Research ArticleA Two-Dimensional CMUT Linear Array for UnderwaterApplications Directivity Analysis and Design Optimization
Wen Zhang Hui Zhang Shijiu Jin and Zhoumo Zeng
State Key Laboratory of Precision Measurement Technology and Instrument Tianjin University Tianjin 300072 China
Correspondence should be addressed to Hui Zhang hzhangtjueducn
Received 12 February 2016 Accepted 24 March 2016
Academic Editor Rui Tang
Copyright copy 2016 Wen Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Capacitive micromachined ultrasonic transducers (CMUTs) are one of the promising MEMS devices This paper proposed anintegrated vibration membrane structure to design a two-dimensional CMUT linear array for underwater applications Theoperation frequencies for different medium have been calculated and simulated which are 25MHz in air and 07MHz in waterThe directivity analyses for the CMUT cell subarray and linear array have been provided According to the product theorems thedirectivity function of the complex array is obtained using a combination of the directivity functions of certain simple structuresResults show that the directivity of a CMUT cell is weak due to the small size but the directivity of the designed linear array isvery strong Influential parameters of the linear array have been discussed including the cell numbers the adjacent distance andthe operation medium In order to further suppress the side lobe interference and improve the resolution and the imaging qualityof the imaging system several weighting methods are used for optimization and comparison Satisfactory side lobe suppressionresults are obtained which can meet the actual requirements
1 Introduction
As the crucial component to achieve the conversion betweenacoustic energy and electrical energy ultrasonic transducersare widely used in medical imaging nondestructive evalua-tion flow measurement environmental chemical detectionand so on Compared to traditional transducers microma-chined ultrasonic transducer (MUT) fabricated by micro-electromechanical systems (MEMS) technology has greatadvantages in integration which can structure system-inpackage (SIP) and even system-on chip (SOC) technologies[1]Moreover theMEMS technology controls the accuracy inmicrometer (120583m) magnitude which largely reduces the fab-rication errors and improves the consistency between arraysAlso MEMS technology utilizes the silicon piezoresistivityor capacitance change to achieve the detection of acousticsignals so the imaging resolution can be improved too [2]
Currently the MUT family includes capacitive microma-chined ultrasonic transducers (CMUTs) based on flexuralvibrations caused by a field-induced electrostatic attrac-tion between suspended membrane and the substrate [3]and piezoelectric micromachined ultrasonic transducers
(PMUTs) based on flexural vibrations caused by d31-mode or
d33-mode excitation of a piezoelectric membrane [4 5]PMUT is made of a vibration membrane and piezoelec-
tric thin film with the upper and lower electrodes PMUTs donot require a large voltage bias and have fewer geometric anddesign constraints facilitating integration with low voltageelectronics However PMUTrsquos impedance cannot match theacoustic impedance of air or fluid medium so a surfacematching layer is of great need for a better performanceAlso the high sensitivity of the resonant frequency to theresidual stress of the PMUTmembranemay cause difficultiesduring the design process Residual stresses which are aconsequence of the various thermal treatments encounteredduring the fabrication process are expected to result in anincreased resonance frequency of the membrane if they weretensile in nature The level of residual stresses in the layers isvery dependent on the particular fabrication process and theprocessing conditions and is generally difficult to model [6]
Recently CMUTs have been developed as a promisingcandidate for ultrasound transducer arrays for underwa-ter application Unlike PMUTs the ultrasonic emission ofCMUT is caused by the vibration of a very thin film
Hindawi Publishing CorporationJournal of SensorsVolume 2016 Article ID 5298197 8 pageshttpdxdoiorg10115520165298197
2 Journal of Sensors
which lowers CMUTrsquos impedance to the same level of thesurroundings So the defects of PMUT impedance mismatchcan be improved without adding the surface matching layerCMUTbased onMEMS technology is of small size lownoiseand wide operating temperature range Therefore predrivecircuit preamplifier and signal processing circuits can beintegrated on the same silicon wafer Also CMUTs have beendemonstrated to produce fractional immersion bandwidth aswide as 175 and electromechanical coupling coefficient ashigh as 85 which are better than conventional transducers[7] In this paper a two-dimensional MUT linear arrayconsisting of CMUT cells is of research interest
In 1996 Haller and Khuri-Yakub from Stanford Uni-versity used surface micromachined technology and pro-duced a microcapacitive ultrasonic transducer [8] In 1999they developed air-coupled nondestructive evaluation usingmicromachined ultrasonic transducers [9] In 2002 Oralkanet al from Stanford University developed a linear CMUTarray and a 2D CMUT array which could implement 3Dultrasonic imaging [10 11] and also conducted preliminarysimulation experiments on imaging [12 13] In 2006 Carontiet al developed a one-dimensional array of ultrasonic trans-ducers and detectors used in medical ultrasonic imaging[14] In China Tianjin University was the first researchgroup and they launched a research program using a CMUTarray as the imaging and nondestructive detecting planararray [2 15] The Institute of Acoustics Chinese Academy ofSciences developed amicrocapacitivemicrophone of circularstructure [16] The North University of China studied themethod of designing MEMS capacitive ultrasonic transducerbased on silicon wafer bonding process [17] However allthese designs and research mentioned above did not involveactual applications of the device and the finite elementanalysis is time-consuming Therefore carrying out researchinto CMUT design simulation and application helps topromote the development of CMUT and improvement ofrelated technologies which is of great research value andpractical significance
The arrangement optimization of a transducer array hasbeen carried out to improve the radiated sound field direc-tivity Steinberg studied the focusing properties of uniformlinear array composed of many point sources and ignores thearray size and element number [18] Wooh and Shi studiedthe linear array focusing effect where the element lengthis infinite or the element length is much larger than theelement width [19] Actually the element of a transducerarray has certain size and the array could have good effectof the spatial resolution with proper design Compared withtraditional one-dimensional linear array the side leakingenergy is more serious in the MEMS transducer array forsmaller ratio of length to width Therefore the study on thedirectivity performance of the CMUT transducer array isvery necessary
Our aim is to analyze and optimize the directivitycharacteristics of CMUT cell and linear array which wouldbe accurate enough for designing and avoid massive finiteelement modeling In this paper Section 1 summarizes thedevelopment of the transducer community and issues thepossibility of CMUT cell being a MEMS linear array for
Fixed substrateInsulation layer
Membrane
Poly-Si
Si
Cavity
2R
SixNy
tins
h
t
Figure 1 Geometry of a flat circular CMUT cell
underwater application Details of the main problems withformer research are provided Section 2 describes the geom-etry design of both CMUT cell and the two-dimensionallinear array The operation frequencies in different mediumsare provided and proved by COMSOLMultiphysics softwareSection 3 provides the directivity analysis for CMUT cellsubarray and two-dimensional linear array The directiv-ity function of the complex array is obtained using theproduct theorems Section 4 makes further discussion andoptimization forCMUTsubarray and two-dimensional arrayDifferent influential parameters are considered for design andmodeling Side lobe suppression methods are compared anddiscussed Section 5 concludes the paper and assesses theregime of validity of the present analysis
2 Geometry Design of CMUT Celland Linear Array
A CMUT cell is built with a circular square or hexagonalmembrane separated from a fixed substrate by a small airgap[2 20] The geometry of the circular CMUT cell is shown inFigure 1 The vibrating membrane of the CMUT cell is madefrom a conducting ploysilicon membrane [21] A layer ofsilicon dioxide is deposited in order to prevent the electricalshortcut between the two electrodesThehighly doped siliconsubstrate is also utilized as the bottom electrode
Determination of the array resonant frequency has asignificant influence on the array design and optimizationThe CMUT often generates or detects ultrasonic waves bythe vibrating membrane featuring fixed circumference Thenthe resonant frequency of a clamped circular microplate invacuum can be calculated as [22 23]
1198910
= 0467119905
1198772radic
119864
120588 (1 minus 1205902) (1)
where 119905 and 119877 are the membrane thickness and radiusrespectively119864 is Youngrsquosmodulus120588 is themembrane densityand 120590 is Poissonrsquos ratio
When the CMUT cell is working for underwater appli-cations the influence of the surrounding medium cannot
be ignored Due to the effect of the medium the resonantfrequency in water can be expressed as [23 24]
119891119897
=1
radic1 + 067120588119897119877120588119905
1198910 (2)
where 120588119897represents the density of the surrounding liquid
In our case the membrane radius 119877 is 40 120583m and thethickness 119905 is 1 120583m Relevant material properties used intheory analysis are summarized in Table 1 The resonantfrequency of transducer is calculated as 249MHz in vacuumand 071MHz in water
The resonant frequencies of the transducer with thesame structure parameters for airborne and underwaterapplications are also analyzed by finite element method andthe results are comparedwith (1) and (2) As shown in Figures2 and 3 the results of the harmonic analysis simulated by theCOMSOLMultiphysics software are 250MHz and 07MHzwhich are consistentwith the theoretical analysis of a clampedcircular plate For the same geometry the CMUT cell showsa lower operation frequency for underwater applications Inour work (1)sim(2) and COMSOL simulations are adopted tomore accurately predict the array resonant frequencies fordifferent applications
In order to increase radiation sound pressure of thetwo-dimensional CMUT linear array we designed an arraystructure based on CMUT with the circular membrane Asshown in Figure 4 the 119872 CMUT cells in subarray are
In water
000
001
002
003
004
005
006
Vert
ical
disp
lace
men
t (120583
m)
065 070 075 080060
Frequency (MHz)
Figure 3 Harmonic analysis for a CMUT cell in water
y
z
x
ab
r
O
Figure 4 Geometry of a two-dimensional CMUT linear array
arranged by parallel connection where 119886 and 119903 are theintercell spacing and the cell radius The 119873 subarrays areuniformly arranged in 119874119909119910 plane and the distance betweentwo adjacent subarrays is 119887
3 Directivity Analysis for CMUT Linear Array
The directivity is a crucial parameter for CMUT design andit describes that the amplitude of its transmitting response orreceiving response is varying with an azimuth which is alsoa kind of attribute in the far field This is usually evaluatedby using the directivity function directivity diagram beamwidth side lobe level and so on
The following analyses assume that the subarray or thetwo-dimensional array is located along the 119909-axis which isin 119874119909119910 plane of three-dimensional space coordinate systemas shown in Figure 4 and its surface points to the 119874119909119911 plane
The normalized directivity function can be expressed as
where 120572 and 120579 are the standard spherical coordinate angles119875(120572 120579) is the sound pressure of the arbitrary position (120572 120579)
4 Journal of Sensors
y
z
x
P
O
120579
120572
Figure 5 Schematic for directivity analysis using normalized soundpressure
in the far field and 119875(120572119898
120579119898
) is the biggest sound pressureas shown in Figure 5
The directivity function of the complex array is generallysimplified as a combination of the directivity functions ofcertain simple structures Using the Bridge product theoremsthe complex array directivity function can be obtained bytaking the product of the directivity function of the simplestructures
For the two-dimensional CMUT linear array shown inFigure 4 the radiated sound field directivity function is equalto the product of a single subarray directivity function and alinear array directivity function composed of119873 point sourcesin each element center
The CMUT cell as shown in Figure 1 can be taken asa single circular piston with radius 119903 and the directivityfunction of the circular piston in the 119874119909119911 plane is
Considering the uniform linear array composed of 119873
point sources each subarray has the same resonant fre-quency the vibration amplitude and the phase Multipli-cation manipulation using (3)sim(5) leads to the following
expression for the sound pressure normalized directivityfunction
In order to improve the imaging resolution and imagingquality in an ultrasonic imaging system one-dimensional ortwo-dimensional linear array ultrasonic transducer is oftenused to implement the ultrasonic imaging The sound beamthat the CMUT array radiated to the three-dimensionalspace will produce a relative maximum amplitude of thesound pressure in a steering angle direction If the designedparameters are not optimized the radiation of the soundbeam will tend to produce the grating lobes and side lobesaround the main lobe The existence of the grating lobes andthe side lobes means the sound waves propagate in otherdirections which causes the ldquoleakagerdquo of the beam energyand affects the signal-to-noise ratio of the system Besides astrong side lobe inhibits the ability of the array to detect aweaker signal in the presence of a larger nearby signal Thusthe array parameters should be discussed and optimized byminimizing the main lobe width eliminating grating lobesand suppressing side lobes as much as possible
41 CMUT Subarray Optimization To discuss the directivityof a CMUT subarraymany parameters have to be consideredFor a CMUT subarray composed of119872 cells as in Figure 3 theoperation frequency of the CMUT linear array is designedto be 071MHz for underwater application and the soundvelocity in water is 1540ms so the wavelength can becalculated as
120582 =V119897
119891119897
=1540ms071MHz
asymp 2169 120583m (7)
To avoid the grating lobes the distance between twoadjacent cells in one subarray is supposed to be nomore than05120582 Consider the distance between two adjacent cells for ouranalysis to be 05120582 When the azimuth angle is 0∘ and there isno steering the directivity of a subarray varies with differentcell number 119872 as shown in Figure 6
From Figure 6 it can be seen that when the cell numberincreases the main lobe width decreases indicating a betterresolution and a more sensitive receiving angle range Alsowith more cells in one subarray the amplitude of the sidelobes decreases For more than 16 cells in one subarraythe main lobe width slightly decreases unlike the obviousdecrease from 119872 = 4 to 119872 = 8 So for the following analysis16 cells linearly arranged in one subarray have been chosen
Journal of Sensors 5
minus50
minus40
minus30
minus20
minus10
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
M = 4
M = 8
M = 16
M = 32
M = 64
Figure 6 Directivity analysis with different cell number in asubarray
minus50
minus40
minus30
minus20
minus10
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
025120582
05120582
075120582
1120582
