[C034] L. Yan, J. Wu, and W. C. Tang, “High frequency filters based on piezoelectrically transduced micromechanical resonators,” Proc. 2004 IEEE Int.Ultrasonics, Ferroelectrics, and Frequency Control Joint 50th Anniversary Conf., August 23 – 27, 2004, Montréal, Canada, in press.

High Frequency Filters Based on PiezoelectricallyTransduced Micromechanical Resonators

Le Yan1, Jian Wu2, and William C. Tang2,3

1Department of Mechanical and Aerospace Engineering2Department of Electrical Engineering and Computer Science

3Department of Biomedical EngineeringUniversity of California, Irvine

Irvine, CA, USA

Abstract—This paper presents the design, simulation, fabrication,and preliminary test results of a novel micromechanical filterbased on coupled piezoelectrically transduced resonators. Thiswork is the first report of two identical microfabricated free-freebeam resonators coupled with two torsional beams forming asecond-order mechanical filter. Piezoelectric transducers fromthin-film ZnO were used to drive and sense resonance,eliminating the need for precision fabrication of nanometer-scalegaps in contrast to electrostatic transduction. Fabrication wasdone with a four-mask process on SOI wafers with maximumtemperature capped at 250°C, allowing post-CMOS integration.Preliminary tests showed a resonant peak of 10.83 MHz and aquality factor of 41 under atmospheric pressure.

Keywords—MEMS; piezoelectric; resonator; filter

I. INTRODUCTION

Discrete mechanical filters (SAW, quartz, etc.) have beenthe target of replacement with microelectromechanical systems(MEMS) technology since the invention of the electrostaticcomb drive resonator in 1989 [1]. The motivation is to integratethe filtering functions on the signal processing chip to achieveradio-on-a-chip with low manufacturing cost, highperformance, and high reliability.

A common metric to measure the performance ofresonators is the frequency-Q product. It is observed that agiven technology will yield resonators with resonant frequencyand Q factor tradeoffs. Recent state-of-research with advancedmicrofabrication technology using electrostatically transduceddisk resonators fabricated from nanocrystalline diamond [2]and polycrystalline silicon (polysilicon) [3] achieved afrequency-Q product of 1.7 1013, exceeding that of some ofthe best quartz crystals. In order to realize on-chip MEMSfront-end, however, multi-pole mechanical filters withpercentage bandwidth on the level of 0.01% are required.Mechanical coupling technique has been used extensively indeveloping such filters. Percentage bandwidth of 1.3% at 35MHz was demonstrated in [4] and was push to 68 MHz with abandwidth less than 2% in a later design [5]. Percentagebandwidth of 0.01% was achieved at center frequency of 600kHz using a novel electrostatic coupling method [6]. Thesefilters relied on electrostatic drive and sense and nanometer-scale capacitive gaps to achieve detectable transduction.Impedance matching and fabrication challenges are the focusesfor improvement.

The motivation of this work is to develop a mechanicalfilter that works at a moderately high center frequency andsmaller percentage bandwidth by maximizing the effectivespring constant of the resonator. For the first time,piezoelectrically transduced free-free beam resonators are usedto synthesize a mechanical filter, avoiding the need fornanometer-scale capacitive gap. Preliminary test results show aresonant peak at 10.83 MHz with an observed Q at 41 underatmospheric pressure, demonstrating the feasibility andpromise of the current approach.

II. DESIGN CONCEPT

The equation for the resonant frequency of a lumped one-degree-of-freedom (DOF) undamped system is given by

12 2

eff

eff

kf

m

(1)

where effk and effm are the effective spring constant and

mass, respectively. For the case of a beam with density ,width w , thickness h , length l ,

2

2 2 0

2( ) ( )

( ) ( )

lE

eff

K whm x x dxv x x

(2)

where EK is the total kinetic energy of the beam and ( )v xis the velocity of the beam element at location x along thelength of the beam, and is the mode shape of the beam. For afree-free beam [7],

( ) cos( ) cosh( ) sin( ) sinh( )x kx kx kx kx (3)

where 0.9825 and 4.730 /k l .

