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Sensors and Actuators A 206 (2014) 42– 50

Contents lists available at ScienceDirect

Sensors and Actuators A: Physical

jo u r n al homep age: www.elsev ier .com/ locate /sna

podization technique for spurious mode suppression in AlNontour-mode resonators

arco Giovannini, Serkan Yazici, Nai-Kuei Kuo, Gianluca Piazza ∗

arnegie Mellon University, United States

r t i c l e i n f o

rticle history:eceived 31 December 2012eceived in revised form0 November 2013ccepted 20 November 2013vailable online 3 December 2013

a b s t r a c t

This paper reports on the application of apodization techniques to 900 MHz–1 GHz MEMS AlN Contour-Mode Resonators (CMRs [1–6]) to efficiently suppress spurious modes in close proximity of the mainmechanical resonance. This concept has been applied with excellent results to a variety of one portresonators formed by patterned top electrodes made out of aluminum, and a floating bottom electrodemade out of platinum sandwiching the AlN film. As also predicted by 3D COMSOL analysis, a completeelimination of the spurious responses (>90% suppression) is attained without significantly impacting the

eywords:luminum nitrideesonatorEMS

quality factor, Q, and electromechanical coupling coefficient, k2t , of the device. On average, the Q improves

except for resonators with thick (220 nm) top electrodes for which <11% degradation in Q is recorded.The k2

t reduction is <20% and it has an absolute value > 1% for all designs.© 2013 Elsevier B.V. All rights reserved.

podizationpurious modes

. Introduction

The presence of spurious modes in the response of micromech-nical resonators hinders the performance of acoustic filters [7–10]y generating ripples in the pass-band and unwanted responsesut-of-band. Additionally, in most micromechanical resonators thebility to set the device impedance by changing its geometry isimited by the appearance of spurious modes for certain devicespect ratios. Although some methods to suppress out-of-bandpurious modes by means of anchoring techniques [11,12], or thentroduction of dummy electrodes [13] have been implemented,he problem of in-band spurious suppression for aluminum nitrideontour mode resonators (CMRs), an emerging class of high fre-uency resonators [1], has never been addressed.

This paper introduces the concept of apodization for AlN MEMSesonators (Figs. 1 and 2) — a new method to shape the geometry ofhe electrodes to obtain a consistent reduction of spurious modes inhe electrical response of one port CMRs. The concept of apodizationonsists of confining the vibration energy in specific regions of theMR body by shaping its electrodes. This technique helps suppressransversal spurious modes as it modifies the shape of the acousticeam in a direction orthogonal to the direction of propagation of

he main mode.

Apodization techniques were first introduced with surfacecoustic wave (SAW) transducers in order to improve the

∗ Corresponding author. Tel.: +1 412 268 7762.E-mail address: piazza@ece.cmu.edu (G. Piazza).

924-4247/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.sna.2013.11.023

sampling of the signal coming from an unapodized SAW device[16]. This technique is the most widely used method for weight-ing the response of a SAW transducer and exclusively picking upthe desired mode of vibration [17]. It relies on properly varyingthe shape of the electrodes so that the sampled electrical signal isproperly weighted (Fig. 3) by a prescribed window (sampling) func-tion. This technique simultaneously suppresses transversal modespropagating in a direction orthogonal to the main mode of vibration[17].

Two apodization techniques were studied and applied to oneport CMRs formed by patterned top electrodes (25, 33, 49 and 65fingers) made out of aluminum (120 nm thick), and a floating bot-tom electrode made out of platinum (90 nm thick) sandwichingthe AlN film (500 nm and 1 �m thick) (see Fig. 1). This concept wasapplied to a variety of one port CMRs having different aspect ratiosto prove its effectiveness and repeatability. Each solution has beendesigned, simulated, and fabricated. The paper first describes thegeneral concept of apodization for mode selection, then it focuseson the design of the apodized CMRs and introduces the finiteelement analysis used to provide evidence of spurious mode sup-pression. Finally, experimental results showing the performance ofthe apodization techniques are presented and discussed.

