Thin film Lamb wave resonators in frequency control and sensing applications: a review

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2013 J. Micromech. Microeng. 23 043001

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J. Micromech. Microeng. 23 (2013) 043001 (14pp) doi:10.1088/0960-1317/23/4/043001

TOPICAL REVIEW

Thin film Lamb wave resonators infrequency control and sensingapplications: a reviewVentsislav Yantchev and Ilia Katardjiev

Department of Engineering Sciences, Uppsala University, Uppsala, Sweden

E-mail: veya@angstrom.uu.se

Received 4 December 2012, in final form 23 January 2013Published 7 March 2013Online at stacks.iop.org/JMM/23/043001

AbstractThis work makes an overview of the progress made during the last decade with regard to anovel class of piezoelectric microwave devices employing acoustic Lamb waves inmicromachined thin film membranes. This class of devices is referred to as either thin filmLamb wave resonators or piezoelectric contour-mode resonators both employing thin filmaluminum nitride membranes. These devices are of interest for applications in both frequencycontrol and sensing. High quality factor Lamb wave resonators exhibiting low noise, low lossand thermally stable performance are demonstrated and their application in high resolutiongravimetric and pressure sensors further discussed. A specific emphasis is put on the ability ofthese devices to operate in contact with liquids. Future research directions are further outlined.

(Some figures may appear in colour only in the online journal)

1. Introduction

Microwave electro-acoustics offers unique features in termsof low losses and small form factors for filter applications aswell as low noise frequency sources. At the same time thistechnology enables fabrication of high-resolution sensors forchemical, physical and biochemical sensor applications.

Two general types of electroacoustic technologies arecurrently used in commercial application in a concurrentmanner. Namely, the thin film bulk acoustic wave resonator(FBAR) technology and the microwave surface acousticwave (SAW) technology. The FBAR technology employsthin piezoelectric, polycrystalline aluminum nitride (AlN)films on Si substrates which are acoustically isolated fromthe substrate typically by micromachining (figure 1(a)). TheFBAR technology is a planar technology and as such is fullycompatible with the IC technology. The SAW technologyemploys single crystal substrates with high mechanical qualityand high electromechanical coupling. Typical examples areLiTaO3 and LiNbO3. The main building blocks of a SAWresonator are the interdigital transducer (IDT) (figure 1(b)) and

the reflector gratings (the end gratings of the SAW resonatorin figure 1(b)). Both approaches have specific advantagesand shortcomings. For example, the SAW technology offersrobust designs with low sensitivity to technological toleranceson the one hand while being inherently incompatible withthe IC technology on the other because of the use of singlecrystalline substrates. The FBAR technology is IC compatibleand has demonstrated impressive performance in the lowerGHz range but is quite sensitive to technological toleranceswhich limits the development of fully integrated systems.In an attempt to fill this technological gap a new classof micromachined electroacoustic devices employing plate-guided waves propagating in micromachined AlN thin filmmembranes has been recently developed. Electrical excitationof the wave is also achieved, as in the SAW case, by IDTsand hence retains the robustness of the SAW technology.Device fabrication, on the other hand, employs the FBARtechnological platform and is hence IC compatible. Thisunique combination makes the Lamb wave technology an ICcompatible alternative to the commercially established SAWtechnology.

0960-1317/13/043001+14$33.00 1 © 2013 IOP Publishing Ltd Printed in the UK & the USA

J. Micromech. Microeng. 23 (2013) 043001 Topical Review

(a )

(b)

Figure 1. Sketches of common piezoelectric resonator topologies:(a) FBAR, (b) SAW resonator.

(a )

(b)

Figure 2. Sketches of Lamb wave resonator topologies employing:(a) grating reflectors, (b) edge reflectors.

The development of the Lamb wave resonator (LWR)technology was initiated about 8 years ago with thedemonstration of the first thin-film-based resonator employingthe lowest order symmetric Lamb wave (S0) [1]. Currently theS0 mode in AlN membranes has mostly been explored becauseof its unique combination of extremely high velocity, lowdispersion and moderate piezoelectric coupling. In figure 2,we illustrate the two Lamb wave resonator topologies whichonly differ in the way the acoustic energy is confined withinthe cavity.

Specifically, the grating-type Lamb wave resonatorsemploy reflective gratings (spatially distributed (Bragg)reflectors) in an identical manner as in most of the SAWresonators (see figure 1(b)). The edge-type Lamb waveresonators employ reflection from the suspended edges of

Figure 3. Lamb acoustic modes.

the membrane (spatially fixed reflectors). Most generally theedge-type LWRs are smaller in size as compared to thegrating-type LWR. Such a type of reflection was previouslyemployed in some shear SAW resonators [2] as well as invarious resonant microelectromechanical systems (MEMS)[3]. Accordingly, the term contour-mode-resonators (CMR)is sometimes adopted to specify Lamb wave resonatorsemploying suspended edges [4]. For simplicity, Lamb waveresonators will be referred to in this work as grating-type andedge-type LWR, respectively.

Most of the experimental data presented here refers to aspecific set of LWR design parameters. These are AlN filmthickness d = 2 μm and acoustic wavelength λ = 12 μm.The demonstrated characteristics are found in good agreementwith the results obtained independently by other researchers,thus revealing the underlying Lamb wave properties which inturn determine the observed performance improvements.

2. The lowest order symmetric Lamb wave (S0)

The AlN membrane, usually employed in FBARs, itselfrepresents a plate in which laterally propagating plate modesare allowed. Most generally, the plate waves are divided intotwo groups with respect to the acoustic wave polarization.The first type is the so-called Lamb waves which exhibitan elliptical polarization while the second type is the so-called shear acoustic plate modes which exhibits a shearor quasi-shear polarization. In here, focus is primarily onLamb waves. Generally, the plate supports a number ofthese waves depending on the plate thickness to acousticwavelength ratio. Each type of plate waves consists of twodifferent modes. These are the symmetric and the asymmetricmodes respectively indicating the symmetry of the particledisplacements associated with the wave relative to the medianplane of the plate (see figure 3). For simplicity the differentplate modes are denoted with symbols. Thus, the nth ordersymmetric Lamb wave is denoted as Sn, while the nth orderasymmetric Lamb wave is denoted as An, where ‘n’ is aninteger ranging from 0 to infinity and represents the numberof standing waves along the plate thickness. In this context, aLamb wave has two characteristic wavelengths, one along theplate thickness and another along the plate surface. Throughout

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Figure 4. Theoretical dispersion presented in coordinatesnormalized to the wavelength λ and the shear velocity VS.

this overview, we will refer only to the latter one and denote itby λ.

Figure 4 shows the typical dispersion of the first few Lambmodes in c-textured AlN as a function of the relative platethickness d/λ. Unlike their first order counterparts the zerothorder symmetric and asymmetric Lamb waves do not exhibitcritical ‘cut-off’ frequencies at zero wavenumber (infinite λ).More specifically, the lowest order symmetric Lamb waveS0 demonstrates an almost linear dependence of frequencyfor small values of the relative membrane thickness. In otherwords, the S0 mode exhibits a low velocity dispersion whenpropagating in acoustically thin membranes. It should be notedthat the cut-off frequencies of the A1 and S1 modes coincidewith the fundamental resonance frequency of the thicknessexcited shear and longitudinal modes, respectively. Thus, theS1 Lamb wave represents a more general ‘2D-wavenumber’presentation of the one-dimensional thickness-excited FBARmode. At the cut-off frequency, the mode has an infinite λ,which represents exactly the thickness-excited mode.

