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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS 1
Optimization of a Collapsed Mode CMUT Receiverfor Maximum Off-Resonance Sensitivity
Mansoor Khan , Talha M. Khan, Akif Sinan Tasdelen, Mehmet Yilmaz, Abdullah Atalar , Fellow, IEEE,and Hayrettin Köymen , Senior Member, IEEE
Abstract— We propose an airborne collapse capacitivemicromachined ultrasonic transducer (CMUT) as a practicalviable ultrasound transducer capable of providing a stable per-formance at the off-resonance frequencies. Traditional practice isto bias the CMUT plate close to collapse voltage to achieve highcoupling coefficient and sense the incoming ultrasound as anopen-circuit receive voltage signal of the transducer or short-circuit receive current (SCRC). Maintaining CMUT plate inthe vicinity of collapse threshold is rather difficult. In thispaper, an analytic approach to design an airborne collapsed-mode CMUT for maximum off-resonance sensitivity is presented.We use small-signal circuit model to evaluate the performanceof a collapsed CMUT for varying operating conditions. CMUToperational parameters that yield the highest off-resonanceSCRC are directly obtained from performance design curves.Collapsed CMUT plate is then biased in a critical biasing regionthat produces a stable and maximum off-resonance sensitivity.We experimentally verify and measure a stable sensitivity of afabricated collapsed CMUT cell of −60 dB V/Pa at 100 kHzwhen biased between 50 to 65 V. We characterize our linearcircuit model performance against the measured performance ofcollapsed CMUT in air within 4-dB tolerance. [2018-0058]
OWING to standard silicon integrated circuit (IC) fab-rication technology and potential for integration with
electronics, CMUTs have proved to be a viable technol-ogy in medical ultrasound. For example, the first pulse-echo128-element, 1-D linear CMUT array was fabricated usingsimple photolithography process and was characterized witha wider bandwidth and higher sensitivity than piezoelectricceramics in 2001 [1]. Commercial scanners using 1-D CMUTarrays are also reported to have produced clinical-quality
Manuscript received March 12, 2018; revised July 13, 2018; acceptedJuly 15, 2018. This work was supported by the Scientific and TechnologicalResearch Council of Turkey under Project Grant 114E588. The work ofA. Atalar was supported by the Turkish Academy of Sciences. (Correspondingauthor: Mansoor Khan.)
M. Khan, A. Atalar, and H. Köymen are with the Electrical and ElectronicsEngineering Department, Bilkent University, 06800 Ankara, Turkey (e-mail:[email protected]).
T. M. Khan is with the Institute of Materials Science and Nanotechnology,Bilkent University, 06800 Ankara, Turkey.
A. S. Tasdelen is with the Bilkent University Acoustic and UnderwaterTechnologies Research Center, Bilkent University, 06800 Ankara, Turkey.
M. Yilmaz is with the National Nanotechnology Research Center, BilkentUniversity, Ankara 06800, Turkey.
Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JMEMS.2018.2857444
images [2], [3]. 2-D CMUT arrays with 128 × 128 elementshave also been successfully fabricated and characterized [4].These 2-D arrays can be integrated with electronics in theform of a 3-D multichip module by flip-chip bonding [5].Recently [6], tuning of the center frequency of collapsed-mode CMUT is investigated for inter-cardiac echo imaging.The center frequency of a collapsed CMUT is tuned between8.7 MHz and 15.3 MHz by varying the DC bias. Maximumtransmit sensitivity of 52 kPa/V is achieved at the centerfrequency of 9 MHz.
In this paper we demonstrate both analytically and exper-imentally that an airborne CMUT in collapsed mode couldbe optimized and used for the detection of ultrasound moreefficiently and in a stable manner than that in conventionalmode. The electric field sustained between the biased collapsedplate and the substrate is larger than an un-collapsed plateowing to small insulation layer at the contact region. Thissmall separation increases the capacitance, resulting in animproved electromechanical transformer ratio [7], [8]. Thismakes collapsed-mode CMUT operation a viable choice forhigher acoustic output [9] with lower bandwidth than conven-tional CMUTs [10]. Many studies have developed and usedaccurate FEM models to show superior power transmissionand efficiency for a collapsed mode CMUT [11].
We derive and use linear equivalent circuit model to evaluatethe performance of a collapsed CMUT. SCRC normalized toincident pressure is derived from the model in terms of itslumped circuit elements. We compare SCRC with open circuitreceive voltage (OCRV) and show that SCRC performance isnot impaired due to electrical losses. The normalized SCRCis then optimized with bias for varying CMUT operationalparameters.
