Skyworks Solutions, Inc., Irvine, California, USA 2 Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Illinois, USA

Transcription

1 A Review of Lamé and Lamb Mode Crystal Resonators for Timing Applications and Prospects of Lamé and Lamb Mode PiezoMEMS Resonators for Filtering Applications C.S. Lam 1, Anming Gao 2, Chih-Ming Lin 1, Jie Zou 1 1 Skyworks Solutions, Inc., Irvine, California, USA 2 Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Illinois, USA cs.lam@skyworksinc.com Abstract- The first resonator based on Extensional Mode anchored at nodal points using the GT-cut of quartz crystal appeared in the 1940s. Though AT- and SC-cut Thickness-Shear (ThS) Mode of quartz crystal have been the resonant elements of choice in the timing market for decades, Lamé and Lamb Mode quartz crystal appeared a few years ago to complement the ATand SC-cut in the low MHz and hundreds of MHz small size quartz crystal market, respectively. For timing applications, high Q (Quality Factor) and low TCF (Temperature Coefficient of Frequency) of the quartz crystal are critical for frequency stability and the Coupling Factor (separation of series resonant frequency and parallel resonant frequency- very small for quartz crystal) impacts mainly the oscillator pullability. MEMS resonators (MRs)- capacitive, piezoresistive, piezoelectric (PiezoMEMS), etc. began to appear about 15 years ago to support the development of MEMS oscillators in competing with the entrenched crystal oscillators. PiezoMEMS resonators of different piezoelectric materials (AlN, LiTaO3, LiNbO3) and of different configurations/nomenclatures (Lamé Mode Resonator, Lamb Mode/Wave Resonator, Contour Mode Resonator, Laterally Vibrating Mode Resonator, Cross-Sectional Lamé Mode Resonator, etc.) have been studied by different research groups and startups and with the AlN one mainly for timing applications. As the timing market seems to have softened in recent years, the authors, from the industry s point of view, review the different PiezoMEMS resonator technologies from the Q, Coupling Factor and TCF aspects and their prospects in the filtering market which is experiencing tremendous growth. Keywords- Quartz Crystal, Plate Mode, Lamé Mode, Lamb Mode, PiezoMEMS Resonators, RF Filters, Timing, Filtering 1. Introduction In a 2016 review [1] one of the authors wrote The explosive growth of the smartphone market especially in supporting LTE (Long Term Evolution) to meet continuous demand for more and faster data transfer has drawn interest from many who want to know how timing and filtering components are used in smartphones to support the crowded spectrum and their future market opportunities. A smartphone is unequivocally a brilliant product and necessity of the digital age. However, its timing (frequency generation) and filtering (frequency control) functions still have to be processed by analog timing and filtering components. At the smartphone RF Front-End (RFFE), a clock is needed to set the frequency such that the door is opened at the right position in the RF spectrum. Then a filter is needed to ensure the door has the right width to pass the needed bandwidth. Both timing and filtering functions are important. Known to many, the timing and filtering functions in smartphones have been diligently supported for many years by some physically moving electromechanical components based on piezoelectric materials- quartz-based crystal, lithium tantalite (LT)- and lithium niobate (LN)-based surface acoustic wave (SAW) RF filter, and aluminum nitride (AlN)-based bulk acoustic wave (BAW) RF filter. At the end of the review the author wrote The evolving of hybrid SAW-BAW technology has also attracted attention. When the piezoelectric substrate is very thin, SAW IDT (Interdigital Transducer) excites BAW (plate) modes efficiently. This MEMS-type development is primarily for timing applications. As the filter/duplexer market continues to expand, it s expected to see more development effort in this area (Fig. 1). Fig. 1 Plate Mode Resonator [1] The first resonator based on Extensional Mode anchored at nodal points using the GT-cut of quartz crystal appeared in the 1940s. Though AT- and SC-cut Thickness-Shear (ThS) Mode of quartz crystal have been the resonant elements of choice in the timing market for decades, Lamé and Lamb Mode quartz crystal appeared a few years ago to complement the AT- and SC-cut in the low MHz and hundreds of MHz small size quartz crystal market, respectively. For timing applications, high Q (Quality Factor) and low TCF (Temperature Coefficient of Frequency) of the quartz crystal are critical for frequency stability and the Coupling Factor (separation of series resonant frequency and parallel resonant frequency- very small for quartz crystal) impacts mainly the oscillator pullability. MEMS resonators (MRs)- capacitive, piezoresistive, piezoelectric (PiezoMEMS), etc. began to appear about 15 years ago to support the development of MEMS oscillators in competing with the entrenched crystal oscillators. PiezoMEMS resonators of different piezoelectric materials (AlN, LiTaO 3, LiNbO 3) and of different configurations/nomenclatures (Lamé Mode Resonator, Lamb Mode/Wave Resonator, Contour Mode Resonator, Laterally Vibrating Mode Resonator, Invited Paper, 2018 International Symposium on Acoustic Wave Devices for Future Mobile Communication Systems, March 6~7, 2018, Chiba, Japan.

