Design of Efficient Focused Surface Acoustic Wave Devices for Potential Microfluidic Applications

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Design of efficient focused surface acoustic wave devices for potentialmicrofluidic applicationsSubramanian K. Sankaranarayananand Venkat R. BhethanabotlaCitation: J. Appl. Phys. 103, 064518 (2008); doi: 10.1063/1.2891577View online: http://dx.doi.org/10.1063/1.2891577View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v103/i6Published by theAIP Publishing LLC.Additional information on J Appl PhysJournal Homepage: http://jap.aip.org/Journal Information: http://jap.aip.org/about/about_the_journalTop downloads: http://jap.aip.org/features/most_downloaded

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Design of efficient focused surface acoustic wave devices for potentialmicrofluidic applications

Subramanian K. R. S. Sankaranarayanan and Venkat R. Bhethanabotlaa

Sensors Research Laboratory, Department of Chemical Engineering, University of South Florida, Tampa,Florida 33620, USA

Received 12 August 2007; accepted 6 January 2008; published online 31 March 2008

Focused interdigital transducers

F-IDTspatterned on surfaces of piezoelectric substrates can be

used to generate surface acoustic waves SAW with high intensity and high beam-widthcompression ratio. A three dimensional coupled field finite element model of a focused SAWF-SAW device with interdigital transducers shaped as concentric circular arcs based on a YZLiNbO3 substrate is developed in this study. This model was utilized to investigate the effect ofgeometric shape of transducers on the focusing properties of F-IDTs to identify the optimal designfor potential microfluidic applications. The transducer design parameters investigated in the currentstudy include number of finger pairs, degree of arc, geometric focal length, and wavelength ofF-SAW. The transient response of the device on application of impulse and ac electrical inputs at thetransmitting FIDT fingers were utilized to deduce the device frequency response and propagationcharacteristics of F-SAWs, respectively. The influence of applied input voltage on the propagationcharacteristics is also investigated. The insertion loss calculated for the various F-IDT designs wasused to identify the optimal transducer configuration for sensing and microfluidic applications. The

focusing properties as well as the wave propagation characteristics for the various F-IDT designswere evaluated in terms of the amplitude field and displacement contours generated in regions closeto and at the focal point. Comparison with a conventional SAW device operating at megahertzfrequency range and uniform IDT design is also made. Our study indicates that the focusingproperty of the device is significantly influenced by the geometric shape of the F-IDTs. Thestreaming phenomenon induced by F-SAW propagation, when in contact with a fluid medium, isdiscussed in detail. The simulated amplitude fields generated using ac analysis for the variousdesigns in conjunction with wave propagation parameters derived using perturbational techniquessuch as CampbellJones are utilized to calculate the streaming forces and velocities based onsuccessive approximation technique applied to NavierStokes equation Nyborgs theory. Themaximum streaming force and velocity are obtained at the focal point of the F-SAW device. Themagnitude of the generated streaming force and induced streaming velocity are strongly influencedby the transducer configurations. Based on the simulation results of this study, we provide guidelines

for designing various F-IDTs to suite desired applications. F-SAW devices operating with higherapplied input voltages and at higher frequencies, with optimal geometric length and larger degree ofarc, are best suited for actuation and fluid microtransport. 2008 American Institute of Physics.DOI:10.1063/1.2891577

I. INTRODUCTION

Microfluidics represents the science of designing, manu-facturing, and formulating devices and processes that dealwith volumes of fluid on the order of picoliters to nanoliters.Surface acoustic wave SAW devices find applications inmicrofluidics and in actuation.15 In particular, SAWs can be

used to actuate and process smallest amounts of fluid on theplanar surface of a piezoelectric chip.1,4 The small size ofthese pumps or devices can minimize the dead volume offluid in the system. This feature is especially useful when thereagents or products are precious or when the device needs tobe cleaned or reused.

Applications of microfluidic systems include biologicalor chemical analysis and synthesis, micromixing, microdis-

pensing, and precision chemical dilution and mixing. In par-ticular, microfluidic devices can be used to obtain a varietyof interesting measurements including molecular diffusioncoefficients, fluid viscosity, pH, chemical binding coeffi-cients, and enzyme reaction kinetics.69 Other potential ap-plications for microfluidic devices include capillary electro-phoresis, isoelectric focusing, immunoassays, flowcytometry, sample injection of proteins for analysis via massspectrometry, polymerase chain reaction PCR amplifica-tion, DNA analysis, cell manipulation, cell separation, cellpatterning, and chemical gradient formation.1014 Several ofthese applications have utility for clinical diagnostics.

The flow through a microfluidic channel is characterizedby Reynolds number Re=Lu/, where L is the relevantlength scale, represents the fluid density, and is the fluidviscosity. The fluid velocities u in these devices are typi-cally in the range ofm /s and, hence, the Reynolds numbers

aAuthor to whom correspondence should be addressed. Electronic mail:[email protected].

JOURNAL OF APPLIED PHYSICS 103, 0645182008

0021-8979/2008/1036/064518/17/$23.00 2008 American Institute of Physics103, 064518-1

http://dx.doi.org/10.1063/1.2891577http://dx.doi.org/10.1063/1.2891577http://dx.doi.org/10.1063/1.2891577http://dx.doi.org/10.1063/1.2891577http://dx.doi.org/10.1063/1.2891577http://dx.doi.org/10.1063/1.2891577


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involved in the field of microfluidics are usually below 100. 4

This prevents turbulent flow and, hence, processes are essen-tially diffusion limited. For applications involving chemicaland biological analysis, micromixing, dispensing, and actua-tion, the device performance is determined by its ability toeffectively generate high enough fluid velocity in a smallchannel or chamber.15 High frequency acoustic waves, how-

ever, can circumvent such difficulties.SAW devices used for pumping and actuation purposes

rely on the acoustic streaming phenomenon induced by theinteraction of high frequency ultrasonic waves with the fluidmedium.9 At first, the periodic wave motion might seem tobe of little use for fluid manipulation. However, the inertialnonlinearity can rectify oscillatory fluid motion resulting in atime-averaged flow called steady or acoustic streaming, asshown by Rayleigh1884. Details of the ultrasonic radiationmechanism leading to streaming induced flows can be foundin Ref.16.Most research efforts have focused on methods toincrease the acoustic streaming phenomenon, thereby in-

creasing the efficiency of ultrasonic microtransport. TheSAW induced streaming phenomenon depends mainly ongeneration and propagation characteristics of the acousticwaves as well as the coupling of these ultrasonic acousticwaves with the fluid medium. The wave propagation charac-teristics are in turn affected by several device design param-eters such as applied input voltage, the device frequency,transducer geometry, as well as fluid properties such as den-sity and viscosity. Optimization of these parameters to maxi-mize the SAW streaming phenomenon is necessary to realizeits potential microfluidic applications. In this work, we focuson the effect of device design parameters on the surfaceacoustic wave propagation and qualitatively discuss the im-

plications of the same on the streaming induced flows.Our previous experimental and theoretical work hasshown that the SAW streaming phenomenon is strongly af-fected by wave propagation characteristics which are prima-rily dependent on the crystallographic orientation as well asthe transducer design and geometry.17,18 Recent studies haveindicated that SAW devices with focused interdigital trans-ducers can be used to excite waves with high intensity,highbeam-width compression ratio, and small localized area.1922