II. ANALYSIS OF COLLAPSED CMUTA cross-sectional view of collapsed CMUT plate is shown
in Fig. 1 where a is the clamped circular plate radius, b is thecontact radius, tg is the gap height, ti is the insulation layerthickness and tm is the plate thickness.
A static analysis of CMUT can be done using the normal-ized form of the Timoshenko’s equation [12], [13]. We sum-marize this method in Appendix A for completeness.
III. LINEAR SMALL-SIGNAL MODEL
A collapsed-mode CMUT receiver, under small signal con-ditions can be represented by a linear equivalent-circuit-model,shown in Fig. 2. The small signal circuit parameters are
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2 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS
Fig. 1. Cross-sectional view of a collapsed CMUT cell.
Fig. 2. Small-signal model of collapsed mode CMUT with both mechanicaland electrical losses.
TABLE I
CIRCUIT PARAMETERS OF SMALL SIGNAL MODEL
derived by linearizing the transduction and plate restoringforce at the static operating point. These parameters aredescribed in Table I.
The receive CMUT signal is the ac voltage, Vac at theelectrical port and resulting plate rms displacement is xr .1
The electrical terminal voltage, V and resulting total rms platedisplacement xR is expressed as:
V 2 = [VDC + Vac]2 ≈ V 2DC + 2VDC Vac (1)
xR = X R + xr since |Vac| � VDC and |xr | � X R (2)
fR is the electrical transduction force derived from the instan-taneous energy, E , due to charge accumulated on the CMUTelectrode in presence of electrical terminal voltage, V :
fR = d E
dxR= d
dxR
(1
2CV 2
)= C0V 2
2tgeg�
c(xR
tge) (3)
where C0 is the clamped CMUT capacitance and gc(.) is thecapacitance polynomial defined in Appendix B. tge = tg +ti/εr is the effective gap height, εr is the relative permittivity
1rms displacement is defined as xr =√
1πa2
∫ a0 2π x2(r)rdr .
of insulation layer. C is the non-linear electrical capacitancegiven by,
C = C0 gc
(xR
tge
)(4)
C0 = ε0πa2
tge(5)
Using (1) in (3) we linearize the transduction force, fR aroundstatic X R as:
fR = FR + fr
= C0(V 2
DC + 2VDC Vac)
2tge
[g�
c(X R
tge) + xr
tgeg��
c (X R
tge)
](6)
Ignoring the higher order terms, and the DC force FR , we writeour linear transduction force fr in terms of normalized rmsplate displacement X R/tge as:
fr = C0VDC Vac
tgeg�
c(X R
tge) + xr
tge
C0V 2DC
2tgeg��
c (X R
tge)
= nR Vac + xr
CRS(7)
where
nR = C0VDC
tgeg�
c(X R
tge) and CRS = 2t2
ge
C0V 2DC g��
c ( X Rtge
)(8)
nR is the electromechanical turns ratio at the static operatingpoint, and CRS is the spring softening capacitance due toapplied VDC whose effect opposes the plate restoring force.In terms of normalized quantities (8) can be expressed as:
n2R = 4
15
C0
CRm0
[VDC
Vrg�
c(X R
tge)
]2
(9)
CRS = CRm0
[2
15
V 2DC
V 2r
g��c (
X R
tge)
]−1
(10)
In (9) and (10) CRm0 is the linear spring compliance of anun-collapsed plate:
CRm0 = 9(1 − σ 2)a2
80πY0t3m
(11)
and Vr is the bias required to collapse the plate in vacuumgiven by (31). In collapsed mode, the restoring force has anon-linear dependence on the plate displacement, therefore therestoring force is also linearized around X R :
fR + FRb = xR
CRm(xR)(12)
where FRb = (√
5/3)πa2 Pb is the uniform rms force dueto ambient pressure Pb [14]. Ignoring the higher order terms,we can write the linearized compliance at X R as:
fR + FRb = X R
CRm+ xr
[d(xR/CRm(xR))
dxR
∣∣∣∣xR=X R
]
= X R
CRm+ xr
(1
CRm− X R
C2Rm
dCRm(xR)
dxR
∣∣∣∣xR=X R
)
(13)
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KHAN et al.: OPTIMIZATION OF A COLLAPSED-MODE CMUT RECEIVER 3
Fig. 3. Normalized series compliance, CRms/CRm0 as a function ofnormalized bias voltage, VDC/Vr for varying normalized gap heights, tg/tgeand normalized force, Fb/Fg of 1 and 2.
