANUARY 1996

with no sign of contamination. This is an important feature of these transducers for enabling them to be usable in airborne applications.

Another advantage of electrostatic transducers over piezo- electric devices is their temperature insensitivity. PZT based transducers are very sensitive to temperature and can only be used near room temperature. Electrostatic devices are only limited by melting point and the different thermal expansions of the materials used. For the devices described here, the upper temperature limit is approximately 400OC. The temperature dependence was tested by placing a soldering iron tip on the sample during operation. There was no effect on the acoustic signal after 30 s of contact with soldering iron tip. This is another large advantage of electrostatic transducers over conventional piezoelectric devices.

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[l] W. P. Mason, Electromechanical Transducers and Wave Filters. New York: D. Van Nostrand, 1942, pp. 163-165, 193-195.

[Z] F. Massa, “Ultrasonic transducer for use in air,” in Proc. IEEE Ultrason., vol. 53, no. 10, pp. 1363-1371, Oct. 1965.

[3] P. Kleinschmidt and V. Magori, “Ultrasonic robotic-sensors for exact short range distance measurement and object indentification,” in Proc. IEEE Ultrason. Symp., 1985, pp. 457462.

[4] “Ultrasonic ranging system,” Polaroid Corp., Cambridge, MA, Docu- ment P1834B, 1981.

151 G. L. Miller, R. A. Boie, and M. J. Sibilia, “Active damping of ultrasonic transducers for robotic applications,” in Proc. IEEE Ultrason. Symp.,

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[7] G. Decicco, B. Morten, M. Prudenziati, and A. Taroni, “A 250 kHz piezoelectric transducer for operation in air: Application to distance and wind velocity measurements,” in Proc. IEEE Ultrason. Symp., vol. 1,

[SI G. Cadet, J. L. Valdes, and J. W. Mitchell, “Ultrasonic time-of-flight method for on-line quantitation of semiconductor gases,” in Proc. IEEE Ultrason. Symp., 1991, pp. 192-195.

191 J. D. Fox, B. T. Khuri-Yakub, and G. S. Kino, “High-frequency ultrasonic transducers operating in air,” in Proc. IEEE Ultrason. Symp.,

[lo] C. M. Fortunko and W. P. Dube, “Gas-coupled acoustic microscopy in pulse-echo mode,” in Proc. IEEE Ultrason. Symp., 1993, pp. 661471.

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IEEE Ultrason. Symp., 1988, pp. 503-506. 1131 M. 1. Haller and B. T. Khuri-Yakub, “1-3 composites for ultrasonic air

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[15] J. T. Kung and H.-S. Lee, “An integrated air-gap-capacitor prescure sensor and digital readout with sub- 100 attofarad resolution,” J. Micro- electromech. Syst., vol. 1, no. 3, pp. 121-129, Sept. 1992.

[16] Y . E. Park and K. D. Wise, “An MOS switched-capacitor readout amdifier for capacitive pressure sensors.” Rec. IEEE Custom IC C o d . 1986, pp. 380-384. ~

1171 H. Guckel, “Surface micromachined pressure transducers,” Sensors ~

Acfuarors A , vol. 28, pp. 133-146, 1991. [IS] D. W. Schindel and D. A. Hutchins, “Applications of micromachined

capacitance transducers in air-coupled ultrasonics and nodestructive evaluation,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 42, pp. 51-58, 1995.

[19] M. Rafiq and C. Wykes, “The performance of capacitive ultrasonic transducers using v-grooved backplates,” Measurement Sci. Technol., vol. 2, pp. 168-174, 1991.

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[21] S . P. Sandejas, Ginzton Lab., Stanford Univ., Stanford, CA, private communication.

Matthew I. Haller was born in New York City, NY, on October 26, 1964 He received the B S degree in electrical engineering from the University of Cali- fornia at San Diego in 1986 In 1989, he received the M S degree in electrical engineering from Stanford University, Stanford. CA He completed the Ph D in electrical engineering dt Stanford University in 1994 His Ph D dissertation was in the field of using mcromachining technology to fabncate ultrasonic matenals and devices

Between 1986 and 1988, he worked at G T E Government Systems as a Systems Engineer, writing free-space optical communications simulation software From 1988 to 1990, he worked at Acuson Corporation as an Image Analysis Engineer for Medical Ultrasound Equipment In 1994, he returned to Acuson to continue his work in image analysis He is interested in micromachining, medical ultrasound, and the blending of these two fields to open up new applications

Butrus T. Khuri-Yakub (S’70-S’73-M’76- SM’87-F‘95) was born in Beirut, Lebanon, on August 15, 1948. He received the B.S. degree in 1970 from the American University of Beirut, the M.S. degree in 1972 from Dartmoutb College, and the Ph.D. degree in 1975 from Stanford University, CA all in electrical engineering.

He joined the Research Staff at the E. L. Ginzton Laboratory of Stanford University in 1976 as a Research Associate. He was uromoted to a Senior Research Associate in 1978, and to a Professor

of Electrical Engineering (Research) in 1982. He is involved in teaching graduate and undergraduate courses in the Electrical Engineering Department at Stanford. His current research interests include thin film deposition, acoustic fluid ejection, the nondestructive evaluation of structural materials, acoustic imaging and microscopy, photo-acoustic interactions, in-process monitoring, and silicon micromachining and its applications to ultrasonic materials.

Dr. Khuri-Yahb is a senior member of the Acoustical Society of America and a member of Tau Beta Pi. He is also Associate Editor of Research in Nondestructive Evaluation, a journal of the American society for nondestructive testing, and a member of the Ad Comm of the IEEE group on Ultrasonics, Ferroelectrics, and Frequency Control. He received the Stanford University School of Engineering Distinguished Advisor Award in June 1987, and the Medal of the City of Bordeaux for contributions to NDE in 1983.