Surface Micromachined Capacitive Ultrasonic Transducers · coupled ultrasonic inspections motivate the development of air transducers [1]{[5] and the advantages of limited di raction

678 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 45, no. 3, may 1998

Surface Micromachined CapacitiveUltrasonic Transducers

Igal Ladabaum, Student Member, IEEE, Xuecheng Jin, Student Member, IEEE,Hyongsok T. Soh, Abdullah Atalar, Senior Member, IEEE,

and Butrus T. Khuri-Yakub, Fellow, IEEE

Abstract—The current state of a novel technology, sur-face microfabricated ultrasonic transducers, is reported.Experiments demonstrating both air and water transmis-sion are presented. Air-coupled longitudinal wave transmis-sion through aluminum is demonstrated, implying a 110 dBdynamic range for transducers at 2.3 MHz in air. Watertransmission experiments from 1 to 20 MHz are performed,with a measured 60 dB SNR at 3 MHz. A theoretical modelis proposed that agrees well with observed transducer be-havior. Most significantly, the model is used to demonstratethat microfabricated ultrasonic transducers constitute anattractive alternative to piezoelectric transducers in manyapplications.

I. Introduction

Ultrasound is used in a wide variety of applicationsthat can be characterized as either sensing modalities

or actuating modalities. Sensing applications include med-ical imaging, nondestructive evaluation (NDE), ranging,and flow metering. Practical uses of ultrasound as an ac-tuating mechanism include industrial cleaning, soldering,and therapeutic ultrasound (heating, lithotripsy, tissue ab-lation, etc.). Current theoretical understanding indicates,however, that many fruitful applications of ultrasound re-main unrealized. Often a lack of adequate transducersprecludes theoretically interesting ultrasonic systems frommaterializing. Thus, we find ourselves at a familiar point inthe scientific process; practical applications motivate tech-nological progress; and the technological progress, if real-ized, can serve to further refine theory. Specifically, air-coupled ultrasonic inspections motivate the developmentof air transducers [1]–[5] and the advantages of limiteddiffraction beams motivate the realization of 2-dimensionaltransducer matrices [6]–[8]. In this paper, we present mi-cromachined ultrasonic transducers (MUTs) and reportthat they overcome many of the current transducer prob-lems. MUTs are shown to work in air with the largestdynamic range reported to date, they are shown to workin water, and simulations are used to demonstrate thatoptimized immersion MUTs can perform comparably topiezoelectric transducers with fewer practical limitations.

In order to harness the practical potential of ultrasound,

Manuscript received May 6, 1997; accepted November 20, 1997.I. Ladabaum, X. Jin, H. T. Soh, and B. T. Khuri-Yakub are with

the E. L. Ginzton Laboratory, Stanford University, Stanford, CA94305 (e-mail: [email protected]).

A. Atalar is with Bilkent University, Ankara, Turkey.

waves must be efficiently launched at, or in, the subject ofinterest. In all sensing applications and most actuating ap-plications, the waves also need to be detected. Ultrasoundis usually introduced into and detected from the subjectvia a coupling medium; it is rare for the vibrating elementof the transducer to be placed in direct contact with thesubject [9]. The coupling medium can be solid, such as thequartz rods used in wafer temperature measurements [10],[11]; it can be liquid, as in many NDE and medical applica-tions, or it can be gaseous, as in air-coupled applications.Ultrasonic excitation and detection also can occur on thesubject via laser light [12]–[14]. Currently, the vast major-ity of ultrasonic transducers are fabricated using piezoelec-tric crystals and composites. When performing ultrasonicinvestigations directly on solids, piezoelectric transducersare the best choice because the acoustic impedance of thepiezoelectric ceramic is of the same order of magnitudeas that of the solid. Laser based ultrasound also performswell with solids. However, when the objective is to exciteand detect ultrasound in fluids (as is the case in most ap-plications), piezoelectric transducers have drawbacks thatmotivate our approach to transducer design.

Piezoelectric transducers are problematic in fluid-coupled applications because of the impedance mismatchbetween the piezoelectric and the fluid of interest. In air,for example, the generation of ultrasound is challengingbecause the acoustic impedance of air (400 kg/m2s) ismany orders of magnitude smaller than the impedanceof piezoelectric materials commonly used to excite ultra-sonic vibrations (approximately 30 × 106 kg/m2s). Thelarge impedance mismatch implies that piezoelectric airtransducers are inherently inefficient. In order to improveefficiency, a matching layer is usually placed in betweenthe piezoelectric and the air [9]. The matching layer solu-tion is problematic for three reasons. First, the impedancemismatch is so large that matching layer materials withthe necessary characteristic impedance are rarely avail-able. Second, the improved energy coupling comes at theexpense of bandwidth. Third, high frequency transducersrequire impractically thin matching layers. Attempts tomaximize the energy transfer from the piezoelectric ele-ment to the air and vice versa have achieved moderatesuccess. However, the increased complexity of the more ef-ficient devices reduces their reliability and increases theircost.

In the case of water-coupled ultrasound, the impedancemismatch is not as severe (approximately 30×106 kg/m2s

0885–3010/98$10.00 c© 1998 IEEE

ladabaum et al.: micromachined capacitive transducers 679

for piezoceramics versus 1 × 106 kg/m2s for water), butnevertheless leads to system limitations. Matching layersare still necessary, and both the ceramic and the match-ing layers need to be manufactured to tight mechanicaltolerances. Thus, theoretically interesting designs, such ascomplex arrays, are limited to realizable configurations.

