Q-Factor Enhancement of Thin-Film Piezoelectric-On-Silicon MEMS Resonator by Phononic Crystal-Reﬂector Composite Structure

micromachines

Article Q-Factor Enhancement of Thin-Film Piezoelectric-on-Silicon MEMS Resonator by Phononic Crystal-Reﬂector Composite Structure

Jiacheng Liu 1,* , Temesgen Bailie Workie 1 , Ting Wu 1, Zhaohui Wu 1, Keyuan Gong 1, Jingfu Bao 1,* and Ken-ya Hashimoto 1,2

1 School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China; [email protected] (T.B.W.); [email protected] (T.W.); [email protected] (Z.W.); [email protected] (K.G.); [email protected] (K.-y.H.) 2 Department of Electrical and Electronic Engineering, Chiba University, Chiba 263-8522, Japan * Correspondence: [email protected] (J.L.); [email protected] (J.B.)

Received: 28 November 2020; Accepted: 18 December 2020; Published: 20 December 2020

Abstract: Thin-film piezoelectric-on-silicon (TPoS) microelectromechanical (MEMS) resonators are required to have high Q-factor to offer satisfactory results in their application areas, such as oscillator, filter, and sensors. This paper proposed a phononic crystal (PnC)-reflector composite structure to improve the Q factor of TPoS resonators. A one-dimensional phononic crystal is designed and deployed on the tether aiming to suppress the acoustic leakage loss as the acoustic wave with frequency in the range of the PnC is not able to propagate through it, and a reflector is fixed on the anchoring boundaries to reflect the acoustic wave that lefts from the effect of the PnC. Several 10 MHz TPoS resonators are fabricated and tested from which the Q-factor of the proposed 10 MHz TPoS resonator which has PnC-reflector composite structure on the tether and anchoring boundaries achieved offers a loaded Q-factor of 4682 which is about a threefold improvement compared to that of the conventional resonator which is about 1570.

Keywords: MEMS resonator; Q-factor; phononic crystals; acoustic reﬂector

1. Introduction With the development trend of miniaturization of electronic equipment, microelectromechanical (MEMS) resonators has shown promising prospects in the field of sensing and wireless communication systems for their property of smaller size, lower power, and higher integration compared to the traditional electrical resonators. However, the quality factor of MEMS resonators with piezoelectric transduction is usually relatively low, which severely limits its practical applications in many fields, such as low phase noise oscillators, high sensitivity sensors, and narrowband filters [1–4]. For this cause, studying Q-factor enhancement strategy for thin film piezoelectric on silicon (TPoS) resonators has paramount importance to promote the practical application of piezoelectric MEMS resonators 2 in many fields. Unlike its quality factor, the effective electromechanical coupling coefficient (Ke f f ) of TPoS structure is relatively high and can also achieve single-chip multi-frequency [5–7]. As it is well known, the Q-factor is defined as the ratio of the energy stored in the resonator to the energy dissipated for each electromechanical conversion cycle:

E Q f actor = 2π stored (1) − Edissipated

Micromachines 2020, 11, 1130; doi:10.3390/mi11121130 www.mdpi.com/journal/micromachines Micromachines 2020, 11, x FOR PEER REVIEW 2 of 14 Micromachines 2020, 11, 1130 2 of 13 where 𝐸 is the vibration energy stored in the resonator and 𝐸 denotes the energy dissipated per cycle of vibration, respectively. It is clear that to obtain a higher Q-factor, it requires whereless energyEstored isdissipation. the vibration In energythe last stored few indecades, the resonator scholars and haveEdissipated beendenotes studying the energythe energy dissipated loss permechanism cycle of vibration,of MEMS respectively. resonators Itfrom is clear which that most to obtain relevant a higher loss Q-factor, mechanisms it requires in piezoelectric less energy dissipation.resonators are In thethe lastanchor few decades,loss [8], interface scholars haveloss, beenthermoelastic studying thedamping energy (T lossED), mechanism material damping, of MEMS resonatorsand other fromunknown which losses. most relevantHowever, loss it mechanisms has been found in piezoelectric that the anchor resonators loss areaccounts the anchor for a loss larger [8], interfaceproportion loss, of thermoelasticthe various energy damping losses (TED), of the material resonator. damping, In this andwork other too, unknownthe anchor losses. loss is However,assumed itto hasbe the been main found contributor that the anchor of various loss energy accounts dissipat for a largerion sources, proportion so the of total the various quality energyfactor increases losses of the resonator. In this work too, the anchor loss is assumed to be the main contributor of various energy with a higher 𝑄 [9,10]. The anchor loss is caused by the mechanical deformation of the dissipationresonator during sources, operation, so the total which quality generates factor increases acoustic withwaves a higher that propagateQanchor [9, 10outward]. The anchor through loss the is causedtether to by the the anchoring mechanical substrate. deformation The energy of the carrie resonatord by duringthe acoustic operation, waves which leaky generatescannot be acousticused by waveselectromechanical that propagate conversion outward in through the next the cycle. tether For tothis the reason, anchoring different substrate. loss reduction The energy schemes carried were by theproposed, acoustic which waves can leaky be cannotsummarized be used into by two electromechanical categories: One conversion is to optimize in the the next structure cycle. For of thisthe reason,resonator diff itself,erent such loss reductionas protrusions schemes on the were side proposed, edges of which the resonator can be summarized body, etched into stress two relief categories: holes Oneand anchor is to optimize points on the the structure resonator of thebody. resonator The other itself, one such is the as introduction protrusions onof additional the side edges structures of the resonatoraround the body, resonator, etched such stress as relief suspended holes and frames anchor for pointsenergy on decoupling the resonator [11–25]. body. In The this other study, one the is theconjunction introduction of 1D-phononic of additional crystals structures (PnCs) around on the the tether resonator, and reflectors such as suspendedon the anchoring frames boundaries for energy decouplingis used to reduce [11–25 the]. In anchor this study, loss of the TPoS conjunction resonators. of 1D-phononic Among them, crystals the phononic (PnCs) oncrystals the tether structure and reflectorsexhibits a ongood the effect, anchoring and the boundaries method only is used needs to reduceto design the the anchor band loss gap of that TPoS includes resonators. the resonance Among them,frequency, the phononic which has crystals a wide structure range of exhibitsapplications. a good Moreover, effect, and the the acou methodstic reflector only needs is designed to design with the banda radius gap of that quarter includes wavelength the resonance for better frequency, performance. which has a wide range of applications. Moreover, the acoustic reflector is designed with a radius of quarter wavelength for better performance. 2. Phononic Crystal Design 2. Phononic Crystal Design Figure 1 shows the structure of one-dimensional PnC proposed in this paper. Thickness of the Figure1 shows the structure of one-dimensional PnC proposed in this paper. Thickness of the PnC must be consistent with the tether as it is intended to be placed on the tether. The holes on the PnC must be consistent with the tether as it is intended to be placed on the tether. The holes on the rectangular block are called scatterers, their shape and size affect the band gap of the PnC. The length rectangular block are called scatterers, their shape and size affect the band gap of the PnC. The length and width of the PnC are called lattice constants, which also affect the position of the band gap center and width of the PnC are called lattice constants, which also affect the position of the band gap center frequency and the width of the band gap frequency range [26]. frequency and the width of the band gap frequency range [26].

(a) (b)

Figure 1.1. The structure of one-dimensiona one-dimensionall phononic crystal (PnC). ( a) 3D schematic view of the proposed PnC conﬁguration;configuration; ((bb)) TopTop viewview ofof thethe PnC.PnC.

Since the one-dimensional PnC has periodicity only in one direction, Bloch-floquentBloch-floquent boundary condition isis imposed imposed on on the the wave wave vector vector k along k along the path the frompath point fromΓ pointto point Γ Xto in point the first X in irreducible the first brillouinirreducible zone brillouin (IBZ). zone (IBZ). The blue surface and arrow in Figure 2 2 indicate indicate thethe positionposition andand directiondirection ofof thethe BlochBloch boundaryboundary conditions applied for the simulation. The dispersion relation of the proposed 1D-PnC is computedcomputed using finitefinite elementelement method method (FEM) (FEM) resulting resulting in ain complete a complete acoustic acoustic bandgap bandgap of about of about 4 MHz 4 MHz (7.54 MHz(7.54 toMHz 11.64 to MHz).11.64 MHz). The band The gap band structure gap structure of a phononic of a phononic crystal is crystal closely is dependent closely dependent on the geometric on the parametersgeometric parameters of a single phononicof a single crystal phononic unit. crystal Its size unit. not only Its size determines not only the determines existence ofthe the existence band gap, of

Micromachines 2020, 11, x FOR PEER REVIEW 3 of 14 Micromachines 2020, 11, 1130 3 of 13 the band gap, but also affects the width of the band gap [27]. In addition, the PnCs are usually designed with some special geometric shapes and relatively small in size, so accuracy errors are prone but also aﬀects the width of the band gap [27]. In addition, the PnCs are usually designed with some to occur during processing, causing the actual size to be different from the setting during simulation, special geometric shapes and relatively small in size, so accuracy errors are prone to occur during thereby changing the band gap of the phononic crystal [28,29]. processing, causing the actual size to be diﬀerent from the setting during simulation, thereby changing the band gap of the phononic crystal [28,29].