Unlike the FBAR, LWRs are mostly employing the lowestorder symmetric Lamb wave S0. The physical characteristicsthat make the lowest order Lamb wave attractive for practicaluse are the possibility of employing simultaneously highvelocity, weak dispersion and moderate electromechanicalcouplings [5], as also predicted theoretically using Adler’smatrix approach [6] and Green’s function formalism [7, 8].In figure 5(a), the calculated dependence of the acousticvelocity on the AlN film thickness for the lowest symmetricLamb mode (S0) in a thin c-oriented AlN membrane isshown. Clearly the S0 mode exhibits low dispersion for amembrane thickness d smaller than 0.4λ where λ is theacoustic wavelength, offering at the same time an acousticwave velocity of up to around 10 000 m s−1. This uniquefeature makes the Lamb wave resonators less sensitive toAlN technological thickness tolerances, while enables theelimination the frequency sensitivity toward small variationsin transducer electrodes thickness [9].

Further, the electromechanical couplings achievable inthe low dispersion region are of the order of up to 3%. Infigure 5(b), the electromechanical couplings of two basictypes of transducers are shown. Here, the electromechanicalcoupling is defined as twice the fractional change of the

(a )

(b)

Figure 5. Calculated characteristics of the S0 Lamb wave inc-oriented AlN: (a) acoustic wave velocity and (b)electromechanical couplings.

velocity of the S0 mode propagating under electrically open andshorted top surface, respectively. The dashed line representsthe electromechanical coupling corresponding to excitationwith a standard IDT, while the dotted line represents theelectromechanical coupling to an IDT transducer with anadditional bottom electrode. In the latter case, the electric fieldis confined predominantly in the vertical direction, thus givingrise to lateral field excitation (LFE) of the longitudinal wave(LW) polarization through the e31 piezoelectric coefficient.The LFE term has initially been introduced from the theoryof bulk acoustic wave devices and denotes acoustic wavepropagation orthogonal to the applied electric field. In contrast,the thickness field excitation (TFE) denotes acoustic wavepropagation parallel to the applied electric field. In the theoryof SAW devices, the same principles of excitations are referredto as cross-field and inline-field excitation, respectively.

3. S0 mode Lamb wave resonators

3.1. LWR design and microfabrication

As mentioned above, LWRs are classified in the way theenergy is confined but they can also be classified in accordancewith the transducer topology used. Three major transducertopologies are used as shown in the right corner of figure 6.

These are respectively an IDT over-floating bottomelectrode, a longitudinal wave (LW) transducer formed bya periodic array of a half wavelength wide metal strip overgrounded bottom electrode and a classical IDT configuration.

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Figure 6. Calculated harmonic admittances of common LWRtransducer configurations.

In figure 6 the harmonic admittances of each transducerconfiguration is shown for the case of d/λ = 0.1 ascalculated with COMSOL finite element frequency responseanalysis (FEA). The fractional frequency shift between theresonance f R and the antiresonance f A is related to theeffective transducer coupling kEFF

2 = 0.25π2( f A− f R)/ f A.Evidently, the IDT/floating electrode transducer offers amuch higher transduction coefficient at relatively small plate-thickness-to-wavelength ratios. Thus, the use of a giventransducer architecture is application specific. If strongerelectromechanical couplings are pursued, the IDT/floatingelectrode configuration is to be preferred [10], since themaximum achievable effective device coupling in this caseapproaches 3.5% (see in figure 6). On the other hand LWRswith reduced technological complexity employ classical IDTsat the expense of reduced effective transducer couplings. TheLW transducer could be advantageous when the resonantfrequency of the first order asymmetric Lamb wave S1 is closeto the resonance frequency of the S0 Lamb mode since LWtransducers on c-textured AlN do not couple to anti-symmetricLamb waves.

Most generally, the device technology resembles to a verylarge extent the FBAR technology. The devices are typicallyfabricated on a micromachined free-standing AlN membrane.In the specific case of edge-type LWRs, suspended edges ofthe AlN membrane are additionally formed by etching the AlNemploying a SiO2 hard mask to ensure vertical edges with finequality. Here we illustrate the general process flow of sucha device including also an electrical contact to the bottomelectrode. All other configurations require a reduced numberof lithographic steps and processes.

As a supporting substrate, a Si wafer is used. Aftercleaning the substrate, a thin metal film is sputter deposited,and then patterned (see figure 7(a)). This structure serves asa bottom electrode of the LWR and should be continuousthroughout the device to eliminate macro-defects evolvingfrom the electrode edges. Subsequently, an etch stop layeris grown, and subsequently a 1–2 μm thick c-textured AlNfilm having a slightly tensile stress is deposited by reactivesputtering onto the bottom electrode (see figure 7(b)). The fullwidth at half maximum of the (0 0 2) x-ray rocking curveshould be bellow 2◦ to ensure good material properties of the

(a)

(b)

(c)

(d )

(e)

(f )

Figure 7. LWR micromachining. (a) Bottom electrode. (b) Etchstop. (c) Via holes. (d) Contact pads. (e) Top electrodes. ( f )Micromachining of the substrate.

active layer. Contact via-holes through the AlN film are thendry etched by reactive ion etching (RIE) (see figure 7(c)). Thickcontact metallization pads are subsequently formed on topof the AlN (see figure 7(d)). The top electrodes are definedby a standard deposition/lithography/dry etch steps (seefigure 7(e)). Finally, the Lamb wave devices are acousticallyisolated from the supporting Si substrate by etching the Sisubstrate from the backside using a standard, three-step, dryetch Bosch process (see figure 7( f )). Alternatively, surfacemicromachining can be employed as in FBARs. Note that thefabrication of IDT-based LWRs needs only the last three of theabove six lithographic steps.

Figure 8 represents a top view of grating types one-portLWRs as fabricated, employing both classical IDTs and LWtransducers, respectively. Specifically, S0 Lamb waves witha 12 μm central wavelength are excited in 2 μm thick AlNmembrane. The central wavelength is defined by the 6-μmpitch of the reflecting grating used in the LWRs. The thicknessof the Al strips is 300 nm and the reflecting gratings have 50–60aluminum strips. More specifically, the IDT-based LWR (seefigure 8(a)) consists of 53 reflecting strips in each reflectivegrating, 79 strips in the IDT and a 40 wavelength aperture.The LW transducer-based LWRs (see figure 8(b)) consistof 62 reflecting strips in each reflector, 30 half-wavelengthwide strips forming the LW transducer and a 30 wavelengthsaperture. The Al bottom electrode (see figure 7( f )) has athickness of 300 nm. In both resonators, the grating reflectorsare spatially shifted by nλ/2 (n—an integer number) fromthe transducer which is further referred to as synchronouslydesigned resonators.

3.2. Performance of LWR

Both edge-type and grating-type LWRs have demonstratedcomparable performances at similar frequencies. Table 1summarizes the results regarding the Q × f product achievedby various research groups.

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(a )

(b)

Figure 8. Top view of the fabricated devices. (a) IDT-based LWR.(b) LW-transducer-based LWR.

Table 1. LWR Q factors.