Figure 7 Directivity analysis with different distance betweenadjacent cells
When the azimuth angle is 0∘ and there is no steering thedirectivity of a 16-cell subarray varies with different distancebetween two adjacent cells as shown in Figure 7
From Figure 7 it can be noticed that when the distancebetween two adjacent cells in a subarray increases themain lobe width decreases However increasing the adjacentdistance can also arouse grating lobes such as in the 1120582 caseTake both the main lobe width and the grating lobes intoconsideration the adjacent distance 05120582 is preferred for thefollowing analysis
The operation medium also has big influence on thedirectivity performance of the CMUT linear subarray Thedistance between two adjacent cells is set to be 1085120583m
Figure 8 Directivity analysis with different operation medium
which is 05120582 for underwater applications When the samearray is operated in air the directivity performance is differ-ent as shown in Figure 8
From Figure 8 it can be observed that for different oper-ation medium directivity performances are different Forthe same cell dimensions subarray geometry and adjacentdistance the grating lobes appear for airborne applicationsThe sound velocity in air is about 340ms and the operationfrequency is 25MHz so the wavelength in air can beexpressed as
120582air =Vair1198910
=340ms25MHz
= 136 120583m (8)
Compared to the wavelength in water (1540120583m) thewavelength in air is much smaller From Figure 7 it canbe obtained that when the distance between two adjacentcells is bigger than wavelength there will be grating lobesIn this case the adjacent distance is 1085 120583m which is muchbigger than the wavelength in air So the grating lobes appearand the energy leakage increases which also proves that aCMUT linear array for underwater applications may not besuitable for airborne applications without modification andoptimization
From Figures 6ndash8 several influential parameters havebeen discussed including the cell numbers the adjacentdistance and the operationmediumDuring the design phaseof a CMUT array these parameters have to be considered forbetter and more stable performance
42 Two-Dimensional CMUT Linear Array Optimization Adisadvantage of the CMUT linear subarray is its large sidelobes A strong side lobe inhibits the ability of the array todetect a weaker signal in the presence of a larger nearbysignal In this section the two-dimensional CMUT lineararray consisting of 16times8 cells (Figure 4) is chosen for analysis
Tapering functions can be used to suppress the sidelobes and the generalized cosine windows are one of the
6 Journal of Sensors
NoneHammingHann
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
Figure 9 Directivity analyses before and after the HannHammingmethods
most commonmethods including the Hann window and theHammingwindowThemathematical expression of theHannwindow is
119908 (119898) =1
2[1 minus cos(
2120587119898
119872)] 0 le 119898 le 119872 (9)
and the Hamming window expression is
119908 (119898) = 054 minus 046 cos(2120587119898
119872) 0 le 119898 le 119872 (10)
where 119872 represents the cell numberDirectivity analyses before and after the generalized
cosine methods are shown in Figure 9 Results show thatbothHamming andHannmethods can decrease the side lobeamplitude but both at the expense of broadening the mainlobe width The two methods are quite similar and the Hannmethod appears to have a faster decreasing rate
Another side lobe suppression method is the Kaiser win-dow weighting method and the mathematical expression is
119908 (119898) =
1198680
[120573radic1 minus (1 minus 2119898119872)2]
1198680
(120573)0 le 119898 le 119872
(11)
where 1198680(119909) is the zero-order modified Bessel function 120573 is
the shape function with relation to the side lobe amplitude119901119904 and the expression is
120573
=
01102 (119901119904
minus 87) 119901119904
gt 50
05482 (119901119904
minus 21)04
+ 007886 (119901119904
minus 21) 21 le 119901119904
le 50
0 119901119904
lt 21
(12)
For different 120573 values the directivity performances aredifferent as shown in Figure 10 When 120573 = 0 the directivity
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
None120573 = 0
120573 = 1
120573 = 5
120573 = 10
Figure 10 Directivity analyses before and after the Kaiser methodN
orm
aliz
ed so
und
pres
sure
(dB)
NoneChebyshevTaylor
minus90
minus60
minus30
0
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
Figure 11 Directivity analyses before and after the Cheby-shevTaylor methods
performance after the Kaiser weighting method remains thesame as before When 120573 increases the side lobe amplitudedecreases also at the expense of broadening the main lobewidth Compared to other weightingmethods the ratio of themain lobe energy to the side lobe energy of the Kaisermethodis almost the biggest Besides the main lobe width andthe side lobe amplitude can be freely regulated for differentapplications
Besides the Chebyshev and Taylor weighting methodsare also chosen for comparison The minus30 dB side lobe sup-pressions are carried out using the two methods and thedirectivity performances are shown in Figure 11
Journal of Sensors 7
From Figure 11 it can be observed that the Taylor methodis similar to the Chebyshev method Both methods havedecreased the side lobe amplitude to around minus30 dB andthe main lobe width has been broadened Whereas theChebyshev method has the narrowest possible main lobefor a specified side lobe level the Taylor method offerstradeoffs between themain lobe width and the side lobe levelMoreover the Taylor distribution avoids edge discontinuitiesso the Taylor method side lobes decrease monotonically
FromFigures 9ndash11 several common side lobe suppressionmethods have been discussed and compared Since the mainlobe width and the side lobe amplitude are contradictorythe side lobe suppression method must be carefully chosendue to different design requirements For instance when highlateral resolutions are desired the main lobe width is thefirst concernWhen the signal-to-noise ratio is the importantrequirement the side lobe level is the first concern
5 Conclusion
This paper proposed an integrated vibration membranestructure to design a CMUT linear array consisting ofmany subarrays for underwater applications The directivityperformances and side lobe suppression methods have beendiscussed The work in this paper is summarized as follows
(1) A two-dimensional CMUT linear array for underwa-ter applications has been proposedThe operation fre-quencies for different medium have been calculatedwhich are also proved by the COMSOL Multiphysicssoftware The derivation takes the ambient fluid intoconsideration and the operation frequency of theCMUT cell is 25MHz in air and 07MHz in water
(2) The directivity analyses for the CMUT cell sub-array and two-dimensional linear array have beenprovided The directivity of a single circular CMUTcell is very weak so it should be composed intolinear array to enhance the directivity According tothe product theorems the directivity function of thecomplex array is obtained using a combination of thedirectivity functions of certain simple structures
(3) The effects of the correlation parameters of the linearsubarray have been discussed including the cellnumbers the adjacent distance and the operationmedium Results show that both the cell numbers andthe adjacent distance have effect on the main lobewidth However both of them have an upper limit inorder to eliminate grating lobes For the underwaterapplications the wavelength is much bigger than thatfor the airborne applications Thus the directivityperformance of a linear subarray is determined byseveral parameters simultaneously
(4) In order to reduce the side lobe of the CMUT lineararray several weighting methods are used to suppressthe side lobe amplitude which is quite satisfactorybut at the expense of broadening themain lobe widthSince themain lobe width and the side lobe amplitudeare contradictory the side lobe suppression method
must be carefully chosen due to different designrequirements and the imaging quality and resolutionof the imaging system can be improved further
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This work has been supported by the Young Scientists Fundof the National Natural Science Foundation of China (Grantno 61201039)
References
[1] Y Qiu J V Gigliotti M Wallace et al ldquoPiezoelectric micro-machined ultrasound transducer (PMUT) arrays for integratedsensing actuation and imagingrdquo Sensors vol 15 no 4 pp8020ndash8041 2015
[2] W Zhang H Zhang F Du J Shi S Jin and Z Zeng ldquoPull-inanalysis of the flat circular CMUT cell featuring sealed cavityrdquoMathematical Problems in Engineering vol 2015 Article ID150279 9 pages 2015
[3] O Oralkan A S Ergun J A Johnson et al ldquoCapacitivemicromachined ultrasonic transducers next generation arraysfor acoustic imagingrdquo IEEE Transactions on Ultrasonics Ferro-electrics and Frequency Control vol 49 no 11 pp 1596ndash16102002
[4] D E Dausch J B Castellucci D R Chou and O T vonRamm ldquoTheory and operation of 2-D array piezoelectricmicromachined ultrasound transducersrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 55 no 11pp 2484ndash2492 2008
[5] A Hajati D Latev D Gardner et al ldquoThree-dimensional microelectromechanical system piezoelectric ultrasound transducerrdquoApplied Physics Letters vol 101 no 25 Article ID 253101 2012
[6] F Akasheh J D Fraser S Bose and A Bandyopadhyay ldquoPiezo-electric micromachined ultrasonic transducers modeling theinfluence of structural parameters on device performancerdquoIEEE Transactions on Ultrasonics Ferroelectrics and FrequencyControl vol 52 no 3 pp 455ndash468 2005
[7] A S Ergun C-H Cheng O Oralkan et al ldquoBroadbandcapacitive micromachined ultrasonic transducers ranging from10 kHz to 60MHz for imaging arrays and morerdquo in Proceedingsof the IEEE Ultrasonics Symposium pp 1039ndash1043 MunichGermany October 2002
[8] M I Haller and B T Khuri-Yakub ldquoA surface micromachinedelectrostatic ultrasonic air transducerrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 43 no 1pp 1ndash6 1996
[9] S T Hansen B J Mossawir A Sanli Ergun F Degertekinand B T Khuri-Yakub ldquoAir-coupled nondestructive evaluationusing micromachined ultrasonic transducersrdquo in Proceedings ofthe IEEE Ultrasonics Symposium pp 1037ndash1040 Lake TahoeNev USA October 1999
[10] J Johnson O Oralkan U Demirci S Ergun M Karaman andP Khuri-Yakub ldquoMedical imaging using capacitive microma-chined ultrasonic transducer arraysrdquo Ultrasonics vol 40 no 1-8 pp 471ndash476 2002
8 Journal of Sensors
[11] X Zhuang A S Ergun Y Huang I O Wygant O Oralkanand B T Khuri-Yakub ldquoIntegration of trench-isolated through-wafer interconnects with 2d capacitive micromachined ultra-sonic transducer arraysrdquo Sensors and Actuators A Physical vol138 no 1 pp 221ndash229 2007
[12] X Zhuang D-S Lin O Oralkan and B T Khuri-YakubldquoFabrication of flexible transducer arrays with through-waferelectrical interconnects based on trench refilling with PDMSrdquoJournal of Microelectromechanical Systems vol 17 no 2 pp446ndash452 2008
[13] I O Wygant N S Jamal H J Lee et al ldquoAn integratedcircuit with transmit beamforming flip-chip bonded to a 2-DCMUT array for 3-D ultrasound imagingrdquo IEEE Transactionson Ultrasonics Ferroelectrics and Frequency Control vol 56 no10 pp 2145ndash2156 2009
[14] A Caronti G Caliano R Carotenuto et al ldquoCapacitive micro-machined ultrasonic transducer (CMUT) arrays for medicalimagingrdquo Microelectronics Journal vol 37 no 8 pp 770ndash7772006
[15] W Zhang H Zhang Y Wang F Du S Jin and Z ZengldquoSimulation characterization of CMUT with vented squaremembranerdquo in Proceedings of the International Conference onOptical Instrument and Technology (OIT rsquo15) Beijing ChinaMay 2015
[16] Z H Hao L Tang and D H Qiao ldquoAnalysis of the resonantfrequency of capacitive micro-machined ultrasonic transducer(cMUT) with finite element methodrdquo Technical Acoustics vol28 pp 133ndash134 2009 (Chinese)
[17] J Miao C D He D Q Lian et al ldquoDesign of MEMS capacitiveultrasonic transducer based on wafer bonding technologyrdquoChinese Journal of Sensors and Actuators vol 25 no 12 pp1653ndash1658 2012 (Chinese)
[18] B D Steinberg Principles of Aperture and Array System DesignIncluding Random and Adaptive Arrays John Wiley amp SonsNew York NY USA 1976
[19] S-C Wooh and Y Shi ldquoInfluence of phased array element sizeon beam steering behaviorrdquo Ultrasonics vol 36 no 6 pp 737ndash749 1998
[20] C B Doody X Cheng C A Rich D F Lemmerhirt and RD White ldquoModeling and characterization of CMOS-fabricatedcapacitive micromachined ultrasound transducersrdquo Journal ofMicroelectromechanical Systems vol 20 no 1 pp 104ndash118 2011
[21] M L Kuntzman D Kim andN A Hall ldquoMicrofabrication andexperimental evaluation of a rotational capacitive microma-chined ultrasonic transducerrdquo Journal of Microelectromechani-cal Systems vol 24 no 2 pp 404ndash413 2015
[22] M Bao Analysis and Design Principles of MEMS DevicesElsevier New York NY USA 2005
[23] M R Haddara and S Cao ldquoA study of the dynamic response ofsubmerged rectangular flat platesrdquoMarine Structures vol 9 no10 pp 913ndash933 1996
[24] X H Si W X Lu and F L Chu ldquoModal analysis of circularplates with radial side cracks and in contact with water on oneside based on the RayleighndashRitz methodrdquo Journal of Sound andVibration vol 331 no 1 pp 231ndash251 2012
which lowers CMUTrsquos impedance to the same level of thesurroundings So the defects of PMUT impedance mismatchcan be improved without adding the surface matching layerCMUTbased onMEMS technology is of small size lownoiseand wide operating temperature range Therefore predrivecircuit preamplifier and signal processing circuits can beintegrated on the same silicon wafer Also CMUTs have beendemonstrated to produce fractional immersion bandwidth aswide as 175 and electromechanical coupling coefficient ashigh as 85 which are better than conventional transducers[7] In this paper a two-dimensional MUT linear arrayconsisting of CMUT cells is of research interest
In 1996 Haller and Khuri-Yakub from Stanford Uni-versity used surface micromachined technology and pro-duced a microcapacitive ultrasonic transducer [8] In 1999they developed air-coupled nondestructive evaluation usingmicromachined ultrasonic transducers [9] In 2002 Oralkanet al from Stanford University developed a linear CMUTarray and a 2D CMUT array which could implement 3Dultrasonic imaging [10 11] and also conducted preliminarysimulation experiments on imaging [12 13] In 2006 Carontiet al developed a one-dimensional array of ultrasonic trans-ducers and detectors used in medical ultrasonic imaging[14] In China Tianjin University was the first researchgroup and they launched a research program using a CMUTarray as the imaging and nondestructive detecting planararray [2 15] The Institute of Acoustics Chinese Academy ofSciences developed amicrocapacitivemicrophone of circularstructure [16] The North University of China studied themethod of designing MEMS capacitive ultrasonic transducerbased on silicon wafer bonding process [17] However allthese designs and research mentioned above did not involveactual applications of the device and the finite elementanalysis is time-consuming Therefore carrying out researchinto CMUT design simulation and application helps topromote the development of CMUT and improvement ofrelated technologies which is of great research value andpractical significance
The arrangement optimization of a transducer array hasbeen carried out to improve the radiated sound field direc-tivity Steinberg studied the focusing properties of uniformlinear array composed of many point sources and ignores thearray size and element number [18] Wooh and Shi studiedthe linear array focusing effect where the element lengthis infinite or the element length is much larger than theelement width [19] Actually the element of a transducerarray has certain size and the array could have good effectof the spatial resolution with proper design Compared withtraditional one-dimensional linear array the side leakingenergy is more serious in the MEMS transducer array forsmaller ratio of length to width Therefore the study on thedirectivity performance of the CMUT transducer array isvery necessary