In (13) CRm is defined as:
CRm = CRm0 hc(X R
tge) (14)
hc(.) is the plate compliance polynomial in X R/tge. Coeffi-cients for capacitance and compliance polynomials are tabu-lated in Appendix B. From (13) we obtain our small signalcompliance capacitance, CRms as:
CRms = CRm0
[ h2c(
X Rtge
)
hc(X Rtge
) − X Rtge
h�c(
X Rtge
)
](15)
In Fig. 3, the normalized series compliance capacitance,CRms/CRm0 is plotted for varying normalized gap heights,tg/tge and normalized force, Fb/Fg of 1 and 2. For Fb/Fg = 2case, the plate makes large initial contact with the substrate andtherefore is less compliant. As VDC/Vr increases, plate stiffenseven more with increasing contact making it less compliant.
The inductance is equal to the mass of plate in rms model:
L Rm = πa2tmρ (16)
The small signal model is finally terminated with the collapsedCMUT radiation impedance of acoustic medium [15] as:
Z R R = πa2ρ0c0{R(ka, kb) + j X (ka, kb)} (17)
where R(ka, kb) and X (ka, kb) are the normalized radiationresistance and reactance of collapsed-CMUT transducer, k isthe wavenumber, co is the speed of sound and ρo is the density,all specified in the immersion medium.
On the electrical side the small signal capacitance, C0dc,is defined at the static X R/tge as [16]:
C0dc = C0 gc(X R
tge) (18)
Fig. 4 plots gc(.) as normalized CMUT electrical capacitanceof (18), C0dc/C0 versus X R/tge for varying normalized gapheights, tg/tge and normalized force, Fb/Fg of 1. For large
Fig. 4. CMUT capacitance polynomial, gc(X R/tge) as a function of X R/tgefor varying normalized gap heights, tg/tge and normalized force Fb/Fg = 1.
tg/tge values collapsed CMUT capacitance is higher owingto thin insulation layer gap between the electrodes. As VDC
increases, plate contact area becomes large resulting in ahigher capacitance. Calculation of CMUT capacitance fromthe static deflection profiles is done in Appendix B.
We add lumped elements to our model to represent bothelectrical and mechanical losses in the CMUT. On the electri-cal side, Cp is the parasitic capacitance. Dielectric loss in theinsulator can be modeled as a conductance, Gi = ωCi tan δwhich appears parallel to the insulation capacitance, Ci . tan δis the loss tangent of insulating material (for silicon diox-ide tan δ = 0.001). This insulation dielectric loss can beapproximated by a resistance Rp described by [17, eq. (13)]as Rp = 1
ω(C p+Codc) tan δ . The series resistance, rloss , in themechanical side accounts for the frictional loss of the collapsedplate.
The loss to substrate in the form of spherical waves intothe solid half-space or in the form of surface waves in theinterfaces is modeled by a parallel impedance branch [18] atthe node after −CRS shown in Fig. 2. For a solid backing,RB is much higher than the plate radiation resistance in air.CRb is the series compliance of backing material.
IV. COLLAPSED CMUT RECEIVER PERFORMANCE
A. Open Circuit Receive Voltage (OCRV) Sensitivity
OCRV normalized to the incident pressure, p, is derivedfrom the small signal equivalent circuit of collapsed CMUTof Fig. 2 as:
VOC
p=
πa2nRjω(C0dc+C p)
RR + jω(L Rm + X R) + 1jω
(n2
RC0dc+C p
+ 1CRms
− 1CRS
)
(19)
At frequencies much lower than the resonance frequency,both the inductive reactance, jωL Rm and the self-radiation
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4 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS
Fig. 5. Collapsed CMUT sensitivity multiplier term h1
(X Rtge
,FbFg
,tgtge
,CpC0
)
in dB for C p = 0.
impedance, RR + jωX R of a collapsed CMUT cell are smalland can be ignored, we rewrite (19) as:
VOC
p=
[3
8
√2(1 − σ 2)
ε0Y0
(a2
tm
)√tge
tm
]h1
(X R
tge,
Fb
Fg,
tgtge
,Cp
C0
)
(20)
with units of V/Pa. The first term of, Voc/p, gives insightinto the dimensional parameters of CMUT for highest receivervoltage sensitivity. It implies that the plate diameter must beas large as possible and it must be thin compared to both thediameter and the effective gap. The second term of (20), h1,is given by,
h1
(X R
tge,
Fb
Fg,
tgtge
,Cp
C0
)
=
√32
(VDCVr
)g�
c
(X Rtge
)[
VDCVr
g�c
(X Rtge
)]2
+ 154
[C pC0
+ gc
(X Rtge
)][1
C Rms− 1
C RS
]
(21)
h1 of (21) is plotted in Fig. 5 for Cp = 0 for variousnormalized gap heights and Fb/Fg = 1 and 2.