LWR topology Resonant frequency Q factor

Edge type (CMR) [11] 1.17 GHz 2200Biconvex edge type [12] 591.8 MHz 3280Grating type [13] 884 MHz 3100

Q factors of about 3000 at a frequency of about 900 MHzhave been demonstrated determining a Q × f product ofabout 2.7 × 1012 Hz [14]. Further improvements arestill feasible by reducing, for example, acoustic leakagethrough wave diffraction. A significant increase of thisfigure in edge-type LWRs can be achieved by reducingwave coupling to the supporting beams through bi-convexreflecting edges [12] or acoustic isolation of the supportedbeams [3]. Initial experimental data have demonstrated Q · f =4.6 × 1012 Hz at 4.7 GHz [15], i.e. scaling of this productwith operation frequency. The possibility to scale Q · f productwith frequency should be further studied.

Figure 9. Close-to-resonance characteristics of 12-μm wavelengthLWR employing a ‘hiccup’ geometry.

The input impedance of the LWRs can easily be tailoredfor each transducer type through the number of strips in thetransducers and the transducer aperture. When low impedancesat resonance are required the IDT/floating electrode topologyis preferred because of its higher effective coupling [10].Classical IDT-based 900 MHz LWRs have demonstrated aninput admittance at resonance as low as 20 � while the LWtransducer-based 900 MHZ LWRs have demonstrated an inputadmittance at resonance as low as 7 � [13].

Figure 9 illustrates the performance of a high Q grating-type one-port LWR employing classical IDT. This specificdesign uses a quarter wavelength shift introduced inside theregular electrode IDT (hiccup geometry), while the gratingreflectors are placed synchronously around the IDT (in thisspecific case the grating reflectors are spatially shifted bya half wavelength each from the IDT). It is further notedthat this design is referred to as non-synchronous becausethe resonance cavity length deviates from the nλ/2 condition.More specifically, the fabricated device (similar in topology tothat in figure 8(a)) employs a 2 μm thick AlN membrane,has a central wavelength λ = 12 μm, 50λ-wide aperture,reflectors consisting of 62 strips and an IDT consisting of 62electrodes with an internal gap of 2.25λ. The Q factor of theLWR considered is determined through the phase slope of theimpedance as Q = 0.5· f ·∂ϕZ/∂ f . The measured device Q atresonant frequency approaches 3000 at a frequency of about875 MHz. LWR maximum effective device coupling of about2% has been demonstrated [16] although the IDT/floatingelectrode configuration enables effective device couplings ofup to 3.5%. Accordingly, LWRs having Q × f products inexcess of 3 × 1012 Hz and electromechanical couplings ofabout 3% are feasible in the lower GHz frequency range.

Another common LWR topology is the two-port LWRwhich inherits the topology of the two-port SAW resonators.Such LWR types can be used, for example, in low-noiseintegrated feedback loop oscillators (FLO) [17] or as integratednarrowband coupled-resonator filters [18]. Figure 10 showsa two-port 12 μm wavelength LWR as fabricated alongwith its close-to-resonance response. The response shown infigure 10(b) corresponds to a device employing a 2 μm thickAlN membrane with central wavelength λ = 12 μm, 41 stripsin each IDT and 52 strips in the reflectors, a cavity length L =1.125λ and an aperture of 50λ. The device has an insertion loss

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(a )

(b)

Figure 10. A 12-μm wavelength two-port LWR. (a) Top view asfabricated. (b) Close-to-resonance S21 measurement.

of IL = 3.87 dB, a loaded QL =π f τ ( f = frequency, τ = groupdelay) of 1110 and a corresponding unloaded QU = QL/(1–10−IL/20) of 3150 at 885.7 MHz resonance frequency. Thedemonstrated QU · f product of 2.79 × 1012 Hz is comparableto the Q · f products demonstrated by the one-port LWRs.

3.3. Analysis of LWRs

The design of LWRs with given specifications requires thedevelopment of adequate analytical tools. The physical modelscommonly used in SAW analysis are found applicable tothe analysis of LWRs. The LWR response can be roughlyestimated by a 1D Mason network model [19] assuming a 1Dnature of the propagating mode. The Mason model is amongthe simplest and has found broad application in the analysis ofboth FBAR and SAW resonant devices although with a limitedaccuracy. Accordingly, 2D models which take into account theLamb wave energy distribution across the membrane thicknesswere shown to be more accurate [20–22]. Specifically,the coupling-of-modes (COM) theory has shown excellentagreement with experiment [23]. Most generally, COM is aphenomenological model for guided wave propagation andexcitation, which is widely employed for the design of high-performance SAW devices [24, 25]. The analysis based on the

COM model gives very simple and analytical solutions with asurprisingly good accuracy provided that the COM parametersare properly determined. The COM model has been used withsuccess to describe also dispersive SAWs in layered structures[26] as well as Leaky SAWs [25]. In comparison to the latter,the S0 Lamb wave demonstrates weak dispersion and well-defined waveguiding. Conversion losses induced by reflectionare known to be suppressed in acoustically thin plates, thuspresuming relative simplicity of the loss mechanisms. Thisspecific feature made possible the design of high-Q contour-extensional-mode resonators employing free-edge reflections[27, 28]. Accordingly, the use of the COM approach toward theanalysis of S0 Lamb wave FPARs seems convincingly justified.

The COM equations used in this study are [24]:

dR(x)

dx= − jδR(x) + jk12S(x) + jαV

dS(x)

dx= − jk12R(x) + jδS(x) − jαV (1)

dI(x)

dx= −2 jαR(x) − 2 jαS(x) + jωCV,

where R(x) and S(x) are slowly varying fields describing theamplitudes of the forward and the backward propagatingmodes, k12 is the COM reflectivity parameter, α is theCOM transduction coefficient, C is the transducer capacitanceper unit length, V is the applied voltage and δ =ω/V(ω) − (π /p) − jγ is a detuning parameter describingthe effects of the unperturbed velocity dispersion and thepropagation losses induced by the material viscosity andthe wave diffraction. Here ω is the angular frequency, V(ω) isthe dispersive unperturbed velocity, p = λ/2 is the grating pitchand γ is the acoustic attenuation. For convenience here wepresent the COM parameters described above in a normalizedfashion:

• kP = −k12 · λ: dimensionless reflectivity per finger pair;• VS0: S0 Lamb wave unperturbed velocity in AlN at central

frequency;• αn: normalized COM transduction coefficient, αn =

α·λ√W/λ

, where W is the device aperture;• γP = γ · λ0: attenuation per wavelength (Np/λ);• D: dimensionless velocity dispersion (V (ω) ≈ VS0(1 −

D(ω − ω0)/ω0));• Cn: normalized capacitance Cn = Cλ0/W (F/m) (per IDT

pair, per unit aperture).

To demonstrate the applicability of the COM approach,we first extract the COM parameters by fitting to the close-in-resonance response of a 12 μm wavelength synchronousone-port FPAR (identical to the one shown in figure 8(a)). Theexperimental curves (solid lines) in figure 11 are fitted to theCOM model (dashed lines) by means of least-squares fitting.Table 2 shows the values of the COM parameters extractedfrom the fitting procedure in figure 11. These parameterscan alternatively be theoretically deduced by modal andGreen’s function analyses as discussed elsewhere [21, 23].The agreement between theory and experiment was foundexcellent.

To further demonstrate the applicability of the COMapproach, the extracted parameters are used in the analysis

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Table 2. Values of the extracted COM parameters.

Layout: 2 μm thick AlN, 270 nm thick Al electrodes, λ = 12 μmCOM parameters Value

S0 unperturbed velocity (VS0, m s−1) 10 435.05Velocity dispersion (D) 3.5 × 10-2

Normalized reflection coefficient (kP) 16.5 × 10-2

Normalized capacitance (Cn, pF m−1) 81.9Normalized transduction coefficient (αn, �-1/2) 13.3 × 10-5

Attenuation (γ P, Np λ−1) 9.48 × 10-4

Parasitic electrical resistance (RS, �) 1.81

Figure 11. Measured versus COM-fitted LWR admittance.