2. Apodization theory

Apodization techniques, conventionally developed for surfaceacoustic wave (SAW) transducers, have been adopted for CMRs inorder to excite their main mode of vibration and suppress undesiredspurious vibrations. SAW transducers and CMRs use interdigitated

M. Giovannini et al. / Sensors and Actuators A 206 (2014) 42– 50 43

Fig. 1. Schematic representation of the finger pair forming the basic element of a lat-eral field excited CMR. The color gradient in the AlN body represents the magnitudeof displacement.

etdif

adsurgttttss

FeTt(i

Fig. 2. Apodization: shape I (a), shape II (b).

lectrodes and their geometries resemble the Fourier transform ofhe truncated impulse response. The similarity might be more evi-ent if we compare the classical SAW delay line filter (formed by

nput and output interdigitated transducers) to the same structureormed by the AlN MEMS transducers [18].

Although the CMR does not excite a surface acoustic wave, but lamb wave, the same concept of apodization introduced for SAWevices can be implemented. As it will be shown in the followingection by finite element analysis (FEA), apodization can also besed to suppress transversal vibrations that cause undesired spu-ious vibrations in standard, unweighted CMRs. In this section, theeneral concept of apodization is introduced and shown to be ableo effectively couple energy into the main mode of vibration despitehe reduction in the overlap of adjacent electrode pairs. As apodiza-ion modifies the acoustic beam profile in a direction orthogonal to

he direction of propagation of the main acoustic wave, transver-al modes are affected and can be eliminated. The suppression ofpurious modes is better captured by a 3D model. This effect is

ig. 3. Schematic representation of the apodization technique for interdigitatedlectrodes and the equivalent impulse response (in red) of the overall transducer.he time domain response of the transducer can be mapped into space and showno be equivalent to the strain field distribution determined by electrode pair overlappeaks and thoroughs of h(t)) [14,16]. (For interpretation of the references to colorn figure legend, the reader is referred to the web version of the article.)

Fig. 4. Schematic representation of a 13 finger CMR, its impulse response and theassociated vector that maps such response in space.

studied by FEA in section III. In analogy with SAW devices, this anal-ysis shows that apodization enables the suppression of transversalspurious modes without impacting the excitation of the main modeof vibration.

As for SAW devices, the electric field in CMRs is applied to theAlN body through a set of interdigitated electrodes (also known asfingers). Hence, shaping of the CMR fingers permits to accuratelyweigh the electric field distribution that is applied to the CMR.

Effectively, the apodization concept consists of finding a methodto shape the electrodes so that the applied electric field excitesexclusively the main vibration mode of interest. Apodization tech-niques are based on the idea that there exists a relationshipbetween the impulse response of the piezoelectrically generatedacoustic waveform, the electrodes geometry and its frequencyresponse [14]. Because of the nature of the piezoelectric actua-tion, the device impulse response is seen as a sequence of Diracfunctions at times that can be mapped to the electrode locations,and with amplitudes proportional to the electrode overlap length,a (Fig. 3). The idea of apodization consists of placing the electrodesat the locations that correspond to the peaks and thorough of theimpulse response waveform, and shaping their overlap to exciteexclusively the main mode of vibration. This means that the elec-trode overlap, a, needs to be maximized at those locations wherethe strain amplitude is maximum, and shaped to follow the desiredtime response.

For the standard CMR device, the electrodes are completelyoverlapped throughout the structure, hence its impulse responseis formed by Dirac functions of constant amplitude. For example,the specific case of a 13 fingers one port CMR is shown in Fig. 4.The electrode layout is identified by a vector formed exclusively byzeros and ones. The number 1, positive or negative, represents thefact that the electrode (signal or ground) extends over the entirelength of the device. The + or − sign is used to establish whetherthe electrode is a signal or ground electrode, and effectively rep-resent a 180◦ phase difference between adjacent electrodes. Azero represents that no electrode is present in that specific region(generally in between electrode pairs). As it is done for SAW trans-ducers, we can assume that this spatial distribution maps to thetime domain impulse response of the resonator. The transducer fre-quency response can be found by a Fourier transform of this samevector (Fig. 5).