Figure 2. Band gap simulation results of PnC units. (a)the blue surface and arrows indicate the position Figure 2. Band gap simulation results of PnC units. (a)the blue surface and arrows indicate the and direction of the applied Bloch boundary conditions; (b)the band gap simulation results of the PnC. position and direction of the applied Bloch boundary conditions; (b)the band gap simulation results of the PnC. For this reason, several simulations are done to verify the changing trend of the band gap of the phononic crystal with different radius of the circular hole. In this regard, the radius of the circular hole For this reason, several simulations are done to verify the changing trend of the band gap of the is swept from 0.5 µm to 2.5 µm, while keeping other structural parameters unchanged. The simulated phononic crystal with different radius of the circular hole. In this regard, the radius of the circular changing trend of the center frequency and width of the phononic crystal bandgap is shown in Table1 hole is swept from 0.5 μm to 2.5 μm, while keeping other structural parameters unchanged. The from which it could be observed that the radius of the circular hole affects the center frequency and simulated changing trend of the center frequency and width of the phononic crystal bandgap is width of the band gap. The center frequency shows a downward trend from which it sharply drops shown in Table 1 from which it could be observed that the radius of the circular hole affects the center when the radius increases more than 1.5 µm, while the band gap width has a decreasing trend for the frequency and width of the band gap. The center frequency shows a downward trend from which it radius less than 1.5 µm and then increased with the increase in the radius. The optimum value can be sharply drops when the radius increases more than 1.5 μm, while the band gap width has a taken as 1.5 µm considering changing trend of band gap center frequency and width changes at this decreasing trend for the radius less than 1.5 μm and then increased with the increase in the radius. point. The main reason is that as the radius of the hole increases, the distance between two adjacent The optimum value can be taken as 1.5 μm considering changing trend of band gap center frequency holes is too small. For example, for radius of 2.5 µm, the distance between the two circular holes is and width changes at this point. The main reason is that as the radius of the hole increases, the only 1 µm, and the air in the circular hole and the material between the two circular holes are used as distance between two adjacent holes is too small. For example, for radius of 2.5 μm, the distance high and low acoustic impedance materials, respectively. As a result, the periodicity will be affected. between the two circular holes is only 1 μm, and the air in the circular hole and the material between In addition, when determining the size of the circular hole, the limitations of the processing technology the two circular holes are used as high and low acoustic impedance materials, respectively. As a must be considered. Although reducing the radius can increase the band gap width, too small radius result, the periodicity will be affected. In addition, when determining the size of the circular hole, the may change the shape and size of the scatterer during the processing [26]. After this all comprehensive limitations of the processing technology must be considered. Although reducing the radius can consideration, a radius of 1.5 µm is finally selected as an optimum value. increase the band gap width, too small radius may change the shape and size of the scatterer during the processing [26]. After this all comprehensive consideration, a radius of 1.5 μm is finally selected Table 1. Illustration for the effect of Scatterer hole radius on band gap structure of the PnC. as an optimum value. Band Gap Frequency (MHz) Hole Radius (µm) Percent Band Gap (%) Table 1. Illustration10.23 for the effect of Scatterer hole 0.5 radius on band gap structure 39.56 of the PnC. 9.48 1.0 41.23 Band Gap Frequency (MHz) Hole Radius(μm) Percent Band Gap (%) 9.10 1.5 40.08 9.3710.23 2.00.5 33.4739.56 10.349.48 2.51.0 39.2641.23 9.10 1.5 40.08 9.37 2.0 33.47 10.34 2.5 39.26

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Micromachines 2020, 11, x FOR PEER REVIEW 4 of 14 Furthermore, transmission characteristics of the PnC is simulated and compared with that of a siliconFurthermore, bar used as transmission a transmission characteristics medium by usingof the thePnC setup is simulated given Figure and 3compareda. In order with to reduce that of the a siliconeﬀect ofbar interference used as a transmission by the reﬂected medium waves, by both using sides the of setup the delay given line Figure are set3a. toIn beorder perfectly to reduce matched the effectlayers of (PML). interference Prescribed by the displacementreflected waves, is appliedboth sides on of the the input delay probe line are and set the to outputbe perfectly probe matched is set to layersmeasure (PML). the transmitted Prescribed response.displacement The is transmission applied on characteristicsthe input probe is investigatedand the output using probe transmission is set to measureparameter the which transmitted is the measure response. of transmitted The transmi wavesssion from inputcharacteristics port to output is portinvestigated (S21) in decibels,using transmissionis expressed asparameter which is the measure of transmitted waves from input port to output port ! (𝑆) in decibels, is expressed as P0 T = S21(dB) = 10log10 (2) 𝑷𝟎Pi 𝑻=𝑺𝟐𝟏(dB)=10𝒍𝒐𝒈𝟏𝟎( ) (2) 𝑷𝒊 where P0 is output power and Pi is input power. Figure3b reveals a very large drop in the wheretransmission(dB) 𝑷𝟎 is output of power the delay and line 𝑷𝒊 made is input up ofpower. 1D-PnC Figure which 3b shows reveals its a tendency very large in inhibitingdrop in the the transmission(dB)propagation of acoustic of the delay waves line with made frequencies up of 1D in-PnC the bandgap which shows range. its tendency in inhibiting the propagation of acoustic waves with frequencies in the bandgap range.