Figure 12. Calculated COM response of a 12-μm wavelengthtwo-port LWR.

of the two-port LWR shown in figure 10. The simulated COMfrequency response is shown in figure 12. The result is in verygood agreement with the experimental response in figure 10.

We further note the ability to extend the method towardthe analysis of edge-type LWRs utilizing multi-wavelengthtransducers and free edge reflections. In such structures theperiodic transducer can be analyzed through the COM modelincluding charge distribution and propagation effects, whilethe reflection from the suspended membrane edges can bedefined by their amplitude and phase [22].

Last but not the least the COM approach has beendeveloped to also account for the specific waveguiding intransversal direction, i.e. assuming changing wave amplitudealong the device aperture [29]. Thus, the COM approachprovides an opportunity to analytically describe LWR in a

Table 3. Phase noise at 1 kHz offset.

LWR topology Central Frequency Noise (dBc Hz−1)

Edge type (CMR) 222 MHz −88 [17]Edge type (CMR) 483 MHz −88 [30]Edge type (CMR) 583 MHz −93 [31]Grating type 888 MHz −92 [32]Edge type (CMR) 1.05 GHz −81 [12]

3D fashion, which seems to be beneficial especially for thedesign of edge-type LWRs.

Recently, finite element analysis (FEA) has also beenapplied to the analysis of SAW, FBAR and LWR devices.In a 2D approximation FEA agrees very well with the 2Danalytical techniques employing COM and Green’s functionanalyses. FEA can also be used to accurately deduce the COMparameters in view of improving their accuracy.

In its 3D form, FEA is found a quite useful tool especiallyfor the edge-type LWRs because of their generally smallerdimensions. Grating-type LWRs can also be simulated in 3Dbut require increased computer power.

4. LWR-stabilized oscillators

IC compatibility and integration of S0 Lamb wave resonatorshas been successfully demonstrated in system on-chipfrequency references [12]. Currently, the thin film Lambwave technology allows easy integration of high-Q acousticresonators on Si for oscillators with a low close-in phasenoise. Lamb wave-based oscillators in the frequency bandof 200 MHz to 1 GHz have shown a phase noise of about−90 dBc Hz−1 at 1 kHz offset frequency independently on theLWR topology used. Close-in phase noise of various LWR-based oscillators is summarized in table 3.

The thermal noise floor (TNF) in these resonators isdependent to a very large extent on the LWR power-handlingabilities. Most generally, TNF is a function of the loop powerP0, the overall loop loss G and the noise figure (NF) of thesustaining amplifier as follows [33]:

TNF [dBc Hz−1] = −174 − P0 + NF + G. (2)

Thus, oscillators with higher power in the loop demonstratelower TNF provided that the LWR can sustain sufficientlyhigh powers. This can be achieved by making the device areasufficiently large while providing efficient heat dissipationat the same time. It is noted that AlN is a material withhigh thermal conductivity which allows for efficient heat

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Figure 13. Block and level diagram of the power oscillator loop.

dissipation. In this respect the use of beam supporters (in edge-type LWRs) must be avoided. Instead, only two, instead of four,free-standing edges may be utilized, as suggested earlier [34].In this way the heat can dissipate through the complete devicelength [35] unlike the case of edge-type LWRs employingbeam supporters.

Here we discuss the specific realization of a grating-typeLWR-stabilized clock in the 900 MHz range running at upto 27 dBm (0.5 W) loop power and exhibiting a phase noiseof −92 dBc Hz−1 at 1 kHz [32]. The close-in phase noise 1 Hzintercept point of the oscillator was measured as £(1 Hz) =−2 dBc Hz−1 which was then used to determine the LWRflicker noise constant αR = 2.1 × 10−36/Hz [36]. This valueis comparable with some of the best SAW resonators built todate and suggests that the LWR technology is a low noise one.This conclusion has been further supported by an independentstudy where a 222 MHz edge-type LWR has demonstrated aphase noise as low as −110 dBc Hz−1 at 1 kHz offset [17].

The two-port LWR shown in figure 10 is connectedin a feedback oscillator loop, as shown in figure 13, witha sustaining RF amplifier capable of generating 27 dBm(0.5 W) of RF power at the 880 MHz resonant frequency. Inthis power oscillator configuration, the FPARs were operatedat an incident power level of 24 dBm (250 mW) for5 weeks [36]. The power dissipated resulted in a moderatetemperature increase of about 6–7◦ K. An inspection under anoptical microscope and a detailed analysis of their electricalcharacteristics prior to and after the power test did not showany measurable performance degradation or any evidence ofelectro-migration and aging effects.

The feasible TNF = −186 dBc Hz−1 that can be achievedin this configuration has been estimated by equation (2) takinginto account the experimentally obtained loop power P0 = 27dBm, the overall loop loss G = 8 dB (5 dB loss in the two-portLWR used and 3 dB output coupler loss) and the noise figureof the sustaining amplifier NF = 7 dB.

The LWR driving power level Pd = 250 mW can befurther related to the longitudinal peak stress |T11|P through arelatively simple one-dimensional model, initially introducedto describe the stress levels in SAW resonators [37]. It is furthernoted that the S0 mode can be treated as one dimensional witha sufficient accuracy when propagating in acoustically thinplates. Accordingly, the peak stress is given by [32]

|T11|P = Jm

√QU Pd/(L.W ), (3)

where Jm = √ρV/π

√λ/d = 3310

√λ/d, ρ is the AlN mass

density, V is the S0 phase velocity, λ the acoustic wavelength,

Figure 14. LWR vibration mode at resonance.

Figure 15. Topology of a thermally compensated LWR.

QU is the unloaded Q, L is the effective resonant cavitylength and W is the effective cavity width determined bythe profile of the fundamental waveguiding mode as W = 3W0/8 (W 0: device aperture). Accordingly the peak stress level|T11|P in the LWR operating at 250 mW drive power is foundto exceed 3 × 108 N m−2. It is noted that Rayleigh SAWquartz resonators with pure aluminum metallization showirreversible degradation due to acoustically induced migrationat stress peak levels exceeding 6 × 107 N m−2 [21]. In thesame experiment, SAW resonators on Quartz using a similargeometry would fail within a few seconds at a power of24 dBm as a result of metal electro-migration in the transducerelectrode structure.

The demonstrated high power handling of the S0 LWR isattributed to the favorable combination between the specificmode of vibration (see figure 14), where the deformationis symmetric within the electrodes resulting in a zero netmomentum induced in them, and the high thermal conductivityof the AlN.

5. LWR thermal stability

LWR are appicable in low noise frequency sources and low lossnarrow band filters with 3-dB bandwidth of up to about 3%.Both applications require compenstion of the thermal drift.LWRs typically exhibit a teperature coefficient of frequency(TCF) of about −23 ppm [15] which requires the developmentof a specific temeprature compensation scheme. Here wediscuss LWR toplogies with intrinsic zero first order TCF.In the proposed designs composite membranes consistingof reactively sputtered AlN and thermally grown SiO2 areused as a platform for the design of temperature-compensatedLWR since the two materials exhibit opposite TCF [38–40].A schematic view of a grating-type LWR employing such acomposite membrane is illustrated in figure 15.