These high amplitude waves can be utilized to increase theinduced streaming velocities to facilitate micromixing andmicrotransport. Similarly, acoustically focused two dimen-sional micromachined microdroplet ejector arrays fabricated

on piezoelectric substrateswere able to achieve formation offocal point by leaky SAWs.1 This allowed for controlled gen-eration and ejection of picoliter droplets for spinless photo-resist deposition. Several other applications might exist inthe multidisciplinary areas involving physics, chemistry, en-gineering, and biotechnology, where the increased streamingachieved using focused SAW F-SAW is desirable. To ex-

plore the same, it is necessary to gain a complete understand-ing of the generation and propagation characteristics of fo-cused surface acoustic waves.

In the present work, we evaluate the design and perfor-mance of one such potential microfluidic surface acousticwave device, based on concentric circular arc fabricated on aLiNbO3 substrate, by analyzing the wave generation andpropagation characteristics for various focused interdigitaltransducer configurations in devices operating at megahertzfrequencies. We develop coupled field finite element struc-tural models to investigate the dependence of acoustic wavegeneration and propagation characteristics on the varioustransducer configurations in F-SAW devices. The transientresponse of the model to various electrical inputs is used toidentify the focused interdigital transducer F-IDTconfigu-ration that would allow for enhanced streaming and in-creased microtransport. The generated displacement profilesobtained at the receiving transducer port as well as otherlocations are used in conjunction with wave propagation pa-rameters derived from perturbational models to calculatestreaming forces and velocities based on successive approxi-mation theory applied to NavierStokes equation. The find-ings are used to identify the optimum transducer configura-tion for potential biosensing and microfluidic applications.The details are discussed in subsequent sections.

II. SURFACE ACOUSTIC WAVE DEVICE DESIGN

Surface acoustic waves are generated by the applicationof an alternating voltage signal to interdigital transducerspatterned on a piezoelectric substrate.23 The phase velocityof the generated wave depends on the material properties ofthe waveguide, the piezoelectric and electrodes, as well as onthe geometric shape of the electrode. The IDT geometry dic-tates the wavelength of the excited wave and, therefore, thecenter frequency of the device Fig.1a. Modifications tothe transducer geometry can result in significant changes inthe acoustic wave propagation characteristics. In this work,

FIG. 1. Color onlineSchematic dia-gram of a transducer design for aconventional SAW device and b fo-cused interdigitated transducer FIDTdesign for a F-SAW device.

064518-2 S. K. R. Sankaranarayanan and V. R. Bhethanabotla J. Appl. Phys. 103, 064518 2008



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we model the acoustic wave generation and propagation re-sulting from the use of concentrically oriented interdigitaltransducer fingers on the surface of a piezoelectric substrate.

An illustration of a F-SAW device constructed usingpairs of FIDTs based on concentric circular arcs is shown inFig.1b.The F-IDTs are characterized by design parameterssuch as degree of arcDa, geometric focal length fL, andthe wavelength . The effect of variation of these param-eters on the acoustic wave propagation characteristics is pre-sented in this work. The wave modes that are generated foreach of the transducer designs are evaluated using three di-mensional3D finite element transient analysis for variousapplied electrical input conditions at the transmitter IDT fin-gers. The simulated displacement and voltage waveforms ob-tained at the output transducer and at different locationsalong the delay path are analyzed to deduce the dependenceof the acoustic wave propagation characteristics on the de-

vice design parameters.The amplitudes of the SAWs depend on the applied volt-age input and frequency as well as device design character-istics and are typically in the nanometer range.23 SAWs suchas Rayleigh waves are generated in piezoelectric devicesbased on LiNbO3with a conventional IDT design and have adisplacement component normal to the propagation direc-tion. When in contact with a liquid, they tend to couplestrongly with the liquid and leak ultrasonic power into thefluid in the form of acoustic waves called leaky SAWs. Theleaky SAWs decay exponentially with distance from thesource. The SAW interaction with the fluid creates a net pres-sure gradient in the direction of sound propagation in the

fluid which leads to an internal, acoustically induced stream-ing phenomenon. SAW induced streaming finds applicationsin various processes ranging from micromixing, surface re-actions, sonic cleaning, to biological detection among severalothers. Altering the transducer electrode design from linearto circular causes the acoustic energy of the SAW device tobe focused. This results in larger amplitude waves and, cor-respondingly, larger streaming velocities are generated. At-tempts to identify transducer designs which would increasethe acoustic wave coupling with the fluid media and maxi-mize the induced streaming phenomenon are made usingstructural 3D finite element models. In particular, the trans-ducer designs listed in TableIare simulated in the present

work and used to identify the effect of the transducer designparameters on the focusing property of F-SAW device. Thesedetails are discussed in subsequent sections.

III. COMPUTATIONAL DETAILS

The propagation of acoustic waves in piezoelectric ma-terials is governed by the mechanical equations of motionand Maxwells equations for electrical behavior.23,24 Theconstitutive equations of piezoelectric media in linear rangecoupling the two are given by25

Tij=cijklE

Sklekijt

Ek, 3.1

Di=eiklSkl+ ikS

Ek. 3.2

In the above equations, Tij represent the components ofstress,cijkl

E the elastic constant for constant electric field, Sklthe strain, Ekthe electric field intensity, Di the electric dis-placement,eki j

t the piezoelectric constant, and ikS the permit-

tivity for constant strain. The acoustic wave propagation ve-locity is five orders of magnitude smaller than that of

electromagnetic waves. Therefore, the quasistatic assump-tions help reduce Maxwells equation to Di /xi =0 and Ei=/xi, where represents the electric potential.