Our aim is to analyze and optimize the directivitycharacteristics of CMUT cell and linear array which wouldbe accurate enough for designing and avoid massive finiteelement modeling In this paper Section 1 summarizes thedevelopment of the transducer community and issues thepossibility of CMUT cell being a MEMS linear array for
Fixed substrateInsulation layer
Membrane
Poly-Si
Si
Cavity
2R
SixNy
tins
h
t
Figure 1 Geometry of a flat circular CMUT cell
underwater application Details of the main problems withformer research are provided Section 2 describes the geom-etry design of both CMUT cell and the two-dimensionallinear array The operation frequencies in different mediumsare provided and proved by COMSOLMultiphysics softwareSection 3 provides the directivity analysis for CMUT cellsubarray and two-dimensional linear array The directiv-ity function of the complex array is obtained using theproduct theorems Section 4 makes further discussion andoptimization forCMUTsubarray and two-dimensional arrayDifferent influential parameters are considered for design andmodeling Side lobe suppression methods are compared anddiscussed Section 5 concludes the paper and assesses theregime of validity of the present analysis
2 Geometry Design of CMUT Celland Linear Array
A CMUT cell is built with a circular square or hexagonalmembrane separated from a fixed substrate by a small airgap[2 20] The geometry of the circular CMUT cell is shown inFigure 1 The vibrating membrane of the CMUT cell is madefrom a conducting ploysilicon membrane [21] A layer ofsilicon dioxide is deposited in order to prevent the electricalshortcut between the two electrodesThehighly doped siliconsubstrate is also utilized as the bottom electrode
Determination of the array resonant frequency has asignificant influence on the array design and optimizationThe CMUT often generates or detects ultrasonic waves bythe vibrating membrane featuring fixed circumference Thenthe resonant frequency of a clamped circular microplate invacuum can be calculated as [22 23]
1198910
= 0467119905
1198772radic
119864
120588 (1 minus 1205902) (1)
where 119905 and 119877 are the membrane thickness and radiusrespectively119864 is Youngrsquosmodulus120588 is themembrane densityand 120590 is Poissonrsquos ratio
When the CMUT cell is working for underwater appli-cations the influence of the surrounding medium cannot
be ignored Due to the effect of the medium the resonantfrequency in water can be expressed as [23 24]
119891119897
=1
radic1 + 067120588119897119877120588119905
1198910 (2)
where 120588119897represents the density of the surrounding liquid
In our case the membrane radius 119877 is 40 120583m and thethickness 119905 is 1 120583m Relevant material properties used intheory analysis are summarized in Table 1 The resonantfrequency of transducer is calculated as 249MHz in vacuumand 071MHz in water
The resonant frequencies of the transducer with thesame structure parameters for airborne and underwaterapplications are also analyzed by finite element method andthe results are comparedwith (1) and (2) As shown in Figures2 and 3 the results of the harmonic analysis simulated by theCOMSOLMultiphysics software are 250MHz and 07MHzwhich are consistentwith the theoretical analysis of a clampedcircular plate For the same geometry the CMUT cell showsa lower operation frequency for underwater applications Inour work (1)sim(2) and COMSOL simulations are adopted tomore accurately predict the array resonant frequencies fordifferent applications
In order to increase radiation sound pressure of thetwo-dimensional CMUT linear array we designed an arraystructure based on CMUT with the circular membrane Asshown in Figure 4 the 119872 CMUT cells in subarray are
In water
000
001
002
003
004
005
006
Vert
ical
disp
lace
men
t (120583
m)
065 070 075 080060
Frequency (MHz)
Figure 3 Harmonic analysis for a CMUT cell in water
y
z
x
ab
r
O
Figure 4 Geometry of a two-dimensional CMUT linear array
arranged by parallel connection where 119886 and 119903 are theintercell spacing and the cell radius The 119873 subarrays areuniformly arranged in 119874119909119910 plane and the distance betweentwo adjacent subarrays is 119887
3 Directivity Analysis for CMUT Linear Array
The directivity is a crucial parameter for CMUT design andit describes that the amplitude of its transmitting response orreceiving response is varying with an azimuth which is alsoa kind of attribute in the far field This is usually evaluatedby using the directivity function directivity diagram beamwidth side lobe level and so on
The following analyses assume that the subarray or thetwo-dimensional array is located along the 119909-axis which isin 119874119909119910 plane of three-dimensional space coordinate systemas shown in Figure 4 and its surface points to the 119874119909119911 plane
The normalized directivity function can be expressed as
where 120572 and 120579 are the standard spherical coordinate angles119875(120572 120579) is the sound pressure of the arbitrary position (120572 120579)
4 Journal of Sensors
y
z
x
P
O
120579
120572
Figure 5 Schematic for directivity analysis using normalized soundpressure
in the far field and 119875(120572119898
120579119898
) is the biggest sound pressureas shown in Figure 5
The directivity function of the complex array is generallysimplified as a combination of the directivity functions ofcertain simple structures Using the Bridge product theoremsthe complex array directivity function can be obtained bytaking the product of the directivity function of the simplestructures
For the two-dimensional CMUT linear array shown inFigure 4 the radiated sound field directivity function is equalto the product of a single subarray directivity function and alinear array directivity function composed of119873 point sourcesin each element center
The CMUT cell as shown in Figure 1 can be taken asa single circular piston with radius 119903 and the directivityfunction of the circular piston in the 119874119909119911 plane is
Considering the uniform linear array composed of 119873
point sources each subarray has the same resonant fre-quency the vibration amplitude and the phase Multipli-cation manipulation using (3)sim(5) leads to the following
expression for the sound pressure normalized directivityfunction
In order to improve the imaging resolution and imagingquality in an ultrasonic imaging system one-dimensional ortwo-dimensional linear array ultrasonic transducer is oftenused to implement the ultrasonic imaging The sound beamthat the CMUT array radiated to the three-dimensionalspace will produce a relative maximum amplitude of thesound pressure in a steering angle direction If the designedparameters are not optimized the radiation of the soundbeam will tend to produce the grating lobes and side lobesaround the main lobe The existence of the grating lobes andthe side lobes means the sound waves propagate in otherdirections which causes the ldquoleakagerdquo of the beam energyand affects the signal-to-noise ratio of the system Besides astrong side lobe inhibits the ability of the array to detect aweaker signal in the presence of a larger nearby signal Thusthe array parameters should be discussed and optimized byminimizing the main lobe width eliminating grating lobesand suppressing side lobes as much as possible
41 CMUT Subarray Optimization To discuss the directivityof a CMUT subarraymany parameters have to be consideredFor a CMUT subarray composed of119872 cells as in Figure 3 theoperation frequency of the CMUT linear array is designedto be 071MHz for underwater application and the soundvelocity in water is 1540ms so the wavelength can becalculated as
120582 =V119897
119891119897
=1540ms071MHz
asymp 2169 120583m (7)
To avoid the grating lobes the distance between twoadjacent cells in one subarray is supposed to be nomore than05120582 Consider the distance between two adjacent cells for ouranalysis to be 05120582 When the azimuth angle is 0∘ and there isno steering the directivity of a subarray varies with differentcell number 119872 as shown in Figure 6
From Figure 6 it can be seen that when the cell numberincreases the main lobe width decreases indicating a betterresolution and a more sensitive receiving angle range Alsowith more cells in one subarray the amplitude of the sidelobes decreases For more than 16 cells in one subarraythe main lobe width slightly decreases unlike the obviousdecrease from 119872 = 4 to 119872 = 8 So for the following analysis16 cells linearly arranged in one subarray have been chosen
Journal of Sensors 5
minus50
minus40
minus30
minus20
minus10
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
M = 4
M = 8
M = 16
M = 32
M = 64
Figure 6 Directivity analysis with different cell number in asubarray
minus50
minus40
minus30
minus20
minus10
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
025120582
05120582
075120582
1120582
Figure 7 Directivity analysis with different distance betweenadjacent cells
When the azimuth angle is 0∘ and there is no steering thedirectivity of a 16-cell subarray varies with different distancebetween two adjacent cells as shown in Figure 7
From Figure 7 it can be noticed that when the distancebetween two adjacent cells in a subarray increases themain lobe width decreases However increasing the adjacentdistance can also arouse grating lobes such as in the 1120582 caseTake both the main lobe width and the grating lobes intoconsideration the adjacent distance 05120582 is preferred for thefollowing analysis
The operation medium also has big influence on thedirectivity performance of the CMUT linear subarray Thedistance between two adjacent cells is set to be 1085120583m
Figure 8 Directivity analysis with different operation medium
which is 05120582 for underwater applications When the samearray is operated in air the directivity performance is differ-ent as shown in Figure 8
From Figure 8 it can be observed that for different oper-ation medium directivity performances are different Forthe same cell dimensions subarray geometry and adjacentdistance the grating lobes appear for airborne applicationsThe sound velocity in air is about 340ms and the operationfrequency is 25MHz so the wavelength in air can beexpressed as
120582air =Vair1198910
=340ms25MHz
= 136 120583m (8)
Compared to the wavelength in water (1540120583m) thewavelength in air is much smaller From Figure 7 it canbe obtained that when the distance between two adjacentcells is bigger than wavelength there will be grating lobesIn this case the adjacent distance is 1085 120583m which is muchbigger than the wavelength in air So the grating lobes appearand the energy leakage increases which also proves that aCMUT linear array for underwater applications may not besuitable for airborne applications without modification andoptimization
From Figures 6ndash8 several influential parameters havebeen discussed including the cell numbers the adjacentdistance and the operationmediumDuring the design phaseof a CMUT array these parameters have to be considered forbetter and more stable performance
42 Two-Dimensional CMUT Linear Array Optimization Adisadvantage of the CMUT linear subarray is its large sidelobes A strong side lobe inhibits the ability of the array todetect a weaker signal in the presence of a larger nearbysignal In this section the two-dimensional CMUT lineararray consisting of 16times8 cells (Figure 4) is chosen for analysis
Tapering functions can be used to suppress the sidelobes and the generalized cosine windows are one of the
6 Journal of Sensors
NoneHammingHann
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
Figure 9 Directivity analyses before and after the HannHammingmethods
most commonmethods including the Hann window and theHammingwindowThemathematical expression of theHannwindow is
119908 (119898) =1
2[1 minus cos(
2120587119898
119872)] 0 le 119898 le 119872 (9)
and the Hamming window expression is
119908 (119898) = 054 minus 046 cos(2120587119898
119872) 0 le 119898 le 119872 (10)
where 119872 represents the cell numberDirectivity analyses before and after the generalized
cosine methods are shown in Figure 9 Results show thatbothHamming andHannmethods can decrease the side lobeamplitude but both at the expense of broadening the mainlobe width The two methods are quite similar and the Hannmethod appears to have a faster decreasing rate
Another side lobe suppression method is the Kaiser win-dow weighting method and the mathematical expression is
119908 (119898) =
1198680
[120573radic1 minus (1 minus 2119898119872)2]
1198680
(120573)0 le 119898 le 119872
(11)
where 1198680(119909) is the zero-order modified Bessel function 120573 is
the shape function with relation to the side lobe amplitude119901119904 and the expression is
120573
=
01102 (119901119904
minus 87) 119901119904
gt 50
05482 (119901119904
minus 21)04
+ 007886 (119901119904
minus 21) 21 le 119901119904
le 50
0 119901119904
lt 21
(12)
For different 120573 values the directivity performances aredifferent as shown in Figure 10 When 120573 = 0 the directivity
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
None120573 = 0
120573 = 1
120573 = 5
120573 = 10
Figure 10 Directivity analyses before and after the Kaiser methodN
orm
aliz
ed so
und
pres
sure
(dB)
NoneChebyshevTaylor
minus90
minus60
minus30
0
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
Figure 11 Directivity analyses before and after the Cheby-shevTaylor methods
performance after the Kaiser weighting method remains thesame as before When 120573 increases the side lobe amplitudedecreases also at the expense of broadening the main lobewidth Compared to other weightingmethods the ratio of themain lobe energy to the side lobe energy of the Kaisermethodis almost the biggest Besides the main lobe width andthe side lobe amplitude can be freely regulated for differentapplications
Besides the Chebyshev and Taylor weighting methodsare also chosen for comparison The minus30 dB side lobe sup-pressions are carried out using the two methods and thedirectivity performances are shown in Figure 11
Journal of Sensors 7
From Figure 11 it can be observed that the Taylor methodis similar to the Chebyshev method Both methods havedecreased the side lobe amplitude to around minus30 dB andthe main lobe width has been broadened Whereas theChebyshev method has the narrowest possible main lobefor a specified side lobe level the Taylor method offerstradeoffs between themain lobe width and the side lobe levelMoreover the Taylor distribution avoids edge discontinuitiesso the Taylor method side lobes decrease monotonically
FromFigures 9ndash11 several common side lobe suppressionmethods have been discussed and compared Since the mainlobe width and the side lobe amplitude are contradictorythe side lobe suppression method must be carefully chosendue to different design requirements For instance when highlateral resolutions are desired the main lobe width is thefirst concernWhen the signal-to-noise ratio is the importantrequirement the side lobe level is the first concern
5 Conclusion
This paper proposed an integrated vibration membranestructure to design a CMUT linear array consisting ofmany subarrays for underwater applications The directivityperformances and side lobe suppression methods have beendiscussed The work in this paper is summarized as follows
(1) A two-dimensional CMUT linear array for underwa-ter applications has been proposedThe operation fre-quencies for different medium have been calculatedwhich are also proved by the COMSOL Multiphysicssoftware The derivation takes the ambient fluid intoconsideration and the operation frequency of theCMUT cell is 25MHz in air and 07MHz in water