The TCF of the S0 mode in such composite structures isreadily derived theoretically [38, 39] as illustrated in figure 16.Specifically, the TCF, defined as the relative frequency changeper 1 K of temperature variation, is shown as a function of the

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Figure 16. Temperature coefficient of frequency as a function of theSiO2 thickness for AlN plate of varying thicknesses relative to thewavelength (λ).

relative SiO2 layer thickness for different relative thicknessesof the AlN. It is noted that thicknesses are normalized withrespect to the acoustic wavelength (λ) at room temperature asdefined from the transducer grating pitch. The relative AlNthickness of interest lies in the range where the S0 modeexhibits low dispersion. In this specific range of AlN acousticthicknesses temperature compensation can be achieved withSiO2 of thicknesses smaller than that of the AlN. We also notethe wide applicability of the results obtained with respect tothe frequency of operation required. For a desired frequency ofoperation the optimal AlN/SiO2 combination is to be chosenamong the range of solutions shown in figure 16. From thosesolutions, the one that offers a reasonable trade-off betweenelectromechanical coupling and robustness of fabrication is tobe chosen.

Practical realizations of the proposed scheme weredemonstrated for both types of topologies. It was furtherobserved that the second order TCF2 tends to decreasewith the thickness of the composite membrane. Thus,compensated LWR demonstrated a second order TCF2 ofabout −31 ppb K−2 and −22 ppb K−2, when employingAlN thicknesses of d = 0.167λ [38] and d = 0.09λ [39],respectively (see figure 16). For comparison, the second orderTCF2 demonstrated is slightly larger than that for temperaturecompensated AlN FBAR (TCF2 = −20 ppb K−2) [41]but smaller than that for Rayleigh SAWs on ST-cut quartz(TCF2 = −34 ppb K−2) [42].

6. LWR as sensors

As discussed above, the LWR technology offers robust thermalcompensation along with low noise performance. Further, thespecific membrane configuration (see figure 2(a)) enablesphysical separation between the analyte and the transducerin e.g. biosensor applications. This feature is specificallyadvantageous when operation with liquid or aggressiveenvironments is required.

The specific advances regarding the use of the LWRplatform in sensing applications should be considered through

the possibility to achieve increased resolution as comparedto the other alternative micro-acoustic technologies, namelySAW and FBAR. The resolution R is represented by

R = 3σY (τ )min

S, (4)

where σ Y(τ )min is the minimum Allan deviation [43], whileS is the normalized sensitivity defined as the fractionalfrequency variation per unit increment of the measurand M(S = � f /( f ·�M)). Here, M denotes any physical quantitybeing measured, for instance mass, pressure, temperature, etc.

The theoretical limit of the LWR noise floor can beestimated by the Q factor through the empirical relationσ Y(τ )min = 10−7/Q [44]. Thus, a LWR with a Q factor ofabout 1000 could demonstrate a noise floor down to 10−10.Practically achievable noise floors are larger, i.e. in the rangeof 10−9 which makes the LWR technology comparable,in noise floor, to the commercially established SAW. Agood SAW sensor exhibits a short term stability of about5 × 10−9 s−1 [45]. Accordingly, a sufficient improvementover the state of art of the sensor resolution is most likely tobe achieved by improvements in sensitivity while preservingthe LWR low noise performance. Below we summarize thesensitivity performance of the LWR with respect to pressure,mass and liquid loadings, respectively.

6.1. LWR pressure sensors

The use of a high aspect ratio membrane itself promoteshigher stress levels in the membrane and thus an improvedsensitivity to pressure. Grating-type LWR configurationstypically employ about 2 μm thick AlN membrane with anarea of about 0.5 mm2. The pressure sensitivity can be furtherscaled by improving the aspect ratio of the membrane—eitherby reducing the membrane thickness or by increasing themembrane area. In comparison, the classical SAW resonantsensors have technologically imposed thickness limitations (inthe range down to few hundred μm) while the AlN membranesare typically up to 2 μm thick. Thus, the high aspect ratio inSAWs can be achieved for the expense of inconveniently largesensor areas.

The pressure sensitivity of micro-acoustic resonators isdetermined by the generated deformations and the stress-induced changes in elasticity. These factors determine specificchanges in resonant frequency due to either change inthe resonance cavity dimensions or change in the acousticwave velocity, respectively. The S0 mode has been provedto be more sensitive than all other plate modes in thin AlNmembrane since both factors are uniquely working in synergy[46]. The FBAR, unlike the LWR, is expected to have oppositecontributions from the strain and the stress-induced changesin elasticity, respectively, since ambient pressure induceseffective AlN thickness compression (i.e. frequency increase),while the elastic constants exhibit a relative softening (i.e.frequency decrease). This expectation was further confirmedby the measured lower sensitivity of the S1 mode (as comparedto S0) excited in the LWR [46]. It is further noted that S1 is amode originating from the fundamental thickness longitudinalresonance (i.e. the FBAR mode).

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Figure 17. LWR pressure sensitivity as a function of pressuredifferential.

This finding makes LWR a preferable choice whendeveloping a high resolution pressure sensor. It is also notedthat due to the low losses LWR as well as their SAW andBAW counterparts are well suited for low power wirelessinterrogation [47], thus making these devices preferable inremote sensing applications.

Figure 17 shows the pressure sensitivity of a 900 MHzS0 grating-type LWR as measured experimentally. The deviceis a synchronous LWR with a 12 μm wavelength employinga 2 μm thick AlN membrane having a 0.55 mm2 surface area[46]. The measured fractional sensitivity of the S0 mode isfound in excess of −6 ppm kPa−1. The LWR was measuredin pressure differentials of up to 160 kPa and have showna hysteresis-free performance with good linearity and nodegradation with time [46, 48].

6.2. LWR gravimetric sensors

The S0 Lamb wave platform appeared to be much more masssensitive as compared to its SAW and FBAR counterparts[49, 50]. A common way to estimate the mass sensitivity isthrough the relative frequency shift caused by mass loadingwith thin layers. Figure 18 shows the calculated magnitudeof the fractional frequency shifts as a function of therelative thickness h/λ of a mass-loading, glassy state polymerpp-HMDSO (plasma polymerized hexamethyl di-siloxane)for the four different cases, a S0 LRW and an FBAR bothemploying AlN membranes as well as the Love wave andSAW resonators both employing commercial AT cut Quartzsubstrates. In this specific calculation, the relative membranethickness d/λ for the S0 mode case is 0.166.

Evidently, the S0 mode demonstrates a considerablyhigher mass sensitivity as compared to the FBAR, RSAW andLove waves. This is explained by the fact that the S0 Lamb waveis typically confined in membranes with a smaller thickness towavelength ratio (d/λ ∼ 0.1–0.2) as compared to the classicalFBAR where d/λ = 0.5 and to the SAWs where the depth ofenergy confinement is in the range of one wavelength d/λ ∼1. Therefore, sensitivity can easily be scaled by varying themembrane thickness [51]. However, an increased sensitivitymay not necessarily be the best choice for a practical system.Generally, an improved mass sensitivity correlates with greater

Figure 18. Theoretical mass sensitivity of S0 Lamb wave, BAW,Love wave, SAW and Love wave. Although mass loading causes afrequency downshift, absolute values are presented to underline theincrease of sensitivity.