Piezoelectric transducers have some drawbacks in ad-dition to the impedance mismatch problem. Because apiezoelectric’s frequency range of operation is determinedby its geometry, the size and frequency requirements ofcertain systems may not converge to a realizable config-uration. Furthermore, the device’s geometry defines itselectrical impedance, so that sensitive receiving electron-ics may be forced to operate with loads that worsen theirnoise performance. Two-dimensional transducer matricespresent particular problems because the element size re-quired results in an electrical element impedance that doesnot match conventional driving and receiving electronics.Attempts to match this impedance better, such as throughthe use of multilayer piezoelectrics, lead to significantcross-coupling [7]. In addition, piezoelectrics are limitedto strain levels of approximately 10−4, which translatesto a surface displacement limit of approximately 0.5 µmin the low MHz range. Such amplitudes may not be suf-ficient in certain gas applications. The more widely avail-able piezoelectric ceramics depole at relatively low temper-atures (approximately 80C), which prevents them frombeing used in high temperature environments, while spe-cialized ceramics that depole at higher temperatures havelower coupling constants and are very costly.

Although piezoelectric ceramics and engineering clever-ness have generated a significant number of ultrasonic de-vices and systems, many modern applications would ben-efit from transducers based on a different principle of ac-tuation and detection. Capacitive MUTs overcome manyof piezoelectric transducers’ drawbacks.

II. Previous Work

Analyses of capacitive acoustic transducers have existedfor many decades [15], [16]. The use of capacitive transduc-ers for airborne ultrasonics dates back to the 1950s [17],[18], and the first immersion version appeared in 1979 [19].The use of air-coupled ultrasound in the context of NDE isalso not new [1], [20], [21]. Recently, a report has been pub-lished describing air-coupled longitudinal wave excitationin metals at frequencies below 1 MHz [22].

The application of micromachining techniques to fabri-cate acoustic transducers consisting of suspended mem-branes over a backplate was reported within the lastdecade [23]. Recently, papers have been published describ-ing various designs and models of capacitive ultrasonicair transducers [24]–[27]. However, the papers generallyomit models that are adequate for the design of optimizedtransducers, and a robust explanation of the operationof the devices is usually lacking. More rigorous modelingof grooved backplate electrostatic transducers has been

Fig. 1. Schematic of one element of a MUT.

Fig. 2. SEM of a portion of a MUT.

published [28], but the transducers it describes are lim-ited to 500 KHz operation. A capacitive ultrasonic trans-ducer made with more advanced fabrication technologywas invented in 1993 [29]–[31]. The capabilities, fabrica-tion procedures, and modeling of the device have been im-proved [32]–[36] and have spurred concurrent developmentefforts [37]. The present state of such transducer devel-opment, including a more thorough theoretical treatmentthan in previous publications, is the subject of this paper.

III. Device Description

A MUT consists of metalized silicon nitride membranessuspended above heavily doped silicon bulk. A schematicof one element of the device is shown in Fig. 1. A trans-ducer consists of many such elements, as shown in thescanning electron microscope (SEM) image of Fig. 2. Whena voltage is placed between the metalized membrane andthe bulk, coulomb forces attract the membrane toward thebulk and stress within the membrane resists the attraction.


If the membrane is driven by an alternating voltage, sig-nificant ultrasound generation results. Conversely, if themembrane is biased appropriately and subjected to ultra-sonic waves, significant detection currents are generated.Micromachining is the chosen vehicle for device fabricationbecause the membrane’s dimensions (microns) and resid-ual stress (hundreds of MPas) can be precisely controlled.Silicon and silicon nitride have excellent mechanical prop-erties, and can be readily patterned using the wide reper-toire of procedures invented by the semiconductor indus-try.

Certain qualitative observations about MUT design areworth noting. If the energy associated with a transducer’ssurface motion when unloaded is low compared to the en-ergy associated with the surface motion when loaded bythe medium of interest (e.g., air, water), the transducerthen will have a broad bandwidth. Thus, when operationis intended in lower density media, the surface of motionshould be associated with a light structure. The structurecan be made resonant to further enhance energy trans-fer at the expense of some bandwidth. Our thin resonantmembrane fits these criteria. Also important to the electro-mechanical coupling of a transducer is the fact that largecoulombic forces are realized when an electrical potentialis applied across a small gap. Thus, a thin metalized mem-brane separated from a conducting backplate by a smallgap is a critical feature of our design. Because detectionentails measuring the fractional change of the MUT capac-itance when ultrasonic waves impinge on it, a small gapis also desirable in order to maximize detection sensitiv-ity. Furthermore, to avoid both electrical breakdown andthe mechanical effects of backside air loading, the trans-ducer cavity can be evacuated. It is important to realizethat optimization of transducer design need not be lim-ited to a single solution; a transducer can be optimizedfor emission, and a different transducer can be optimizedfor reception. For example, a sensitive receiver would bemade with a thin gap, which would limit its power outputas an emitter. Thus a thin gap receiver and a thicker gapemitter could each be optimized in a final system.

IV. MUT Fabrication

MUTs are fabricated by using techniques pioneered bythe integrated circuits industry. A fabrication scheme ofthe MUTs used to generate some of the results reportedherein1 is found in Fig. 3.

A p-type (100) 4 in. silicon wafer is cleaned, and a 1 µmoxide layer is grown with a wet oxidation process. A 3500 Alayer of LPCVD nitride is then deposited. The residualstress of the nitride can be varied by changing the pro-portion of silane to ammonia during the deposition pro-cess. The residual stress used is approximately 80 MPa. Apattern of etchant holes is then transferred to the waferwith an electron beam lithography process. The nitride is

1Other fabrication schemes are currently being reduced to practiceand are the subject of upcoming conference proceedings [36].