Fig. 1 shows a lumped mass-spring-dashpot model of asecond-order mechanical filter with two identical resonatorswith mass m and spring constant k , coupled with amechanical spring with spring constant ck The governingequations for this system are

1 1 1 2( )cmx cx k k x kx F (4)

2 2 2 2 1( ) 0cmx cx kx k x x (5)

where c is the damping coefficient, F , the applied force,1x and 2x , the displacements of the two masses. The passband

of this system is proportional to the difference between the in-phase and anti-phase resonances of the two resonant beams.The undamped in-phase resonant frequency, inf , is given by(1). The undamped anti-phase resonant frequency is given by

2 211

2c c

anti in

k k kf f

m k

(6)

The fractional separation of the two resonant frequencies is

21 1anti in c c

in

f f k kf k k for ck k (7)

Therefore, to make the passband narrow, ck should beminimized in comparison to k . Fig. 2 shows the MATLAB©simulation results of the passbands for various values of / ck kand different damping coefficients.

In microfabricated resonators, the coupling spring cannotbe made too soft because of robustness and fabricationuniformity considerations. Therefore, it is better to maximizethe effective spring constant of the resonator at the couplinglocation. Since effk is proportional to effm at a given resonantfrequency, and thus is inversely proportional to the secondorder of the mode displacement, the coupling locations shouldbe at the nodes of the resonant modes. This was the strategyadopted in [8] and [9]. However, in those works, the clamp-clamp beam designs limited the effectiveness of this approachbecause of the absence of nodal points other than the anchors.

In contrast, the free-free beam design in this paper offerstwo quasi-nodes along the length of the beams, where thecoupling springs can be conveniently located. Fig. 3 shows thesimulated mode shape for the first resonant mode of a free-freebeam and the effective spring constant along the length of thebeam. Fig. 4 shows the 3D model. The torsional springconstant of the coupling spring ck is given by [10]

3 4

4

163.36 1

3 12cc

ab b bk G

l a a

(8)

where a and b are the half width and half height of thecross section of the coupling spring, cl , the length of the beam,

k

k k

x Fck

ck2 ck2

mkfin 21

mkkf canti 221

kkff cinanti 21

k

k

k

k

c c

c c

inf antif

k

k k

x Fck

ck2 ck2

mkfin 21

mkkf canti 221

kkff cinanti 21

k

k

k

k

c c

c c

inf antif

Figure 1. The equivalent lumped mass-spring-dashpot model of a coupledmechanical filter.

(a)

(b)

Figure 2. MATLAB© simulation of the passband (a) various ratios of springconstants and (b) at various damping values.

(a)

(b)

Figure 3. Simulation results with MATLAB© for (a) the mode shape of thefirst resonant mode and (b) the effective spring constant along the length of

the beam. The quasi-nodes are where the spring constant approaches infinity.

and G , the modulus of rigidity. The beam height, 2b , isdetermined by the thickness of the top silicon layer in the SOIwafer. The width, 2a , and the length, cl , of the coupling springare the two optimization parameters to tune the passband and atthe same time to suppress spurious modes in the spring. Thereis a low limit on the coupling spring width to 2 µm or so, dueto fabrication limits. Several values of cl have been modeledwith ANSYS©, one of them is shown in Fig. 5, indicating thein-phase and anti-phase resonances at 6.9 MHz and 7.0 MHz,respectively, for a beam geometry of160 ( ) 40 ( ) 20 ( )l w h µm and a coupling spring geometry of20 ( ) 4 (2 ) 20 (2 )cl a b µm. The percentage passbands areplotted as a function of cl and 2a in Fig. 5(c). Within thevariations chosen in this set of simulation, the minimumpercentage passband is 0.094% with a coupling springgeometry of 40 2 20 µm ( 2 2cl a b ).