It is evident that the frequency response of the standard CMRdevice is characterized by a main lobe (corresponding to the devicecenter frequency), and a set of smaller adjacent lobes.

In the case of the apodized CMR structure, the vector represent-ing the device impulse response is rewritten to follow the shape of

the sampling function.

For example, in the case of the same 13 fingers CMR device, a sinefunction could be used to implement the concept of apodization.The vector representing the spatial distribution of the sampling

44 M. Giovannini et al. / Sensors and Actuators A 206 (2014) 42– 50

Fts

ftiotCt

v

sittiaodvrSlpnc

Fo

Fig. 7. The frequency response obtained by Fourier transform of the vector

finement of the electric field over the body of the resonator isattained.

ig. 5. Frequency response for a standard and apodized 13 fingers CMR. The ampli-ude values have been normalized to more clearly highlight the difference in theecondary lobes.

unction is found by making the total device width proportionalo half period of a sine wave, which is then divided into 14 parts ofdentical width (Fig. 6). For each one of these parts, the electrodeverlap is designed to be proportional to the value of the sine func-ion at that point in space. Therefore, for an apodized 13 fingersMR that uses the sine sampling function, the vector representinghe impulse response is given by:

apodized = [ 0 −0.22 0 0.43 0 −0.6 0 0.78 · · · ] (1)

The frequency response associated with this specific vector ishown in Fig. 5. In this figure the response of the apodized devices compared to the standard CMR. It is clear that the response ofhe apodized CMR is characterized by a main lobe centered aroundhe resonance frequency and out-of-band lobes that are smallern magnitude than in the standard CMR case. This implies thatn apodized transducer excites very effectively the main modef vibration. The reduction of the secondary lobe is seen as aemonstration that more energy is focused in the main mode ofibration. It is important to note that the plots in Fig. 6 only rep-esent the ideal Fourier transform of the impulse response of aAW/MEMS transducer and do not contain any information aboutoss or damping in the device. Hence, the widening of the main

eak in the apodized case with respect to the standard device isot related to losses in the device. The width of the peak is mostlyontrolled by the number of fingers forming the device and should

ig. 6. Schematic illustration of the sine shape sampling window. The maximumverlap (a) is placed in the middle of the CMR.

representing the transducer impulse response for standard CMR transducers char-acterized by 13, 49, and65 fingers.

not be used to compare the intrinsic quality factor of transduc-ers.

To highlight the impact of the number of fingers on the con-cept of apodization, the same procedure was repeated for deviceshaving 49 and 65 electrodes. Figs. 7 and 8 show the frequencyresponse for standard and apodized transducers having a numberof electrodes varying between 13 and 65. The magnitude of theFourier transforms have been normalized to 1 in order to bettershow the reduction of the side lobes that is attained via apodiza-tion. Fig. 8 clearly highlights that apodization is more effective asthe number of fingers increases. This is intuitive as a better con-

Fig. 8. The frequency response obtained by Fourier transform of the vectorrepresenting the transducer impulse response for apodized CMR transducers char-acterized by 13, 49, and 65 fingers.

M. Giovannini et al. / Sensors and Actuators A 206 (2014) 42– 50 45

Fw

3

ga

Ficva

ig. 9. (a) Plot of ½ of the finger overlap magnitude (in �m) for the ideal sine shapeindow and the selected Apodization Shape I. (b) Layout view of the apodized CMR.