Fig. 3. Major steps of MUT fabrication.

plasma etched, and the sacrificial oxide is removed withHF. Note that the etchant holes define the elements’ ge-ometry,2 as is shown in Fig. 4. A second 2500 A layer ofLPCVD nitride is then deposited on the released mem-branes, vacuum sealing the etchant holes. The holes arepatterned with an electron beam so that their small sizeallows for adequate sealing of the cavity. A chrome adhe-sion layer and a 500 A film of gold are evaporated onto thewafer.

The wafer is then diced, and the MUTs are mountedon a circuit board with epoxy. A gold wire bond connectsthe top electrode to the circuit board. In an older process,conductive epoxy was used to make contact to the bulkof the silicon (the lower electrode). Currently, a wire bondalso connects the lower electrode to the circuit board.

V. Theory

In both the analysis and design of MUTs, it is impor-tant to differentiate between a MUT as a receiver and a

2Some devices were fabricated with hexagonally close packed mem-branes, whereas some results were obtained with circular membranes.


Fig. 4. Time lapse of sacrificial etch.

MUT as an emitter. The purpose of a receiving MUT isto detect the small ultrasonic signals that result after in-sonification of a sample. Thus, a linearized small signalanalysis is appropriate. In contrast, the aim of an emittingMUT is to launch ultrasonic waves of sufficient magnitudeto enable applications of interest. Hence, the displacementof the emitting MUT’s membrane can be large, and a moreinvolved nonlinear analysis is necessary to quantitativelypredict a collapse voltage and an electromechanical cou-pling factor. In this section, we present a first order anal-ysis of an emitting MUT. We then present a small signalmodel that yields a quantitative description of a receiv-ing MUT.

A. First-order Analysis

Several approximations simplify the analysis and serveto highlight the most significant aspects of MUT behavior.We assume that the membrane’s restoring force is a linearfunction of its displacement. We neglect all electrical fring-ing fields and membrane curvature when considering theelectrical forces on the membrane. Furthermore, we takeall conductors and contacts to be perfect. We then assumethat the MUT operates in a vacuum, which is equivalent toneglecting any loading of the membrane3. Thus, we obtaina lumped electro-mechanical model consisting of a linearspring, a mass, and a parallel plate capacitor, as shown inFig. 5.

The mass is actuated by the resultant of the capacitorand spring forces.

Fcapacitor + Fspring = Fmass

3The lack of dissipative elements implies that a resonant conditionwould result in infinite displacement; nonetheless, dissipative loadsare neglected for clarity.

Fig. 5. First order lumped electro-mechanical model of a MUT ele-ment.

The force exerted by the capacitor is found by differenti-ating the potential energy of the capacitor with respect tothe position of the mass (principle of virtual work):

Fcapacitor = − d

dx

(12CV 2

)= −1

2V 2[d

dx

(εS

d0 − x

)]=

εSV 2

2(d0 − x)2(1)

where V is the voltage across the capacitor, C is capac-itance, ε is the electric permittivity, S is the area of thecapacitor plates, x is displacement in the direction shownin Fig. 5 and d0 is the separation of the capacitor plates atrest. The spring exerts a force that is linearly proportionalto displacement

Fspring = −kxwhere k is the spring constant. Substituting for the forceterms and noting all time dependence explicitly gives:

md2x(t)dt2

− εS[V (t)]2

2[d0 − x(t)]2+ kx(t) = 0. (2)

Equation (2) is a nonlinear differential equation of sec-ond order, and its solution is not trivial. In order to extractthe significant qualitative behavior of the system, we con-sider the case where V (t) = VDC , which implies no timedependence and leads to:

εSV 2DC

2(d0 − x)2 = kx. (3)

Equation (3) can be rearranged into a third degree poly-nomial in x whose solution has two regions of interest.For small VDC , the solution consists of three real roots,of which only one is a physical solution (the other rootscorrespond to an unphysical x > d0 and to an unstable


Fig. 6. Sketch of MUT hysteresis.

point). As VDC is increased, there is a point at which theelectrostatic force overwhelms the spring’s restoring force,and the membrane collapses. This inflection point is foundwhen there is a double real root such that x > d0. Thecollapse point occurs when:

Vcollapse =

√8kd3

0

27εS

xcollapse =d0

3.

In order to prevent the capacitor from shorting aftercollapse, we imagine a thin insulating layer of thicknessdinsulator on one of the electrodes (the metalized mem-brane’s nitride, in a real MUT). Note that we have ne-glected the effect of such an insulating layer until thispoint. It is possible to account for the insulator in (2)and (3), but it is conceptually more clear to assume thatdinsulator and εinsulator can be neglected until collapse. Af-ter the membrane has collapsed, it will not snap back untilthe voltage is reduced below Vcollapse to

Vsnap-back =

√2kd2

insulator(d0 − dinsulator)εinsulatorS

.

A sketch of such hysteretic behavior is found in Fig. 6. Weconclude from such analysis that membrane collapse is apossibility, and we report in the results section that suchcollapse is observed.

In addition to membrane collapse, electrostatic springsoftening also is observed experimentally. Such softeningarises from the fact that, as the capacitor plate displaces inthe +x direction, a spring force is generated in the −x di-rection. However, displacement in the +x direction underconstant VDC also causes an increase in the electrostatic

force in the +x direction. This increase in electrostaticforce can be interpreted as a spring softening. A moremathematical explanation begins by linearizing (2) witha Taylor expansion about the point x(t) = 0:

md2x(t)dt2

−[εSV 2

DC

2d20

+εSV 2

DC

d30

x(t)]

+ kx(t) = 0.(4)

Collecting terms yields an equation in a familiar form

md2x(t)dt2

+(k − εSV 2

DC

d30

)x(t) =

εSV 2DC

2d20

(5)

which we rewrite as

md2x(t)dt2

+ ksoftx(t) =εSV 2

DC

2d20

(6)

where

ksoft = k − εSV 2DC

d30

.