Figure 19. Experimental versus calculated LWR mass sensitivity asa function of the relative thickness h/λ of the HMDSO sensing layer.Layer losses are taken into account in the calculations throughcomplex elastic constants C = C′+i∗C′′.

susceptibility to losses induced by the viscosity of the sensinglayer [52]. This in turn deteriorates the noise performance andthus limits the sensor resolution. Figure 18 further suggests thatmass sensitivity of the S0 mode increases with the thickness ofthe sensing layer. This beneficial effect is in practice inhibitedby the viscosity of the sensing layer. At relatively thickersensing layers the S0 mode also exhibits an improved dampingwhich in turn results in LWR performance degradation in termsof losses and, hence, Q factor. Figure 19 shows the S0 modemass sensitivity taking into account the viscosity of the thinsensing layer. A very good agreement between theory andexperiment is demonstrated.

The gas sensitivity of a HMDSO-coated LWR towardxylene was measured and compared to that of RayleighSAW and Surface Transverse Wave (STW) Quartz resonatorscovered with the same sensing layer. The sensing mechanism

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Table 4. Sensitivity to xylene of HMDSO coated resonators.

Mode Frequency Sensitivity (Hz ppm−1)

SAW on Quartz 430 MHz 7.2 [53]STW on Quartz 700 MHz 9.1 [53]LWR on AlN 890 MHz 33 [49]

in this study is mass-loading caused by the adsorption of thegas molecules onto the HMDSO surface.

Table 4 summarizes the calculated mass sensitivities ofthe three types of resonators toward xylene. In order tocompare the sensitivity values to the theoretical estimates,the relative sensitivity toward xylene, defined as the ratioof the absolute sensitivity (in Hz/ppm) to the unloadedresonance frequency, was calculated for LRW, STW and SAW,respectively. These sensitivities were found to be in relation5.0/1.3/1.0 for LWR versus STW versus SAW, respectively,which is in good agreement with the theoretical expectations.

The results presented suggest that S0 mode resonatorsemploying acoustically thinner sensing films are preferable inorder to preserve the low noise and low loss performance ofthe sensor [49] while benefitting from the improved sensitivityof the LWR technology. Most generally, the design of agravimetric sensor employing the S0 Lamb wave in thin AlNmembranes is application specific. Resolution, exceeding thatof the other competing microacoustic technologies, is quitefeasible. The design of high resolution sensor requires anoptimal ratio between increased sensitivity and added noiseby both the viscosity of the sensing layer and the analyte [49].

6.3. LWR in-liquid sensors

In contact with a liquid, the S0 mode couples weakly tothe liquid due to its predominantly longitudinal polarizationparallel to the plate surface. A small coupling to the liquidis induced by the weak vertical shear component of theS0 mode and by the shear viscosity stress gradient which ismore pronounced in liquids with increased viscosity [54].The observed frequency shift is mostly due to changes in theelectric permittivity of the liquid and changes in the acousticimpedance of the liquid [48]. The S0 mode can be used ascomplementary to shear mode liquid sensors. Recently, a bio-chemical sensor employing the S0 Lamb wave in a thin GaNmembrane has been demonstrated showing weak susceptibilityto water and high mass sensitivity [55].

To further clarify the sensing mechanisms of LWRimmersed in a liquid, we used a frequency responsefinite element method analysis (COMSOL) to calculate theharmonic admittance of the LWR as a function of the dielectricand the acoustic loads caused by the liquid. The resultsobtained are then used to explain the experimental observationsas follows.

Figures 20(a), (b) show the harmonic admittance ofa LWR unit cell (an IDT pair of electrodes with appliedperiodic boundary conditions) calculated by means ofCOMSOL multiphysics FEM frequency response analysis.Three physical modules, namely the piezoelectric strainmodule, the acoustic-structure interaction module and the

(a )

(b)

Figure 20. COMSOL FEM simulations. (a) Acoustic loading.(b) Electric loading.

quasi-static electric module, are simultaneously used in acomplementary manner to describe the phenomena involved.The first module is used to describe the excitation of a12 μm wavelength S0 mode in 2 μm thick AlN membraneand is further coupled to the other two modules to describeacoustic and electric couplings to the liquid. At the bottomend in the liquid domain, an absorbing perfectly matchedlayer (PML) is added. The electrical condition at the bottommembrane surface is assumed to be that of an open electricalcircuit. The liquid in this simulation is represented by itsdensity, acoustic wave velocity, bulk viscosity and dielectricpermittivity. Figure 20(a) presents the effect of the acousticloading by the liquid. The harmonic admittances are calculatedassuming outside media having the dielectric permittivity ofthe water. The acoustic loading is simulated by coupling anddecoupling the fluid–structure interaction module. It is seenthat the admittance amplitude decreases significantly withthe loading while the resonance frequency remains almostunaffected. The observed behavior is due to the acousticradiation in liquid. This effect is further demonstrated infigure 20(a) in terms of square root of the pressure. It isfurther noted that the square root of pressure is plotted inorder to make the weak acoustic radiation in the liquid domainvisible as compared to the acoustic field in the solid domain.The acoustic pressure in the solid domain (the AlN plate)

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Figure 21. FPAR in-liquid performance.

is represented by the negative S0 mean stress. Figure 20(b)presents the effect of electrical loading by varying the dielectricpermittivity of the liquid while the liquid acoustic propertiesare considered identical to those of water. An increase of theresonance frequency with dielectric permittivity is observedwhile the amplitude of the response slightly drops. The latteris associated with the effective decrease of electromechanicalcoupling to the S0 mode since a significant part of the electricenergy penetrates in to the liquid and does not contributeto wave excitation. By the same token, initial increase ofthe dielectric permittivity above the vacuum level causes animprovement in the vertical alignment of the electric field,which in turn promotes higher electromechanical couplingthrough the e31 piezoelectric coefficient.

A 12 μm wavelength LWR, identical to the one usedin the pressure sensitivity study, in contact with liquid bydispensing a droplet on the membrane backside has beencharacterized with a network analyzer [48]. The measurementsindicate that the S0 mode has a performance comparable tothat of the state of the art FBAR bio-sensors [56]. Figure 21shows the measured S0-mode LWR responses, demonstratingQ-values of 1700 (in air), 150 (in water) and 70 (in 50%glycerol water solution), respectively. An initial 9.2 MHz(from air to water) and an additional 1.3 MHz (from waterto 50% glycerol solution) frequency shifts were observed.Further, the FPAR static capacitance increases by about40% due to the dielectric permittivity of the water. Thelarge frequency downshift between air and water is primarilydue to the large dielectric permittivity of water, while thecontribution of the acoustic loading remains negligibly small.The acoustic loading in this case is mostly manifested bythe moderate decrease of the LWR Q factor. The responseof the LWR immersed in 50% glycerol solution is affected bythe relative decrease of the liquid permittivity and the increaseof the liquid acoustic impedance along with its viscosity.Using the developed COMSOL-multiphysics model, we haveestimated theoretically that the decrease of the dielectricpermittivity causes about −840 ppm frequency shift, whilethe change in the acoustic impedance causes about −360 ppmfrequency shift. Thus, the total frequency shift is expectedto be about −1200 ppm. Experimentally we have observed afrequency shift of about −1485 ppm which is in very good

agreement with the theoretical prediction. The subsequentdecrease of the Q factor is explained by the improved acousticcoupling to the fluid due to increase of both the acousticimpedance and the viscosity of the fluid.

In summary, the LWR technology is sensitive to both themechanical and the dielectric properties of the liquid. An LWRdesign with metalized bottom side of the membrane wouldelectrically isolate the LWR from the liquid (making the devicesensitive to the liquid mechanical properties only) as well asfurther improving the electromechanical coupling, resultingin higher in-liquid performance. Thus, LWR designs with Aubackside metallization seem to be a promising candidate forbiosensor applications.