The components of strain are defined by

Sij=1

2ui

xj+

uj

xi . 3.3

The equation of motion in the absence of internal bodyforces is given as

Tij

xj

2ui

t2 = 0, 3.4

where is the density and ui

represent the components ofdisplacement. Substituting and rearranging the above set ofequations leads to a system of four coupled wave equationsfor the electric potential and the three component of dis-placement in piezoelectric materials which are solved for thepiezoelectric substrate or the solid domain,

2ui

t2 +cijkl

E 2uk

xjxl+eki j

2

xkxj= 0, 3.5

eikl

2uk

xixl ik

S 2

xixj= 0. 3.6

These coupled wave equations can be solved for generating

displacement profiles and voltages at each element/node us-ing the finite element method.

IV. MODEL PARAMETERS

A three dimensional finite element model was developedin the present study. A micron-sized piezoelectric substratewith dimensions of 800 m propagation length500mdepth400m width was simulated to gain insights intothe wave propagation characteristics in F-SAW as well asconventional SAW devices. In most designs, three IDT fingerpairs for the input port were defined at the surface ofY-cut,Z-propagating LiNbO3 substrate. The fingers were defined

TABLE I. Design parameters of different focused SAW transducers simu-lated in this work.

F-SAW designparameters

Number offinger pairs

NpDegree of arc

Da

Geometricfocal lengthfLin m

Wavelengthin m

Design 1 3 120 45 40Design 2 3 120 45 60Design 3 3 120 45 80

Design 4 3 120 85 40Design 5 3 120 125 40Design 6 3 90 45 40Design 7 3 60 45 40Design 8 4 60 45 40Design 9 5 60 45 40




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with periodicity of 40, 60, and 80 m for simulating F-SAWdevices with varying wavelengths. Eight-node quadrilateralcoupled field solid elements were used to model the solidpiezoelectric domain. The IDT fingers were modeled asmassless conductors and represented by a set of nodescoupled by voltage degrees of freedom DOF. A total ofapproximately 150 000 elements more than 250 000 nodeswere generated. The model was created to ensure higher

node density at the surface and throughout the middle of thedevice to study the different modes of surface acoustic wavesand the use of eight-node coupled field solidelements withthree DOF ensured the same. Three DOFs provided the dis-placements in the longitudinalz, normaly, and the shearhorizontal z directions and a fourth for the voltage. Thetransient response of the F-SAW devices was simulated andused to identify conditions which would allow for enhancedultrasonic microtransport.

A. Structure excitation

The center frequency of SAW devices simulated in this

work is in the range of 50100 MHz. Hence, the structurewas simulated for a total of 200 ns, with a time step of0.5 ns. This enabled precise determination of the device fre-quency operating in the megahertz range. The excitation ofthe piezoelectric solid was provided by applying a time vary-ing voltage signalwith varying peak values and frequenciesequivalent to the device center frequencyon the transmitterIDT fingers of the F-SAW devices, as shown in Fig. 2. Twokinds of analysis were carried out for each of the F-SAWdesigns:1An impulse input of 100 V over 1 ns is appliedto study the frequency response of the device and 2 acanalysis with a 5 V peak-peak input and 100 MHz frequencyto study the wave propagation characteristics. A high inputvoltage impulse ensured that the amplitude of the acousticwave impulse sampled at the output transducer fingers wassufficiently large enabling clear distinction from any possibleinterference arising from edge reflections. The applied volt-age values chosen for ac analysiscorrespond to those used inexperimental investigations.17,4,38

V. RESULTS AND DISCUSSION

Using a 3D transient coupled field finite element model,the effect of transducer design parameters such as degree ofarcDa, geometric focal lengthfL, wavelength, as wellas number of F-IDT finger pairs as listed in TableIon thepropagation characteristicsvoltage and surface normal, lon-gitudinal, and shear horizontal displacement profiles ofF-SAW devices was investigated in the present work. Addi-tionally, the effect of applied input voltages on the displace-ment waveforms along the F-SAW delay path was simulated.The transient response to an applied voltage impulse wasused to calculate the center frequency of the F-SAW deviceand identify the propagation losses associated with each ofthe F-IDT designs. Analysis of particle displacements intothe substrate depth was utilized to determine the acousticenergy confinement for the various F-IDT designs. The simu-lated frequency response as well as wave propagation char-acteristics obtained for an F-SAW are also compared with aconventional SAW device with similar design parameters.The details are presented in the following sections.

A. Frequency response analysis

The frequency response of the F-SAW device is neces-sary in most of their applications, such as filters, sensors,actuators, detectors, etc.23 Although SAW devices with fo-cused interdigital transducers have been studied for severalyears, the models required to calculate the frequency re-sponse are very limited.2628 In case of F-SAW devices, sec-ond order effects of SAW propagation such as SAW diffrac-tion, refraction, and beam steering are much stronger than inthe conventional SAW deviceand deeply influence the ob-tained frequency response.19,29 Most of the simpler modelsare based on perturbational approach and are unable to ac-count for such effects. Therefore, a simulation model such asthe finite element technique which considers these secondorder effects is needed to accurately calculate the frequencyresponse of an F-SAW device.

FIG. 2. Color onlineF-SAW device ameshed structure. bApplied input voltage profile for a 100 MHz SAW device.




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To calculate the frequency response of the F-SAW de-vice using the developed finite element model, an input im-pulse signal of 10 V is applied at the transmission electrode.Three to five IDT fingers at each port were defined with thenodes coupled to 0 V, while the same number of output IDTfingers was coupled separately. The impulse function repre-sented above is applied to the remaining input IDT fingers,and the average voltage profiles calculated at the output IDTfingers were used to derive the frequency response of the

F-SAW device.The simulation is then performed for 100 ns duration

with a time step Ts of approximately 1 ns. The samplinginterval1 ns in our caseis typically chosen as the smallestfrequency which the system can resolve using Fourier trans-form. The transient response of the F-SAW device to theapplied impulse voltage input is then obtained in terms oftime varying output voltage profile at the set of nodes repre-senting the output F-IDT fingers. Then, the frequency re-sponse of a F-SAW device H f can be obtained from itsimpulse response htby taking the Fourier transform of thevoltage data sampled at the output transducer.30,31

Hf=

hte2ftdt. 5.1

The power spectrum can then be calculated from the knownfrequency domain data as follows:

Sxxf=HfH*f=Hf2, 5.2

where, * represents the complex conjugate of Hf. Thepower spectrum was scaled with respect to the number of

sampled data points.The corresponding magnitude of the obtained signal is

converted into decibels insertion loss using the followingequation and represents the insertion loss corresponding tothe given frequency:

Insertion loss = 20 log10Sxxf. 5.3

These features are represented as frequency response plotsshown in Figs. 36. The calculated insertion losses associ-ated with each of the transducer designs are listed in TableIand used to identify the applicability of the various designsin the areas of microfluidics and sensing.