Thus, we expect to see a drop in the resonance frequencyof the system as VDC is increased. Such a frequency shiftis observed, and reported in the results section.

Even though much is left to decipher about the com-plex nonlinear behavior of a MUT under large displace-ment conditions, small signal operation about a bias pointyields fruitful practical and theoretical results. If in (1) weassume that the membrane displacement x is small com-pared to the gap spacing d0, then:

Fcapacitor ≈εSV 2

2d20∝ V 2.

If we let V = VDC + Vac then

Fcapacitor ∝ V 2DC + 2VDCVac + V 2

ac.

If we choose VDC Vac then the time varying forcingfunction

Fac ∝ 2VDCVac.

Thus, reasonable experiments can be performed and in-terpreted even though a full understanding of an emittingMUT’s behavior requires further analysis.

B. Small Signal Model

In order to facilitate the design of systems enabled byMUTs, the goal of the theory is to arrive at an equiva-lent circuit model of the transducer. The equivalent cir-cuit should be a two port network, where the electricaldomain (voltage and current) is represented at one port,and the mechanical domain (force and velocity) is repre-sented at the other port. The equivalent circuit is valid un-der small signal conditions for a receiving MUT, and evenfor an emitting MUT, as long as the membrane displace-ment is not near the collapse point and the bias voltagedoes not cause significant spring softening. The approach,


as first suggested by Mason [15], is to find the mechanicalimpedance of the membrane in vacuum and then to in-sert it in a transformer equivalent circuit. Because the firstmembranes we fabricated were circular, and also to facil-itate analytical treatment, we consider the circular mem-brane solution. We hypothesize that hexagonal membranebehavior is approximated well by circular membrane be-havior. We use Mason’s derivation with some corrections,and preserve his notation as much as possible.

C. Mechanical Impedance of a Membrane in Vacuum

We consider a circular membrane of radius a operatingin vacuum. The membrane has a Young’s modulus of Y0and a Poisson’s ratio of σ. In addition, the membrane isin tension T in units of N/m2. The differential equationgoverning the normal displacement x(r) of the membranecan be written as [15], [38]:

(Y0 + T )l3t12(1− σ2)

∇4x(r)− ltT∇2x(r)− P − ltρd2x(r)dt2

= 0(7)

where lt is the membrane thickness, and P is the externaluniform pressure applied to the membrane. The equationis derived from an energy formulation, and the critical as-sumption is that the tension generated by a displacementx is small compared to the tension T . Assuming a har-monic excitation at an angular frequency ω, (7) is knownto have a solution of the form:

x(r) = AJ0(k1r) +BJ0(k2r) + CK0(k1r)

+DK0(k2r)− P/(ω2ρlt) (8)

where A,B,C, and D are arbitrary constants, J0() is thezeroth order Bessel function of the first kind, and K0() isthe zeroth order Bessel function of the second kind. Weimmediately deduce that C = 0 and D = 0 because theBessel function of the second kind is infinite at r = 0,which is not physical. If we use (8) to substitute for x(r)in (7), we find that k1 and k2 must satisfy the characteristicequations:

(Y0 + T )l2t12(1− σ2)

k41 +

T

σk2

1 − ω2 = 0 (9)

(Y0 + T )l2t12(1− σ2)

k42 +

T

σk2

2 − ω2 = 0. (10)

Following Mason’s notation, we define

c =(Y0 + T )l2t12(1− σ2)

and d =T

ρ. (11)

The quadratic formula then gives the solutions:

k1 =

√√d2 + 4cω2 − d

2cand k2 = j

√√d2 + 4cω2 + d

2c.

(12)

Fig. 7. Calculated displacement as a function of frequency for a 25 µmembrane excited by uniform pressure.

In order to determine the constants A and B, twoboundary conditions are necessary. Physically reasonableboundary conditions at r = a are that x = 0, which im-plies that the membrane undergoes no displacement at itsperiphery, and (d/dr)x = 0, which implies that the mem-brane is perfectly flat (i.e., does not bend) at it’s periph-ery. Both conditions amount to stating that the membraneis perfectly bonded to an infinitely rigid substrate. Usingthese conditions, we determine the constants A and B andfind the displacement of the membrane as:

x(r) =P

ω2ρlt

×[k2J0(k1r)J1(k2a) + k1J0(k2r)J1(k1a)k2J0(k1a)J1(k2a) + k1J1(k1a)J0(k2a)

− 1]. (13)

Fig. 7 is a calculated plot of the displacement of a typi-cal membrane as a function of frequency under a uniformpressure excitation4. For the simulation, values used werea = 25 × 10−6, lt = 0.6 × 10−6, P = 1, Y0 = 3.2 × 1011,σ = 0.263, T = 280 × 106, and ρ = 3270 (all in MKSunits).

Because we have assumed uniform pressure P , the forceon the membrane is simply PS, where S is the area of themembrane. The velocity of the membrane is v(r) = jωx(r),and we take v as the lumped velocity parameter where:

v = (1/πa2)∫ a

0

∫ 2π

0v(r)rdθdr

=jP

ωρlt

×[

2(k21 + k2

2)J1(k1a)J1(k2a)ak1k2(k2J0(k1a)J1(k2a) + k1J1(k1a)J0(k2a))

− 1].

(14)

Mechanical impedance is defined as the ratio of pressureto velocity. Hence, the mechanical impedance of the mem-

4Fig. 7 illustrates the mechanical resonance of the membrane. Thedisplacement in this particular example is too large to be valid forthe small signal equivalent circuit derived in the next section.