. Apodized resonator design

The design of the apodized resonators is driven by the followinguidelines: (i) operate at a center frequency around 1 GHz, (ii) attain

value of device static capacitance, C0, as compatible as possible

ig. 11. Results of COMSOL simulations for (a) a standard and (b) apodized resonatorn correspondence of the spurious frequency. Graphs are referred to resonators operatiharacterized by 33 fingers of 2 �m of width and by a finger length of 38 �m. Application oibrations at 1004 MHz, therefore suppressing the undesired spurious mode. Only the disffects the resonator output current. The displacement in x was two orders of magnitude

Fig. 10. Schematic representation of the resonator used to highlight the boundaryconditions used in the COMSOL 3D FEA.

with 50 � circuits; (iii) achieve quality factor, Q, higher than 1000in air and electromechanical coupling coefficient, k2

t , higher than1%.

The overall finger width (electroded + unelectroded area) (Fig. 1)is determined by the frequency of operation. An electrode pitch of4 �m was used to operate around 1 GHz for the 1 �m AlN film andthe given metal stack. Because of metal loading frequency below1 GHz were attained with 500 nm thick AlN films (∼900 MHz). Theremainder of the device geometry is set by the number of electrode

pairs and their lengths. Finger lengths ranging between 40 �m and85 �m, and a number of fingers between 25 and 65 were selectedto yield device capacitances between 100 fF and 1000 fF. In this way

(with shape I), showing the equivalent admittance, and the in-plane vibrationsng around 1 GHz and formed by 1 �m of AlN, 120 nm of Al and 90 nm of Pt, andf apodization techniques allows decreasing of one order of magnitude the in-planeplacement in the y direction is shown as it has the largest magnitude and directly

smaller and does not directly impact the resonator response.

46 M. Giovannini et al. / Sensors and Actuators A 206 (2014) 42– 50

Fw

ts

otavgowto

FanIi

asasTctlatfwsssiwpcdettt

Fig. 13. COMSOL FEA for a 970 MHz AlN resonator (formed by 1000 nm of AlN,120 nm of Al and 90 nm of Pt) and composed of 33 fingers (finger length of

The two presented apodization shapes were studied and appliedto one port resonators formed by patterned top electrodes (25, 33,49 and 65 fingers) made out of aluminum (120 nm and 200 nmthick), and a floating bottom electrode made out of platinum (90 nm

ig. 12. (a) Plot of ½ of the finger overlap magnitude (in �m) for the ideal sine shapeindow and the selected Apodization Shape II. (b) Layout view of the apodized CMR.

he devices could be interfaced with 50 � circuits, with the largertatic capacitance offering a closer match.

To obtain CMRs characterized by optimal performance in termsf Q and k2

t , the basic geometry of the apodized devices was kepthe same of the standard resonators. To implement the concept ofpodization, the electrode overlap of the CMRs was shaped, amongarious available window functions, as a sine function. With theoal of maximizing the device electromechanical coupling, the lay-ut of the electrode overlap slightly deviated from a perfect sineave function. The length of the overlap for the electrodes at the

wo ends of the CMR was increased, whereas the length of theverlap for the central fingers was reduced (Fig. 9).

The rationale for this selection was confirmed by COMSOL 3DEA, which shows that transversal spurious mode suppression isttained without significantly impacting the series resonance mag-itude. The optimization of this sampling function (named shape

in this paper), was attained by an empirical approach based onntuition and COMSOL 3D analysis.

The 3D FEA was essential in verifying the use of the concept ofpodization explained in the previous section for spurious modeuppression. This analysis validates the analogy with SAW devicesnd justifies the use of apodization for the suppression of transver-al spurious modes without impacting the main mode of vibration.he COMSOL FEA consisted of a frequency domain analysisonducted in the structural mechanics module. The analysis modelshe piezoelectric effect in the AlN film and derives the equiva-ent device admittance by sweeping the resonator response over

set of prescribed frequencies. The frequency response was moni-ored for frequencies 25 MHz above and below the resonator centerrequency. Specific mechanical and electrical boundary conditionsere imposed. For example, in the geometry of Fig. 10 the two

ides of the anchors through which the CMR is connected to theupporting silicon are constrained to be fixed, while the remainingurfaces are set to be free. Half of the top electrode fingers weremposed a 1 V signal whereas the other half (alternating electrode)

as grounded. The bottom Pt electrode was set to have a floatingotential. The device was meshed using a free tetrahedral mesh,haracterized by different density of the elements depending on theirection of the 3D model. This was done to have a higher number oflements available along the direction of propagation of the acous-

ic wave and in the in plane direction transversal to it. The reason forhis choice is motivated by the fact that the transversal direction ishe one of interest in regards to suppression of spurious vibrations.