FIG. 3. Color online Simulated frequency responses of F-SAW devices: a design 1, b design 2, c and design 3. Designs 1, 2, and 3 correspond toF-SAW devices with F-IDTs having similar degree of arcD

a=120and geometric focal lengthf

L= 45 m, but varying wavelengthsi.e., 40, 60, and

80 m, respectively.




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1. Effect of wavelength

To investigate the effect of acoustic wavelength on thepropagation characteristics of F-SAWs, we simulated F-SAWdevices with varying IDT finger spacing, i.e., 10, 15, and20 m. Typically, the SAW device operational frequency isgiven by v /4f, where vis the velocity of the acoustic wavetraveling along any particular crystallographic direction inthe LiNbO3substrate and fis the finger spacing. Therefore,

the spacing between electrodes was modified to simulateF-SAW devices operating in different frequency ranges andgenerating focused acoustic waves with varying wave-lengths. The smallest attenuation is attained when the inputexcitation frequency matches the center frequency of the de-vice. To identify the center frequency for subsequent acanalysis, an impulse input of 100 V was applied to the trans-mitter fingers. The frequency response obtained for the threedesigns with varying IDT finger spacing is shown in Fig. 3.The calculated center frequencies for the three cases arelisted in TableII. It can be seen that the center frequenciesfor 10, 15, and 20 m F-IDT finger spacings correspond to100, 75, and 55 MHz, respectively.

The insertion losses corresponding to the three designsare also listed in TableII. We find that F-SAW devices op-erating at lower frequencies show higher propagation lossesas compared to those operating at higher frequencies. Thisbehavior is different from that seen in conventional SAWdevices, in which the higher frequency devices have higherpropagation losses. It is also worth noting that in the F-SAWdevices operating at 55 and 75 MHz, the frequency re-sponse appears to show significant bulk acoustic waveBAWinterference at the high frequency end of the devicepassband. It is, however, also possible that the high fre-quency signal obtained at 150 MHz is a result of electro-magnetic feedthrough effect. The BAW velocity in YZLiNbO3 is 7220 m /s and, hence, it takes approximately12 ns for the wave to travel the delay-line distance of 45 mbetween the input and output electrodes. The electromagneticfeedthrough, on the other hand, is attributed to the initialsignal which occurs mostly within the first few nanoseconds.Our analysis of the frequency response obtained without theelectromagnetic feedthrough effect, i.e., time domain signalpicked up beyond 12 ns, indicated that the high intensity

FIG. 4. Color onlineSimulated frequency response of F-SAW devices with transducer configurations having varying geometric focal length: adesign 1,b design 4, andcdesign 5. Designs 1, 4, and 5 correspond to F-SAW devices with F-IDTs having similar degree of arc Da =120 and wavelength = 40 m, but varying geometric focal length fL, i.e., 45, 85, and 125 m, respectively.




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signal still existed and is therefore a result of BAW interfer-ence. Although the disappearance of the BAW signal in the100 MHz F-SAW device is unclear, it is evident that thehigher propagation losses associated with the 55 and70 MHz devices, as shown in Table II, are due to BAWinterference.

Based on these simulation findings, it appears that the100 MHz frequency F-SAW device with lesser insertion lossis more suitable for applications involving microfluidics andsensing. Therefore, in the subsequent subsections, we com-pare the variations of geometric focal length and the degreeof arc of F-IDT for the device operating at 100 MHz.

2. Effect of geometric focal length FL

To investigate the effect of geometric focal length on thefrequency response of the F-SAW device, we simulated de-vices with the same degree of arc of 120 and finger spacingof 10 m, but different focal lengths of 45, 85, and 125 m.The simulated frequency response for the different device

TABLE II. Calculated center frequencies and insertion losses for three de-signs with varying finger spacing.

F-SAW transducerdesign Wavelength

Center frequencyMHz

Insertion lossdB

Design 1 40 100 9.5Design 2 60 70 11.6Design 3 80 55 11.9

FIG. 5. Color onlineSimulated frequency response of F-SAW devices with transducer configurations having varying degrees of arc: adesign 1,bdesign

6, andcdesign 7. Designs 1, 6, and 7 correspond to F-SAW devices with F-IDTs having similar geometric focal length fL =45 m and wavelength

= 40 m, but varying degree of arcs Da i.e., 120, 90, and 60, respectively.

FIG. 6. Color online Simulated frequency response of F-SAW deviceswith transducer configurations having varying number of F-IDT fingers.




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designs is shown in Fig. 4. It can be seen that the centerfrequency of the devices is unaffected by changes in thefocal length and depends primarily on the F-IDT finger spac-ing. The calculated insertion losses corresponding to thevarious geometric lengths are summarized in Table III. Asexpected, the F-SAW devices with longer focal length showincreased insertion loss.

The higher propagation losses are attributed to secondorder effects arising from substrate anisotropy such as SAWdiffraction, refraction, and beam steering which are strongerin F-SAW devices in comparison to conventionalSAW ones,

as has been shown in one of our investigations.

29

The calcu-lated insertion loss shows little change for focal length varia-tion from 45 to 85 m. However, it increases significantlyfrom approximately 9.2 to 13.9 dB when the focal lengthchanges from 85 to 125m. It is likely that the insertionloss shows a nonlinear dependence on geometric focallength, although more simulations are needed to confirm thesame. This implies that, beyond a certain optimal focallength, the propagation losses are significantly higher.F-SAW devices, beyond the optimal focal length, with higherinsertion losses are unsuitable for sensing applications andmight find applications primarily in actuation, whereas thosewithin the optimal focal length might be suitable for both

sensing and actuation. The localized amplitude variations inthe focal region for each of the three designs are required tosubstantiate the above arguments. This and other details ofthe propagation characteristics for the three designs are dis-cussed in the ac analysis in a subsequent subsection.