Zm =P

v= jωρlt

[ltak1k2(k2J0(k1a)J1(k2a) + ltk1J1(k1a)J0(k2a))

ak1k2(k2J0(k1a)J1(k2a) + k1J1(k1a)J0(k2a))− 2(k21 + k2

2)J1(k1a)J1(k2a)

]. (15)

Fig. 8. Calculated absolute value of mechanical impedance for a sil-icon nitride membrane as a function of frequency and thickness.

brane, Zm, can be written as: (see equation 15).5 Figs. 8, 9,and 10 show calculated values of this impedance as a func-tion of each critical parameter. In each figure, all param-eters except the one of interest are held constant. The sig-nificance of Figs. 8, 9, and 10 is that they demonstrate howa MUT membrane’s impedance can be tailored to be in-significant compared to the medium’s acoustic impedance,which is the necessary condition for efficient power trans-fer.

D. Electrostatically Excited Membraneand Its Equivalent Circuit

The membrane of thickness lt is coated with a thin layerof conducting material on the top side, and the bottomelectrode is separated from the membrane by a distancela. The electrical capacitance can be written as:

C(t) =ε0εS

ε0lt + εla(t)(16)

where ε is the dielectric constant of the membrane mate-rial, and S is the area of the membrane. If a DC voltageVDC is applied between the top electrode and the bot-tom, the electrostatic attraction force on the membrane isgiven by:

FE = − d

dx

(12CV 2

DC

)=

ε0ε2SV 2

DC

2(ε0lt + εla)2 . (17)

5The choice of lumped parameters for distributed systems can besubtle. A lumped mechanical impedance in series with a lumpedradiation impedance must adequately describe the power deliveredto the medium. Because our analysis is predicated on a small signalapproximation, we do not introduce a rigorous solution here, but itshould nonetheless be pointed out that rigorous lumped parametersfor apodized transducers can be obtained.

Fig. 9. Calculated absolute value of mechanical impedance as a func-tion of frequency and membrane tension.

Fig. 10. Calculated absolute value of mechanical impedance for asilicon nitride membrane as a function of frequency and radius.

Let the total voltage across the capacitor be V = VDC +Vac sin(ωt), where VDC is the bias voltage and Vac VDCis the small signal AC voltage. Then, the current flowingthrough the device is:

I =d

dtQ =

d

dt(C(t)V (t)) = C(t)

d

dtV (t) + V (t)

d

dtC(t).

(18)

Because this is a small signal analysis, we also can as-sume that the capacitor can be described by C(t) =C0 +Cac sin(ωt+φ) where Cac C0. We can then rewrite(18) as:

I = C0d

dtVac(t) + VDC

d

dtCac(t). (19)


Fig. 11. Partial electrical equivalent circuit of MUT.

Fig. 12. Electrical equivalent circuit of MUT.

If we differentiate (16) we obtain:

d

dtCac(t) = − ε0ε

2S

(ε0lt + εla0)2

d

dtla(t) (20)

where la0 is the DC value of the gap spacing. The deriva-tive of the air gap thickness is equal to membrane velocity(d/dt)la = v, which leads to:

I = C0d

dtVac(t)−

VDCε0ε2S

(ε0lt + εla0)2 v. (21)

Equation (21) is significant because it transforms velocity,a mechanical quantity, into electrical current. Thus, we candefine a transformer ratio:

n =VDCε0ε

2S

(ε0lt + εla0)2 (22)

and write the current as sum of electrical and mechanicalcomponents

I = Cd

dtVac(t)− nv. (23)

It is important to note that n can be controlled by varyingthe applied bias voltage or by changing the membrane andair gap thickness. Using (23) we can draw the partial smallsignal equivalent circuit shown in Fig. 11.

In order to complete the equivalent circuit, a relation-ship between force and velocity at the mechanical portis necessary. By definition, an equivalent load impedanceconstitutes such a relationship. By inspection, and usingthe mechanical impedance of (15), the equivalent circuitof Fig. 12 is obtained. The impedance elements are placedin series in order to maintain consistency with definitions.For example, the load impedance of vacuum is zero, so itmust be placed in series with the membrane impedancebecause a parallel combination would imply a total loadof zero.

When loaded by air, the bandwidth of the transducer isdominated by the mechanical impedance of the membrane.As shown in the results section, the typical 3 dB bandwidth

Fig. 13. Electrical equivalent circuit of MUT when Zm Za.

of an air-loaded transducer is 5% of the center frequency.The bandwidth can be further increased at the cost ofefficiency.

In contrast to an air-loaded transducer, an immersionMUT has its bandwidth determined by the transformerratio. In most configurations of a MUT element, the me-chanical impedance of the immersion medium, Za, is muchgreater than the membrane impedance, Zm. In this casethe equivalent circuit of the MUT simplifies to that shownin Fig. 13, where the equivalent resistance is given by:

Req = ZaS/n2 = Za

(ε0lt + εla)4

V 2DCε

20ε

4S. (24)

The Q factor of the MUT is thus given by:

Q = ωReqC =ωZa(ε0lt + εla)3

V 2DCε0ε

3 for Zm Za.(25)

It is clear that, for wide band operation, lt and la shouldbe chosen as small as possible, and the DC bias voltageVDC should be kept as high as possible. The bias voltage,however, is limited by the collapse voltage (discussed inthe first order analysis). Thus, there exists a lower boundon the quality factor. The determination of this lowerbound entails more involved nonlinear analysis, and it isthe subject of current research. Nonetheless, a conserva-tive assumption is that a configuration with parameterslt = 0.3 µm, la = 0.2 µm, and VDC = 80 V does notcollapse. Such a configuration has a Q, according to (25),of 23.