7. Conclusions

In summary, the LWR technology has demonstrated a numberof unique features stemming from the nature of the S0 Lambwave propagating in silicon micromachined AlN membranes.These are as follows:

• technologically compatible with IC;• very high velocity at low dispersion;• moderate electromechanical coupling �3%;• low loss and low noise performance;• robust first order temperature compensation with a low

second order temperature coefficient of frequency;• highly sensitive to mass and pressure. Sensitivity is

inversely proportional to the membrane thickness;• able to operate in liquids, highly sensitive to liquid

permittivity.

LWR technology continues to develop simultaneouslyin several directions. The AlN/Si LWR platform is furtherdeveloped employing AlN/SiC composite membranes aimingat increasing the device Q [57, 58]. Other Lamb waves andprinciples of energy confinement are under investigation.Recently LWR employing other principles than reflectionwere demonstrated in proof of concept studies [59, 60]. Morespecifically, these include the employment of the zero groupvelocity characteristic of the S1 Lamb wave as well as theconversion of the S0 mode into the fundamental thickness shearplate resonance. Further, new piezoelectric thin films [61] withincreased piezoelectricity and retained mechanical qualityare being employed toward boosting the electromechanicalcoupling and thus the bandwidths of the LWR-based filters.Promising materials candidates are the Sc doped AlN films,and LiNbO3 thin plates released by means of smart cuttechnology.

Acknowledgments

This work was supported by the Swedish Research Council(VR) through the Forskarassistent grant ‘Thin Film GuidedMicroacoustic Waves in Periodical Systems: Theory andApplications’.

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References

[1] Bjurstrom J, Katardjiev I and Yantchev V 2005Lateral-field-excited thin film Lamb wave resonatorAppl. Phys. Lett. 86 154103

[2] Kadota M, Ago J, Horiuchi H and Ikeura M 2002 Very smallIF resonator filters using reflection of shear horizontal waveat free edges of substrate IEEE Trans. Ultrason. Ferroelectr.Freq. Control 49 1269–79

[3] Harrington B P and Abdolvand R 2011 In-plane acousticreflectors for reducing effective anchor loss inlateral–extensional MEMS resonators J. Micromech.Microeng. 21 085021

[4] Stephanou P and Pisano A 2006 GHz contour extensionalmode aluminum nitride MEMS resonators Proc. IEEE Int.Ultrason. Symp. pp 2401–4

[5] Benetti M, Cannata D, Di Pietrantonio F and Verona E 2007Guided Lamb waves in AlN free strips Proc. 2007 IEEE Int.Ultrasonics Symp. pp 1673–6

[6] Adler E 1990 Matrix methods applied to acoustic waves inmultilayers IEEE Trans. Ultrason. Ferroelectr. Freq.Control 37 485–90

[7] Joshi S and Jin Y 1991 Excitation of ultrasonic Lamb waves inpiezoelectric plates J. Appl. Phys. 69 8018–24

[8] Yantchev V and Katardjiev I 2006 Quasistatic transduction ofthe fundamental symmetric Lamb mode in longitudinalwave transducers Appl. Phys. Lett. 88 214101

[9] Yantchev V 2009 Zero mass loading sensitivity of the S0 lambwave resonance in thin film plate acoustic resonators(FPAR) Proc. 2009 Int. IEEE Ultrasonic Symp. pp 2181–4

[10] Lin C-M, Yantchev V, Chen Y-Y, Felmetsger V and Pisano A2011 Characteristics of AlN Lamb wave resonators withvarious bottom electrode configurations Proc. IEEE Int.Freq. Control Symp. 505–9

[11] Zuo C, Van der Spiegel J and Piazza G 2010 1.05 GHz CMOSoscillator based on lateral-field-excited piezoelectric AlNcontour-mode MEMS resonators IEEE Trans. Ultrason.Ferroelectr. Freq. Control 57 82–7

[12] Lin C-M, Lai Y-J, Hsu J-C, Chen Y-Y, Senesky D Gand Pisano A P 2011 High-Q aluminum nitride Lamb waveresonators with biconvex edges Appl. Phys. Lett. 99 143501

[13] Yantchev V and Katardjiev I 2007 Micromachined thin filmplate acoustic resonators utilizing the lowest ordersymmetric lamb wave mode IEEE Trans. Ultrason.Ferroelectr. Freq. Control 54 87–95

[14] Yantchev V, Arapan L and Katardjiev I 2009 Micromachinedthin film plate acoustic wave resonators (FPAR): part IIIEEE Trans. Ultrason. Ferroelectr. Freq. Control56 2701–10

[15] Rinaldi M, Zuniga C and Piazza G 2009 5–10 GHz AlNcontour-mode nanoelectromechanical resonators Proc. 2009IEEE MEMS Conf. pp 916–9

[16] Zuo C, Sinha N, Van der Spiegel J and Piazza G 2010Multifrequency pierce oscillators based on piezoelectricAlN contour-mode MEMS technologyJ. Microelectromech. Syst. 19 570–80

[17] Avramov I, Walls F, Parker T and Montress G 1996 Extremelylow thermal noise floor, high power oscillators usingsurface transverse wave devices IEEE Trans. Ultrason.Ferroelectr. Freq. Control 43 20–9

[18] Morgan D P 2004 Idealized analysis of SAW longitudinallycoupled resonator filters IEEE Trans. Ultrason. Ferroelectr.Freq. Control 51 1165–70

[19] Joshi S, Zaitsev B and Kuznetsova I 2002 Reflection of plateacoustic waves produced by a periodic array of mechanicalload strips or grooves IEEE Trans. Ultrason., Ferroelect.,Freq. Control 49 1730–4

[20] Yantchev V and Katardjiev I 2005 Propagation characteristicsof the fundamental symmetric lamb wave in thin aluminum

nitride membranes with infinite gratings J. Appl. Phys.98 084910

[21] Kuypers J and Pisano A 2009 Interpolation techniques for fastanalysis of surface acoustic wave and lamb wave devicesJapan. J. Appl. Phys. 48 07GG07

[22] Chen Y-Y 2009 Exact analysis of Lamb waves in piezoelectricmembranes with distinct electrode arrangements Japan. J.Appl. Phys. 48 07GA06

[23] Yantchev V 2010 Coupling-of-modes analysis of thin filmplate acoustic wave resonators utilizing the S0 lamb modeIEEE Trans. Ultrason. Ferroelectr. Freq. Control 57 801–7

[24] Chen D P and Haus H A 1985 Analysis of metal-strip SAWgratings and transducers IEEE Trans. Ultrason. Ferroelectr.Freq. Control SU-32 395–408

[25] Plessky V and Koskela J 2001 Advances in Surface AcousticWave Technology, Systems and Applications 2 (Singapore:World Scientific) pp 1–82

[26] Iriarte G, Engelmark F, Katardjiev I, Plessky Vand Yantchev V 2003 SAW COM-parameter extraction inAlN/Diamond layered structures IEEE Trans. Ultrason.Ferroelectr. Freq. Control 50 1542–7

[27] Volatier A, Caruyer G, Pellissier Tanon D, Ancey P, Defay Eand Dubus B 2005 UHF/VHF resonators using Lamb wavesco-integrated with bulk acoustic wave resonatorsProc. 2005 IEEE Int. Ultrasonics Symp. pp 902–5

