800 IEEE ELECTRON DEVICE LETTERS, VOL. 40, NO. 5, MAY 2019

A Non-Reciprocal Filter Using AsymmetricallyTransduced Micro-Acoustic Resonators

Mayur Ghatge , Student Member, IEEE, Glen Walters, Student Member, IEEE,Toshikazu Nishida, Senior Member, IEEE, and

Roozbeh Tabrizian , Member, IEEE

Abstract— This letter reports a non-reciprocalfilter basedon the use of nonlinearities in high quality-factor (Q) sili-con micro-acoustic resonators with asymmetric piezoelec-tric transducers. The two-port resonators are created bythe integration of 120-nm piezoelectric aluminum nitrideand 10-nm ferroelectric hafnium–zirconium-oxide transduc-ers atop of 70-nm single-crystal silicon. The asymmet-ric electromechanical transduction architecture results inhighly contrasted power-handing of the micro-acoustic res-onator when excited at different ports, resulting in non-reciprocal transmission response for excitation powersbeyond a certain threshold. A proof-of-concept filter at253 MHz with 0.25% −3-dB bandwidth is implementedthrough electrical coupling of two asymmetrically trans-duced resonators with individual Q of ∼870. The filterdemonstrates a non-reciprocal transmission ratio of ∼16 dBfor input power exceeding 5 dBm.

Index Terms— Non-reciprocal filter, nonlinear resonator,hafnium-zirconium-oxide transducer, high-Q acousticresonator.

I. INTRODUCTION

FULL-DUPLEX (FD) integrated RF front-end (RFFE)systems are one of the key enabling modules for real-

ization of the emerging wireless communication protocols(i.e. 5G and beyond). FD RFFE can essentially double the datacommunication capacity through simultaneous transmissionand receive at the same frequency-band and address the ever-growing need for network capacity. Realization of FD RFFEfor wireless systems requires integrated non-reciprocal com-ponents, such as isolators and circulators, to avoid destructiveself-interference between the transmitter (Tx) and receiver (Rx)signals. Such integrated non-reciprocal architectures, however,are not currently available due to the fundamental limitationof current analogue signal processing modules, such as filtersand amplifiers that operate inherently on reciprocal physics.Besides FD RFFE, frequency selective limiters (FSL), whichare pivotal components in tactical communication systems,require non-reciprocal blockage of in-band signals with large

Manuscript received March 1, 2019; revised March 17, 2019; acceptedMarch 17, 2019. Date of publication March 22, 2019; date of currentversion April 25, 2019. This work was supported in part by the NSFunder Grant ECCS 1610387 and Grant ECCS 1752206. The review ofthis letter was arranged by Editor S. Pourkamali. (Corresponding author:Mayur Ghatge.)

The authors are with the Electrical and Computer EngineeringDepartment, University of Florida, Gainesville, FL 32611 USA (e-mail:ruyam@ufl.edu).

Color versions of one or more of the figures in this letter are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LED.2019.2907089

powers that saturate Rx amplifiers. Currently, all FSL tech-nologies rely on ferromagnetic resonators that are very largein size and incompatible with monolithic integration [1]. Thisleads to the need for research on the development of integratednon-reciprocal architectures based on novel components andsystems that break the reciprocity and operate at diverse powerratings. Prominent examples of such architectures are time-varying electronic systems [2]–[4] and active electroacousticcomponents [5]–[6]. These systems are typically highly com-plex and impose excessive power-consumption and integrationchallenges.

In this letter, we introduce a new high quality-factor (Q)micro-acoustic resonator technology that exploits the nonlin-ear operation regime to enable realization of non-reciprocalRF filters. The presented technology is based on the integra-tion of piezoelectric aluminum nitride (AlN) and ferroelectrichafnium-zirconium-oxide (Hf0.5Zr0.5O2) films on a thin singlecrystal silicon (SCS) to realize asymmetrically transducedLamb-wave resonator with non-reciprocal operation.

II. ASYMMETRICALLY TRANSDUCED RESONATORS

The non-reciprocal filter presented in this letter are real-ized through electrical coupling of asymmetrically transducedwaveguide-based resonators. Dispersion engineering of theLamb-waves result in acoustic energy trapping for high-Qwaveguide-based resonators [7]. These devices are formedby stacking two piezoelectric transducer films with largethickness variation atop of a thin 70nm SCS layer. Thelarge contrast between the electromechanical transduction effi-ciency of the two piezoelectric films with large thicknessratio (>10) results in the non-reciprocal power handling of theresonator when excited through different ports. Fig. 1 showsthe top view of the asymmetrically transduced resonator.The asymmetric piezoelectric stack is formed by sputtering120nm piezoelectric AlN film, followed by atomic layerdeposition (ALD) of 10nm ferroelectric Hf0.5Zr0.5O2 film. The10nm ferroelectric Hf0.5Zr0.5O2 is the thinnest ever-reportedelectromechanical transducer that provides a large piezoelec-tric coupling when sufficiently polarized [8]. Fig. 2 illustratesthe resonator stack, highlighting the diffraction pattern ofthe orthorhombic Hf0.5Zr0.5O2 layer, sandwiched between themolybdenum (Mo) and TiN electrodes. Fig. 2 (b-inset) showsthe ferroelectric hysteresis loop of the TiN/Hf0.5Zr0.5O2/Mocapacitor where a large instantaneous polarization is evident.Application of a sufficiently large DC voltage across theHf0.5Zr0.5O2 film enables polarization of the transducer toprovide linear piezoelectric coupling. The large difference