3. Effect of degree of arc

The effect of degree of arc of the F-IDTs on the fre-quency response of the F-SAW device is shown in Fig. 5.The simulated devices shown in Fig.5have the degree of arcvarying from 120 for design 1 to 60for design 7. The in-crease in the degree of arc of an F-IDT does not change the

passband width of the device. However, there exist signifi-cant differences in the insertion loss of the device as listed inTableIV.For smaller degree of arc such as 60, the insertionlosses are significantly reduced 3.8 dB. However, if thedegree of arc is excessively large, then the insertion lossbecomes larger, for example, it is 9.5 dB for a 120 arc. Anincrease in the degree of arc of F-IDTs results in an increasein SAW diffraction which results from the high anisotropy ofthe piezoelectric substrate. This typically occurs when thepropagation direction is not along one of the pure-mode axesof the crystal, but at an angle with respect to it. In suchcases, as in an F-SAW device with the transducers based onconcentric circular arcs, the acoustic group velocity will

propagate off at angle with respect to the phase velocity.The higher the degree of arc, the higher would be the SAWdiffraction effect and hence greater would be the insertionloss, as seen in Fig.5.

It is expected that an increase in the degree of arc of theFIDTs might lead to better focusing property with the ampli-tude field possibly reaching a focal point. This can be usefulto build devices that are more suitable as actuators in micro-fluidic applications. However, as brought out earlier, F-SAWdevices with higher propagation losses are not best suited forsensing applications. Hence, it is likely that F-SAW deviceswith smaller degree of arc and lower insertion losses are

more qualified to be applied as sensors or filters. This mightimply that standard nonfocusing IDTs which represent a spe-cial case of F-SAWs with Da =0 are best suited for sensingapplications. However, our simulation study indicates thatwhile the insertion losses of F-SAW devices with smallerdegree of arc are higher than those of standard nonfocusingIDTs, the corresponding wave amplitudes in the focal regionare also significantly higher for F-IDTs with smaller arcswhen compared to standard nonfocusing IDTs. Therefore, itappears that there exists an optimum F-IDT design with de-gree of arc between Da =0 and 60 which might be bestsuited for sensing applications. Identification of the optimumsensor design requires correlation of device sensitivity with

the extracted simulation data and is beyond the scope of thecurrent work. Instead, the main focus of the current work isto identify F-IDT designs which are best suited for microflu-idic applications and geometric parameters which couldmaximize streaming forces and velocities and can thus beused effectively for actuation and droplet dispensing applica-tions. A detailed ac analysis of the propagation characteris-tics of F-SAW devices with varying degrees of arc is pre-sented in a subsequent section.

4. Effect of number of finger pairs

To simulate the effect of number of F-IDT finger pairson the frequency response of the F-SAW device, we utilizeddesign 7 with three F-IDT finger pairs as the base case. Thenumber of F-IDT fingers was subsequently increased to fourand five and the results are shown in Fig.6. We find that thepassband width becomes narrower with an increase in thenumber of finger pairs while the insertion loss of the devicesbecomes smaller. It has been reported by Wu et al.that, forlarge enough number of finger pairs 120, the insertionloss of the F-SAW device does not decrease any further withincrease of this number. However, the increase in finger pairsalso increases the size of the device. As a result, it is neces-

TABLE III. Calculated insertion loss for F-IDTs with varying focal length.

F-SAW transducerdesign

Geometric focallengthfL in

mInsertion loss

dB

Design 1 45 9.5Design 4 85 9.2Design 5 125 13.9

TABLE IV. Calculated insertion loss for F-IDTs with varying degrees of arc.

F-SAW transducerdesign Degree of arc

Insertion lossdB

Design 1 120 9.5Design 6 90 8.6Design 7 60 3.8




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sary to optimize the number of F-IDT finger pairs in an

F-SAW device according to the required pass-band and in-sertion loss.The simulation model developed by Wu et al.19 was

based on effective permittivity approach and perturbationtheory. In the present case, although more robust, the finiteelement FE simulations involving larger number of fingerpairs led to a considerable increase in the number of ele-ments to model the F-SAW device and leading to a signifi-cant increase in the simulation time. The computationallyintensive nature of the FE model makes it difficult to simu-late F-SAW having increased number of finger pairs. Theseand other limitations of the FE model are discussed in aseparate investigation.32

B. ac response analysis

ac analysis for the various F-IDT designs considered inthe above section was carried out to investigate the focusingproperty as well as understand the propagation characteris-tics of F-SAWs. The simulated displacement contours show-ing F-SAW propagation along the substrate surface for the acanalysis of design 4 are shown in Fig.7.The focusing effect,which is clearly evident from Fig. 7, is analyzed for thevarious designs listed in TableI.

The propagation of acoustic waves in the F-SAW deviceis evaluated in terms of the displacement waveforms in the

surface normal, longitudinal, and shear horizontal directionsat various locations along the delay path including the outputtransducer fingers. The voltage waveforms analyzed at theoutput transducer are used to gain insights into the extent ofwave attenuation. The wave propagation into the depth of thesubstrate is analyzed to understand the acoustic energy con-finement as well as wave conversion into the bulk mode.

1. Effect of degree of arc Of F-IDT

ac analysis of F-SAW devices with varying degrees ofarc of F-IDTs ranging from 120 to 60 was carried out toinvestigate the focusing property and propagation character-istics of F-SAWs. An increase in the degree of arc also

causes an increase in the aperture width of the F-IDT fingers.

The simulated amplitude field obtained after the wave hasstabilizedafter 40 ns is shown in Fig. 8.It can be clearlyseen that the amplitudes for designs 1 and 6 attain a sharpmaximum at regions close to the focal point, whereas thosefor design 7 are much broader and do not approach a focalpoint. The displacement amplitudes at the focal region de-crease with degree of arc of the F-IDTs. The maximum incase of designs 6 and 1 i.e., withDa =90 and 120appearsto be shifted away from the focal point. The deviation resultsfrom SAW diffraction and is attributed to the anisotropy ofthe piezoelectric substrate. The SAW diffraction effect in-creases with the degree of arc. As a result, the frequencyresponse of devices with larger degrees of arc shows higher

insertion loss.The snapshots obtained at the end of 70 ns of simulation

time for the three F-IDT designs are shown in Fig. 9.Theamplitude fields appear to converge to the focal point as thedegree of arc increases from 60 to 120. Hence, it can be

FIG. 7. Color onlineSimulated acoustic wave propa-gation in an F-SAW device. The parameters correspond

to those of design 4. Design 4 corresponds to F-SAWdevice with F-IDTs having degree of arc Da =120,geometric focal length fL= 85m, and wavelength=40 m.

FIG. 8. Color onlineSimulated amplitude field for F-SAWs with varyingdegrees of arc. Designs 1, 6, and 7 correspond to F-SAW devices withF-IDTs having similar geometric focal length fL= 45m and wavelength=40 m, but varying degree of arcs Da, i.e., 120, 90, and 60,

respectively.