(2) The directivity analyses for the CMUT cell sub-array and two-dimensional linear array have beenprovided The directivity of a single circular CMUTcell is very weak so it should be composed intolinear array to enhance the directivity According tothe product theorems the directivity function of thecomplex array is obtained using a combination of thedirectivity functions of certain simple structures
(3) The effects of the correlation parameters of the linearsubarray have been discussed including the cellnumbers the adjacent distance and the operationmedium Results show that both the cell numbers andthe adjacent distance have effect on the main lobewidth However both of them have an upper limit inorder to eliminate grating lobes For the underwaterapplications the wavelength is much bigger than thatfor the airborne applications Thus the directivityperformance of a linear subarray is determined byseveral parameters simultaneously
(4) In order to reduce the side lobe of the CMUT lineararray several weighting methods are used to suppressthe side lobe amplitude which is quite satisfactorybut at the expense of broadening themain lobe widthSince themain lobe width and the side lobe amplitudeare contradictory the side lobe suppression method
must be carefully chosen due to different designrequirements and the imaging quality and resolutionof the imaging system can be improved further
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This work has been supported by the Young Scientists Fundof the National Natural Science Foundation of China (Grantno 61201039)
References
[1] Y Qiu J V Gigliotti M Wallace et al ldquoPiezoelectric micro-machined ultrasound transducer (PMUT) arrays for integratedsensing actuation and imagingrdquo Sensors vol 15 no 4 pp8020ndash8041 2015
[2] W Zhang H Zhang F Du J Shi S Jin and Z Zeng ldquoPull-inanalysis of the flat circular CMUT cell featuring sealed cavityrdquoMathematical Problems in Engineering vol 2015 Article ID150279 9 pages 2015
[3] O Oralkan A S Ergun J A Johnson et al ldquoCapacitivemicromachined ultrasonic transducers next generation arraysfor acoustic imagingrdquo IEEE Transactions on Ultrasonics Ferro-electrics and Frequency Control vol 49 no 11 pp 1596ndash16102002
[4] D E Dausch J B Castellucci D R Chou and O T vonRamm ldquoTheory and operation of 2-D array piezoelectricmicromachined ultrasound transducersrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 55 no 11pp 2484ndash2492 2008
[5] A Hajati D Latev D Gardner et al ldquoThree-dimensional microelectromechanical system piezoelectric ultrasound transducerrdquoApplied Physics Letters vol 101 no 25 Article ID 253101 2012
[6] F Akasheh J D Fraser S Bose and A Bandyopadhyay ldquoPiezo-electric micromachined ultrasonic transducers modeling theinfluence of structural parameters on device performancerdquoIEEE Transactions on Ultrasonics Ferroelectrics and FrequencyControl vol 52 no 3 pp 455ndash468 2005
[7] A S Ergun C-H Cheng O Oralkan et al ldquoBroadbandcapacitive micromachined ultrasonic transducers ranging from10 kHz to 60MHz for imaging arrays and morerdquo in Proceedingsof the IEEE Ultrasonics Symposium pp 1039ndash1043 MunichGermany October 2002
[8] M I Haller and B T Khuri-Yakub ldquoA surface micromachinedelectrostatic ultrasonic air transducerrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 43 no 1pp 1ndash6 1996
[9] S T Hansen B J Mossawir A Sanli Ergun F Degertekinand B T Khuri-Yakub ldquoAir-coupled nondestructive evaluationusing micromachined ultrasonic transducersrdquo in Proceedings ofthe IEEE Ultrasonics Symposium pp 1037ndash1040 Lake TahoeNev USA October 1999
[10] J Johnson O Oralkan U Demirci S Ergun M Karaman andP Khuri-Yakub ldquoMedical imaging using capacitive microma-chined ultrasonic transducer arraysrdquo Ultrasonics vol 40 no 1-8 pp 471ndash476 2002
8 Journal of Sensors
[11] X Zhuang A S Ergun Y Huang I O Wygant O Oralkanand B T Khuri-Yakub ldquoIntegration of trench-isolated through-wafer interconnects with 2d capacitive micromachined ultra-sonic transducer arraysrdquo Sensors and Actuators A Physical vol138 no 1 pp 221ndash229 2007
[12] X Zhuang D-S Lin O Oralkan and B T Khuri-YakubldquoFabrication of flexible transducer arrays with through-waferelectrical interconnects based on trench refilling with PDMSrdquoJournal of Microelectromechanical Systems vol 17 no 2 pp446ndash452 2008
[13] I O Wygant N S Jamal H J Lee et al ldquoAn integratedcircuit with transmit beamforming flip-chip bonded to a 2-DCMUT array for 3-D ultrasound imagingrdquo IEEE Transactionson Ultrasonics Ferroelectrics and Frequency Control vol 56 no10 pp 2145ndash2156 2009
[14] A Caronti G Caliano R Carotenuto et al ldquoCapacitive micro-machined ultrasonic transducer (CMUT) arrays for medicalimagingrdquo Microelectronics Journal vol 37 no 8 pp 770ndash7772006
[15] W Zhang H Zhang Y Wang F Du S Jin and Z ZengldquoSimulation characterization of CMUT with vented squaremembranerdquo in Proceedings of the International Conference onOptical Instrument and Technology (OIT rsquo15) Beijing ChinaMay 2015
[16] Z H Hao L Tang and D H Qiao ldquoAnalysis of the resonantfrequency of capacitive micro-machined ultrasonic transducer(cMUT) with finite element methodrdquo Technical Acoustics vol28 pp 133ndash134 2009 (Chinese)
[17] J Miao C D He D Q Lian et al ldquoDesign of MEMS capacitiveultrasonic transducer based on wafer bonding technologyrdquoChinese Journal of Sensors and Actuators vol 25 no 12 pp1653ndash1658 2012 (Chinese)
[18] B D Steinberg Principles of Aperture and Array System DesignIncluding Random and Adaptive Arrays John Wiley amp SonsNew York NY USA 1976
[19] S-C Wooh and Y Shi ldquoInfluence of phased array element sizeon beam steering behaviorrdquo Ultrasonics vol 36 no 6 pp 737ndash749 1998
[20] C B Doody X Cheng C A Rich D F Lemmerhirt and RD White ldquoModeling and characterization of CMOS-fabricatedcapacitive micromachined ultrasound transducersrdquo Journal ofMicroelectromechanical Systems vol 20 no 1 pp 104ndash118 2011
[21] M L Kuntzman D Kim andN A Hall ldquoMicrofabrication andexperimental evaluation of a rotational capacitive microma-chined ultrasonic transducerrdquo Journal of Microelectromechani-cal Systems vol 24 no 2 pp 404ndash413 2015
[22] M Bao Analysis and Design Principles of MEMS DevicesElsevier New York NY USA 2005
[23] M R Haddara and S Cao ldquoA study of the dynamic response ofsubmerged rectangular flat platesrdquoMarine Structures vol 9 no10 pp 913ndash933 1996
[24] X H Si W X Lu and F L Chu ldquoModal analysis of circularplates with radial side cracks and in contact with water on oneside based on the RayleighndashRitz methodrdquo Journal of Sound andVibration vol 331 no 1 pp 231ndash251 2012
be ignored Due to the effect of the medium the resonantfrequency in water can be expressed as [23 24]
119891119897
=1
radic1 + 067120588119897119877120588119905
1198910 (2)
where 120588119897represents the density of the surrounding liquid
In our case the membrane radius 119877 is 40 120583m and thethickness 119905 is 1 120583m Relevant material properties used intheory analysis are summarized in Table 1 The resonantfrequency of transducer is calculated as 249MHz in vacuumand 071MHz in water
The resonant frequencies of the transducer with thesame structure parameters for airborne and underwaterapplications are also analyzed by finite element method andthe results are comparedwith (1) and (2) As shown in Figures2 and 3 the results of the harmonic analysis simulated by theCOMSOLMultiphysics software are 250MHz and 07MHzwhich are consistentwith the theoretical analysis of a clampedcircular plate For the same geometry the CMUT cell showsa lower operation frequency for underwater applications Inour work (1)sim(2) and COMSOL simulations are adopted tomore accurately predict the array resonant frequencies fordifferent applications
In order to increase radiation sound pressure of thetwo-dimensional CMUT linear array we designed an arraystructure based on CMUT with the circular membrane Asshown in Figure 4 the 119872 CMUT cells in subarray are
In water
000
001
002
003
004
005
006
Vert
ical
disp
lace
men
t (120583
m)
065 070 075 080060
Frequency (MHz)
Figure 3 Harmonic analysis for a CMUT cell in water
y
z
x
ab
r
O
Figure 4 Geometry of a two-dimensional CMUT linear array
arranged by parallel connection where 119886 and 119903 are theintercell spacing and the cell radius The 119873 subarrays areuniformly arranged in 119874119909119910 plane and the distance betweentwo adjacent subarrays is 119887
3 Directivity Analysis for CMUT Linear Array
The directivity is a crucial parameter for CMUT design andit describes that the amplitude of its transmitting response orreceiving response is varying with an azimuth which is alsoa kind of attribute in the far field This is usually evaluatedby using the directivity function directivity diagram beamwidth side lobe level and so on
The following analyses assume that the subarray or thetwo-dimensional array is located along the 119909-axis which isin 119874119909119910 plane of three-dimensional space coordinate systemas shown in Figure 4 and its surface points to the 119874119909119911 plane
The normalized directivity function can be expressed as
where 120572 and 120579 are the standard spherical coordinate angles119875(120572 120579) is the sound pressure of the arbitrary position (120572 120579)
4 Journal of Sensors
y
z
x
P
O
120579
120572
Figure 5 Schematic for directivity analysis using normalized soundpressure
in the far field and 119875(120572119898
120579119898
) is the biggest sound pressureas shown in Figure 5
The directivity function of the complex array is generallysimplified as a combination of the directivity functions ofcertain simple structures Using the Bridge product theoremsthe complex array directivity function can be obtained bytaking the product of the directivity function of the simplestructures
For the two-dimensional CMUT linear array shown inFigure 4 the radiated sound field directivity function is equalto the product of a single subarray directivity function and alinear array directivity function composed of119873 point sourcesin each element center
The CMUT cell as shown in Figure 1 can be taken asa single circular piston with radius 119903 and the directivityfunction of the circular piston in the 119874119909119911 plane is
Considering the uniform linear array composed of 119873
point sources each subarray has the same resonant fre-quency the vibration amplitude and the phase Multipli-cation manipulation using (3)sim(5) leads to the following
expression for the sound pressure normalized directivityfunction
In order to improve the imaging resolution and imagingquality in an ultrasonic imaging system one-dimensional ortwo-dimensional linear array ultrasonic transducer is oftenused to implement the ultrasonic imaging The sound beamthat the CMUT array radiated to the three-dimensionalspace will produce a relative maximum amplitude of thesound pressure in a steering angle direction If the designedparameters are not optimized the radiation of the soundbeam will tend to produce the grating lobes and side lobesaround the main lobe The existence of the grating lobes andthe side lobes means the sound waves propagate in otherdirections which causes the ldquoleakagerdquo of the beam energyand affects the signal-to-noise ratio of the system Besides astrong side lobe inhibits the ability of the array to detect aweaker signal in the presence of a larger nearby signal Thusthe array parameters should be discussed and optimized byminimizing the main lobe width eliminating grating lobesand suppressing side lobes as much as possible
41 CMUT Subarray Optimization To discuss the directivityof a CMUT subarraymany parameters have to be consideredFor a CMUT subarray composed of119872 cells as in Figure 3 theoperation frequency of the CMUT linear array is designedto be 071MHz for underwater application and the soundvelocity in water is 1540ms so the wavelength can becalculated as
120582 =V119897
119891119897
=1540ms071MHz
asymp 2169 120583m (7)
To avoid the grating lobes the distance between twoadjacent cells in one subarray is supposed to be nomore than05120582 Consider the distance between two adjacent cells for ouranalysis to be 05120582 When the azimuth angle is 0∘ and there isno steering the directivity of a subarray varies with differentcell number 119872 as shown in Figure 6
From Figure 6 it can be seen that when the cell numberincreases the main lobe width decreases indicating a betterresolution and a more sensitive receiving angle range Alsowith more cells in one subarray the amplitude of the sidelobes decreases For more than 16 cells in one subarraythe main lobe width slightly decreases unlike the obviousdecrease from 119872 = 4 to 119872 = 8 So for the following analysis16 cells linearly arranged in one subarray have been chosen
Journal of Sensors 5
minus50
minus40
minus30
minus20
minus10
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
M = 4
M = 8
M = 16
M = 32
M = 64
Figure 6 Directivity analysis with different cell number in asubarray
minus50
minus40
minus30
minus20
minus10
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
025120582
05120582
075120582
1120582
Figure 7 Directivity analysis with different distance betweenadjacent cells
When the azimuth angle is 0∘ and there is no steering thedirectivity of a 16-cell subarray varies with different distancebetween two adjacent cells as shown in Figure 7
From Figure 7 it can be noticed that when the distancebetween two adjacent cells in a subarray increases themain lobe width decreases However increasing the adjacentdistance can also arouse grating lobes such as in the 1120582 caseTake both the main lobe width and the grating lobes intoconsideration the adjacent distance 05120582 is preferred for thefollowing analysis
The operation medium also has big influence on thedirectivity performance of the CMUT linear subarray Thedistance between two adjacent cells is set to be 1085120583m
Figure 8 Directivity analysis with different operation medium
which is 05120582 for underwater applications When the samearray is operated in air the directivity performance is differ-ent as shown in Figure 8
From Figure 8 it can be observed that for different oper-ation medium directivity performances are different Forthe same cell dimensions subarray geometry and adjacentdistance the grating lobes appear for airborne applicationsThe sound velocity in air is about 340ms and the operationfrequency is 25MHz so the wavelength in air can beexpressed as
120582air =Vair1198910
=340ms25MHz
= 136 120583m (8)
Compared to the wavelength in water (1540120583m) thewavelength in air is much smaller From Figure 7 it canbe obtained that when the distance between two adjacentcells is bigger than wavelength there will be grating lobesIn this case the adjacent distance is 1085 120583m which is muchbigger than the wavelength in air So the grating lobes appearand the energy leakage increases which also proves that aCMUT linear array for underwater applications may not besuitable for airborne applications without modification andoptimization
From Figures 6ndash8 several influential parameters havebeen discussed including the cell numbers the adjacentdistance and the operationmediumDuring the design phaseof a CMUT array these parameters have to be considered forbetter and more stable performance
42 Two-Dimensional CMUT Linear Array Optimization Adisadvantage of the CMUT linear subarray is its large sidelobes A strong side lobe inhibits the ability of the array todetect a weaker signal in the presence of a larger nearbysignal In this section the two-dimensional CMUT lineararray consisting of 16times8 cells (Figure 4) is chosen for analysis
Tapering functions can be used to suppress the sidelobes and the generalized cosine windows are one of the
6 Journal of Sensors