III. FABRICATION

The resonant disks are fabricated with a four-mask processfrom SOI wafers, similar to the one reported in [11] (Fig. 6).SOI wafers are used because of the high intrinsic materialquality and uniformity, near-zero built-in stress, andpredictable mechanical and electrical properties of the topsingle-crystal silicon layer, which is used as the structuralmaterial. Also, the embedded oxide is used as the sacrificiallayer, conveniently bypassing the needs to deposit bothstructural and sacrificial layers in contrast to a conventionalsurface micromachining process. The maximum processingtemperature is capped at 250°C, which is the temperature at theZnO sputtering step, and thus allowing post-CMOS integration.The process begins by patterning the structural layer and deep-reactive-ion etching (DRIE) through the 20 µm thickness of thetop silicon layer [Fig. 6(a)]. A 0.8-µm-thick ZnO layer issputter deposited, with deposition parameters optimized toachieve c-orientation [Fig. 6(b)]. The top electrode is formedby E-beam evaporation of a layer of 500Å of gold [Fig. 6(c)].The backside is then etched to open a window to facilitateetching of the sacrificial oxide layer [Fig. 6(d)]. The processconcludes with device release with 6:1 BOE etch [Fig. 6(e)].Fig. 7 shows the SEM pictures of the fabricated device.

Figure 4. 3D drawing of the coupled free-free beam resonators withpiezoelectric transducers.

(a)

(b)

(c)

Figure 5. FEA simulated mode shapes of (a) in-phase at 6.9 MHz and (b)anti-phase at 7.0 MHz. (c) Percentage bandwidth with different coupling spring

geometries.

(a)

(b)

(c)

(d)

(e)

Figure 6. Cross-sectional drawings of the fabrication flow. (a) DRIE etch of20 µm-thick top silicon layer. (b) Sputter 0.8 µm of ZnO thin film. (c)

Evaporate 500 Å of Au. (d) Etch backside window. (e) Device release in 6:1BOE oxide etchant.

IV. MEASUREMENT

The prototype filters were measured as two-port deviceswith an Agilent® E4407B spectrum analyzer underatmospheric pressure. The built-in tracking generator of thespectrum analyzer was used as the signal source in combinationwith a DC offset voltage through a bias-T. The output signalwas measured at the input port and analyzed. Preliminaryresults on a pair of 160 ( ) 40 ( ) 20 ( )l w h µm resonatorbeams coupled with two 20 ( ) 4 (2 ) 20 (2 )cl a b µm torsionalbeams is shown in Fig. 8. A resonant peak of 10.83 MHz wasmeasured, which was 1.5 times the simulated value. Theobserved Q was 41. This rather low Q value probably maskedthe two expected resonant peaks, resulting in the observedsingle peak. The four supporting tethers on the outsides of thetwo resonant beams, each with a width of 10 µm, contributed tothe increase in the overall effective spring constant, causing theunderestimation in the modeling.

V. DISCUSSION AND CONCLUSION

This paper reported and demonstrated the feasibility of thefirst use of piezoelectric transduction on a coupled pair of free-free resonant beams to achieve a second-order bandpassmechanical filter. Several important improvements areidentified for future research. Fig. 9 shows the secondgeneration of an optimized design, in which two supportingtethers are connected to the coupling springs instead of fourconnecting to the resonant beams directly. The width of thecoupling springs is also reduced to 1 µm. The resonantfrequency of this improved design is expected to be morepredictable. Also, operation in vacuum is expected to improvethe Q of the filter.

ACKNOWLEDGMENT

The authors thank Prof. E. S. Kim of the University ofSouthern California and his research group for providing theZnO sputtering capability and valuable technical discussions.

REFERENCES

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[10] Young, W. C., Roark’s formulas for stress and strain, 7th Ed., NewYork: McGraw-Hill, 2002.

[11] L. Yan, W. Pang, J. Wu, W. C. Tang, and E.-S. Kim, “High frequencymicromechanical piezo actuated disk resonator,” Tech. Dig., Solid-StateSensor, Actuator and Microsyst. Workshop, Hilton Head Island, SC, Jun.6–10, 2004, pp. 372–375.

Figure 7. SEM pictures of a free-free beam coupled mechanical filter. Eachof the resonant beam is 160 ( ) 40 ( ) 20 ( )l w h µm. The coupling springs are

each 40 ( ) 4 (2 ) 20 (2 )cl a b µm.

Figure 8. Output of the two-port measurement of the device in Fig. 7. Centerfrequency is at 10.83 MHz with a Q of 41.

Electrodes

Anchoring beams

Coupling Springs

Free-freeresonators

Piezoelectricthin film

Electrodes

Anchoring beams

Coupling Springs

Free-freeresonators

Piezoelectricthin film

Figure 9. 3D model of the next-generation optimized design, where theoriginal four tethers have been reduced to two, and is connected to the

coupling springs instead of the resonator beams.