B. Discussion
To maximize h1, the collapsed CMUT cell must be designedfor the lowest static force, Fb/Fg and the highest possibletg/tge with a bias equal to or slightly larger than that requiredfor maximum sensitivity. Increasing the bias thereafter makesthe plate less compliant and harder to move implying lowersensitivity. For example, when Fb/Fg = 1, and tg/tge = 0.85,we obtain h1 = −24 dB for 0.45 < VDC/Vr < 0.65.
We observe similar maximum sensitivity regions for higherFb/Fg , however it is not prudent to choose the dimensions ofCMUT for large Fb/Fg , as the plate becomes pre-stiffeneddue to large static force, resulting in more contact and
Fig. 6. Effect of relative parasitic capacitance on collapsed CMUT sensitivitymultiplier term, h1 for various normalized gap heights and Fb/Fg = 1.
less sensitivity. Fig. 5 shows a loss of 6 dB for the samenormalized gap height if the static normalized force, Fb/Fg isdoubled.
Fig. 6 demonstrates the effect of relative parasitic capaci-tance on sensitivity multiplier, h1, for Fb/Fg = 1 and varioustg/tge values. Cp/C0 = 1 at tg/tge = 0.85 introduces loss of3 dB in the maximum sensitivity region. This loss increasesto 4 dB if tg/tge = 0.65 is employed at Fb/Fg = 1 .
C. Short Circuit Receive Current (SCRC) Sensitivity
SCRC current, iSC (normalized to incident pressure, p) onthe electrical side at off-resonance is given by,
isc
p= πa2ωnR
CRmsCRS
CRS − CRms(22)
(22) can be rewritten as:
isc
p= ωπ
5
[√ε0(1 − σ 2)
2Y0
(a4
tm
)1√
tmtge
]h2
(X R
tge,
Fb
Fg,
tgtge
)
(23)
with units of A/Pa. The first term contains CMUT geomet-rical parameters. For high SCRC sensitivity, CMUT must bedesigned with thin plate and small effective gap height, tge
but with larger aperture radius, a. The second term of (23) isgiven by,
h2
(X R
tge,
Fb
Fg,
tgtge
)=
√32
(VDCVr
)g�
c
(X Rtge
)[
1C Rms
− 1C RS
] (24)
We can use a transimpedance amplifier to measure SCRC.If we use a capacitance, C f , as the feedback element, we geta transimpedance gain of 1/(ωC f ), which eliminates ω depen-dence of (23). Note that h2 is independent of Cp unlike OCRVmultiplier term, h1. Fig. 7 plots h2 for various normalizedgap heights and Fb/Fg = 1 and 2. h2 variation with VDC/Vr
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KHAN et al.: OPTIMIZATION OF A COLLAPSED-MODE CMUT RECEIVER 5
Fig. 7. Collapsed-mode CMUT SCRC sensitivity multiplier term, h2 in dBfor various normalized gap heights and Fb/Fg = 1 and 2.
TABLE II
DIMENSIONAL PARAMETERS OF A FABRICATED CMUT CELL
indicates that a collapsed-mode CMUT has a better SCRCperformance than its OCRV counterpart. This is becausecurrent on electrical side is scaled by turns ratio, nR , whichincreases with the bias and improves the SCRC performance.
D. Collapsed-Mode CMUT Design for MaximumSCRC Performance
We find collapsed CMUT physical dimensions from theoperational parameters that maximize, h2. For example for,Fb/Fg = 1 and tg/tge = 0.85, employing ti = 1 μmthick silicon oxide (εr = 3.9), with tg = 1.45 μm producestge = 1.7 μm. A silicon plate with tm = 16 μm anda = 487 μm yields Fb/Fg = 1. From (27) and silicon materialproperties described in Table II, the vacuum collapse voltage,Vr = 121.7 V, that is VDC = 92 V is required to obtainh2 = −4 dB. If a transimpedance amplifier is employed witha feedback capacitance, C f = 1 pF then we get a maximumtransimpedance amplifier output as −57 dB V/Pa.
V. FABRICATION OF COLLAPSED CMUT RECEIVER
We employ anodic wafer bonding technology similar tothe one described in [19] to produce collapsed CMUTs.
Fig. 8. Optical photo of CMUT bottom electrodes taken from the rear Pyrexside after bonding.
A (100) orientation, p-type, boron doped, wafer having 1 μmtop layer thermal oxide on 15 μm thick device Si layer is usedas a CMUT plate. A (4-inch wide, 3.3 mm-thick) Pyrex waferis used as the substrate. The SOI wafer has 1 μm thick buriedoxide (BOX) layer between the device layer and 350 μm thicksilicon handle layer. The total plate thickness, tm of Table-IIhas a variation of ±1 μm as measured by FIB/SEM.