NoneHammingHann
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
Figure 9 Directivity analyses before and after the HannHammingmethods
most commonmethods including the Hann window and theHammingwindowThemathematical expression of theHannwindow is
119908 (119898) =1
2[1 minus cos(
2120587119898
119872)] 0 le 119898 le 119872 (9)
and the Hamming window expression is
119908 (119898) = 054 minus 046 cos(2120587119898
119872) 0 le 119898 le 119872 (10)
where 119872 represents the cell numberDirectivity analyses before and after the generalized
cosine methods are shown in Figure 9 Results show thatbothHamming andHannmethods can decrease the side lobeamplitude but both at the expense of broadening the mainlobe width The two methods are quite similar and the Hannmethod appears to have a faster decreasing rate
Another side lobe suppression method is the Kaiser win-dow weighting method and the mathematical expression is
119908 (119898) =
1198680
[120573radic1 minus (1 minus 2119898119872)2]
1198680
(120573)0 le 119898 le 119872
(11)
where 1198680(119909) is the zero-order modified Bessel function 120573 is
the shape function with relation to the side lobe amplitude119901119904 and the expression is
120573
=
01102 (119901119904
minus 87) 119901119904
gt 50
05482 (119901119904
minus 21)04
+ 007886 (119901119904
minus 21) 21 le 119901119904
le 50
0 119901119904
lt 21
(12)
For different 120573 values the directivity performances aredifferent as shown in Figure 10 When 120573 = 0 the directivity
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
None120573 = 0
120573 = 1
120573 = 5
120573 = 10
Figure 10 Directivity analyses before and after the Kaiser methodN
orm
aliz
ed so
und
pres
sure
(dB)
NoneChebyshevTaylor
minus90
minus60
minus30
0
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
Figure 11 Directivity analyses before and after the Cheby-shevTaylor methods
performance after the Kaiser weighting method remains thesame as before When 120573 increases the side lobe amplitudedecreases also at the expense of broadening the main lobewidth Compared to other weightingmethods the ratio of themain lobe energy to the side lobe energy of the Kaisermethodis almost the biggest Besides the main lobe width andthe side lobe amplitude can be freely regulated for differentapplications
Besides the Chebyshev and Taylor weighting methodsare also chosen for comparison The minus30 dB side lobe sup-pressions are carried out using the two methods and thedirectivity performances are shown in Figure 11
Journal of Sensors 7
From Figure 11 it can be observed that the Taylor methodis similar to the Chebyshev method Both methods havedecreased the side lobe amplitude to around minus30 dB andthe main lobe width has been broadened Whereas theChebyshev method has the narrowest possible main lobefor a specified side lobe level the Taylor method offerstradeoffs between themain lobe width and the side lobe levelMoreover the Taylor distribution avoids edge discontinuitiesso the Taylor method side lobes decrease monotonically
FromFigures 9ndash11 several common side lobe suppressionmethods have been discussed and compared Since the mainlobe width and the side lobe amplitude are contradictorythe side lobe suppression method must be carefully chosendue to different design requirements For instance when highlateral resolutions are desired the main lobe width is thefirst concernWhen the signal-to-noise ratio is the importantrequirement the side lobe level is the first concern
5 Conclusion
This paper proposed an integrated vibration membranestructure to design a CMUT linear array consisting ofmany subarrays for underwater applications The directivityperformances and side lobe suppression methods have beendiscussed The work in this paper is summarized as follows
(1) A two-dimensional CMUT linear array for underwa-ter applications has been proposedThe operation fre-quencies for different medium have been calculatedwhich are also proved by the COMSOL Multiphysicssoftware The derivation takes the ambient fluid intoconsideration and the operation frequency of theCMUT cell is 25MHz in air and 07MHz in water
(2) The directivity analyses for the CMUT cell sub-array and two-dimensional linear array have beenprovided The directivity of a single circular CMUTcell is very weak so it should be composed intolinear array to enhance the directivity According tothe product theorems the directivity function of thecomplex array is obtained using a combination of thedirectivity functions of certain simple structures
(3) The effects of the correlation parameters of the linearsubarray have been discussed including the cellnumbers the adjacent distance and the operationmedium Results show that both the cell numbers andthe adjacent distance have effect on the main lobewidth However both of them have an upper limit inorder to eliminate grating lobes For the underwaterapplications the wavelength is much bigger than thatfor the airborne applications Thus the directivityperformance of a linear subarray is determined byseveral parameters simultaneously
(4) In order to reduce the side lobe of the CMUT lineararray several weighting methods are used to suppressthe side lobe amplitude which is quite satisfactorybut at the expense of broadening themain lobe widthSince themain lobe width and the side lobe amplitudeare contradictory the side lobe suppression method
must be carefully chosen due to different designrequirements and the imaging quality and resolutionof the imaging system can be improved further
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This work has been supported by the Young Scientists Fundof the National Natural Science Foundation of China (Grantno 61201039)
References
[1] Y Qiu J V Gigliotti M Wallace et al ldquoPiezoelectric micro-machined ultrasound transducer (PMUT) arrays for integratedsensing actuation and imagingrdquo Sensors vol 15 no 4 pp8020ndash8041 2015
[2] W Zhang H Zhang F Du J Shi S Jin and Z Zeng ldquoPull-inanalysis of the flat circular CMUT cell featuring sealed cavityrdquoMathematical Problems in Engineering vol 2015 Article ID150279 9 pages 2015
[3] O Oralkan A S Ergun J A Johnson et al ldquoCapacitivemicromachined ultrasonic transducers next generation arraysfor acoustic imagingrdquo IEEE Transactions on Ultrasonics Ferro-electrics and Frequency Control vol 49 no 11 pp 1596ndash16102002
[4] D E Dausch J B Castellucci D R Chou and O T vonRamm ldquoTheory and operation of 2-D array piezoelectricmicromachined ultrasound transducersrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 55 no 11pp 2484ndash2492 2008
[5] A Hajati D Latev D Gardner et al ldquoThree-dimensional microelectromechanical system piezoelectric ultrasound transducerrdquoApplied Physics Letters vol 101 no 25 Article ID 253101 2012
[6] F Akasheh J D Fraser S Bose and A Bandyopadhyay ldquoPiezo-electric micromachined ultrasonic transducers modeling theinfluence of structural parameters on device performancerdquoIEEE Transactions on Ultrasonics Ferroelectrics and FrequencyControl vol 52 no 3 pp 455ndash468 2005
[7] A S Ergun C-H Cheng O Oralkan et al ldquoBroadbandcapacitive micromachined ultrasonic transducers ranging from10 kHz to 60MHz for imaging arrays and morerdquo in Proceedingsof the IEEE Ultrasonics Symposium pp 1039ndash1043 MunichGermany October 2002
[8] M I Haller and B T Khuri-Yakub ldquoA surface micromachinedelectrostatic ultrasonic air transducerrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 43 no 1pp 1ndash6 1996
[9] S T Hansen B J Mossawir A Sanli Ergun F Degertekinand B T Khuri-Yakub ldquoAir-coupled nondestructive evaluationusing micromachined ultrasonic transducersrdquo in Proceedings ofthe IEEE Ultrasonics Symposium pp 1037ndash1040 Lake TahoeNev USA October 1999
[10] J Johnson O Oralkan U Demirci S Ergun M Karaman andP Khuri-Yakub ldquoMedical imaging using capacitive microma-chined ultrasonic transducer arraysrdquo Ultrasonics vol 40 no 1-8 pp 471ndash476 2002
8 Journal of Sensors
[11] X Zhuang A S Ergun Y Huang I O Wygant O Oralkanand B T Khuri-Yakub ldquoIntegration of trench-isolated through-wafer interconnects with 2d capacitive micromachined ultra-sonic transducer arraysrdquo Sensors and Actuators A Physical vol138 no 1 pp 221ndash229 2007
[12] X Zhuang D-S Lin O Oralkan and B T Khuri-YakubldquoFabrication of flexible transducer arrays with through-waferelectrical interconnects based on trench refilling with PDMSrdquoJournal of Microelectromechanical Systems vol 17 no 2 pp446ndash452 2008
[13] I O Wygant N S Jamal H J Lee et al ldquoAn integratedcircuit with transmit beamforming flip-chip bonded to a 2-DCMUT array for 3-D ultrasound imagingrdquo IEEE Transactionson Ultrasonics Ferroelectrics and Frequency Control vol 56 no10 pp 2145ndash2156 2009
[14] A Caronti G Caliano R Carotenuto et al ldquoCapacitive micro-machined ultrasonic transducer (CMUT) arrays for medicalimagingrdquo Microelectronics Journal vol 37 no 8 pp 770ndash7772006
[15] W Zhang H Zhang Y Wang F Du S Jin and Z ZengldquoSimulation characterization of CMUT with vented squaremembranerdquo in Proceedings of the International Conference onOptical Instrument and Technology (OIT rsquo15) Beijing ChinaMay 2015
[16] Z H Hao L Tang and D H Qiao ldquoAnalysis of the resonantfrequency of capacitive micro-machined ultrasonic transducer(cMUT) with finite element methodrdquo Technical Acoustics vol28 pp 133ndash134 2009 (Chinese)
[17] J Miao C D He D Q Lian et al ldquoDesign of MEMS capacitiveultrasonic transducer based on wafer bonding technologyrdquoChinese Journal of Sensors and Actuators vol 25 no 12 pp1653ndash1658 2012 (Chinese)
[18] B D Steinberg Principles of Aperture and Array System DesignIncluding Random and Adaptive Arrays John Wiley amp SonsNew York NY USA 1976
[19] S-C Wooh and Y Shi ldquoInfluence of phased array element sizeon beam steering behaviorrdquo Ultrasonics vol 36 no 6 pp 737ndash749 1998
[20] C B Doody X Cheng C A Rich D F Lemmerhirt and RD White ldquoModeling and characterization of CMOS-fabricatedcapacitive micromachined ultrasound transducersrdquo Journal ofMicroelectromechanical Systems vol 20 no 1 pp 104ndash118 2011
[21] M L Kuntzman D Kim andN A Hall ldquoMicrofabrication andexperimental evaluation of a rotational capacitive microma-chined ultrasonic transducerrdquo Journal of Microelectromechani-cal Systems vol 24 no 2 pp 404ndash413 2015
[22] M Bao Analysis and Design Principles of MEMS DevicesElsevier New York NY USA 2005
[23] M R Haddara and S Cao ldquoA study of the dynamic response ofsubmerged rectangular flat platesrdquoMarine Structures vol 9 no10 pp 913ndash933 1996
[24] X H Si W X Lu and F L Chu ldquoModal analysis of circularplates with radial side cracks and in contact with water on oneside based on the RayleighndashRitz methodrdquo Journal of Sound andVibration vol 331 no 1 pp 231ndash251 2012
Figure 5 Schematic for directivity analysis using normalized soundpressure
in the far field and 119875(120572119898
120579119898
) is the biggest sound pressureas shown in Figure 5
The directivity function of the complex array is generallysimplified as a combination of the directivity functions ofcertain simple structures Using the Bridge product theoremsthe complex array directivity function can be obtained bytaking the product of the directivity function of the simplestructures
For the two-dimensional CMUT linear array shown inFigure 4 the radiated sound field directivity function is equalto the product of a single subarray directivity function and alinear array directivity function composed of119873 point sourcesin each element center
The CMUT cell as shown in Figure 1 can be taken asa single circular piston with radius 119903 and the directivityfunction of the circular piston in the 119874119909119911 plane is
Considering the uniform linear array composed of 119873
point sources each subarray has the same resonant fre-quency the vibration amplitude and the phase Multipli-cation manipulation using (3)sim(5) leads to the following
expression for the sound pressure normalized directivityfunction
In order to improve the imaging resolution and imagingquality in an ultrasonic imaging system one-dimensional ortwo-dimensional linear array ultrasonic transducer is oftenused to implement the ultrasonic imaging The sound beamthat the CMUT array radiated to the three-dimensionalspace will produce a relative maximum amplitude of thesound pressure in a steering angle direction If the designedparameters are not optimized the radiation of the soundbeam will tend to produce the grating lobes and side lobesaround the main lobe The existence of the grating lobes andthe side lobes means the sound waves propagate in otherdirections which causes the ldquoleakagerdquo of the beam energyand affects the signal-to-noise ratio of the system Besides astrong side lobe inhibits the ability of the array to detect aweaker signal in the presence of a larger nearby signal Thusthe array parameters should be discussed and optimized byminimizing the main lobe width eliminating grating lobesand suppressing side lobes as much as possible
41 CMUT Subarray Optimization To discuss the directivityof a CMUT subarraymany parameters have to be consideredFor a CMUT subarray composed of119872 cells as in Figure 3 theoperation frequency of the CMUT linear array is designedto be 071MHz for underwater application and the soundvelocity in water is 1540ms so the wavelength can becalculated as
120582 =V119897
119891119897
=1540ms071MHz
asymp 2169 120583m (7)
To avoid the grating lobes the distance between twoadjacent cells in one subarray is supposed to be nomore than05120582 Consider the distance between two adjacent cells for ouranalysis to be 05120582 When the azimuth angle is 0∘ and there isno steering the directivity of a subarray varies with differentcell number 119872 as shown in Figure 6
From Figure 6 it can be seen that when the cell numberincreases the main lobe width decreases indicating a betterresolution and a more sensitive receiving angle range Alsowith more cells in one subarray the amplitude of the sidelobes decreases For more than 16 cells in one subarraythe main lobe width slightly decreases unlike the obviousdecrease from 119872 = 4 to 119872 = 8 So for the following analysis16 cells linearly arranged in one subarray have been chosen
Journal of Sensors 5
minus50
minus40
minus30
minus20
minus10
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
M = 4
M = 8
M = 16
M = 32
M = 64
Figure 6 Directivity analysis with different cell number in asubarray
minus50
minus40
minus30
minus20
minus10
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
025120582
05120582
075120582
1120582
Figure 7 Directivity analysis with different distance betweenadjacent cells
When the azimuth angle is 0∘ and there is no steering thedirectivity of a 16-cell subarray varies with different distancebetween two adjacent cells as shown in Figure 7
From Figure 7 it can be noticed that when the distancebetween two adjacent cells in a subarray increases themain lobe width decreases However increasing the adjacentdistance can also arouse grating lobes such as in the 1120582 caseTake both the main lobe width and the grating lobes intoconsideration the adjacent distance 05120582 is preferred for thefollowing analysis
The operation medium also has big influence on thedirectivity performance of the CMUT linear subarray Thedistance between two adjacent cells is set to be 1085120583m
Figure 8 Directivity analysis with different operation medium
which is 05120582 for underwater applications When the samearray is operated in air the directivity performance is differ-ent as shown in Figure 8
From Figure 8 it can be observed that for different oper-ation medium directivity performances are different Forthe same cell dimensions subarray geometry and adjacentdistance the grating lobes appear for airborne applicationsThe sound velocity in air is about 340ms and the operationfrequency is 25MHz so the wavelength in air can beexpressed as