60 �m–note sample name 3360 representing the finger number and length). Thefigure shows the comparison between the admittance plot of standard and apodized(shape I and II) CMRs.

The results of the FEA performed in COMSOL for a specific res-onator geometry are shown in Fig. 11. The apodized device exhibitsspurious vibrations characterized by a displacement that is approx-imately one order of magnitude lower than the standard device, asseen in the color scale of each plot. The maximum vibration is onthe order of 0.1 �m for the standard device and 0.02 �m for theapodized one. It is also evident that the y displacement is morehomogeneous and focused in the central region of the fingers inthe apodized device, whereas it goes through maxima and minimaalong the transversal direction, x, (transversal spurious vibration)for the standard resonator.

With the purpose of further improving the device electricalresponse, a second apodized shape (shape II) was also studied theo-retically and experimentally (Figs. 2 and 12). In shape II, the lengthof the electrode overlap toward the two ends of the resonator isfurther increased and made constant for the last group of fingers.The overall electrode layout is similar to shape I, except for the endparts (Fig. 12).

Although intuitively this design should strengthen the resonatorresponse at the series resonance (higher electromechanical cou-pling), both shapes (shape I and shape II) show a similar behaviorwhen modeled with COMSOL FEA (Fig. 13).

4. Fabrication

Fig. 14. Representation of the 3 mask fabrication process used for the making ofthe apodized resonator: (a) sputtering and patterning by lift-off of the bottom elec-trode and sputtering of the thin AlN film; (b) deposition and patterning of the topelectrode; (c) etching of AlN; (d) release of AlN resonator in XeF2 atmosphere.

M. Giovannini et al. / Sensors and Actuators A 206 (2014) 42– 50 47

al colors, and (b) false colors in order to highlight the apodized shape (shape I).

tpwir

5

astdoi

i

-

TSaopcve

�

Fig. 15. Scanning electron micrograph of an apodized CMR, (a) with origin

hick) sandwiching the AlN film (500 nm and 1 �m thick). For com-arison, the same identical geometries were laid out and fabricatedithout apodization (standard resonator). The device fabrication

s based on a standard 3-mask manufacturing process previouslyeported for AlN CMRs [15] and schematically shown here in Fig. 14.

. Experimental results

The fabricated devices (example shown in Fig. 15) were tested in micromanipulated RF probe station under ambient conditions. Ahort open and load calibration was performed prior to measuringhe devices and extracting their admittance response. The apodizedevice response is compared to standard CMR devices. An examplef such comparison for a specific device formed by 1 �m thick AlNs shown in Fig. 16.

A total of 84 different resonator geometries were tested. Specif-

cally, the following classes of resonators were measured:

33 resonators formed by 1 �m of AlN, 90 nm of Pt and Al top elec-trodes of 120 nm, all operating around 1 GHz. The experimental

Fig. 16. Experimental results for standard and apodized (shape I) 1 GHz AlN CMRformed by 1 �m of AlN, 120 nm of Al, 90 nm of Pt, and 49 fingers (finger length of85 �m).