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observed that F-IDTs with larger degree of arc produce asmaller focal area. Therefore, the focusing property becomesbetter as we increase the degree of arc, with the amplitudefield approaching the focal point. For devices having suffi-ciently larger degree of arc, i.e., greater than 90, it can beseen that the variations in the azimuthal direction are negli-gible, especially at regions near the focal point. As we moveaway from the focal region, i.e., distances greater than 4,variations in the azimuthal direction become significant as

seen from the displacement contours shown in Fig. 9.Theacoustic wave propagation characteristics in devices havingF-IDTs with smaller degree of arc approach that of a conven-tional SAW device. At longer simulation times, wave reflec-tions from the edge of the substrates are also captured bythese coupled field finite element models.

We further analyze the displacement profiles along thedepth of the piezoelectric substrate for a section cut throughthe region close to the focal point of the F-SAW device, asshown in Fig.10.Insights into the acoustic energy confine-ment at regions near the focal point and substrate surface canbe obtained using Fig.10.The waves are confined within oneto two wavelengths from the device surface. The acoustic

intensity rapidly attenuates with depth into the device surfacefor the three designs shown. However, we find higher acous-tic wave penetration into the substrate surface for F-SAWdevices having larger degree of arc. As brought out earlier,the displacement amplitudes are higher for devices havingF-IDTs with larger degrees of arc.

Based on the findings of the ac and impulse analysis, itappears difficult to design F-SAW devices having degree ofarc that results in best possible focusing properties and low-

est insertion loss at the same time. Among the various simu-lated designs, F-IDTs with Da =90 appears to be the opti-mum transducer configuration for use in both microfluidicand sensing applications. On the other hand, FIDTs withDa =120 have better focusing property, but higher insertionloss and are most suitable for use in actuation or excitation.FIDTs with Da =60 have moderate focusing property, butsmaller insertion loss and hence are most suitable for sensingapplications.

Furthermore, comparison of propagation characteristicsof an F-SAW device design 1 with a conventional SAWdevice having uniform transducer fingers can also be carriedout. In Ref.29,we simulated a 100 MHz conventional SAW

FIG. 9. Color onlineSimulated displacement contours for F-SAW devices for adesign 1, bdesign 6, and cdesign 7. Designs 1, 6, and 7 correspondto F-SAW devices with F-IDTs having similar geometric focal lengthfL =45 mand wavelength= 40 m, but varying degree of arcs Dai.e., 120, 90,and 60, respectively.




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device having a finger periodicity of 40 m, an aperture

width of 200 m, and delay line equivalent to twice the focallength in design 1. An ac electrical input of 5 V peak-peakwas applied at its transmitting fingers. We analyzed the dis-placement contours as well as the amplitude field at variouslocations along the device delay line as well as at the outputtransducer fingers after the system had stabilized after70 ns.

Our simulation results indicated that the surface wavesgenerated in a conventional SAW device with uniform fin-gers and aperture width has smaller amplitudes of particledisplacement compared to F-SAWs. The analysis of particledisplacement profiles indicated that the depth penetration ofthe surface waves in a conventional SAW is smaller than thatobserved for a focused SAW device. Additionally, the local-ized variations observed near the focal point in an F-SAWdevice are absent in conventional SAWs. Our analysis of thevoltage profiles obtained at the receiving IDT fingers indi-cates the propagation losses in the conventional SAW arelower than that in F-SAW, owing to reduced second ordereffects such as SAW diffraction, refraction, and beam steer-ing. The analysis of particle displacement profiles along thesubstrate depth at various locations along the F-SAW delaypath corroborated the above argument. We found that theconventional SAW devices are better suited for sensing ap-plications than for actuation and microfluidic application. On

the other hand, depending on the design specifications,

F-SAW devices can be applied for both sensing as well asactuation and microfluidic applications.

2. Effect of geometric focal length

ac analysis, as brought out in the above subsection, ofF-SAW devices with varying geometric focal length45, 85,and 125 mwas carried out to investigate its effect on thepropagation characteristics of F-SAWs. The amplitude fieldsobtained near the focal point for the three designs are quali-tatively similar. The simulated displacement contours ob-tained for the three designs, i.e., designs 1, 4, and 5 shown inFigs.9a,7,and11, respectively, were analyzed to study the

dependence of the focusing property on the geometric focallength. Our analysis indicated that the displacement ampli-tudes attain a maximum near the focal point, which increaseswith F-IDT focal length. At first sight, this might appearcounterintuitive as one would expect higher propagationlosses and smaller displacement amplitudes for devices withlonger geometric focal length. However, for the same degreeof arc and number of finger pairs, the aperture width of theF-IDT fingers would increase with distance from the focalpointFig.1b. Hence, the increased propagation losses arecompensated by a corresponding increase in the aperturewidth and, therefore, higher displacement amplitudes as wellas increased focusing property result in devices with in-

FIG. 10. Color onlineSimulated displacement profiles along the depth of the piezoelectric substrate for a section cut through a region close to the center ofdelay path and normal to the propagation direction for adesign 1, bdesign 6, andcdesign 7. Designs 1, 6, and 7 correspond to F-SAW devices withF-IDTs having similar geometric focal lengthfL = 45mand wavelength=40 m, but varying degree of arcs Dai.e., 120, 90, and 60, respectively.




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creased geometric focal length. For the same reason, ouranalysis of displacement profiles along the depth of the sub-strate for a section cut through the focal point also indicated

higher acoustic energy penetration for F-SAW devices hav-ing longer geometric focal length.Although the current simulations suggest that longer fo-

cal lengths might be needed typically 20for the amplitudefield to approach a concise focal point, the scale of the devicewould also increase significantly, making the simulationcomputationally intensive. This, and other limitations of thefinite element simulations, can be found in Ref.32.

3. Effect of wavelength

ac analysis of F-SAW devices with varying F-IDT fingerspacing was carried out to understand the effect of F-SAW

wavelength on its propagation characteristics, in particular,the focusing property. An applied voltage of 5 Vpeak-peakwith frequency determined from the frequency responseshown in Fig. 3 was input at the transmitting F-IDTs. Theamplitude fields obtained for the three designs are shown inFig.12. Although the F-SAW amplitude at the focal point is

not very different for the three designs, the distribution of theF-SAW amplitude field shows significant differences. Com-parison of the peak amplitudes of the F-SAW crest at regions

near the focal point for the three different wavelengthsFig.12suggests that the focusing effect is enhanced for deviceswith smaller wavelengths and higher frequency. The local-ized variations are more prominent in design 1, whereas de-sign 3 appears to have a more uniform particle displacementnear the focal point.