Following the standard Pyrex wafer clean process,2 35 nmof Cr is first deposited on the Pyrex wafer in an e-beam evap-oration chamber. Using a standard photolithography process,circular CMUT features are UV exposed and developed.Before the Pyrex wet-etch process to carve the circular cav-ities, exposed Cr is removed by a Cr wet etch remover.Pyrex wafer was kept in a wet-etch (BOE 7:1) bath for50 mins at room temperature. This produced circular CMUTcavities of tg = 1.12 μm. CMUT cavities and electrical padsare connected by a 50 μm wide channel. Bottom electrodeswere deposited in an e-beam evaporation chamber and consistof 100 nm Ti, 30 nm Pt and 50 nm Au, patterned by a lift-off process. The processed Pyrex wafer containing CMUTfeatures is then bonded with the SOI at a commerciallyavailable bonding facility.3 After bonding, the interface of theair gaps between SOI and glass substrate, are sealed witha low-viscosity epoxy resin4 which is cured in a vacuumchamber. To reveal the collapsed CMUT profiles and forsubsequent electrical connections, first 350 μm thick siliconhandle layer is removed by SF6 based RIE process run insidean ICP chamber, while exposed gold pads are being protectedby a metal shadow mask made from aluminum alloy. TheBOX acts like an etch stop layer for this process, which isthen removed by BOE 7:1 to reveal device silicon layer.
VI. MEASUREMENTS AND MODEL CHARACTERIZATION
To validate the model predictions we use a fabricatedCMUT, (see Fig. 8) parameters of which are given in Table II.
A. Admittance Measurements
The small signal model is experimentally validated by firstmeasuring the conductance and susceptance of the fabricatedCMUT in air with an impedance analyzer (HP 4194A).
2Acetone Sonication/IPA/DI water/Nitrogen blowDevice Si layer has a 0.01-100 �cm resistivity range.3Applied Microengineering Ltd., Oxfordshire, UK.4Biresin CR122 epoxy resin and CH122-3 hardener, Sika, Baar, Switzerland.
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6 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS
Fig. 9. Measured and simulated conductance of collapsed CMUT.
Fig. 10. Collapsed CMUT plate modes obtained in FEM modal analysis(a) first symmetrical mode at 645 kHz (b) first asymmetrical mode at 684 kHz(c) second asymmetrical mode at 872 kHz (d) third asymmetrical modeat 1220 kHz.
The admittance measurements are made in long averagingmode with 20 V of bias voltage and 0.5 Vpp of AC volt-age. As seen in Fig. 9 measured fundamental resonance isat 650 kHz, and the quality factor is 68.
Fig.10 shows the lowest order symmetrical and asymmetri-cal modes of the collapsed CMUT plate as obtained from FEMsimulations.5 The lowest order symmetrical mode (Fig. 10(a))occurs at 645 kHz as verified by the experiment. Asymmetricalmodes of the plate are also excited due to small asymmetriesarising from production inaccuracies. These resonances arealso visible in the measurement results as small peaks.
5FEM simulations are carried out in Ansys R14.5 (Ansys Inc., Canonsburg,PA). Modal analysis of a 3D collapsed CMUT cell is done and lowest platesymmetrical and asymmetrical modes are extracted.
Fig. 11. Pulse measurement setup with lock-in amplifier.
The radiation resistance of spherical waves propagating inisotropic solids is derived by Blake, Jr., [20]. Baseline of themeasured conductance is reproduced by RB which is 10 timeslarger than plate radiation resistance in air with a series lossof 5.6Sρ0co. This series loss (due to friction of collapsed plate)together with the backing loss, lowers the overall SNR of thereceived signal. We measure Cp as 0.98 times C0.
To match the measured resonance, we need to set tm =15.4 μm and a = 492 μm. The peak conductance is adjustedby setting tge = 1.53 μm which does not result in a significantshift in the resonance frequency.
B. Receive Sensitivity Performance Measurements
SCRC sensitivity of CMUT is measured at low ultrasoundfrequency of 100 kHz using the setup shown in Fig. 11.First, the CMUT wafer is covered with a metal shield toreduce the coupling. A low noise OPAMP (MAX4475)6 ina shield is placed right next to CMUT with R f = 1 G�and C f = 1 pF as its parallel feedback impedance. CMUTis connected directly to the inverting input while the non-inverting input of the OPAMP is connected to the ground.CMUT bias voltage is applied to the bottom electrode. Theoutput voltage of amplifier, (isc/ωC f ) is recorded with varyingbias at each frequency. The small-signal model of Fig. 2 issimulated in a circuit simulator7 using the employed OPAMPat off-resonance, to include the pre-amplifier gain in SCRC asshown in Fig. 12c.