Si slab

1D-PnC array

(a)

-20

-40

Transmission (dB) Transmission Si-slab 1D-PnC -60 1D-PnC(No hole)

-80 0.0 2.5 5.0 7.5 10.0 12.5 15.0 Frequency (MHz)

(b)

Figure 3. Illustration of transmission characteristics of the proposed 1D-PnC (a) delay lines set up to Figure 3. Illustration of transmission characteristics of the proposed 1D-PnC (a) delay lines set up to test test the transmission of 1D-PnC taking the Si-slab based delay line and a 1D-PnC without hole as a the transmission of 1D-PnC taking the Si-slab based delay line and a 1D-PnC without hole as a control control device. The mode shapes are taken at 10 MHz; (b) Transmission (dB) of the delay line made-up device. The mode shapes are taken at 10 MHz; (b) Transmission (dB) of the delay line made-up of 1D- of 1D-PnC with and without scatterer holes in comparison with the Control Si slab based delay line. PnC with and without scatterer holes in comparison with the Control Si slab based delay line. 3. Resonator Design and Analysis 3. Resonator Design and Analysis The TPoS resonator with PnC-reﬂector Composite Structure designed in this paper is shown in FigureThe4. TPoS The ﬁgureresonator omits with the PnC-reflector silicon dioxide Composite layer in the Structure silicon on designed insulator in (SOI)this paper substrate is shown and the in Figure 4. The figure omits the silicon dioxide layer in the silicon on insulator (SOI) substrate and the back-substrate silicon. The wave equation for a resonator vibrating along its width(y-axis) in one space dimension can be written as

Micromachines 2020, 11, 1130 5 of 13 back-substrate silicon. The wave equation for a resonator vibrating along its width(y-axis) in one space dimension can be written as ∂2u ∂2u ρ = Ep (3) ∂t2 ∂y2 where ρ and Ep are the equivalent density and Young’s modulus of the material stack forming the bar respectively, u is the displacement, t is time, and y is the direction of vibration. The general solution for Equation (20) can be taken as

u(y, t) = [asin(βy) + bcos(βy)]ejω0t (4) where βy is the wave vector component in the y-axis. Considering a rectangular plate of width Wr and applying the boundary conditions that there is no stress and no stress gradient at the free lateral boundaries of the plate (y = 0 and y = Wr), the fundamental mode of the vibration of the structure can be derived as s n Ep fr = (5) 2Wr ρ Micromachines 2020, 11, x FOR PEER REVIEW 6 of 14

(a) (b)

FigureFigure 4. Illustration4. Illustration of the proposedof the aluminum proposed nitride-on-silicon aluminum (AlN-on-Si)nitride-on-silicon microelectromechanical (AlN-on-Si) (MEMS)microelectromechanical resonators. (a) 3D (MEMS) schematic resonators. view of ( thea) 3D proposed schematic configuration view of the thatproposed integrates configuration PnC-reflector that compositeintegrates structure;PnC-reflector (b) The composite top view structure; and the enlarged (b) The viewtop view of the and PnC the structure enlarged at theview tether. of the PnC structure at the tether. From Newton–Laplace equation, the acoustic velocity, v in the resonator could be approximated q 4. FabricationEp and Measurement by ρ [30–34]: nv The TPoS resonators designed in this articlef = are all based on MEMSCAP’s AlN-on-SOI standard(6) r 2W process, where by the <110> direction of the wafer is alignedr with the y-axis direction of the resonator. whereAs shownv is thein Figure acoustic 5, the velocity fabrication of the process resonator, of theWr TPoSis the resonators width of the follows resonator, the following and n is thesteps: mode numberStep of 1. the Select respective the SOI harmonic, wafer whichwith the is set <100> as one crystal in this orientation, work. The resonatorand deposit is designed a layer toof vibratePhosphosilicate in symmetrical glass (PSG) width on extension the upper (WE) surface mode of o theffering wafer a resonance after polishing. frequency Next, of the 10 MHz.wafer Thewas resonatingannealed in body Argon of the at resonator1050 °C for is aone rectangular hour, so platethat withPSG widthwas doped (wr) = onto420 µ them, lengthtop silicon ( Lr) =to180 formµm. a Theconductive plate is actuatedlayer, which through served the as input the ground electrodes electr byode the of inverse the entire piezoelectric device. Then effect, the while remaining the output PSG electrodeslayer is removed are used by to wet readout etching; the output current converted from the plate vibration through the direct piezoelectricStep 2. The effect. top The silicon tether thermally width and oxidized perfectly to generate matched a layer200 nm width thick (PML) silicon were dioxide tuned layer, to be and 10 µthenm and wet 3 etching times wavelength( is used to patternλ) respectively the silicon using dioxi FEM.de layer The radiusto obtain of an the insulating reflector is layer designed between to be the a quarterelectrode of theand wavelength, the ground; 210 µm, of the acoustic wave propagated in the resonator [27]. The resonant bodyStep comprises 3. A 500 a thin-filmnm thick piezoelectric aluminum nitride layer (0.5filmµ ism deposited thick aluminum on the nitride,wafer by AlN) reactive sandwiched sputtering, by theand upper the designed metallic piezoelectric electrodes (1 µlayerm thick size aluminum, is obtained Al) by andwet theetching; bottom substrate (10 µm thick silicon, Si). AnStep isotropic 4. Using silicon electron with beam orientation: evaporation<110> technology, for a higher 1 μ phasem thick velocity aluminum [35], is is deposited used. The and various 0.02 elasticμm thick coe ffichromium,cients are shownand the in electrodes Table2[36 ].were patterned through a stripping process and the metal electrodes and wiring of the resonator are obtained; Step 5. Hard mask deep reactive ion etching (DRIE) is used to etch the top silicon of SOI to the silicon dioxide layer of SOI and support beam structure, mirror structure and phononic crystal structure are obtained; Step 6. Polyimide is applied as a protective layer on the top of the device to protect the top structure, and then reactive ion etching (RIE) is used to etch the bottom oxide layer for the first time, and then DRIE used to etch from the bottom of the wafer to the second part of the SOI. The silicon oxide layer is then etched with hydrofluoric acid to remove the silicon dioxide layer, so that the resonator body forms a suspension structure. After releasing the top protective layer, the designed TPoS resonator is obtained.