The electrical equivalent circuit allows analysis and op-timization of the MUT structure. Furthermore, circuitscan be designed to tune a particular transducer. As isshown in the results section, the model agrees well withexperimental observations. Nevertheless, the model doesnot take into account several factors. There is no term torepresent the mechanical impedance of the cavity behindthe membrane, nor of the supporting structure, which canpresent significant real and imaginary loads. Also absentare terms for the parasitic electrical elements present inany real device. The careful derivation of such terms, aswell as the investigation of the nonlinear nature of the de-vice when operated at large displacements, are topics ofcurrent research.


VI. Results

The present results, which include air-coupled through-transmission of aluminum, constitute a significant im-provement over previously reported results [32]–[35]. Thetransmission results herein presented are generated with asimple experimental setup. A function generator and volt-age source excite the emitter, and a custom transconduc-tance amplifier with approximately 40 dB of gain detectsthe signal at the receiver. When appropriate, a series in-ductor is used to tune the transducer to match the elec-tronics’ impedance. The signal is digitized by an 8 bit dig-itizing oscilloscope, and it is transferred to a computer fordisplay. The impedance curves herein reported are takenwith an HP 8752A network analyzer connected to the bi-ased transducer with a bias-T. The theoretical curves aregenerated by a computer program that incorporates thetheory developed in this paper.

In preliminary transmission experiments with no alu-minum slab present, transducer membranes were observedto transmit at a low frequency of 1.8 MHz (100 micronmembrane) to a high frequency of 12 MHz (12 micronmembrane). Fig. 14 shows the ultrasound detected afterpassing through air, then into a 1.9 mm slab of aluminum(longitudinal mode), then air. The excitation was at the2.3 MHz resonance frequency of the transducer, and con-sisted of a 20 cycle tone burst of 16 V riding on a biasof 30 V. The received signal was averaged 16 times, andpresents a 30 dB signal-to-noise ratio. The emitter haddimensions of 1 cm2, the receiver was 0.25 cm2, and thetransducers were placed 1 cm apart. Because the aluminumslab causes 70 dB of signal loss, 0.8 cm of air cause 5 dBof loss, and electrical impedance mismatch between thetransducer and the receiving electronics cause an addi-tional 5 dB of loss, the transducer dynamic range is ap-proximately 110 dB6. The dynamic range of 110 dB wasfurther verified by removing the aluminum and reducingthe excitation voltage of the emitter until it was barely de-tectable at the receiver, which occurred at 0.2 mV. Thus,assuming a linear variation of power with excitation volt-age, the range from 0.2 mV to 16 V represents 98 dB ofdynamic range. The 5 dB electrical impedance mismatchand a loss of 6 dB from 1 cm of air contribute to a to-tal dynamic range of 109 dB; 16 V is taken as the upperlimit of excitation power because it was the highest voltageused in the experiments and it is the approximate limit ofa linearized analysis. It is possible that the transducers’dynamic range actually exceeds 110 dB.

The transducers used for the aluminum experimentwere unsealed. However, a vacuum sealed pair of transduc-ers is able to operate in both water and air. Water trans-

6The acoustic properties of aluminum are taken from [9] and areused in the well-known formula for the power transmission coefficient(see for example [39]) to predict the 70 dB of mismatch loss. It shouldbe noted that a 1.9 mm slab of aluminum is far from its thicknessmode resonance, thus giving a large loss factor. Experiments per-formed since the original submission of the manuscript with 1.6 mmof steel also verify 110 dB of dynamic range. Details of steel resultswill be presented in future publications.

Fig. 14. Air coupled aluminum through-transmission at 2.3 MHz.

Fig. 15. Water transmission at 3 MHz.

mission is shown in Fig. 15 for transducers placed 0.5 cmapart. When the noise floor of the receiver was measured,it was found to be 60 dB below the peak received sig-nal (the receiving MUT’s capacitance was tuned out witha series inductor). Interesting features of Fig. 15 are theacoustic echoes, which indicate that the receiver’s acous-tic impedance is not perfectly matched to water. Such amismatch implies a loss in efficiency, and it is due to un-optimized electrical tuning and physical construction. AMUT is comprised of thousands of active elements joinedby supporting structure. The inactive supporting struc-ture is responsible for reduced efficiency, so its surface areashould be minimized in future designs. When the devicesare operated untuned, they exhibit a fractional bandwidthin excess of 100%. The same pair of transducers was usedto observe transmission from 1 to 20 MHz, but the signalwas almost at the noise level at the high frequencies. Thedesign of the devices used for water transmission was not


Fig. 16. Real part of impedance under vacuum: experiment and the-ory.

optimized. It is anticipated that future generations of de-vices, based on the analysis herein reported, will approachthe dynamic range of piezoelectric devices [34].

The transmission experiments show that practical ap-plications of MUTs are feasible. In fact, the aluminum re-sults show that air-coupled ultrasound is likely to playan increasingly important role in nondestructive testing.The water transmission results show that the significantadvantages of microfabrication (on chip electronics, cost,repeatability) may soon find their way into the ultrasonictransducer industry.

The more significant result from an academic point ofview, however, is that the theoretical model of the deviceagrees well with experimental observation. Fig. 16 showsgood agreement between the measured and simulated val-ues of the real electrical impedance of the receiving trans-ducer used in the aluminum experiment. The small dis-crepancy can be attributed to the approximations in themodel, the most significant of which is that the hexag-onal membranes can be treated as circular membranes.The parameters used in the program agree with the ex-pected parameters of the fabrication process (lt = 0.6 µm,la = 0.75 µm, T = 170 MPa, a = 48 µm). In order to fitthe theory to the experiment, a load of 3000 Ohms wasplaced on the acoustic port of the circuit model. This loadrepresents all acoustic losses in vacuum. When this lossload is also used in an air impedance experiment, excel-lent agreement exists with theory7 (see Fig. 17).