The simulated displacement contours for designs 1, 2,and 3 obtained after the system has stabilized 70 ns isshown in Figs. 9a, 13a,and 13b, respectively. We findthat the scattering of the waves after the focal point reduceswith increase in the wavelength and the amplitude field be-comes more uniform. The size of the focal area increaseswith the increase in F-SAW wavelength. For larger wave-

lengths, the amplitude field has no concise focal point. In-stead, the F-SAW propagates as a narrow, long, strong SAWbeam, as shown in Fig. 13b.

Our simulation results indicate that the focusing proper-ties increase with decrease in the wavelength of the F-SAW.Additionally, F-SAW devices operating at higher frequenciesor smaller wavelengths also incur smaller propagation losses.Hence, for both sensing and microfluidic applications, de-vices operating at higher frequencies or generating F-SAWswith smaller wavelengths are preferred.

4. Effect of applied input voltage

The simulations results reported above for the variousF-IDT designs were obtained for an applied ac electrical in-put of 5 V peak-peak at the transmitter F-IDT fingers. Toinvestigate the effect of voltage intensity on the propagationcharacteristics of the wave, we simulated an F-SAW devicewith transducer design parameters corresponding to design 1and operating at 100 MHz, but with varying applied inputvoltages of 5, 10, 20, and 30 Vpeak-peak. Our simulationresults indicated that similar wave propagation characteris-tics and displacement contours, but with varying wave am-plitudes, are generated for the various applied power inputs.As brought out earlier, the maximum amplitudes were ob-tained at the focal point of the F-SAW device. The ampli-

FIG. 11. Color online Simulated displacement con-tours for design 5, i.e., F-SAW device having F-IDTs

with wavelength = 40 m, focal length fL=125 m, and degree of arcDa =120.

FIG. 12. Color onlineSimulated amplitude fields for F-SAWs with vary-ing wavelengths. Designs 1, 2, and 3 correspond to F-SAW devices withF-IDTs having similar degree of arcDa =120and geometric focal lengthfL= 45 m, but varying wavelengths , i.e., 40, 60, and 80m,respectively.




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tudes of the wave generated at the focal point in the F-SAWdevice for the various simulated voltage inputs are shown inFig.14. We find that the amplitude of the generated focusedwave varies linearly with the applied input voltage.

Similar linear variation was observed theoretically forconventional SAW devices simulated in our previous inves-tigations and was also reported experimentally by Chono etal. for SAW devices operating at 50 MHz frequency. TheSAW amplitudes in these experiments were measured usingoptical methods for varying input voltages.9 When in contactwith the fluid medium, the increased wave amplitudes areexpected to result in enhanced streaming forces and in-creased streaming velocities. The effect of these amplitudevariations in the F-SAW device on the induced streaming

force and the streaming velocities for the various transducerconfigurations and applied electrical input is discussed in thenext subsection.

C. F-SAW induced streaming

In this section, we investigate the applicability ofF-SAW devices with the various transducer designs simu-

lated in the present work. Specifically, the streaming forcethat is induced by the F-SAW devices when in contact withthe fluid medium as well as the induced streaming velocitiesare derived using the successive approximation techniqueap-plied to NavierStokes equation, i.e., Nyborgs theory.16 Theamplitude field generated by the coupled field finite elementsimulations are used in conjunction with the wave propaga-tion parameters derived using perturbational techniques, suchas that due to CampbellJones, to calculate the inducedstreaming velocities. The governing equations for acousticstreaming have been derived by Nyborg some time ago andare given by

2v2p2=F, 5.4

F= 0v1v1+ v1 v1. 5.5

In the above equations,is shear viscosity, 0is the constantequilibrium density, v1is the oscillatory particle velocity, v2is the acoustic streaming velocity, p 2is the steady state dcpressure, Fis the nonlinear driving force term, and the an-gular brackets denote the time average over sufficiently largenumber of cycles.33,34

The particle displacements in a F-SAW device can bederived in terms of components along the principal cylindri-cal coordinates. The conversion function f from cylindricalto Cartesian coordinates is denoted by fx,y ,z=r cos ,r sin , h. The variations in the displacement com-ponent along the azimuthaldirection are negligible as canbe seen in the simulations, especially at regions near the

TABLE V. Leaky SAW velocity and attenuation coefficient calculated basedon the CampbellJones methodRefs.35 and36.

CrystalOrientation

Rayleigh wavevelocitym/s

Water loadedleaky SAWvelocity

Leaky SAWwave-number/m

Attenuationcoefficient

128 Y-XLiNbO3

3994 3931+j68.1 2768 2.47

Y-ZLiNbO3 3487 3194+j268.3 16409 1.92

FIG. 13. Color online Simulated displacement contours for a design 2 and b design 3; i.e., F-SAW device having F-IDTs with similar degree of arcDa =120 and geometric focal length fL= 45 m, but with varying wavelengths of 60 and 80 m, respectively.

FIG. 14. Color onlineEffect of applied input voltage on the wave ampli-tudes at the focal point in an F-SAW device.




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focal point. Therefore, the wave propagation in the F-SAWdevice occurs primarily along the radial denoted byuxandsurface normaluzdirections and can be set in the followingform to derive the components of leaky F-SAW when incontact with the liquid medium:

ux=AexpjtexpjkLxexp kLz, 5.6

uz= j Aexpjtexpj kLxexp kLz,

where = 1 vL/vw2. 5.7

Arefers to the amplitude of F-SAW displacement, =2fis

the angular frequency; vL and vw represent the leaky andlongitudinal wave velocities, respectively. The leaky F-SAWpropagates along the boundary and excites longitudinalwaves into the liquid. The wave number kL for leakyF-SAW is a complex number, with the imaginary part ac-counting for the extent of energy dissipation into the fluidmedium. The wave number kL and velocity vL of theleaky F-SAW can be computed by extending the method of

CampbellJones to solid-liquid structures assuming displace-ment and stress continuity at the interface.35,36

The oscillatory particle velocity v1 can be found usingv=u /t. Substituting the first order velocity into Eq. 5.5,we obtain the following components of streaming force Fs:

Fx= 01 + 12A22kiexp 2kix+ 1kiz, 5.8

Fz= 01 + 12A221kiexp 2kix+ 1kiz, 5.9

where, =j1, and kL = kr+jki. The streaming force Fs canbe calculated by Fs =Fx2 + Fz2 and is given as

Fs= 01 + 123/2A22kiexp 2kix+ 1kiz. 5.10

The force calculated above acts as a body force near theSAW-fluid interface, with the direction being at the sameangle as the radiation of leaky SAW. The decaying exponen-tial factors in v1limit the extent of force into the fluid. Thisforce, which varies as the square of the first order velocity, inturn produces the second order velocity v2. Substitution of

TABLE VI. Calculation of streaming force and velocities, generated by F-SAW devices with different trans-ducer configurations, based on Nyborgs theory. The FE simulations were carried out with three finger pairs ofFIDT fingers. In calculating the streaming velocities and forces generated by F-SAW, we scaled the simulationamplitudes to match the number of FIDT finger pairs 150that are used in an actual device. The attenuation

constant =1.92 and leaky SAW velocity v=3194+j268.3 for water loading were calculated using theCampbellJones method.