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Table 2. Speciﬁc parameters of silicon.

Parameter Name Value

Young’s modulus (E) Ex = Ey = 169 GPa, Ez = 130 GPa Poisson’s ratio (σ) σxy = 0.064, σyz = 0.36, σzx = 0.28 Shear modulus (G) Gxy = 50.9 GPa, Gyz = Gzx = 79.6 GPa Density (ρ) 2330 kg/m3

4. Fabrication and Measurement The TPoS resonators designed in this article are all based on MEMSCAP’s AlN-on-SOI standard process, where by the <110> direction of the wafer is aligned with the y-axis direction of the resonator. AsMicromachines shown in 2020 Figure, 11, 5x, FOR the PEER fabrication REVIEW process of the TPoS resonators follows the following steps: 7 of 14

Figure 5. Process flow of thin-film piezoelectric-on-silicon (TPoS) resonator. (i) silicon on insulator Figure 5. Process flow of thin-film piezoelectric-on-silicon (TPoS) resonator. (i) silicon on insulator (SOI) substrate top silicon doping; (ii) Thermal oxidation generates insulating layer; (iii) Generate (SOI) substrate top silicon doping; (ii) Thermal oxidation generates insulating layer; (iii) Generate piezoelectric film; (iv) Generate metal electrodes; (v) Top etch; (vi) Back etching. piezoelectric film; (iv) Generate metal electrodes; (v) Top etch; (vi) Back etching. Step 1. Select the SOI wafer with the <100> crystal orientation, and deposit a layer of A series of four TPoS resonators with different structures are designed and processed to verify Phosphosilicate glass (PSG) on the upper surface of the wafer after polishing. Next, the wafer whether the proposed composite structure of phononic crystal and acoustic reflectors can effectively was annealed in Argon at 1050 ◦C for one hour, so that PSG was doped onto the top silicon to form a enhance the Q-factor by reducing the anchor loss of the resonator, as shown in Figure 6. The resonant conductive layer, which served as the ground electrode of the entire device. Then the remaining PSG structure of the four TPoS resonators are completely the same except the different additional layer is removed by wet etching; structures on the supporting structures to suppress anchor loss, and they are all designed to resonate Step 2. The top silicon thermally oxidized to generate a 200 nm thick silicon dioxide layer, and at a resonance frequency of 10 MHz lateral vibration mode. then wet etching is used to pattern the silicon dioxide layer to obtain an insulating layer between the electrode and the ground; Step 3. A 500 nm thick aluminum nitride film is deposited on the wafer by reactive sputtering, and the designed piezoelectric layer size is obtained by wet etching;

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Step 4. Using electron beam evaporation technology 1 µm thick aluminum is deposited and 0.02 µm thick chromium, and the electrodes were patterned through a stripping process and the metal electrodes and wiring of the resonator are obtained; Step 5. Hard mask deep reactive ion etching (DRIE) is used to etch the top silicon of SOI to the silicon dioxide layer of SOI and support beam structure, mirror structure and phononic crystal structure are obtained; Step 6. Polyimide is applied as a protective layer on the top of the device to protect the top structure, and then reactive ion etching (RIE) is used to etch the bottom oxide layer for the first time, and then DRIE used to etch from the bottom of the wafer to the second part of the SOI. The silicon oxide layer is then etched with hydrofluoric acid to remove the silicon dioxide layer, so that the resonator body forms a suspension structure. After releasing the top protective layer, the designed TPoS resonator is obtained. A series of four TPoS resonators with different structures are designed and processed to verify whether the proposed composite structure of phononic crystal and acoustic reflectors can effectively enhance the Q-factor by reducing the anchor loss of the resonator, as shown in Figure6. The resonant structure of the four TPoS resonators are completely the same except the different additional structures on the supporting structures to suppress anchor loss, and they are all designed to resonate at a Micromachinesresonance frequency 2020, 11, x FOR of 10 PEER MHz REVIEW lateral vibration mode. 8 of 14