Confirmation of behavior predicted by the first orderanalysis was also obtained. Fig. 18 shows a decrease inresonant frequency with increasing voltage. This changein frequency is due to an effective softening of the spring,as has been explained.

Figs. 19 and 20 demonstrate the hysteretic collapse be-

7A change in the tension parameter was made to reflect the in-creased stiffness of an air-backed membrane versus a vacuum backedmembrane.

Fig. 17. Impedance in air: experiment and theory.

Fig. 18. Evidence of spring softening: change in resonant frequencywith bias voltage.

havior predicted in Fig. 6. As the bias voltage is increased,the baseline of the imaginary impedance shifts, implyingthe reduction of gap spacing. When the voltage is increasedbeyond 40 V, the characteristic signature of resonance dis-appears, and no further change is observed. The membranedoes not snap back until the voltage is reduced well belowthe collapse voltage8.

Because our theoretical understanding is verified by ex-periment, we are basing future transducer designs on thetheory herein reported. It is a critical feature of MUTsthat their geometric characteristics (gap thickness, mem-brane thickness and radius) can control their electricalimpedance. Thus, transducers can be made to match themost sensitive electronics available at a center frequency of

8The membrane used to generate Fig. 19 is thicker than the onethat generated Fig. 17, which explains the difference of resonancefrequencies.


Fig. 19. Evidence of membrane collapse: imaginary impedance as afunction of bias voltage.

Fig. 20. Evidence of hysteresis: imaginary impedance as a functionof bias voltage.

interest. Currently, we plan to fabricate transducers with a50 Ω real impedance, which would allow them to be usedwith readily available electronic components. The simu-lated impedance of a proposed design is found in Fig. 21.

As has been explained, the bandwidth of the device isgreatest when the bias voltage is as large as possible andthe electrode separation is as small as possible. Because wehave not completed and verified a quantitative model forthe nonlinear behavior of the device, we hesitate to proposea quantitative limit to the transducer’s bandwidth9. Usingthe conservative parameters of Fig. 21 and a series tuninginductor, the absolute impedance of Fig. 22 is obtained.The figure shows a 5% 3 dB bandwidth, which enables therealization of an impressive system. The room temperature

9For example, if the collapse point occurs at electric fields greaterthan 4.108 V/m, a 3 dB bandwidth in excess of 100% is possible.

Fig. 21. Simulation of a 50 Ω immersion device (a = 10 µm, la =0.2 µm, lt = 0.3 µm, VDC = 80 V).

Fig. 22. Tuned immersion device (a = 10 µm, la = 0.2 µm, lt =0.3 µm,VDC = 80 V, L = 19 µH).

thermal noise due to a 50 Ω resistor with 5% bandwidthcentered at 10 MHz is 63 nV, or 1.26 nA. The thermalcurrent noise is comparable to that of well-designed elec-tronics, and can be taken as the limiting noise floor of thesystem. Thus, a transmitter capable of generating 13 mAof current (or for a 50 Ω transmitter, 8 mW of acousticpower all directed at the receiver) will result in a systemwith 140 dB dynamic range at 10 MHz with 5% band-width. Trading some dynamic range for bandwidth yieldsa system with 120 dB of dynamic range and 50% band-width. In short, the extrapolation of the theoretical mod-els herein presented and verified indicates that optimizedMUTs may have liquid-coupled performance comparableto piezoelectric transducers’ performance.


VII. Conclusion

We have reported that microfabricated ultrasonic trans-ducers are capable of transmitting sound in air with adynamic range of 110 dB. Such transducers are usedto demonstrate air-coupled through transmission in alu-minum. MUTs are also shown to work well in water,though their optimized configuration awaits future fabri-cation runs. Most significantly, we have proposed a theo-retical model which agrees with observed behavior. Admit-tedly, the model only accounts for the electrical impedancebehavior of the transducers, which does not completelydescribe the acoustic behavior of the devices. More directmeasurements of the displacements at the transducers’ sur-face and of the directivity of the transducers are planned,and future theoretical models should also describe the ob-served behavior. The current model nevertheless indicatesthat MUTs offer better performance than piezoelectrictransducers in air-coupled applications, and that MUTshave the potential to approach piezoelectrics’ performancein liquids. MUTs enjoy the inherent advantages of micro-fabrication, which include low cost, array fabrication, andthe possibility to integrate electronics either on chip oras a multi-chip module. Additional plans for future workinclude obtaining a better understanding of the devices’non-linear characteristics when operated at large displace-ments, the realization of optimized immersion transducers,and the use of the air transducers in several newly enabledapplications. More distant plans include array and elec-tronics fabrication and integration.

Acknowledgments

This work was made possible with support from theU.S. Office of Naval Research. X. J. would also like to ac-knowledge the support of an NUS fellowship. During thecourse of study, A. A. was with Ginzton Lab, on leavefrom Bilkent University, Turkey. The staff of the Stan-ford Nanofabrication Facility, as well as Tom Carver andPauline Prather of the Ginzton Lab, provided valuabletechnician support. I. L. also wishes to thank Joseph Mal-lon for preliminary discussions that resulted in the hexag-onal design.