120582air =Vair1198910
=340ms25MHz
= 136 120583m (8)
Compared to the wavelength in water (1540120583m) thewavelength in air is much smaller From Figure 7 it canbe obtained that when the distance between two adjacentcells is bigger than wavelength there will be grating lobesIn this case the adjacent distance is 1085 120583m which is muchbigger than the wavelength in air So the grating lobes appearand the energy leakage increases which also proves that aCMUT linear array for underwater applications may not besuitable for airborne applications without modification andoptimization
From Figures 6ndash8 several influential parameters havebeen discussed including the cell numbers the adjacentdistance and the operationmediumDuring the design phaseof a CMUT array these parameters have to be considered forbetter and more stable performance
42 Two-Dimensional CMUT Linear Array Optimization Adisadvantage of the CMUT linear subarray is its large sidelobes A strong side lobe inhibits the ability of the array todetect a weaker signal in the presence of a larger nearbysignal In this section the two-dimensional CMUT lineararray consisting of 16times8 cells (Figure 4) is chosen for analysis
Tapering functions can be used to suppress the sidelobes and the generalized cosine windows are one of the
6 Journal of Sensors
NoneHammingHann
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
Figure 9 Directivity analyses before and after the HannHammingmethods
most commonmethods including the Hann window and theHammingwindowThemathematical expression of theHannwindow is
119908 (119898) =1
2[1 minus cos(
2120587119898
119872)] 0 le 119898 le 119872 (9)
and the Hamming window expression is
119908 (119898) = 054 minus 046 cos(2120587119898
119872) 0 le 119898 le 119872 (10)
where 119872 represents the cell numberDirectivity analyses before and after the generalized
cosine methods are shown in Figure 9 Results show thatbothHamming andHannmethods can decrease the side lobeamplitude but both at the expense of broadening the mainlobe width The two methods are quite similar and the Hannmethod appears to have a faster decreasing rate
Another side lobe suppression method is the Kaiser win-dow weighting method and the mathematical expression is
119908 (119898) =
1198680
[120573radic1 minus (1 minus 2119898119872)2]
1198680
(120573)0 le 119898 le 119872
(11)
where 1198680(119909) is the zero-order modified Bessel function 120573 is
the shape function with relation to the side lobe amplitude119901119904 and the expression is
120573
=
01102 (119901119904
minus 87) 119901119904
gt 50
05482 (119901119904
minus 21)04
+ 007886 (119901119904
minus 21) 21 le 119901119904
le 50
0 119901119904
lt 21
(12)
For different 120573 values the directivity performances aredifferent as shown in Figure 10 When 120573 = 0 the directivity
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
None120573 = 0
120573 = 1
120573 = 5
120573 = 10
Figure 10 Directivity analyses before and after the Kaiser methodN
orm
aliz
ed so
und
pres
sure
(dB)
NoneChebyshevTaylor
minus90
minus60
minus30
0
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
Figure 11 Directivity analyses before and after the Cheby-shevTaylor methods
performance after the Kaiser weighting method remains thesame as before When 120573 increases the side lobe amplitudedecreases also at the expense of broadening the main lobewidth Compared to other weightingmethods the ratio of themain lobe energy to the side lobe energy of the Kaisermethodis almost the biggest Besides the main lobe width andthe side lobe amplitude can be freely regulated for differentapplications
Besides the Chebyshev and Taylor weighting methodsare also chosen for comparison The minus30 dB side lobe sup-pressions are carried out using the two methods and thedirectivity performances are shown in Figure 11
Journal of Sensors 7
From Figure 11 it can be observed that the Taylor methodis similar to the Chebyshev method Both methods havedecreased the side lobe amplitude to around minus30 dB andthe main lobe width has been broadened Whereas theChebyshev method has the narrowest possible main lobefor a specified side lobe level the Taylor method offerstradeoffs between themain lobe width and the side lobe levelMoreover the Taylor distribution avoids edge discontinuitiesso the Taylor method side lobes decrease monotonically
FromFigures 9ndash11 several common side lobe suppressionmethods have been discussed and compared Since the mainlobe width and the side lobe amplitude are contradictorythe side lobe suppression method must be carefully chosendue to different design requirements For instance when highlateral resolutions are desired the main lobe width is thefirst concernWhen the signal-to-noise ratio is the importantrequirement the side lobe level is the first concern
5 Conclusion
This paper proposed an integrated vibration membranestructure to design a CMUT linear array consisting ofmany subarrays for underwater applications The directivityperformances and side lobe suppression methods have beendiscussed The work in this paper is summarized as follows
(1) A two-dimensional CMUT linear array for underwa-ter applications has been proposedThe operation fre-quencies for different medium have been calculatedwhich are also proved by the COMSOL Multiphysicssoftware The derivation takes the ambient fluid intoconsideration and the operation frequency of theCMUT cell is 25MHz in air and 07MHz in water
(2) The directivity analyses for the CMUT cell sub-array and two-dimensional linear array have beenprovided The directivity of a single circular CMUTcell is very weak so it should be composed intolinear array to enhance the directivity According tothe product theorems the directivity function of thecomplex array is obtained using a combination of thedirectivity functions of certain simple structures
(3) The effects of the correlation parameters of the linearsubarray have been discussed including the cellnumbers the adjacent distance and the operationmedium Results show that both the cell numbers andthe adjacent distance have effect on the main lobewidth However both of them have an upper limit inorder to eliminate grating lobes For the underwaterapplications the wavelength is much bigger than thatfor the airborne applications Thus the directivityperformance of a linear subarray is determined byseveral parameters simultaneously
(4) In order to reduce the side lobe of the CMUT lineararray several weighting methods are used to suppressthe side lobe amplitude which is quite satisfactorybut at the expense of broadening themain lobe widthSince themain lobe width and the side lobe amplitudeare contradictory the side lobe suppression method
must be carefully chosen due to different designrequirements and the imaging quality and resolutionof the imaging system can be improved further
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This work has been supported by the Young Scientists Fundof the National Natural Science Foundation of China (Grantno 61201039)
References
[1] Y Qiu J V Gigliotti M Wallace et al ldquoPiezoelectric micro-machined ultrasound transducer (PMUT) arrays for integratedsensing actuation and imagingrdquo Sensors vol 15 no 4 pp8020ndash8041 2015
[2] W Zhang H Zhang F Du J Shi S Jin and Z Zeng ldquoPull-inanalysis of the flat circular CMUT cell featuring sealed cavityrdquoMathematical Problems in Engineering vol 2015 Article ID150279 9 pages 2015
[3] O Oralkan A S Ergun J A Johnson et al ldquoCapacitivemicromachined ultrasonic transducers next generation arraysfor acoustic imagingrdquo IEEE Transactions on Ultrasonics Ferro-electrics and Frequency Control vol 49 no 11 pp 1596ndash16102002
[4] D E Dausch J B Castellucci D R Chou and O T vonRamm ldquoTheory and operation of 2-D array piezoelectricmicromachined ultrasound transducersrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 55 no 11pp 2484ndash2492 2008
[5] A Hajati D Latev D Gardner et al ldquoThree-dimensional microelectromechanical system piezoelectric ultrasound transducerrdquoApplied Physics Letters vol 101 no 25 Article ID 253101 2012
[6] F Akasheh J D Fraser S Bose and A Bandyopadhyay ldquoPiezo-electric micromachined ultrasonic transducers modeling theinfluence of structural parameters on device performancerdquoIEEE Transactions on Ultrasonics Ferroelectrics and FrequencyControl vol 52 no 3 pp 455ndash468 2005
[7] A S Ergun C-H Cheng O Oralkan et al ldquoBroadbandcapacitive micromachined ultrasonic transducers ranging from10 kHz to 60MHz for imaging arrays and morerdquo in Proceedingsof the IEEE Ultrasonics Symposium pp 1039ndash1043 MunichGermany October 2002
[8] M I Haller and B T Khuri-Yakub ldquoA surface micromachinedelectrostatic ultrasonic air transducerrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 43 no 1pp 1ndash6 1996
[9] S T Hansen B J Mossawir A Sanli Ergun F Degertekinand B T Khuri-Yakub ldquoAir-coupled nondestructive evaluationusing micromachined ultrasonic transducersrdquo in Proceedings ofthe IEEE Ultrasonics Symposium pp 1037ndash1040 Lake TahoeNev USA October 1999
[10] J Johnson O Oralkan U Demirci S Ergun M Karaman andP Khuri-Yakub ldquoMedical imaging using capacitive microma-chined ultrasonic transducer arraysrdquo Ultrasonics vol 40 no 1-8 pp 471ndash476 2002
8 Journal of Sensors
[11] X Zhuang A S Ergun Y Huang I O Wygant O Oralkanand B T Khuri-Yakub ldquoIntegration of trench-isolated through-wafer interconnects with 2d capacitive micromachined ultra-sonic transducer arraysrdquo Sensors and Actuators A Physical vol138 no 1 pp 221ndash229 2007
[12] X Zhuang D-S Lin O Oralkan and B T Khuri-YakubldquoFabrication of flexible transducer arrays with through-waferelectrical interconnects based on trench refilling with PDMSrdquoJournal of Microelectromechanical Systems vol 17 no 2 pp446ndash452 2008
[13] I O Wygant N S Jamal H J Lee et al ldquoAn integratedcircuit with transmit beamforming flip-chip bonded to a 2-DCMUT array for 3-D ultrasound imagingrdquo IEEE Transactionson Ultrasonics Ferroelectrics and Frequency Control vol 56 no10 pp 2145ndash2156 2009
[14] A Caronti G Caliano R Carotenuto et al ldquoCapacitive micro-machined ultrasonic transducer (CMUT) arrays for medicalimagingrdquo Microelectronics Journal vol 37 no 8 pp 770ndash7772006
[15] W Zhang H Zhang Y Wang F Du S Jin and Z ZengldquoSimulation characterization of CMUT with vented squaremembranerdquo in Proceedings of the International Conference onOptical Instrument and Technology (OIT rsquo15) Beijing ChinaMay 2015
[16] Z H Hao L Tang and D H Qiao ldquoAnalysis of the resonantfrequency of capacitive micro-machined ultrasonic transducer(cMUT) with finite element methodrdquo Technical Acoustics vol28 pp 133ndash134 2009 (Chinese)
[17] J Miao C D He D Q Lian et al ldquoDesign of MEMS capacitiveultrasonic transducer based on wafer bonding technologyrdquoChinese Journal of Sensors and Actuators vol 25 no 12 pp1653ndash1658 2012 (Chinese)
[18] B D Steinberg Principles of Aperture and Array System DesignIncluding Random and Adaptive Arrays John Wiley amp SonsNew York NY USA 1976
[19] S-C Wooh and Y Shi ldquoInfluence of phased array element sizeon beam steering behaviorrdquo Ultrasonics vol 36 no 6 pp 737ndash749 1998
[20] C B Doody X Cheng C A Rich D F Lemmerhirt and RD White ldquoModeling and characterization of CMOS-fabricatedcapacitive micromachined ultrasound transducersrdquo Journal ofMicroelectromechanical Systems vol 20 no 1 pp 104ndash118 2011
[21] M L Kuntzman D Kim andN A Hall ldquoMicrofabrication andexperimental evaluation of a rotational capacitive microma-chined ultrasonic transducerrdquo Journal of Microelectromechani-cal Systems vol 24 no 2 pp 404ndash413 2015
[22] M Bao Analysis and Design Principles of MEMS DevicesElsevier New York NY USA 2005
[23] M R Haddara and S Cao ldquoA study of the dynamic response ofsubmerged rectangular flat platesrdquoMarine Structures vol 9 no10 pp 913ndash933 1996
[24] X H Si W X Lu and F L Chu ldquoModal analysis of circularplates with radial side cracks and in contact with water on oneside based on the RayleighndashRitz methodrdquo Journal of Sound andVibration vol 331 no 1 pp 231ndash251 2012
Figure 6 Directivity analysis with different cell number in asubarray
minus50
minus40
minus30
minus20
minus10
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
025120582
05120582
075120582
1120582
Figure 7 Directivity analysis with different distance betweenadjacent cells
When the azimuth angle is 0∘ and there is no steering thedirectivity of a 16-cell subarray varies with different distancebetween two adjacent cells as shown in Figure 7
From Figure 7 it can be noticed that when the distancebetween two adjacent cells in a subarray increases themain lobe width decreases However increasing the adjacentdistance can also arouse grating lobes such as in the 1120582 caseTake both the main lobe width and the grating lobes intoconsideration the adjacent distance 05120582 is preferred for thefollowing analysis
The operation medium also has big influence on thedirectivity performance of the CMUT linear subarray Thedistance between two adjacent cells is set to be 1085120583m
Figure 8 Directivity analysis with different operation medium
which is 05120582 for underwater applications When the samearray is operated in air the directivity performance is differ-ent as shown in Figure 8
From Figure 8 it can be observed that for different oper-ation medium directivity performances are different Forthe same cell dimensions subarray geometry and adjacentdistance the grating lobes appear for airborne applicationsThe sound velocity in air is about 340ms and the operationfrequency is 25MHz so the wavelength in air can beexpressed as
120582air =Vair1198910
=340ms25MHz
= 136 120583m (8)
Compared to the wavelength in water (1540120583m) thewavelength in air is much smaller From Figure 7 it canbe obtained that when the distance between two adjacentcells is bigger than wavelength there will be grating lobesIn this case the adjacent distance is 1085 120583m which is muchbigger than the wavelength in air So the grating lobes appearand the energy leakage increases which also proves that aCMUT linear array for underwater applications may not besuitable for airborne applications without modification andoptimization
From Figures 6ndash8 several influential parameters havebeen discussed including the cell numbers the adjacentdistance and the operationmediumDuring the design phaseof a CMUT array these parameters have to be considered forbetter and more stable performance
42 Two-Dimensional CMUT Linear Array Optimization Adisadvantage of the CMUT linear subarray is its large sidelobes A strong side lobe inhibits the ability of the array todetect a weaker signal in the presence of a larger nearbysignal In this section the two-dimensional CMUT lineararray consisting of 16times8 cells (Figure 4) is chosen for analysis
Tapering functions can be used to suppress the sidelobes and the generalized cosine windows are one of the
6 Journal of Sensors
NoneHammingHann
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
Figure 9 Directivity analyses before and after the HannHammingmethods
most commonmethods including the Hann window and theHammingwindowThemathematical expression of theHannwindow is
119908 (119898) =1
2[1 minus cos(
2120587119898
119872)] 0 le 119898 le 119872 (9)
and the Hamming window expression is
119908 (119898) = 054 minus 046 cos(2120587119898
119872) 0 le 119898 le 119872 (10)
where 119872 represents the cell numberDirectivity analyses before and after the generalized
cosine methods are shown in Figure 9 Results show thatbothHamming andHannmethods can decrease the side lobeamplitude but both at the expense of broadening the mainlobe width The two methods are quite similar and the Hannmethod appears to have a faster decreasing rate
Another side lobe suppression method is the Kaiser win-dow weighting method and the mathematical expression is