Figure 6. SEMSEM photo photo of TPoS resonator. ( (aa)) Conventional Conventional structure; structure; ( (bb)) Resonator Resonator with quarter wavelength reﬂectorreflector structure;structure; ( c()c Resonator) Resonator with with 1D-PnC 1D-PnC on on the the supporting supporting tether tether (d) Resonator (d) Resonator with 1Dwith PnC-Reﬂector 1D PnC-Reflector Composite Composite Structure. Structure.

In Figure 6 6,, (a)(a) is is a a conventional conventional rectangular rectangular plate plate laterally laterally vibrating vibrating resonator, resonator, named named N; N; (b) (b) is ais aresonator resonator with with acoustic acoustic reﬂector reflector structure structure added added to to the the anchoringanchoring boundaries,boundaries, namednamed R, where the reflectorreﬂector structure is used as proposed in [[26].26]. This This is is only used as a control group to compare the anchor loss suppression effect of a 1D-PnC deployed on the tether. (c) is 1D-PnC deployed on the tether of resonator, named P, (d) is a resonator with a reflector and a 1D-PnC composite structure deployed on the anchoring boundaries and tethers respectively, named R+P. The combination of the two techniques can help the resonator to have reduced anchor loss than that of the techniques used independently as the reflectors can prevent the propagation of acoustic waves leaked from the phononic crystal. The electrical performance of the resonator obtained after fabrication is tested. The dust in the air, changes in ambient temperature and humidity should be taken in to considerations during measurement and testing as it will affect the output characteristics of the resonator as the size of the resonator is in the micron level, and the vibration amplitude during operation is usually only tens of nanometers. Due to the aforementioned reasons, the processed resonator is generally packaged to protect the stability of the device output, and for the resonator that is not packaged, the test work must be carried out in a clean room. There is no need for vacuum packaging as TPoS resonator is a piezoelectric resonator for which electromechanical conversion is through a piezoelectric film. Moreover, air is a natural high acoustic impedance material, and its acoustic impedance is much greater than the material of the resonator itself. The acoustic impedance mismatch between the two can effectively prevent the energy in the resonator from leaking into the air. Therefore, even the bare chip test will not have a large impact on its Q-factor. The resonators tested in this article are all bare chips as shown in Figure 7. The test environment is an ordinary clean room at room temperature and standard atmospheric pressure. The test platform used is shown in Figure 8.

Micromachines 2020, 11, 1130 8 of 13 anchor loss suppression effect of a 1D-PnC deployed on the tether. (c) is 1D-PnC deployed on the tether of resonator, named P, (d) is a resonator with a reflector and a 1D-PnC composite structure deployed on the anchoring boundaries and tethers respectively, named R+P. The combination of the two techniques can help the resonator to have reduced anchor loss than that of the techniques used independently as the reflectors can prevent the propagation of acoustic waves leaked from the phononic crystal. The electrical performance of the resonator obtained after fabrication is tested. The dust in the air, changes in ambient temperature and humidity should be taken in to considerations during measurement and testing as it will affect the output characteristics of the resonator as the size of the resonator is in the micron level, and the vibration amplitude during operation is usually only tens of nanometers. Due to the aforementioned reasons, the processed resonator is generally packaged to protect the stability of the device output, and for the resonator that is not packaged, the test work must be carried out in a clean room. There is no need for vacuum packaging as TPoS resonator is a piezoelectric resonator for which electromechanical conversion is through a piezoelectric film. Moreover, air is a natural high acoustic impedance material, and its acoustic impedance is much greater than the material of the resonator itself. The acoustic impedance mismatch between the two can effectively prevent the energy in the resonator from leaking into the air. Therefore, even the bare chip test will not have a large impact on its Q-factor. The resonators tested in this article are all bare chips as shown in Figure7. The test environment is an ordinary clean room at room temperature and standard atmospheric pressure. The test platform used is shown in Figure8. The equipment used for the test are:

1. Kesight N9914A 4GHz handheld vector network analyzer 2. Cascade EPS150RF Video Probe Station 3. GGB Picoprobe Model 10 Active Probe Holder 4. GGB Model 30-60-W-2-R-125 RF probe 5. Calibration chip (used for vector network calibration) 6.Micromachines SMA adapter 2020, 11, andx FOR coaxial PEER REVIEW cable 9 of 14

Figure 7. Resonator testing platform. Figure 7. Resonator testing platform.

The equipment used for the test are: 1. Kesight N9914A 4GHz handheld vector network analyzer 2. Cascade EPS150RF Video Probe Station 3. GGB Picoprobe Model 10 Active Probe Holder 4. GGB Model 30-60-W-2-R-125 RF probe 5. Calibration chip (used for vector network calibration) 6. SMA adapter and coaxial cable

Figure 8. Schematic diagram of the measurement platform.