C. Time Domain Pulse Measurements
Receiver CMUT is mounted 40 cm away on a planarwooden hardboard baffle, and is insonified by a widebandairborne transmitter8 which is driven by a signal gener-ator with a 3Vp pulse of 1 ms duration (100 cycles at100 kHz). A gain of 75 is provided by an amplifier.9
6Maxim Integrated 160 Rio Robles, San Jose, CA 95134 USA,www.maximintegrated.com
7Advanced Design Systems, Keysight Technologies, Santa Rosa, CA.8Series 600 Instrument Grade, Ultrasonic Transmitter, SensComp Inc.
Livonia, USA9Krohn-Hite 7500, Krohn-Hite Corporation, Brockton, MA
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KHAN et al.: OPTIMIZATION OF A COLLAPSED-MODE CMUT RECEIVER 7
Fig. 12. Pulse Measurements at 100kHz (a) transmitted pulse and measure-ment microphone recorded pressure (b) received signal envelopes for varyingDC bias is recorded on an oscilloscope (c) squares in the figure shows therecorded sensitivity at 100kHz of CMUT at preamplifier output in dB V/Pafrom the time domain pulse data.
Pulse repetition rate is kept 200 ms, to avoid any interfer-ence due to reflections or incoming transmitting pulse (SeeFig.12a). A lock-in amplifier (Stanford Research Systems,
Fig. 13. Variation of measured CMUT sensitivity against model at 110kHz.
SRS 830) with a set time constant of 100μs and filter rolloff of 12 dB/octave is employed to measure the ampli-tudes of receive signal envelopes on an oscilloscope. Theincident acoustic pressure is first measured by a calibratedpressure microphone (pressure-field microphone, B&K 4138)mounted on a preamplifier (B&K 2633) using an adap-tor (B&K UA 160). The microphone is polarized by a powersupply (B&K Type 2807). The sensitivity of the microphonesub system is −66.9 dB V/Pa (or 0.452 mV/Pa). The micro-phone output voltage is converted into pressure using itscalibration data and referred to the second axis at the rightof Fig. 12a. At the same distance of 40 cm, we measurethe baffle pressure of 0.12 Pa. This reference pressure isused to normalize the received CMUT acoustic envelopes ofFig. 12b for varying DC bias. Measured sensitivity of fabri-cated CMUT cell is then compared with the model predictionat 100kHz (Fig. 12c).
We repeat the pulse measurements at an alternate off-resonance frequency of 110kHz, with the same pulse excitationduration of 1 ms (110 cycles at 110kHz). The variation ofmeasured CMUT sensitivity against model is shown in Fig. 13.
D. Discussion
Measured SCRC sensitivity at 100kHz is shownin Fig. 12. We characterize maximum receive performanceof −60 dB V/Pa over the biasing range of 50 to 65 Volts.Measured absolute receive sensitivity of collapsed CMUTreceivers is in very good agreement with what is predicted byour small signal model. We repeat the same measurements atan alternate off-resonance frequency of 110kHz (see Fig. 13)and obtain the same variation of CMUT performance againstvarying bias. The critical biasing region predicted by themodel of fabricated CMUT is characterized within 4 dB onaverage at off-resonance frequencies. We record multiplereceive envelopes at each bias with a variance of lessthan 2 dB. Averaged envelopes are shown in this paper.Average SNR of these measurements for varying bias is
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8 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS
about 21 dB. We report absolute pressure measurementsin air which are affected by the measurement environmentdifferently at different frequencies.
VII. CONCLUSION
This paper shows that an optimized off-resonance CMUTreceiver can be more stable and reasonably sensitive incomparison to an uncollapsed CMUT receiver. A linear-equivalent-circuit model based approach is employed to char-acterize the receive sensitivity of collapse mode CMUTreceiver. We demonstrated through low frequency SCRC mea-surements that a fabricated collapsed CMUT cell maximumreceive sensitivity can be very accurately characterized by ourlinear small signal model. Conductance baseline correction isfirst made by adding backing loss impedance in the model.After impedance characterizations, we rederive CMUT receiveperformance with backing loss and compare it with SCRCmeasurements. Variation of the measured SCRC shows that acollapsed mode CMUT receiver sensitivity can be optimizedwith bias and that if it is biased in the critical maximumsensitivity region a stable maximum performance can beachieved at off-resonance frequencies.