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GHATGE et al.: NON-RECIPROCAL FILTER USING ASYMMETRICALLY TRANSDUCED MICRO-ACOUSTIC RESONATORS 801

Fig. 1. SEM image of two-port asymmetrically transduced resonator.Port-1 (highlighted in green) is a 10nm ferroelectric Hf0.5Zr0.5O2 film andPort-2 (highlighted in pink) is a 120nm AlN film. The insets highlight thedetails of Hf0.5Zr0.5O2 transducer stack formed from 10nm ferroelectricfilm in between 10nm/30nm TiN/Pt on top and 50nm Mo at bottom.AlN transducer is formed from the piezoelectric film with 30nm Pt (top)and 50nm Mo (bottom) electrodes. The device operates based on exten-sional waves propagating in Z direction, with orthogonal displacement inY direction; hence, forming lateral-extensional resonance mode.

Fig. 2. (a) HR-XTEM image of the resonator stack. (b) Zoomed-in viewof the 10nm/10nm Hf0.5Zr0.5O2/TiN layers. The diffraction patters areevident indicating the orthorhombic crystallinity of Hf0.5Zr0.5O2. (inset)Measured hysteresis loop for the 10nm Hf0.5Zr0.5O2. The polarizedtransducer operates at the starred point yielding a large linear electro-mechanical coupling.

between the thicknesses of the two transducers (i.e. 120nmAlN vs 10nm Hf0.5Zr0.5O2) results in highly contrasted powerhandling of the device when excited at different ports. Fig. 3demonstrates the asymmetric power-handling concept usingthe Mason waveguide model for the resonator. For a similarelectrical input power (i.e. Pin ), the mechanical energy storedin the resonator can significantly change, depending on theelectromechanical excitation port. Specifically, when the res-onator is excited at the AlN port, the large k2

eff,AlN can drive thedevice into mechanical nonlinearities with low input powers.The k2

eff,AlN can be expressed as:

k2eff,AlN ≈ k2

31,AlN · EAlNTAlN∑

n (En Tn)(1)

where k231,AlN is the transverse coupling coefficient of AlN

and En and Tn are the Young’s modulus and thickness of

Fig. 3. Mason waveguide model for the resonator with asymmetrictransducers. ZAlN/HZO, kAlN/HZO, tAlN/HZO, CAlN/HZO are the acousticimpedance, wavenumber, thickness and static capacitance of the indi-vidual transducers and Zi, ki, ti, Ci correspond to other non-piezoelectricmaterials in the resonator stack. ηAlN/HZO are transduction efficienciesat two ports and are proportional to k31,AlN/HZO [9]. S21 and S12correspond to the mechanical power injected into the resonator whenactuated using the AlN and Hf0.5Zr0.5O2 transducers, respectively, usingan electric input power Pin; Power-sensitive resistive (DiPMech,i) andreactive (−jEiPMech,i) components in the model represents the thermaland elastic nonlinear behavior in the ith layer of the resonator.

the corresponding layer in the resonator stack. On the otherhand, excitation of the device at the 10nm Hf0.5Zr0.5O2port with similar input powers does not induce mechanicalnonlinearities, due to the significantly smaller k2

eff,HZO. Theratio between the electromechanical transduction of the twoports can be expressed through:

k2eff,AlN

k2eff,HZO

= k231,AlN

A2 · k231,HZO

· EAlNTAlN

EHZOTHZO(2)

Here, A is the ratio of effective transduction areas atport-1 and port-2. The large contrast in electromechanicalcoupling at the two ports, resulting from an order of mag-nitude difference in the transducer thicknesses, induces asignificant change in mechanical energy stored in the res-onator when excited with similar input power. While exci-tation of the resonator at two different ports with sufficientlysmall input power (Pin ) results in a reciprocal transmissionresponse, the reciprocity can be directionally broken withthe increase in Pin . The increase in Pin , beyond a certainthreshold, drives the resonator into mechanical nonlinearitieswhen using AlN transducer as the excitation port. However,application of the same Pin to Hf0.5Zr0.5O2 port does notinduce any nonlinearity in resonator operation. In the nonlinearregime, the frequency response of the resonator is substantiallydistorted resulting in a tremendous increase in the insertionloss. Such distortion can be attributed to the columnar poly-crystalline structure of the AlN film that is comprised ofdense C-axis oriented grains with loose intergranular bonds.Therefore, excitation of the AlN film with large input powersinduces local thermal nonlinearities that essentially distort theresonator frequency response [10]. This behavior is unlikesingle crystal films or substrates where even large nonlin-earities induces a predictable duffing effect in the frequencyresponse of the resonator [11]. The nonlinear operation of thetwo-port resonator, based on thermal and elastic nonlinearities,are incorporated in Mason waveguide model (Fig. 3) as power-dependent resistive and reactive components.