When testing the resonator, first S21 measured with a wider frequency range, as there could be a frequency shift because of the processing accuracy errors. So measuring in a wider frequency range helps to determine the location of the resonant peak, and to observe the remaining multiple resonant peaks produced by the resonator. For this, a wide-band test was conducted first and the results are as shown in Figure 9.

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Figure 7. Resonator testing platform.

The equipment used for the test are: 1. Kesight N9914A 4GHz handheld vector network analyzer 2. Cascade EPS150RF Video Probe Station 3. GGB Picoprobe Model 10 Active Probe Holder 4. GGB Model 30-60-W-2-R-125 RF probe Micromachines 2020, 11, 1130 9 of 13 5. Calibration chip (used for vector network calibration) 6. SMA adapter and coaxial cable

Micromachines 2020, 11, x FOR PEER REVIEW 10 of 14 Figure 8. Schematic diagram of the measurement platform. Figure 8. Schematic diagram of the measurement platform.

FigureFigure 9. Broadband9. Broadband S21 S21 curve curve of of the the resonator, resonator, N isN theis the traditional traditional structure, structure, R isR theis the mirror mirror structure, structure, P isP theis the phononic phononic crystal crystal beam beam structure. structure.

WhenFrom testing Figure the 9, resonator,it can be observed ﬁrst S21 measuredthat an obvious with a resonance wider frequency peak appears range, asat there10.03 couldMHz, bewhich a frequencyis almost shift the same because as the of the resonance processing frequency accuracy obta errors.ined by So simulation measuring (10.05 in a wider MHz), frequency which proves range the helpscorrectness to determine of the the resonator location ofstructure the resonant design peak, regardle and toss observe of the small the remaining fabrication multiple process resonant error. In peaksaddition, produced there by are the many resonator. resonant For peaks this, a besides wide-band the resonant test was conductedfrequency. ﬁrstThe andmode the corresponding results are as to showneach inresonant Figure9 .peak are computed through eigen frequency analysis simulation with COMSOL MultiphysicsFrom Figure as9, shown it can be in observed Figure 10. that Although an obvious the resonancefrequency peakof these appears modes at 10.03is different MHz, whichfrom the is almostdesigned the basic same width as the extension resonance mode, frequency the frequencie obtaineds byare simulationseparated far (10.05 away, MHz), which which will provesnot affect thethe correctness normal operation of the resonator of the designed structure mode. design regardless of the small fabrication process error. In addition, there are many resonant peaks besides the resonant frequency. The mode corresponding to each resonant peak are computed through eigen frequency analysis simulation with COMSOL

Figure 10. The mode corresponding to each resonance peak in the broadband S21 curve.

Micromachines 2020, 11, x FOR PEER REVIEW 10 of 14

Figure 9. Broadband S21 curve of the resonator, N is the traditional structure, R is the mirror structure, P is the phononic crystal beam structure.

From Figure 9, it can be observed that an obvious resonance peak appears at 10.03 MHz, which is almost the same as the resonance frequency obtained by simulation (10.05 MHz), which proves the correctness of the resonator structure design regardless of the small fabrication process error. In addition, there are many resonant peaks besides the resonant frequency. The mode corresponding to Micromachineseach resonant2020 ,peak11, 1130 are computed through eigen frequency analysis simulation with COMSOL10 of 13 Multiphysics as shown in Figure 10. Although the frequency of these modes is different from the designed basic width extension mode, the frequencies are separated far away, which will not affect Multiphysics as shown in Figure 10. Although the frequency of these modes is diﬀerent from the the normal operation of the designed mode. designed basic width extension mode, the frequencies are separated far away, which will not aﬀect the normal operation of the designed mode.

Figure 10. The mode corresponding to each resonance peak in the broadband S21 curve. Figure 10. The mode corresponding to each resonance peak in the broadband S21 curve. By changing the measurement bandwidth, a single resonance peak S21, dB curve as shown in Figure 11 can be obtained, and the test results corresponds to the resonator structure in Figure6. It can be seen from Figure 11 that each S21 curve is very smooth, and there is no spurious mode around the resonance frequency that aﬀects main mode. Through the test, the center frequency ( fc) and insertion loss (IL) of the resonator can be directly obtained, and the loaded quality factor (Ql) of the resonator can be obtained by calculating the 3dB bandwidth given by the following relation:

fc Q = (7) l 3dB(∆ f ) − where ∆f is the 3dB band width. From Figure 11a and Table3, it can be noticed that the quality factor of the TPoS resonator with the conventional structure is very low, only 1570 compared to one with the acoustic reflectors are added to the anchoring boundaries which is about 1.8 times higher as shown in Figure 11b,c shows the electrical response of the resonator for which the 1D-PnC is deployed on the tethers. Compared with the conventional structure, its Q-factor has been significantly improved (about 2.8 times). Figure 11d shows the electrical response of the resonator which incorporated the two techniques (acoustic reflector and 1D-PnC) showing an improvement in the quality factor with about three times compared to the conventional structure. The experimental results show that the proposed method is very effective in enhancing the Q-factor by suppressing the anchor loss. However, the Q values for other resonant modes were not measured as the study gives due emphasis for the fundamental mode only. In this regard, even though there is no complete band gap at the other modes illustrated with Figure9, slight improvements were observed in the S21(dB) characteristics of these modes. This could be due to the increase in the acoustic impedance resulting from the deployment of 1D-PnC with scatterer holes. Micromachines 2020, 11, x FOR PEER REVIEW 11 of 14