APPENDIX ASTATIC ANALYSIS OF COLLAPSED MODE CMUT
Collapsed CMUT bending profile x(r) is determined byemploying radial dependent electrical force in presence ofuniformly distributed mechanical force (due to ambient pres-sure, Pb) in Timoshenko’s formulation’s [21]. To avoid alarge set of collapse bending profile calculations for eachdifferent CMUT design, we start with the normalized formof Timoshenko’s Eq. (3) in [12]:
rd
dr
(1
r
d
dr
(r
dx(r)
dr
)) = 64∫ r
b
(Pb
Pg+ 2(VDC/Vr )
2
9(1 − x(ζ ))2
)ζdζ
(25)
where r is the circular plate radial variable and the normalizedvariables are:
r = r
a, b = b
a, x(.) = x(.)
tge(26)
Pg is the pressure required to deflect the plate by its effectivegap height, tge at zero bias and Vr is the bias required tocollapse the CMUT plate in vacuum.
Pg = 64Dtge
a4 , Vr = 16
3a2
√Dt3
ge
ε0(27)
where D is the plate flexural rigidity constant. D = Y0t3m/
12(1 − σ 2). Y0 and σ are the Young’s modulus and Poisonratio of the plate, respectively. (25) is solved numerically withthe following boundary conditions:
x(r)∣∣r=1 = 0, x(r)
∣∣r=b = tg
tge,
d
drx(r)
∣∣r=1 = 0,
d
drx(r)
∣∣r=b = 0,
d2
dr2 x(r)∣∣r=b = 0 (28)
For different combinations of CMUT operational parametersPb/Pg , VDC/Vr , and tg/tge resulting collapsed rms platedisplacement, X R is calculated numerically in the MATLABroutine described in [22]. The lumped circuit elements are thenuniquely defined as polynomials in X R/tge.
APPENDIX BCOLLAPSED-MODE CMUT CAPACITANCE
AND COMPLIANCE POLYNOMIALS
gc(.) in (4) is a polynomial in X R/tge corresponding to theCMUT nonlinear capacitance
gc
(X R
tge
)=
3∑i=0
ni
(X R
tge
)i
(29)
For a given CMUT design first the operational parametersare determined from its physical dimensional parameters. Forthe obtained fixed normalized static pressure, Pb/Pg , and gapheight, tg/tge, (25) is solved by varying VDC/Vr . This yieldsvalues for the collapsed bending profile, x(r). Correspondingnonlinear CMUT capacitance C for each given deflectionprofile x(r) is obtained from (30) as:
C = C0
∫ 1
0
2r
1 − x(r)dr (30)
For each collapsed profile x(r), (30) is solved numerically inthe MATLAB routine of [22] and corresponding values fornormalized capacitance, C/C0 are obtained. A third degreecurve fitting to C/C0 against X R/tge yields polynomial coef-ficients ni of (29).
Compliance in collapsed mode of operation is a nonlinearfunction of normalized rms plate displacement X R/tge anddecreases with increasing contact of plate on the substrate.We define CRm as the ratio of X R to total rms force on themembrane (including both electrical and ambient force)
CRm = X R
FR + FRb(31)
where FR is the nonlinear electrical force of (6) and FRb isthe rms static force due to ambient pressure Pb. (31) can beexpressed in its normalized form as:
CRm
CRm0=
√5(X R/tge)
2√
515
( VDCVr
)2 dCd X R
+ PbPg
(32)
With C/C0 data in hand, dC/d X R is obtained from the firstderivative of (30) numerically for any given Pb/Pg , and tg/tge.A fourth degree curve fitting to the normalized compliancecurve CRm/CRm0 yields polynomial coefficients mi for hc(.)of (33).
hc
(X R
tge
)=
4∑i=0
mi
(X R
tge
)i
(33)
For any arbitrary CMUT operating conditions once gc(.) andhc(.) polynomials are obtained, the sensitivity multiplier h2 ofthe collapsed CMUT can be calculated from (24). Short circuitreceive performance can then be readily obtained from (23) forgiven material and physical dimensional parameters of CMUT.
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KHAN et al.: OPTIMIZATION OF A COLLAPSED-MODE CMUT RECEIVER 9
TABLE III
POLYNOMIAL COEFFICIENTS FOR Pb/Pg = 1.29 AND tg/tge = 0.79
Table III contains the polynomial coefficients obtained forCMUT capacitance and compliance for normalized staticpressure, Pb/Pg of 1.29 and normalized gap height tg/tge
of 0.79.
ACKNOWLEDGMENT
We gratefully acknowledge the support and recommen-dations of Tony Rogers at Applied Microengineering Ltd.,Oxfordshire, UK for the anodic bonding.
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Mansoor Khan received the B.S. degree in electri-cal and electronics engineering from the NationalUniversity of Sciences and Technology, Karachi,Pakistan, in 2007, and the M.Sc. degree in signalprocessing from Nanyang Technological University,Singapore, in 2009. He is currently pursuing thePh.D. degree in electrical and electronics engineer-ing with Bilkent University, Ankara, Turkey. Since2013, he has been a Research and Teaching Assistantwith Bilkent University. His current research inter-ests include linear circuit modeling and characteri-zation of collapsed CMUTs as ultrasound sensors.