F-SAW Designparameters

Degree ofarcDa

Geometricfocal lengthfLin m

Wavelength inm

F-SAWamplitude

Streaming

forceN /m3

Streamingvelocitym /s

Design 1 120 45 40 46.2 1.4109 528.2Design 2 120 45 60 44.9 4.5108 244.4Design 3 120 45 80 48.0 2.5108 172.4Design 4 120 85 40 66.5 2.9109 1100.0Design 5 120 125 40 70.5 3.3109 1200.0Design 6 90 45 40 41.3 1.1109 422.1Design 7 60 45 40 38.4 9.6108 364.9

FIG. 15. Color online a Calculated streaming force at the substrate surface and along the radius of the F-SAW device design 1 for an applied inputvoltage of 5 V peak-peak. b Second order streaming velocity profile generated in the same F-SAW device. The device operating frequency is approxi-mately 100 MHz. Design 1 corresponds to F-SAW device with F-IDTs having degree of arc Da =120, geometric focal lengthfL =45 m, and wavelength= 40 m.




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VI. LIMITATIONS OF THE FINITE ELEMENT MODEL

The accurate modeling of focused SAW devices requiresgeneration of a very fine mesh. Since it is critical that thenodal densities for the substrate simulated are at least on theorder of 20 nodes per wavelength for the highest device fre-quency, the number of nodes required for the simulation of a3D F-SAW device with the dimensions employed in thepresent study itself is extremely large. Additionally, the

simulations are computationally intensive and time consum-ing, with the required CPU time increasing considerably withmesh size. The current study investigates acoustic wavepropagation in F-SAW devices with three to five IDT fingerpairs. Increasing the number of IDT fingers to match those inan actual device150would require a significant increasein the scale of the device simulated. The computationallyintensive nature of the finite element method makes thesimulation of such a device beyond the scope of the currentlyavailable computational resources. It should also be notedthat acoustic wave reflections from the substrate edges canarise if the simulations are carried for sufficiently longertimes. To overcome this limitation, it is essential to employdamping elements at the ends of the substrate. Althoughlonger simulation times are necessary to attain a stable state,we find that too long a simulation time results in wave re-flections causing instabilities to set in. A simulation time of200 ns was found to be optimum for the substrate dimen-sions considered in the present study.

VII. CONCLUSIONS

A three dimensional coupled field finite element FEmodel of F-SAW devices was developed in this work. TheF-IDTs were modeled as concentric circular arcs patterned

on the surface ofY ZLiNbO3. The model was used to inves-tigate the effect of geometric shape of transducers on thefocusing property of F-IDTs. The effect of several F-IDTdesign parameters such as number of finger pairs, degree ofarc, geometric focal length, the wavelength of F-SAW on itspropagation characteristics, as well as focusing property wasstudied in detail. An impulse and ac electrical input was ap-plied at the transmitting F-IDT fingers to evaluate the devicefrequency response and F-SAW propagation characteristics,respectively. The frequency of the simulated devices rangedfrom approximately 55 to 100 MHz.

The displacement contours as well as the variations inamplitude field at various locations around the focal region

obtained in an ac analysis were used to evaluate the focusingproperty for the various transducer designs. The results indi-cate that the focusing property is significantly influenced bythe geometric shape of the transducers. F-SAW devices withlarger degree of arc of F-IDTs and operating at higher fre-quencies, i.e., generating waves with smaller wavelength, areneeded to obtain better focusing. Also, there exists an opti-mal geometric focal length for the F-SAW devices whichdepends on a compromise between the focusing property andthe associated insertion loss. Longer geometric focal lengthgave better focusing characteristics and increased insertionlosses. The wavelength of F-SAWs also significantly affectedthe focusing property. Larger wavelength F-SAWs generate

long, narrow, strong SAW beams, but the amplitude field isunable to approach a precise focal point. Shorter wavelengthF-SAWs which are generated in devices operating at higherfrequencies are able to achieve the same.

The streaming phenomenon induced by the propagationof F-SAWs, when in contact with the fluid medium, is dis-cussed in detail. The streaming forces and velocities calcu-lated for the various transducer designs based on Nyborgs

theory using the amplitude fields generated by FE simula-tions and wave propagation parameters derived using a per-turbational approach were used to deduce their applicabilityfor potential microfluidic applications. The induced stream-ing forces and velocities attain a maximum at the focal point,with the exact magnitude dependent on the transducer de-sign. The calculated streaming velocities agree well withthose reported in previous experimental and theoretical stud-ies.

Based on the FE simulation results, we have attemptedto identify transducer configurations that are best suited forsensing and microfluidic applications. We find that F-SAWdevices operating at higher frequencies and with high ap-

plied input voltages, optimal geometric focal length, andlarger degree of arc are best suited for actuation and micro-fluidic applications, whereas F-SAW devices with shortergeometric focal length and smaller degree of arc of F-IDTsare better suited for sensing. Additionally, in comparisonwith the conventional SAW devices fabricated with uniforminterdigital transducers, we find that the focused SAW de-vices are more sensitive to variations in the focal area insteadof the whole delay-line region. This makes them suitable forapplication requiring detection or manipulation of localizedvariations, such as those utilizing acousto-optic or acousto-electric effects. The findings of our study have laid thegroundwork for further investigation into the propagation

characteristics and focusing property of F-SAW devices fab-ricated on multilayered substrates and/or with more compli-cated transducer designs.

ACKNOWLEDGMENTS

The authors thank Academic Computing and Engineer-ing Computing at University of South Florida for providingcomputational facilities. The authors thank Samuel J. Ip-polito and Glenn Matthews at RMIT, Melbourne, and StefanCular and Reetu Singh at USF for useful discussions. Fund-ing for this work was provided by NSF-IGERT Grant No.DGE0221681, USF-IDRG, and the Department of DefenseContract No. W81XWH-05-1-0585.

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