able 1ummary of the results for a variety of apodized resonators (33 samples including: 12 standard CMRs, 12 Apodized Shape I CMRs and 9 Apodized Shape II CMRs) operatinground 1 GHz and formed by 1 �m of AlN, 120 nm of Al and 90 nm of Pt. The resonators are identified with a code of four numbers; the first two numbers indicate the numberf fingers and the last two refer to the length of the fingers in �m. So, for instance the code “2560” is referred to a resonator of 25 fingers, with a length of 60 �m. The data arerovided as percentage change with respect to the linear value of the non-apodized case. A negative value of % indicates that a higher value is recorded in the non-apodizedase. The decrease of spurious vibrations has been quantified by evaluating the maximum amplitude of the spurious response in the admittance graph (expressed in linearalues) before (Spstand) and after the application of the apodization technique (Spapod). The same method has been used to calculatethe decrease of quality factor (�Q),lectromechanical coupling coefficient (�k2

t ), and device capactiance (�C0). a �Sp = −100% means that a total suppression of the spurious vibration has been achieved.

Sp = Spap − Spstand

Spstand∗ 100

1 GHz contour mode resonators

CMRs Apodization Shape I Apodization Shape II

�Sp �Q �k2t �C0 �Sp �Q �k2

t �C0

2540 −98.0% −7.1% −19.1% −22.4% −79.3% −0.9% −22.1% −23.0%2560 −97.8% 36.2% −21.8% −7.2% −95.2% 13.3% −15.5% −20.0%2585 −96.0% 0.0% 9.4% −8.7% −100.0% −2.7% 6.0% −14.4%3340 −97.5% 0.1% −22.4% −4.9% −51.2% −1.2% −25.9% −9.5%3360 −90.0% 9.2% −31.0% −9.4% −97.9% −8.5% −17.6% −9.2%3385 −97.8% 33.4% −14.6% −11.9% −100.0% 22.1% −0.8% −12.7%4940 −80.0% −5.8% −33.8% −3.0% −97.4% 8.5% −35.3% −7.8%4960 −79.6% 14.3% −24.7% −9.0% −100.0% 22.1% −28.1% −13.8%4985 −86.0% −15.7% −3.2% −11.8% −100.0% 2.8% −8.1% −15.7%6540 −77.1% 12.5% −44.8% −9.3% – – – –6560 −94.3% 17.6% −33.6% −1.7% – – – –6585 −90.5% 34.4% −26.0% −17.6% – – – –

� −91.4% 7.2% −17.9% −9.8% −91.1% 6.2% −16.4% −14.0%� 7.5% 15.8% 11.6% 4.7% 3.5% 10.7% 13.2% 3.8%

48 M. Giovannini et al. / Sensors and Actuators A 206 (2014) 42– 50

Table 2Summary of the results for a variety of apodized resonators (33 samples including: 12 standard CMRs, 12 Apodized Shape I CMRs and 9 Apodized Shape II CMRs) operatingaround 900 MHz and formed by 500 nm of AlN, 120 nm of Al and 90 nm of Pt. The CMR label convention follows the same explained in Table 1.

900 MHz contour mode resonators

CMRs Apodization Shape I Apodization Shape II

�Sp �Q �k2t �C0 �Sp �Q �k2

t �C0

2540 −69.3% 6.7% −12.1% −281.3% −79.3% −11.4% −18.9% −13.1%2560 −94.0% −2.8% −7.1% 156.3% −95.2% −2.9% 3.2% −12.0%2585 −100.0% −42.1% 10.2% −124.3% −100.0% −35.5% −1.6% −16.0%3340 −62.1% −15.8% −13.3% −15.6% −51.2% −15.7% −14.8% −10.5%3360 −94.7% −2.8% −6.4% 129.6% −97.9% −6.7% 6.4% −10.1%3385 −100.0% 11.1% −6.3% −156.9% −100.0% 0.1% 6.3% −14.5%4940 −97.4% −12.6% −24.8% 97.7% −97.4% −32.8% −25.5% −8.5%4960 −100.0% 4.8% −12.0% −351.5% −100.0% 4.8% −15.5% −16.0%4985 −100.0% 4.7% −8.5% −279.2% −100.0% 4.8% −12.7% −18.6%6540 −78.8% −7.2% −25.0% 249.6% – – – –6560 −100.0% 10.0% −31.0% −410.6% – – – –6585 −100.0% −4.0% −27.8% 587.5% – – – –