Talha M. Khan received the M.S. degree in electri-cal engineering from the National University of Sci-ences and Technology, Islamabad, Pakistan, in 2013.He is currently pursuing the Ph.D. degree with theNational Nanotechnology Center, Bilkent Univer-sity, Ankara, Turkey. He joined the Faculty of theDepartment of Electrical Engineering, PIET, Multan,Pakistan, as a Lecturer. His research interests includeBio-MEMS, MEMS sensors, airborne acoustics, andultrasonic transducer design.
Akif Sinan Tasdelen was born in Ankara, Turkey,in 1981. He received the B.S. and M.S. degrees inelectrical and electronics engineering from BilkentUniversity, Ankara, in 2004 and 2007, respectively.In 2008, he joined the Bilkent University Acousticsand Underwater Technologies Research Center,where he is currently a Chief Technical ResearchEngineer. His research interests include passivecoherent location radar, underwater acoustics, trans-ducer array design, and biomedical ultrasound.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
10 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS
Mehmet Yilmaz received the B.S. degree (Hons.)from the Izmir Institute of Technology, the M.S.degree from Koç University, and the Ph.D. degreefrom Columbia University, all in mechanical engi-neering. During his M.S. and Ph.D. degrees, hehas specialized in design and microfabrication ofMEMS and integration of MEMS with nanostruc-tures. During his Ph.D. degree, he specialized innanomechanical characterization of materials in situscanning electron microscopes. He joined the IBMMicroelectronics Division, Albany Nanotechnology
Research and Development Center, Albany, NY, USA, where he was involvedin developing reactive-ion etching (RIE) processes for via patterning anddeveloping new integration schemes for 10- and 7-nm technology nodes, andsilicon 3-D integration technologies. He is currently a Principal Investiga-tor with the National Nanotechnology Research Center, Bilkent University.In spirit, he is an academician, scientist, engineer, inventor, and entrepreneur.He is a Co-Inventor of two U.S. patents from the research and developmentefforts during his time at IBM. He is interested in mechanical characterization,elastic strain engineering, understanding, and tuning the material properties atsmall length scales for energy and information technology applications, anddeveloping new unit processes and integration processes for batch-compatiblenanofabricated, high yield, MEMS and NEMS devices for energy, informationtechnology, and health applications.
Abdullah Atalar (F’07) received the B.S. degreefrom Middle East Technical University, Ankara,Turkey, in 1974, and the M.S. and Ph.D. degreesfrom Stanford University, Stanford, CA, USA,in 1976 and 1978, respectively, all in electrical engi-neering. From 1978 to 1980, he was a Post-DoctoralFellow and then an Engineering Research Associatewith Stanford University. He was Hewlett PackardLabs, Palo Alto, CA, USA, for one year. From1980 to 1986, he was an Assistant Professor withthe Faculty of the Middle East Technical University.
In 1983, on leave from the University, he was with Ernst Leitz Wetzlar (nowLeica), Wetzlar, Germany. In 1986, he joined Bilkent University as theChairman of the Electrical and Electronics Engineering Department and servedin the founding of the Department, where he is currently a Professor. In 1995,he was a Visiting Professor with Stanford University. From 1996 to 2010, hewas the Provost of Bilkent University, where he is currently the Rector. From2004 and 2011, he served as a member of the Science Board of TUBITAK. Hiscurrent research interests include microwave electronics and micromachinedsensors. He received the Science Award of the Turkish Scientific ResearchCouncil (TUBITAK) in 1994. He has been a member of the Turkish Academyof Sciences since 1997.
Hayrettin Köymen received the B.Sc. and M.Sc.degrees in electrical engineering from Middle EastTechnical University (METU), Ankara, Turkey,in 1973 and 1976, respectively, and the Ph.D. degreein electrical engineering from Birmingham Univer-sity, Birmingham, U.K., in 1979. From 1979 to 1990,he was with the Department of Marine Sciences,METU, Mersin, Turkey, and with the Departmentof Electrical Engineering, METU, Ankara. In 1990,he joined the Faculty of Bilkent University, Ankara,where he is currently a Professor with the Depart-
ment of Electrical and Electronics Engineering. His research interests includeunderwater and airborne acoustic and ultrasonic transducer design, underwateracoustics, underwater and airborne acoustic systems, acoustic microscopy,ultrasonic NDT, biomedical instrumentation, mobile communications, andspectrum management. He is an IET Fellow.