[28] Piazza G, Stephanou P and Pisano A 2006 Piezoelectricaluminum nitride vibrating contour-mode MEMSresonators J. Microelectromech. Syst. 15 1406–18

[29] Wagner K, Mayer M, Bergmann A and Riha G A 2006 2DP-matrix model for the simulation of waveguiding anddiffraction in SAW components Proc. 2006 IEEE Int.Ultrasonics Symp. pp 380–8

[30] Rinaldi M, Zuo C, Van der Spiegel J and Piazza G 2011Reconfigurable CMOS oscillator based on multifrequencyAlN contour-mode MEMS resonators IEEE Trans.Electron. Dev. 58 1281–6

[31] Tazzoli A, Rinaldi M and Piazza G Ultra-high-frequencytemperature-compensated oscillators based on ovenizedAlN contour-mode MEMS resonators Proc. 2011 Int.Electron Devices Meeting (IEDM) pp 20.2.1–2.4

[32] Avramov I, Arapan L, Katardjiev I, Strashilov Vand Yantchev V 2009 IC-compatible power oscillatorsusing thin film plate acoustic resonators (FPAR) Proc. 2009Int. IEEE Ultrasonic Symp. pp 20–3

[33] Rhea R W 2000 Oscillator Design and Computer Simulation(Atlanta, GA: Noble Publishing Cooperation) p 113

[34] Bjurstrom J, Yantchev V and Katardjiev I 2006 Thin film lambwave resonant structures—the first approach Solid StateElectron. 50 322–6

[35] Rinaldi M, Tazzoli A, Segovia-Fernandez J, Felmetsger Vand Piazza G 2012 High power and low temperaturecoefficient of frequency oscillator based on a fully anchoredand oxide compensated AlN contour-mode MEMSresonator Tech. Dig. IEEE Int. Conf. Micro Electro Mech.Syst. pp 696–9

[36] Arapan L, Avramov I and Yantchev V 2011 Thin film plateacoustic resonators for integrated microwave poweroscillator applications Electron. Lett. 47 453–4

[37] Shreve W, Bray R, Elliot S and Chu Y 1981 Powerdependence of aging in SAW resonator Proc. 1981 Int.IEEE Ultrason. Symp. pp 94–9

[38] Wingqvist G, Arapan L, Yantchev V and Katardjiev I 2009 AMicromachined thermally compensated thin film Lambwave resonator for frequency control and sensingapplications J. Micromech. Microeng. 19 035018

[39] Lin C-M, Yen T-T, Lai Y-J, Felmetsger V, Hopcroft M,Kuypers J and Pisano A 2010 Temperature compensatedaluminum nitride Lamb wave resonators IEEE Trans.Ultrason. Ferroelectr. Freq. Control 57 524–32

13

J. Micromech. Microeng. 23 (2013) 043001 Topical Review

[40] Lin C-M, Yen T-T, Felmetsger V, Hopcroft M, Kuypers Jand Pisano A 2010 Thermally compensated aluminumnitride lamb wave resonators for high temperatureapplications Appl. Phys. Lett. 97 083501

[41] Pang W, Ruby R C, Parker R, Fisher P W, Larson J D,Grannen K J, Lee D, Feng C and Callaghan L 2007 Athermally stable CMOS oscillator using temperaturecompensated FBAR Proc 2007 IEEE Ultrasonics Symp.pp 1041–4

[42] Lam C S 2010 A review of the recent development oftemperature stable cuts of quartz for SAW applicationsEpson Application Notes and White Papers (San Jose, CA:Epson) www.eea.epson.com/portal/page/portal/home/TimingDevicesTechnicalPapers

[43] IEEE standard definitions of physical quantities forfundamental frequency and time metrology 1999 RandomInstabilities IEEE Std. 1139, July

[44] Vig J and Walls F 2000 A review of sensor sensitivity andstability Proc. 2000 Int. IEEE Freq. Control Symp. pp 30–3

[45] Avramov I, Kurosawa S, Rapp M, Krawczak P and Radeva E2001 Investigations on plasma polymer coated SAW andSTW resonators for chemical gas sensing applications IEEETrans. Microw. Theory Tech. 49 827–37

[46] Anderas E, Katardjiev I and Yantchev V 2011 Lamb waveresonant pressure micro-sensor utilizing a thin-filmaluminum nitride membrane J. Micromech. Microeng.21 085010

[47] Friedt J, Droit C, Martin G and Ballandras S 2010 A wirelessinterrogation system exploiting narrowband acousticresonator for remote physical quantity measurementRev. Sci. Instrum. 81 014701

[48] Arapan L, Anderas E, Katardjiev I and Yantchev V 2011Sensitivity features of thin film plate acoustic waveresonators IEEE Sens. J. 11 3330–1

[49] Arapan L, Alexieva G, Avramov I, Radeva E, Strashilov V,Katardjiev I and Yantchev V 2011 Highly mass-sensitivethin film plate acoustic resonators (FPAR) Sensors11 6942–53

[50] Rinaldi M, Zuniga C, Nipun S, Taheri M, Piazza G, Khamis Sand Johnson A 2008 Gravimetric chemical sensor based on

the direct integration of SWNT on AlN contour modeMEMS resonators Proc. 2008 IEEE Freq. Control Symp.pp 443–8

[51] Piazza G, Rinaldi M and Zuniga C 2010 Nanoscaledpiezoelectric aluminum nitride contour-mode resonantsensors Proc. IEEE Sensors Conf. pp 2202–7

[52] Yantchev V, Strashilov V, Rapp M, Stahl U and Avramov I2002 Theoretical and experimental mass-sensitivityanalysis of polymer-coated SAW and STW resonators forgas sensing applications IEEE Sens. J. 2 307–13

[53] Avramov I, Rapp M, Kurosawa S, Krawczak P and Radeva E2002 Gas sensitivity comparison of polymer coated SAWand STW resonators operating at the same acoustic wavelength IEEE Sens. J. 2 150–9

[54] Zaitsev B, Kuznetsova I and Joshi S 1997 Propagation ofacoustic waves in plates bordered with viscous load Proc.1997 Int. IEEE Ultrason. Symp. pp 381–4

[55] Lu X, Lee C M, Wu S Y, Ho A and Lau K M 2013GaN-based S0-wave sensors on Silicon for chemical andbiological sensing in liquid environments IEEE Sens. J.13 1245–51

[56] Katardjiev I and Yantchev V 2012 Recent developments inthin film electro-acoustic technology for biosensorapplications Vacuum 86 520–31

[57] Lin C-M, Chen Y-Y, Felmetsger V, Senesky D and Pisano A2012 AlN/3C–SiC composite plate enabling high-frequencyand high-Q micromechanical resonators Adv. Mater.24 2722–7

[58] Lin C-M, Chen Y-Y and Pisano A 2010 Theoreticalinvestigation of Lamb wave characteristics in AlN/3C–SiCcomposite membranes Appl. Phys. Lett. 97 193506

[59] Yantchev V, Arapan L, Katardjiev I and Plessky V 2011Thin-film zerogroup- velocity lamb wave resonatorAppl. Phys. Lett. 99 033505

[60] Arapan L, Katardjiev I and Yantchev V 2012 Anintermode-coupled thin-film micro-acoustic resonatorJ. Micromech. Microeng. 22 085004

[61] Moreira M, Bjurstrom J, Katardjev I and Yantchev V 2011Aluminum scandium nitride thin-film bulk acousticresonators for wide band applications Vacuum 86 23–6

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