−9.0% −91.2% −10.6% −8.1% −11.90%3.7% 16.4% 15.0% 11.9% 3.3%

-

-

-

cbgd

pstropcsdsteatT

sopc

tt

wi

Table 3Summary of the average performance for a variety of apodized resonators (sametested in Tables 1 and 2) and formed by 500 and 1000 nm of AlN, 90 nm of Pt and120 nm of Al top electrodes. Each group (1 GHz and 900 MHz devices) consists of 21samples including 12 CMRs characterized by the Apodization Shape I and 9 CMRscharacterized by the Apodization Shape II.

1 GHz contour mode resonators

Apodization Shape I Apodization Shape II

Q k2t Q k2

t

� 2232 1.05% 2236 1.11%� 355 0.13% 266 0.11%

900 MHz contour mode resonators

Apodization Shape I Apodization Shape II

Q k2t Q k2

t

889 MHz resonator over a broad frequency range (200 MHz–2 GHz).Overall, we can state that the introduction of apodization is

advantageous and has mostly the following impact on the device

� −91.5% −4.2% −13.7%

� 13.3% 14.7% 11.7%

results for these devices are reported in Table 1 and summarizedin Table 4.

33 resonators formed by 1 �m of AlN, 90 nm of Pt and Al top elec-trodes of 220 nm, all operating around 1 GHz. The experimentalresults for these devices are summarized in Table 4.

33 resonators formed by 500 nm of AlN, 90 nm of Pt and Al topelectrodes of 120 nm, all operating around 900 MHz. The exper-imental results for these devices are reported in Table 2 andsummarized in Table 5.

33 resonators formed by 500 nm of AlN, 90 nm of Pt and Al topelectrodes of 220 nm, all operating around 900 MHz. The experi-mental results for these devices are summarized in Table 5.

For each group of 33 resonators, 12 standard resonators wereompared with 21 apodized resonators (12 apodized resonatorsased on shape I and 9 apodized resonators based on shape II). For aiven AlN and metal electrode thickness, the reported experimentalata are for devices fabricated on the same die.

For each tested CMR, admittance peak, electromechanical cou-ling coefficient and Q were extracted and compared. Table 1ummarizes the results for the two apodization shapes appliedo 1 GHz AlN devices, while Table 2 shows similar results, buteferred to 900 MHz AlN devices (effectively the same design lay-ut, but using 500 nm AlN films). The experimental results areresented as percentage change with respect to the non-apodizedase. Tables 1 and 2 clearly show that spurious vibrations areignificantly suppressed with, on average, a minimal impact onevice Q, k2

t and device capacitance, C0. The small value of thetandard deviation (�) for the presented data is a sign that thisechnique can be applied to a large group of devices of differ-nt dimensions (and therefore different impedance). Moreover, thepodized devices are also characterized by optimal performance inerms of Q and k2

t for both 900 MHz and 1 GHz devices, as shown inable 3.

In addition, we verified that the same apodized shapes can beuccessfully applied to CMRs characterized by different thicknessesf the Al top electrode (120 and 220 nm). Table 4 and V reports theerformance of samples of the apodized 900 MHz and 1 GHz CMRsharacterized by 120 nm and 220 nm Al top electrodes (Table 5).

It is worth noting that the experimental results are in line withhe theoretical expectations as shown in the comparison between

he experimental response and the COMSOL FEM model (Fig. 17).

It is also interesting to note that the apodization techniqueorks effectively in suppressing spurious vibrations for frequencies

n close proximity of the main resonance peak without altering the

� 1849 1.14% 1733 1.22%� 367.3 0.16% 409.3 0.10%

broadband response of the resonator. This is evident from Fig. 18,which compares the responses of an apodized and a standard

Fig. 17. COMSOL FEA results compared to the experimental response for apodized(shape I) 900 MHz AlN CMR formed by 1 �m of AlN, 220 nm of Al, 90 nm of Pt and49 fingers (finger length of 76 �m).