Considering the operation principle of the non-reciprocalresonator with asymmetric transducers, the dynamic range of

802 IEEE ELECTRON DEVICE LETTERS, VOL. 40, NO. 5, MAY 2019

Fig. 4. (a) Frequency response of individual resonator for different input powers for (a) Hf0.5Zr0.5O2-actuate / AlN-sense (inset shows simulated modeshape of 3rd width-extensional mode) (b) AlN-actuation / Hf0.5Zr0.5O2-sense transduction schemes. (insets-left) show the transduction schemes(c) Sii response of the resonator with different transduction schemes: Hf0.5Zr0.5O2-actuate (S11) and AlN-actuate (S22) for Pin = 15dBm.

operation can be defined by:{

PMech,forward = k2HZO Pin < PMech,threshold (3.a)

PMech, reverse = k2AlN Pin > PMech,threshold (3.b)

Here, Pin is the input electrical power and Pmech,thresholdis the threshold mechanical power required to drive thedevice into nonlinearity. Eq. (3.a) is required to ensure linearoperation in forward direction, while Eq. (3.b) is neededto enable signal suppression when operated in backwarddirection. Eq. (3.a) and (3.b) can be summarized to yield thedynamic range of non-reciprocal operation as:

Dynamic Range = PMech, threshold

(1

k2H Z O

− 1

k2AlN

)

. (4)

Considering Eq. (4), the dynamic range can be enhanced byincreasing Pmech,threshold, or increasing the mismatch betweenelectromechanical transduction efficiency at the two ports.

Fig. 4 shows the frequency response of the asymmetricallytransduced resonator actuated and sensed at different ports, fordifferent input powers. The 3rd width-extensional bulk acousticmode is excited at ∼253MHz, with a Q of ∼870 in bothtransduction schemes for input powers below 5dBm. However,for the AlN-drive case, the resonator is driven into nonlinearoperation with input powers above 5dBm, showing a highlydistorted frequency response with an increased insertion lossof ∼10dB. On the other hand, in Hf0.5Zr0.5O2-drive scheme,the resonator remains in the linear regime with input powersup to 25dBm, without showing any distortion in response.

III. NON-RECIPROCAL ELECTRICALLY

COUPLED FILTERS

The asymmetrically transduced resonators are electricallycoupled to implement bandpass filters. Opting for a propercoupling architecture, the directional nonlinear response ofthe individual resonators enables realization of a non-reciprocal filter. In the forward configuration, the excitationis applied to port-1 (i.e. resonator-1 at Hf0.5Zr0.5O2 trans-ducer), and the output is measured at port-2 (i.e. resonator-2at AlN transducer), resulting in power-insensitive transmis-sion response (i.e. S21). In the backward configuration, thetransmission response (i.e. S12) is highly sensitive and getsdistorted for input powers above 5dBm. Fig. 5 demonstratesthe frequency response of the filter in forward and backwardconfiguration, for different input powers. A non-reciprocaltransmission ratio (NTR), i.e. the difference between theinsertion losses of forward and backward signal transmission,of ∼16dB is achieved for input powers of 5dBm-25dBm. The20dBm dynamic range of nonreciprocal operation is attributed

Fig. 5. Measured filter response of the electrically coupled filter with alinear BW3dB of 0.25% and NTR of ∼16dB.

to the huge mismatch between electromechanical transductionefficiency at the two ports. This mismatch, however, results ina small k2

eff,overall of the resonator, which limits the maximumattainable bandwidth (i.e. 0.25%) and increases the insertionloss (i.e. −60dB) of the electrically coupled filter. Thesecharacteristics can be significantly improved by opting forthicker transducer films with larger piezoelectric couplingcoefficients, larger device area, and removing electromechani-cally passive layers (i.e. Si and TiN) out of the resonator stack.Alternatively, the dynamic range of operation can be increasedby opting for Pmech,threshold enhancement, while reducing theelectromechanical coupling efficiency mismatch at the twoports; thus, improving k2

eff,overall.

IV. CONCLUSIONThis letter introduces an asymmetrically transduced micro-

acoustic resonator that enables realization of non-reciprocalfilters. The resonators are formed from integration of 120nmpiezoelectric AlN and 10nm ferroelectric Hf0.5Zr0.5O2 trans-ducers. The significant difference in transducer thicknessesresults in a large contrast in resonator power handling whenexcited at different electromechanical transduction ports. Thelarge distortion of the resonator frequency response in thenonlinear operation regime is used to implement a non-reciprocal filter for input powers beyond 5dBm. The filteris created from electrical coupling of identical asymmetri-cally transduced resonators at dissimilar transduction ports tocreate a directional transmission response. Proof of conceptresonators at ∼253 MHz, with Q of ∼870, is demonstratedand used to implemented filters with 0.25% bandwidth. A non-reciprocal transmission ratio of ∼16dB is measured for inputpowers >5dBm. This conceptual demonstration identifies anew approach for realization of non-reciprocal filters to enable5G full-duplex wireless systems and frequency selectivelimiters.

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