119908 (119898) =
1198680
[120573radic1 minus (1 minus 2119898119872)2]
1198680
(120573)0 le 119898 le 119872
(11)
where 1198680(119909) is the zero-order modified Bessel function 120573 is
the shape function with relation to the side lobe amplitude119901119904 and the expression is
120573
=
01102 (119901119904
minus 87) 119901119904
gt 50
05482 (119901119904
minus 21)04
+ 007886 (119901119904
minus 21) 21 le 119901119904
le 50
0 119901119904
lt 21
(12)
For different 120573 values the directivity performances aredifferent as shown in Figure 10 When 120573 = 0 the directivity
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
None120573 = 0
120573 = 1
120573 = 5
120573 = 10
Figure 10 Directivity analyses before and after the Kaiser methodN
orm
aliz
ed so
und
pres
sure
(dB)
NoneChebyshevTaylor
minus90
minus60
minus30
0
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
Figure 11 Directivity analyses before and after the Cheby-shevTaylor methods
performance after the Kaiser weighting method remains thesame as before When 120573 increases the side lobe amplitudedecreases also at the expense of broadening the main lobewidth Compared to other weightingmethods the ratio of themain lobe energy to the side lobe energy of the Kaisermethodis almost the biggest Besides the main lobe width andthe side lobe amplitude can be freely regulated for differentapplications
Besides the Chebyshev and Taylor weighting methodsare also chosen for comparison The minus30 dB side lobe sup-pressions are carried out using the two methods and thedirectivity performances are shown in Figure 11
Journal of Sensors 7
From Figure 11 it can be observed that the Taylor methodis similar to the Chebyshev method Both methods havedecreased the side lobe amplitude to around minus30 dB andthe main lobe width has been broadened Whereas theChebyshev method has the narrowest possible main lobefor a specified side lobe level the Taylor method offerstradeoffs between themain lobe width and the side lobe levelMoreover the Taylor distribution avoids edge discontinuitiesso the Taylor method side lobes decrease monotonically
FromFigures 9ndash11 several common side lobe suppressionmethods have been discussed and compared Since the mainlobe width and the side lobe amplitude are contradictorythe side lobe suppression method must be carefully chosendue to different design requirements For instance when highlateral resolutions are desired the main lobe width is thefirst concernWhen the signal-to-noise ratio is the importantrequirement the side lobe level is the first concern
5 Conclusion
This paper proposed an integrated vibration membranestructure to design a CMUT linear array consisting ofmany subarrays for underwater applications The directivityperformances and side lobe suppression methods have beendiscussed The work in this paper is summarized as follows
(1) A two-dimensional CMUT linear array for underwa-ter applications has been proposedThe operation fre-quencies for different medium have been calculatedwhich are also proved by the COMSOL Multiphysicssoftware The derivation takes the ambient fluid intoconsideration and the operation frequency of theCMUT cell is 25MHz in air and 07MHz in water
(2) The directivity analyses for the CMUT cell sub-array and two-dimensional linear array have beenprovided The directivity of a single circular CMUTcell is very weak so it should be composed intolinear array to enhance the directivity According tothe product theorems the directivity function of thecomplex array is obtained using a combination of thedirectivity functions of certain simple structures
(3) The effects of the correlation parameters of the linearsubarray have been discussed including the cellnumbers the adjacent distance and the operationmedium Results show that both the cell numbers andthe adjacent distance have effect on the main lobewidth However both of them have an upper limit inorder to eliminate grating lobes For the underwaterapplications the wavelength is much bigger than thatfor the airborne applications Thus the directivityperformance of a linear subarray is determined byseveral parameters simultaneously
(4) In order to reduce the side lobe of the CMUT lineararray several weighting methods are used to suppressthe side lobe amplitude which is quite satisfactorybut at the expense of broadening themain lobe widthSince themain lobe width and the side lobe amplitudeare contradictory the side lobe suppression method
must be carefully chosen due to different designrequirements and the imaging quality and resolutionof the imaging system can be improved further
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This work has been supported by the Young Scientists Fundof the National Natural Science Foundation of China (Grantno 61201039)
References
[1] Y Qiu J V Gigliotti M Wallace et al ldquoPiezoelectric micro-machined ultrasound transducer (PMUT) arrays for integratedsensing actuation and imagingrdquo Sensors vol 15 no 4 pp8020ndash8041 2015
[2] W Zhang H Zhang F Du J Shi S Jin and Z Zeng ldquoPull-inanalysis of the flat circular CMUT cell featuring sealed cavityrdquoMathematical Problems in Engineering vol 2015 Article ID150279 9 pages 2015
[3] O Oralkan A S Ergun J A Johnson et al ldquoCapacitivemicromachined ultrasonic transducers next generation arraysfor acoustic imagingrdquo IEEE Transactions on Ultrasonics Ferro-electrics and Frequency Control vol 49 no 11 pp 1596ndash16102002
[4] D E Dausch J B Castellucci D R Chou and O T vonRamm ldquoTheory and operation of 2-D array piezoelectricmicromachined ultrasound transducersrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 55 no 11pp 2484ndash2492 2008
[5] A Hajati D Latev D Gardner et al ldquoThree-dimensional microelectromechanical system piezoelectric ultrasound transducerrdquoApplied Physics Letters vol 101 no 25 Article ID 253101 2012
[6] F Akasheh J D Fraser S Bose and A Bandyopadhyay ldquoPiezo-electric micromachined ultrasonic transducers modeling theinfluence of structural parameters on device performancerdquoIEEE Transactions on Ultrasonics Ferroelectrics and FrequencyControl vol 52 no 3 pp 455ndash468 2005
[7] A S Ergun C-H Cheng O Oralkan et al ldquoBroadbandcapacitive micromachined ultrasonic transducers ranging from10 kHz to 60MHz for imaging arrays and morerdquo in Proceedingsof the IEEE Ultrasonics Symposium pp 1039ndash1043 MunichGermany October 2002
[8] M I Haller and B T Khuri-Yakub ldquoA surface micromachinedelectrostatic ultrasonic air transducerrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 43 no 1pp 1ndash6 1996
[9] S T Hansen B J Mossawir A Sanli Ergun F Degertekinand B T Khuri-Yakub ldquoAir-coupled nondestructive evaluationusing micromachined ultrasonic transducersrdquo in Proceedings ofthe IEEE Ultrasonics Symposium pp 1037ndash1040 Lake TahoeNev USA October 1999
[10] J Johnson O Oralkan U Demirci S Ergun M Karaman andP Khuri-Yakub ldquoMedical imaging using capacitive microma-chined ultrasonic transducer arraysrdquo Ultrasonics vol 40 no 1-8 pp 471ndash476 2002
8 Journal of Sensors
[11] X Zhuang A S Ergun Y Huang I O Wygant O Oralkanand B T Khuri-Yakub ldquoIntegration of trench-isolated through-wafer interconnects with 2d capacitive micromachined ultra-sonic transducer arraysrdquo Sensors and Actuators A Physical vol138 no 1 pp 221ndash229 2007
[12] X Zhuang D-S Lin O Oralkan and B T Khuri-YakubldquoFabrication of flexible transducer arrays with through-waferelectrical interconnects based on trench refilling with PDMSrdquoJournal of Microelectromechanical Systems vol 17 no 2 pp446ndash452 2008
[13] I O Wygant N S Jamal H J Lee et al ldquoAn integratedcircuit with transmit beamforming flip-chip bonded to a 2-DCMUT array for 3-D ultrasound imagingrdquo IEEE Transactionson Ultrasonics Ferroelectrics and Frequency Control vol 56 no10 pp 2145ndash2156 2009
[14] A Caronti G Caliano R Carotenuto et al ldquoCapacitive micro-machined ultrasonic transducer (CMUT) arrays for medicalimagingrdquo Microelectronics Journal vol 37 no 8 pp 770ndash7772006
[15] W Zhang H Zhang Y Wang F Du S Jin and Z ZengldquoSimulation characterization of CMUT with vented squaremembranerdquo in Proceedings of the International Conference onOptical Instrument and Technology (OIT rsquo15) Beijing ChinaMay 2015
[16] Z H Hao L Tang and D H Qiao ldquoAnalysis of the resonantfrequency of capacitive micro-machined ultrasonic transducer(cMUT) with finite element methodrdquo Technical Acoustics vol28 pp 133ndash134 2009 (Chinese)
[17] J Miao C D He D Q Lian et al ldquoDesign of MEMS capacitiveultrasonic transducer based on wafer bonding technologyrdquoChinese Journal of Sensors and Actuators vol 25 no 12 pp1653ndash1658 2012 (Chinese)
[18] B D Steinberg Principles of Aperture and Array System DesignIncluding Random and Adaptive Arrays John Wiley amp SonsNew York NY USA 1976
[19] S-C Wooh and Y Shi ldquoInfluence of phased array element sizeon beam steering behaviorrdquo Ultrasonics vol 36 no 6 pp 737ndash749 1998
[20] C B Doody X Cheng C A Rich D F Lemmerhirt and RD White ldquoModeling and characterization of CMOS-fabricatedcapacitive micromachined ultrasound transducersrdquo Journal ofMicroelectromechanical Systems vol 20 no 1 pp 104ndash118 2011
[21] M L Kuntzman D Kim andN A Hall ldquoMicrofabrication andexperimental evaluation of a rotational capacitive microma-chined ultrasonic transducerrdquo Journal of Microelectromechani-cal Systems vol 24 no 2 pp 404ndash413 2015
[22] M Bao Analysis and Design Principles of MEMS DevicesElsevier New York NY USA 2005
[23] M R Haddara and S Cao ldquoA study of the dynamic response ofsubmerged rectangular flat platesrdquoMarine Structures vol 9 no10 pp 913ndash933 1996
[24] X H Si W X Lu and F L Chu ldquoModal analysis of circularplates with radial side cracks and in contact with water on oneside based on the RayleighndashRitz methodrdquo Journal of Sound andVibration vol 331 no 1 pp 231ndash251 2012
Figure 9 Directivity analyses before and after the HannHammingmethods
most commonmethods including the Hann window and theHammingwindowThemathematical expression of theHannwindow is
119908 (119898) =1
2[1 minus cos(
2120587119898
119872)] 0 le 119898 le 119872 (9)
and the Hamming window expression is
119908 (119898) = 054 minus 046 cos(2120587119898
119872) 0 le 119898 le 119872 (10)
where 119872 represents the cell numberDirectivity analyses before and after the generalized
cosine methods are shown in Figure 9 Results show thatbothHamming andHannmethods can decrease the side lobeamplitude but both at the expense of broadening the mainlobe width The two methods are quite similar and the Hannmethod appears to have a faster decreasing rate
Another side lobe suppression method is the Kaiser win-dow weighting method and the mathematical expression is
119908 (119898) =
1198680
[120573radic1 minus (1 minus 2119898119872)2]
1198680
(120573)0 le 119898 le 119872
(11)
where 1198680(119909) is the zero-order modified Bessel function 120573 is
the shape function with relation to the side lobe amplitude119901119904 and the expression is
120573
=
01102 (119901119904
minus 87) 119901119904
gt 50
05482 (119901119904
minus 21)04
+ 007886 (119901119904
minus 21) 21 le 119901119904
le 50
0 119901119904
lt 21
(12)
For different 120573 values the directivity performances aredifferent as shown in Figure 10 When 120573 = 0 the directivity
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
soun
d pr
essu
re (d
B)
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
None120573 = 0
120573 = 1
120573 = 5
120573 = 10
Figure 10 Directivity analyses before and after the Kaiser methodN
orm
aliz
ed so
und
pres
sure
(dB)
NoneChebyshevTaylor
minus90
minus60
minus30
0
minus60 minus30 0 30 60 90minus90
Azimuth angle (degrees)
Figure 11 Directivity analyses before and after the Cheby-shevTaylor methods
performance after the Kaiser weighting method remains thesame as before When 120573 increases the side lobe amplitudedecreases also at the expense of broadening the main lobewidth Compared to other weightingmethods the ratio of themain lobe energy to the side lobe energy of the Kaisermethodis almost the biggest Besides the main lobe width andthe side lobe amplitude can be freely regulated for differentapplications
Besides the Chebyshev and Taylor weighting methodsare also chosen for comparison The minus30 dB side lobe sup-pressions are carried out using the two methods and thedirectivity performances are shown in Figure 11
Journal of Sensors 7
From Figure 11 it can be observed that the Taylor methodis similar to the Chebyshev method Both methods havedecreased the side lobe amplitude to around minus30 dB andthe main lobe width has been broadened Whereas theChebyshev method has the narrowest possible main lobefor a specified side lobe level the Taylor method offerstradeoffs between themain lobe width and the side lobe levelMoreover the Taylor distribution avoids edge discontinuitiesso the Taylor method side lobes decrease monotonically
FromFigures 9ndash11 several common side lobe suppressionmethods have been discussed and compared Since the mainlobe width and the side lobe amplitude are contradictorythe side lobe suppression method must be carefully chosendue to different design requirements For instance when highlateral resolutions are desired the main lobe width is thefirst concernWhen the signal-to-noise ratio is the importantrequirement the side lobe level is the first concern
5 Conclusion
This paper proposed an integrated vibration membranestructure to design a CMUT linear array consisting ofmany subarrays for underwater applications The directivityperformances and side lobe suppression methods have beendiscussed The work in this paper is summarized as follows
(1) A two-dimensional CMUT linear array for underwa-ter applications has been proposedThe operation fre-quencies for different medium have been calculatedwhich are also proved by the COMSOL Multiphysicssoftware The derivation takes the ambient fluid intoconsideration and the operation frequency of theCMUT cell is 25MHz in air and 07MHz in water
(2) The directivity analyses for the CMUT cell sub-array and two-dimensional linear array have beenprovided The directivity of a single circular CMUTcell is very weak so it should be composed intolinear array to enhance the directivity According tothe product theorems the directivity function of thecomplex array is obtained using a combination of thedirectivity functions of certain simple structures
(3) The effects of the correlation parameters of the linearsubarray have been discussed including the cellnumbers the adjacent distance and the operationmedium Results show that both the cell numbers andthe adjacent distance have effect on the main lobewidth However both of them have an upper limit inorder to eliminate grating lobes For the underwaterapplications the wavelength is much bigger than thatfor the airborne applications Thus the directivityperformance of a linear subarray is determined byseveral parameters simultaneously
(4) In order to reduce the side lobe of the CMUT lineararray several weighting methods are used to suppressthe side lobe amplitude which is quite satisfactorybut at the expense of broadening themain lobe widthSince themain lobe width and the side lobe amplitudeare contradictory the side lobe suppression method
must be carefully chosen due to different designrequirements and the imaging quality and resolutionof the imaging system can be improved further
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This work has been supported by the Young Scientists Fundof the National Natural Science Foundation of China (Grantno 61201039)
References
[1] Y Qiu J V Gigliotti M Wallace et al ldquoPiezoelectric micro-machined ultrasound transducer (PMUT) arrays for integratedsensing actuation and imagingrdquo Sensors vol 15 no 4 pp8020ndash8041 2015
[2] W Zhang H Zhang F Du J Shi S Jin and Z Zeng ldquoPull-inanalysis of the flat circular CMUT cell featuring sealed cavityrdquoMathematical Problems in Engineering vol 2015 Article ID150279 9 pages 2015