By changing the measurement bandwidth, a single resonance peak S21, dB curve as shown in Figure 11 can be obtained, and the test results corresponds to the resonator structure in Figure 6. It can be seen from Figure 11 that each S21 curve is very smooth, and there is no spurious mode around

the resonance frequency that affects main mode. Through the test, the center frequency (𝑓 ) and insertion loss (IL) of the resonator can be directly obtained, and the loaded quality factor (𝑄𝑙) of the resonator can be obtained by calculating the 3dB bandwidth given by the following relation:

𝑓 𝑄 = (7) −3𝑑𝐵(∆𝑓) Micromachineswhere Δf is2020 the, 113dB, 1130 band width. 11 of 13

-20 -20

-30 -30

-40 -40

N R S21(dB) S21 (dB) -50 -50

-60 -60

-70 -70 9.75 9.90 10.05 10.20 10.35 9.75 9.90 10.05 10.20 10.35 Frequency (MHz) Frequency (MHz) (a) (b) -20 -20

-30 -30

-40 -40 P+R P S21 (dB) S21 (dB) -50 -50

-60 -60

-70 -70 9.75 9.90 10.05 10.20 10.35 9.75 9.90 10.05 10.20 10.35 Frequency (MHz) Frequency (MHz) (d) (c) Figure 11. The narrow band S21 curve of the resonator. (a) Conventional structure; (b) With acoustic Figure 11. The narrow band S21 curve of the resonator. (a) Conventional structure; (b) With acoustic reflector on the anchoring boundaries; (c) With 1D-PnC on the tether; (d) With 1D-PnC and acoustic reflector on the anchoring boundaries; (c) With 1D-PnC on the tether; (d) With 1D-PnC and acoustic reflector composite structure. reflector composite structure. Table 3. Average values of the measured electrical characteristics of the fabricated resonators. Table 3. Average values of the measured electrical characteristics of the fabricated resonators. NRPP + R N R P P + R Resonant frequency ( f0), MHz 10.03 10.03 10.03 10.03 InsertionResonant Loss (IL), frequency dB (𝑓),27.01 MHz 10.0322.79 10.03 10.0321.64 10.03 21.59 − − − − Loaded QualityInsertion factor (Q Lossl) (IL), 1570dB −27.01 2809 −22.79 − 444721.64 −21.59 4682 Loaded Quality factor (𝑄) 1570 2809 4447 4682 5. Conclusions From Figure 11a and Table 3, it can be noticed that the quality factor of the TPoS resonator with A new design approach for improving the quality factor of TPoS MEMS resonators is presented. the conventional structure is very low, only 1570 compared to one with the acoustic reflectors are By using the conjunction of acoustic reflectors and phononic crystals (PnCs), the displacement in the added to the anchoring boundaries which is about 1.8 times higher as shown in Figure 11b and Figure tethers is efficiently suppressed and the energy loss via the tethers is reduced. The acoustic reflectors 11c shows the electrical response of the resonator for which the 1D-PnC is deployed on the tethers. enables an unloaded Q-factor of up to 2809, showing a 1.8-fold enhancement over the conventional resonator. Whereas the one-dimensional phononic crystal on the tether shows an increased unloaded Q-factor to about 4447 which is about 2.8-fold enhancement. The conjunction of PnCs and reflectors enables the resonator to offer an unloaded Q up to 4682, showing a threefold enhancement over the conventional resonator. The effect of deploying the proposed 1D-PnC on the acoustic impedance change is taken as the next phase of this study.

Author Contributions: Conceptualization, J.L., T.B.W., J.B. and K.-y.H.; Data curation, J.L. and T.B.W.; Formal analysis, J.L. and T.B.W.; Funding acquisition, J.B.; Methodology, J.L., T.B.W., T.W., Z.W. and K.G.; Project administration, J.B.; Resources, J.L. and J.B.; Software, J.L., T.B.W., T.W., Z.W. and K.G.; Supervision, J.B. and K.-y.H. All authors have read and agreed to the published version of the manuscript. Micromachines 2020, 11, 1130 12 of 13

Funding: This work is financially supported by the grant from the National Natural Science Foundation of China, and the China Academy of Engineering Physics (Project Number: U1430102). Conflicts of Interest: The authors declare no conflict of interest.

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