M. Giovannini et al. / Sensors and Actuators A 206 (2014) 42– 50 49

Table 4Summary of results for a variety of 42 apodized resonators operating around 1 GHz and formed by 1 �m of AlN, 90 nm of Pt and Al top electrodes of either 120 or 220 nm. Foreach case, (120 nm and 220 nm of Al electrodes) the sample group is composed by the same 21 resonators described in Table 1 for shape I (12 samples) and II (9 samples).The apodized response is compared to 12 standard CMRs with the same geometry.

120 nm Al top electrodes

Apodization Shape I Apodization Shape II

�Sp �Q �k2t �C0 �Sp �Q �k2

t �C0

� −91.4% 7.2% −17.9% −9.8% −91.1% 6.2% −16.4% −14.0%� 7.50% 15.80% 11.60% 4.70% 3.5% 10.7% 13.20% 3.80%

220 nm Al top electrodes

Apodization Shape I Apodization Shape II�Sp �Q �k2

t �C0 �Sp �Q �k2t �C0

� −84.5% 37.6% −14.5% −2.3% −99.3% 23.4% −21.8% −7.5%� 22.4% 16.2% 35.10% 7.60% 1.2% 49.2% 13.80% 0.10%

Table 5Summary of results for a variety of 42 apodized resonators operating around 900 MHz and formed by 500 nm of AlN, 90 nm of Pt and Al top electrodes of either 120 or 220 nm.For each case, (120 and 220 nm of Al electrodes) the sample group is composed by the same 21 resonators described in Table 2 for shape I (12 samples) and II (9 samples).The apodized response is compared to 12 standard CMRs with the same geometry.

120 nm Al top electrodes

Apodization Shape I Apodization Shape II

�Sp �Q �k2t �C0 �Sp �Q �k2

t �C0

� −98.9% 3.7% −19.9% −4.7% −95.8% 9.3% −16.3% −5.7%� 2.52% 21.61% 12.69% 5.30% 5.6% 14.8% −13.2% 7.3%

220 nm Al top electrodes

Apodization Shape I Apodization Shape II

�Sp �Q �k2t �C0 �Sp �Q �k2

t �C0

.0%

.7%

p(qittC

Fso

� −91.4% −4.2% −13.7% −9� 13.3% 14.7% 11.7% 3

erformance: (i) complete suppression of the spurious modes>90% in almost all cases); (ii) a minimum improvement of theuality factor, likely due to the ability of apodization to focus energy

nto the main resonance peak (Q reduction is recorded only for thehick electrodes and it is <11%); (iii) minimal decrease of the elec-

romechanical coupling coefficient (k2

t ) (<20% in all cases) and of0.

ig. 18. Experimental response over a wide frequency span (200 MHz–2 GHz) fortandard and apodized (shape I) 889 MHz AlN CMR formed by 500 nm of AlN, 120 nmf Al, 90 nm of Pt, and 49 fingers with a finger length of 60 �m;.

−91.2% −10.6% −8.1% −11.9%16.4% 15.0% 11.9% 3.3%

6. Conclusions

This paper presented the design, fabrication, analysis and exper-imental verification of the apodization technique in AlN MEMSCMRs. Application of apodization to MEMS AlN CMRs has beendemonstrated in order to efficiently suppress spurious modes inclose proximity of the main mechanical resonance without signifi-cantly impacting the Q (Q increases in most cases and decreases forthick electrodes by <11%) or k2

t (decrease < 20% for all cases) of thedevice. The obtained results show that the introduced apodizationtechniques, until now exclusively applied to SAW devices, are alsorelevant to CMRs and could be extended to several other laterallyvibrating MEMS resonator technologies. Furthermore, most of theapodized CMRs that were fabricated showed a quality factor closeto 2000 with an electromechanical coupling coefficient higher than1%, making them ideal candidates for the synthesis of narrowband,spurious-free filters.

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