[3] O Oralkan A S Ergun J A Johnson et al ldquoCapacitivemicromachined ultrasonic transducers next generation arraysfor acoustic imagingrdquo IEEE Transactions on Ultrasonics Ferro-electrics and Frequency Control vol 49 no 11 pp 1596ndash16102002
[4] D E Dausch J B Castellucci D R Chou and O T vonRamm ldquoTheory and operation of 2-D array piezoelectricmicromachined ultrasound transducersrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 55 no 11pp 2484ndash2492 2008
[5] A Hajati D Latev D Gardner et al ldquoThree-dimensional microelectromechanical system piezoelectric ultrasound transducerrdquoApplied Physics Letters vol 101 no 25 Article ID 253101 2012
[6] F Akasheh J D Fraser S Bose and A Bandyopadhyay ldquoPiezo-electric micromachined ultrasonic transducers modeling theinfluence of structural parameters on device performancerdquoIEEE Transactions on Ultrasonics Ferroelectrics and FrequencyControl vol 52 no 3 pp 455ndash468 2005
[7] A S Ergun C-H Cheng O Oralkan et al ldquoBroadbandcapacitive micromachined ultrasonic transducers ranging from10 kHz to 60MHz for imaging arrays and morerdquo in Proceedingsof the IEEE Ultrasonics Symposium pp 1039ndash1043 MunichGermany October 2002
[8] M I Haller and B T Khuri-Yakub ldquoA surface micromachinedelectrostatic ultrasonic air transducerrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 43 no 1pp 1ndash6 1996
[9] S T Hansen B J Mossawir A Sanli Ergun F Degertekinand B T Khuri-Yakub ldquoAir-coupled nondestructive evaluationusing micromachined ultrasonic transducersrdquo in Proceedings ofthe IEEE Ultrasonics Symposium pp 1037ndash1040 Lake TahoeNev USA October 1999
[10] J Johnson O Oralkan U Demirci S Ergun M Karaman andP Khuri-Yakub ldquoMedical imaging using capacitive microma-chined ultrasonic transducer arraysrdquo Ultrasonics vol 40 no 1-8 pp 471ndash476 2002
8 Journal of Sensors
[11] X Zhuang A S Ergun Y Huang I O Wygant O Oralkanand B T Khuri-Yakub ldquoIntegration of trench-isolated through-wafer interconnects with 2d capacitive micromachined ultra-sonic transducer arraysrdquo Sensors and Actuators A Physical vol138 no 1 pp 221ndash229 2007
[12] X Zhuang D-S Lin O Oralkan and B T Khuri-YakubldquoFabrication of flexible transducer arrays with through-waferelectrical interconnects based on trench refilling with PDMSrdquoJournal of Microelectromechanical Systems vol 17 no 2 pp446ndash452 2008
[13] I O Wygant N S Jamal H J Lee et al ldquoAn integratedcircuit with transmit beamforming flip-chip bonded to a 2-DCMUT array for 3-D ultrasound imagingrdquo IEEE Transactionson Ultrasonics Ferroelectrics and Frequency Control vol 56 no10 pp 2145ndash2156 2009
[14] A Caronti G Caliano R Carotenuto et al ldquoCapacitive micro-machined ultrasonic transducer (CMUT) arrays for medicalimagingrdquo Microelectronics Journal vol 37 no 8 pp 770ndash7772006
[15] W Zhang H Zhang Y Wang F Du S Jin and Z ZengldquoSimulation characterization of CMUT with vented squaremembranerdquo in Proceedings of the International Conference onOptical Instrument and Technology (OIT rsquo15) Beijing ChinaMay 2015
[16] Z H Hao L Tang and D H Qiao ldquoAnalysis of the resonantfrequency of capacitive micro-machined ultrasonic transducer(cMUT) with finite element methodrdquo Technical Acoustics vol28 pp 133ndash134 2009 (Chinese)
[17] J Miao C D He D Q Lian et al ldquoDesign of MEMS capacitiveultrasonic transducer based on wafer bonding technologyrdquoChinese Journal of Sensors and Actuators vol 25 no 12 pp1653ndash1658 2012 (Chinese)
[18] B D Steinberg Principles of Aperture and Array System DesignIncluding Random and Adaptive Arrays John Wiley amp SonsNew York NY USA 1976
[19] S-C Wooh and Y Shi ldquoInfluence of phased array element sizeon beam steering behaviorrdquo Ultrasonics vol 36 no 6 pp 737ndash749 1998
[20] C B Doody X Cheng C A Rich D F Lemmerhirt and RD White ldquoModeling and characterization of CMOS-fabricatedcapacitive micromachined ultrasound transducersrdquo Journal ofMicroelectromechanical Systems vol 20 no 1 pp 104ndash118 2011
[21] M L Kuntzman D Kim andN A Hall ldquoMicrofabrication andexperimental evaluation of a rotational capacitive microma-chined ultrasonic transducerrdquo Journal of Microelectromechani-cal Systems vol 24 no 2 pp 404ndash413 2015
[22] M Bao Analysis and Design Principles of MEMS DevicesElsevier New York NY USA 2005
[23] M R Haddara and S Cao ldquoA study of the dynamic response ofsubmerged rectangular flat platesrdquoMarine Structures vol 9 no10 pp 913ndash933 1996
[24] X H Si W X Lu and F L Chu ldquoModal analysis of circularplates with radial side cracks and in contact with water on oneside based on the RayleighndashRitz methodrdquo Journal of Sound andVibration vol 331 no 1 pp 231ndash251 2012
From Figure 11 it can be observed that the Taylor methodis similar to the Chebyshev method Both methods havedecreased the side lobe amplitude to around minus30 dB andthe main lobe width has been broadened Whereas theChebyshev method has the narrowest possible main lobefor a specified side lobe level the Taylor method offerstradeoffs between themain lobe width and the side lobe levelMoreover the Taylor distribution avoids edge discontinuitiesso the Taylor method side lobes decrease monotonically
FromFigures 9ndash11 several common side lobe suppressionmethods have been discussed and compared Since the mainlobe width and the side lobe amplitude are contradictorythe side lobe suppression method must be carefully chosendue to different design requirements For instance when highlateral resolutions are desired the main lobe width is thefirst concernWhen the signal-to-noise ratio is the importantrequirement the side lobe level is the first concern
5 Conclusion
This paper proposed an integrated vibration membranestructure to design a CMUT linear array consisting ofmany subarrays for underwater applications The directivityperformances and side lobe suppression methods have beendiscussed The work in this paper is summarized as follows
(1) A two-dimensional CMUT linear array for underwa-ter applications has been proposedThe operation fre-quencies for different medium have been calculatedwhich are also proved by the COMSOL Multiphysicssoftware The derivation takes the ambient fluid intoconsideration and the operation frequency of theCMUT cell is 25MHz in air and 07MHz in water
(2) The directivity analyses for the CMUT cell sub-array and two-dimensional linear array have beenprovided The directivity of a single circular CMUTcell is very weak so it should be composed intolinear array to enhance the directivity According tothe product theorems the directivity function of thecomplex array is obtained using a combination of thedirectivity functions of certain simple structures
(3) The effects of the correlation parameters of the linearsubarray have been discussed including the cellnumbers the adjacent distance and the operationmedium Results show that both the cell numbers andthe adjacent distance have effect on the main lobewidth However both of them have an upper limit inorder to eliminate grating lobes For the underwaterapplications the wavelength is much bigger than thatfor the airborne applications Thus the directivityperformance of a linear subarray is determined byseveral parameters simultaneously
(4) In order to reduce the side lobe of the CMUT lineararray several weighting methods are used to suppressthe side lobe amplitude which is quite satisfactorybut at the expense of broadening themain lobe widthSince themain lobe width and the side lobe amplitudeare contradictory the side lobe suppression method
must be carefully chosen due to different designrequirements and the imaging quality and resolutionof the imaging system can be improved further
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This work has been supported by the Young Scientists Fundof the National Natural Science Foundation of China (Grantno 61201039)
References
[1] Y Qiu J V Gigliotti M Wallace et al ldquoPiezoelectric micro-machined ultrasound transducer (PMUT) arrays for integratedsensing actuation and imagingrdquo Sensors vol 15 no 4 pp8020ndash8041 2015
[2] W Zhang H Zhang F Du J Shi S Jin and Z Zeng ldquoPull-inanalysis of the flat circular CMUT cell featuring sealed cavityrdquoMathematical Problems in Engineering vol 2015 Article ID150279 9 pages 2015
[3] O Oralkan A S Ergun J A Johnson et al ldquoCapacitivemicromachined ultrasonic transducers next generation arraysfor acoustic imagingrdquo IEEE Transactions on Ultrasonics Ferro-electrics and Frequency Control vol 49 no 11 pp 1596ndash16102002
[4] D E Dausch J B Castellucci D R Chou and O T vonRamm ldquoTheory and operation of 2-D array piezoelectricmicromachined ultrasound transducersrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 55 no 11pp 2484ndash2492 2008
[5] A Hajati D Latev D Gardner et al ldquoThree-dimensional microelectromechanical system piezoelectric ultrasound transducerrdquoApplied Physics Letters vol 101 no 25 Article ID 253101 2012
[6] F Akasheh J D Fraser S Bose and A Bandyopadhyay ldquoPiezo-electric micromachined ultrasonic transducers modeling theinfluence of structural parameters on device performancerdquoIEEE Transactions on Ultrasonics Ferroelectrics and FrequencyControl vol 52 no 3 pp 455ndash468 2005
[7] A S Ergun C-H Cheng O Oralkan et al ldquoBroadbandcapacitive micromachined ultrasonic transducers ranging from10 kHz to 60MHz for imaging arrays and morerdquo in Proceedingsof the IEEE Ultrasonics Symposium pp 1039ndash1043 MunichGermany October 2002
[8] M I Haller and B T Khuri-Yakub ldquoA surface micromachinedelectrostatic ultrasonic air transducerrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 43 no 1pp 1ndash6 1996
[9] S T Hansen B J Mossawir A Sanli Ergun F Degertekinand B T Khuri-Yakub ldquoAir-coupled nondestructive evaluationusing micromachined ultrasonic transducersrdquo in Proceedings ofthe IEEE Ultrasonics Symposium pp 1037ndash1040 Lake TahoeNev USA October 1999
[10] J Johnson O Oralkan U Demirci S Ergun M Karaman andP Khuri-Yakub ldquoMedical imaging using capacitive microma-chined ultrasonic transducer arraysrdquo Ultrasonics vol 40 no 1-8 pp 471ndash476 2002
8 Journal of Sensors
[11] X Zhuang A S Ergun Y Huang I O Wygant O Oralkanand B T Khuri-Yakub ldquoIntegration of trench-isolated through-wafer interconnects with 2d capacitive micromachined ultra-sonic transducer arraysrdquo Sensors and Actuators A Physical vol138 no 1 pp 221ndash229 2007
[12] X Zhuang D-S Lin O Oralkan and B T Khuri-YakubldquoFabrication of flexible transducer arrays with through-waferelectrical interconnects based on trench refilling with PDMSrdquoJournal of Microelectromechanical Systems vol 17 no 2 pp446ndash452 2008
[13] I O Wygant N S Jamal H J Lee et al ldquoAn integratedcircuit with transmit beamforming flip-chip bonded to a 2-DCMUT array for 3-D ultrasound imagingrdquo IEEE Transactionson Ultrasonics Ferroelectrics and Frequency Control vol 56 no10 pp 2145ndash2156 2009
[14] A Caronti G Caliano R Carotenuto et al ldquoCapacitive micro-machined ultrasonic transducer (CMUT) arrays for medicalimagingrdquo Microelectronics Journal vol 37 no 8 pp 770ndash7772006
[15] W Zhang H Zhang Y Wang F Du S Jin and Z ZengldquoSimulation characterization of CMUT with vented squaremembranerdquo in Proceedings of the International Conference onOptical Instrument and Technology (OIT rsquo15) Beijing ChinaMay 2015
[16] Z H Hao L Tang and D H Qiao ldquoAnalysis of the resonantfrequency of capacitive micro-machined ultrasonic transducer(cMUT) with finite element methodrdquo Technical Acoustics vol28 pp 133ndash134 2009 (Chinese)
[17] J Miao C D He D Q Lian et al ldquoDesign of MEMS capacitiveultrasonic transducer based on wafer bonding technologyrdquoChinese Journal of Sensors and Actuators vol 25 no 12 pp1653ndash1658 2012 (Chinese)
[18] B D Steinberg Principles of Aperture and Array System DesignIncluding Random and Adaptive Arrays John Wiley amp SonsNew York NY USA 1976
[19] S-C Wooh and Y Shi ldquoInfluence of phased array element sizeon beam steering behaviorrdquo Ultrasonics vol 36 no 6 pp 737ndash749 1998
[20] C B Doody X Cheng C A Rich D F Lemmerhirt and RD White ldquoModeling and characterization of CMOS-fabricatedcapacitive micromachined ultrasound transducersrdquo Journal ofMicroelectromechanical Systems vol 20 no 1 pp 104ndash118 2011
[21] M L Kuntzman D Kim andN A Hall ldquoMicrofabrication andexperimental evaluation of a rotational capacitive microma-chined ultrasonic transducerrdquo Journal of Microelectromechani-cal Systems vol 24 no 2 pp 404ndash413 2015
[22] M Bao Analysis and Design Principles of MEMS DevicesElsevier New York NY USA 2005
[23] M R Haddara and S Cao ldquoA study of the dynamic response ofsubmerged rectangular flat platesrdquoMarine Structures vol 9 no10 pp 913ndash933 1996
[24] X H Si W X Lu and F L Chu ldquoModal analysis of circularplates with radial side cracks and in contact with water on oneside based on the RayleighndashRitz methodrdquo Journal of Sound andVibration vol 331 no 1 pp 231ndash251 2012
[11] X Zhuang A S Ergun Y Huang I O Wygant O Oralkanand B T Khuri-Yakub ldquoIntegration of trench-isolated through-wafer interconnects with 2d capacitive micromachined ultra-sonic transducer arraysrdquo Sensors and Actuators A Physical vol138 no 1 pp 221ndash229 2007
[12] X Zhuang D-S Lin O Oralkan and B T Khuri-YakubldquoFabrication of flexible transducer arrays with through-waferelectrical interconnects based on trench refilling with PDMSrdquoJournal of Microelectromechanical Systems vol 17 no 2 pp446ndash452 2008
[13] I O Wygant N S Jamal H J Lee et al ldquoAn integratedcircuit with transmit beamforming flip-chip bonded to a 2-DCMUT array for 3-D ultrasound imagingrdquo IEEE Transactionson Ultrasonics Ferroelectrics and Frequency Control vol 56 no10 pp 2145ndash2156 2009
[14] A Caronti G Caliano R Carotenuto et al ldquoCapacitive micro-machined ultrasonic transducer (CMUT) arrays for medicalimagingrdquo Microelectronics Journal vol 37 no 8 pp 770ndash7772006
[15] W Zhang H Zhang Y Wang F Du S Jin and Z ZengldquoSimulation characterization of CMUT with vented squaremembranerdquo in Proceedings of the International Conference onOptical Instrument and Technology (OIT rsquo15) Beijing ChinaMay 2015
[16] Z H Hao L Tang and D H Qiao ldquoAnalysis of the resonantfrequency of capacitive micro-machined ultrasonic transducer(cMUT) with finite element methodrdquo Technical Acoustics vol28 pp 133ndash134 2009 (Chinese)
[17] J Miao C D He D Q Lian et al ldquoDesign of MEMS capacitiveultrasonic transducer based on wafer bonding technologyrdquoChinese Journal of Sensors and Actuators vol 25 no 12 pp1653ndash1658 2012 (Chinese)
[18] B D Steinberg Principles of Aperture and Array System DesignIncluding Random and Adaptive Arrays John Wiley amp SonsNew York NY USA 1976
[19] S-C Wooh and Y Shi ldquoInfluence of phased array element sizeon beam steering behaviorrdquo Ultrasonics vol 36 no 6 pp 737ndash749 1998
[20] C B Doody X Cheng C A Rich D F Lemmerhirt and RD White ldquoModeling and characterization of CMOS-fabricatedcapacitive micromachined ultrasound transducersrdquo Journal ofMicroelectromechanical Systems vol 20 no 1 pp 104ndash118 2011
[21] M L Kuntzman D Kim andN A Hall ldquoMicrofabrication andexperimental evaluation of a rotational capacitive microma-chined ultrasonic transducerrdquo Journal of Microelectromechani-cal Systems vol 24 no 2 pp 404ndash413 2015
[22] M Bao Analysis and Design Principles of MEMS DevicesElsevier New York NY USA 2005
[23] M R Haddara and S Cao ldquoA study of the dynamic response ofsubmerged rectangular flat platesrdquoMarine Structures vol 9 no10 pp 913ndash933 1996
[24] X H Si W X Lu and F L Chu ldquoModal analysis of circularplates with radial side cracks and in contact with water on oneside based on the RayleighndashRitz methodrdquo Journal of Sound andVibration vol 331 no 1 pp 231ndash251 2012