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Igal Ladabaum (S’91) received a B.S. inBioengineering from U.C. Berkeley in 1992.He then went to Paris, France where he was aJean Monnet scholar (1992–93) at the EcolePolytechnique. He was also a staff engineer atAir Liquide. In 1996, he received an M.S. inElectrical Engineering from Stanford Univer-sity. Currently a doctoral candidate at Stan-ford, Mr. Ladabaum is interested in the tech-niques of micromachining and their applica-tion to the realization of novel transducers.Most of his effort is directed toward the devel-

opment and application of ultrasonic transducers. He is a member ofthe IEEE and the Acoustical Society of America. He has received nu-merous awards through the course of his studies, including being thestudent speaker at every commencement ceremony since 8th grade.He received the best student paper prize at the International Con-ference of Micro and Nano-Engineering in Aix en Provence, France,1995, and the RWB Stephens Best Student Paper Prize in Ultrason-ics International Conference, Delft, the Netherlands, in July 1997.He has contributed several journal and conference papers, and ispursuing patents for some of his work on ultrasonic transducers.

XueCheng Jin (S’93) received the BEngDegree in Biomedical Engineering from Ts-inghua University, PR China, in 1990 and theMEng Degree in Computer Engineering fromthe National University of Singapore, Singa-pore, in 1994. He is currently studying towardthe Ph.D. degree in Electrical Engineering atStanford University. He worked for OrientalStar Microcomputers, PR China, until 1992,where he designed analog and digital circuitsfor various instrumentation. He then workedfor Texas Instruments Pte Ltd, Singapore,

where he designed computer vision algorithms and software codes forreal time post mount die inspection in die bonder machines. In 1995,he joined the faculty of Electrical Engineering Department, NationalUniversity of Singapore, as a Senior Tutor, where he is primarily en-gaged in research into solid-state sensor and actuator, MEMS andmicromachining technology, CMOS integrated circuit design, bioin-strumentation and its miniaturization, medical image processing andcomputer vision.

XueCheng Jin is a member of IEEE. He serves as a reviewer forseveral international journals with about 20 publications. He receivedRWB Stephens Best Student Paper Prize in Ultrasonics International

Conference, Delft, the Netherlands, in July 1997 and Whitaker Stu-dent Paper Finalist Certificate in IEEE International Conference onEngineering in Medicine and Biology, Baltimore, MD, in November1994.

Hyongsok T. Soh received a B.S. degreewith Distinction in 1992 with a double ma-jor in Mechanical Engineering and MaterialsScience, and an M.Eng degree in 1993 in Elec-trical Engineering all from Cornell University.He is currently working on the Ph.D. degreein Electrical Engineering at Stanford. His re-search is on scanning probe lithography andnanometer scale electron devices.

Abdullah Atalar (M’88–SM’90) was born in Gaziantep, Turkey, in1954. He received a B.S. degree from Middle East Technical Univer-sity, in 1974; M.S. and Ph.D. degrees from Stanford University in1976 and 1978, respectively, all in Electrical Engineering. His thesiswork was on reflection acoustic microscopy. From 1978 to 1980 hewas first a Post Doctoral Fellow and later an Engineering ResearchAssociate in Stanford University continuing his work on acoustic mi-croscopy. For 8 months he was with Hewlett Packard Labs, PaloAlto, engaged in photoacoustics research. From 1980 to 1986 he wason the faculty of the Middle East Technical University as an Assis-tant Professor. From 1982 to 1983 on leave from University, he waswith Ernst Leitz Wetzlar, West Germany, where he was involved inthe development of the commercial acoustic microscope. In 1986 hejoined the Bilkent University as the chairman of the Electrical andElectronics Engineering Department and served in the founding ofthe Department where he is now a Professor. He is presently theProvost of Bilkent University. He teaches undergraduate and grad-uate courses on VLSI design and microwave electronics. His currentresearch interests include micromachined sensors and actuators andcomputer aided design in Electrical Engineering. He is the projectdirector of a NATO SFS project: TU-MIMIC. He is a senior memberof IEEE.

Butrus T. Khuri-Yakub (S’70–S’73–M’76–SM’87–F’95) was born in Beirut, Lebanon.He received the B.S. degree in 1970 from theAmerican University of Beirut, the M.S. de-gree in 1972 from Dartmouth College, and thePh.D. degree in 1975 from Stanford Univer-sity, all in electrical engineering. He joined theresearch staff at the E. L. Ginzton Laboratoryof Stanford University in 1976 as a researchassociate. He was promoted to a Senior Re-search Associate in 1978, and to a Professor ofElectrical Engineering (Research) in 1982. He

has served on many university committees such as graduate admis-sions, undergraduate academic council of the school of engineering,and others. He has been teaching both at the graduate and under-graduate levels for over 15 years, and his current research interestsinclude in-situ acoustic sensors (temperature, film thickness, resistcure) for monitoring and control of integrated circuits manufactur-ing processes, micromachining silicon to make acoustic materials anddevices such as air borne and water immersion ultrasonic transducersand arrays, and fluid ejectors, and in the field of ultrasonic nonde-structive evaluation and acoustic imaging and microscopy.

Professor Khuri-Yakub is a fellow of the IEEE, a senior memberof the Acoustical Society of America, and a member of Tau BetaPi. He is associate editor of Research in Nondestructive Evaluation,a Journal of the American Society for Nondestructive Testing; anda member of the AdCom of the IEEE group on Ultrasonics Ferro-electrics and Frequency Control (1/1/94–1/1/97). He has authoredabout 300 publications and has been principal inventor or coinventoron over 30 patents. He received the Stanford University School of En-gineering Distinguished Advisor Award, June 1987, and the Medalof the City of Bordeaux for contributions to NDE, 1983.

Documents

Surface Micromachined Capacitive Ultrasonic Transducers · coupled ultrasonic inspections motivate the development of air transducers [1]{[5] and the advantages of limited di raction