2 Cross-Sectional Lamé Mode Resonator, etc.) have been studied by different research groups and startups and with the AlN one mainly for timing applications. As the timing market seems to have softened in recent years, the authors, from the industry s point of view, review the different PiezoMEMS resonator technologies from the Q, Coupling Factor, and TCF aspects and their prospects in the filtering market which is experiencing tremendous growth. 2. Lamé Mode Quartz Crystal for Timing GT-cut quartz crystal (XZ-Plane Extensional Mode) was first developed in the 1940s for hundreds of khz frequency generation applications. Extensional vibrations (Fig. 4) of square/rectangular GT-cut quartz crystal plates were studied extensively by Lee et al. [6] in the 1980s. The earliest mounting of the GT-cut crystal had to be non-trivially soldered at the crystal plate center nodal points. [7] Kawashima et al. proposed holding the crystal at the plate corner/edge nodal points (Fig. 5) as at then photolithographic processing of the quartz crystal plates had become possible. In the last 15 years or so of miniaturizing efforts of quartz crystal for the portable equipment market, the focus was on the tens of MHz of ThS Mode AT-cut quartz (35.25 YX-cut). In some applications customers preferred using lower frequency (<20 MHz) quartz crystal for a few reasons including lower power planning. [2] Unfortunately, it s difficult to fabricate thick (Y-Axis) and small XZ dimensions AT-cut quartz crystal with beveled edges for energy trapping. [3] In 1996, Kawashima et al. [4] reported a 3 MHz Lamé Mode quartz crystal- based on the GT-cut [5] (Fig. 2) processed using photolithographic method. Fig. 4 Extensional Mode Vibrations [6] Fig. 2 GT-Cut Quartz [5] Kawashima et al. wrote When a ratio of width 2z 0 and length 2x 0 for a rectangular plate of isotropy in plane becomes integer, a Lamé mode resonator with nodal points at the four corners can be realized. For an anisotropic material of quartz crystal and LiNbO 3, it was reported that Lamé mode quartz crystal and LiNbO 3 resonators are achieved an aspect ratio Rxz (length 2x 0 / width 2z 0) = 1 for a GT-cut resonator coupled between width extensional mode and length extensional mode and at an aspect ratio R xz (=integer) for a LiNbO 3 resonator, respectively (Fig. 3). Fig. 5 Earlier 100 khz GT-Cut Quartz Crystal Mounted at the Plate Center Nodal Points (Left) [7] and Lamé Mode Quartz Crysal Mounted at Plate Corner Nodal Points (Right) [4] In the 1996 paper, Kawashima et al. [4] referred to a 1995 paper Lamé-Mode Piezoelectric Resonators using LiNbO3 Crystals (in Japanese) which became available in English in [8] In that paper by Mizumoto et al. of River Eletec, Q of 10,400 and motional resistance of 4.1Ω were reported for a khz LiNbO 3 Lamé Mode resonator (155 YX-cut LiNbO 3 square plate 4-corner mounted). Following the effort by Kawashima et al., Mizumoto et al. [9] (Fig. 6) revealed in 2006 the development of a 3.5x2.5x0.7 (mm) 4 MHz Lamé Mode quartz crystal as compared with a conventional bulky 11.9x2.6x2.6 (mm) 4 MHz AT-cut quartz crystal. Q of 145,000 and motional resistance of 79Ω were reported for the 4 MHz quartz Lamé Mode resonator. Fig. 6 Lamé Mode Simulations by Mizumoto et al [9] Fig. 3 Lamé Mode Simulations by Kawashima et al [4] 2

3 In 2014 River Eletec [10] formally announced its first 8~20 MHz Lamé Mode quartz crystal product family in 1.6x1.2 (mm) size (Table 1). The exceptional frequency-temperature (f-t) characteristic of GT-cut quartz crystal was also reported (Fig. 7). increases but the PMs also attenuate more compared with the Rayleigh mode. In the early days, substrates were thickness-increased to attenuate or bottom-roughened to scatter the PMs. The SSBWs can t be attenuated with such means. Assuming XY is the sagittal plane, SSPMs and FSPMs have predominant particle motion in the XY-Plane ( Lamb Mode ) and in the Z-Axis ( Shear Horizontal (SH) Mode ), respectively. As recently as 2015 McHugh et al. [13] studied the impact of Lamb and SH Plate Modes on thin 42 YX LiTaO 3 on Si TC-SAW (Temperature Compensated SAW). It s known that 42 YX LT operates in Leaky SAW (LSAW- right below the FSPM [14] ) mode. Table 1 Charateristics of Small Size Lamé Mode (GT-Cut) Quartz Crystals [10] Fig. 7 Frequency-Temperature Charateristics of Lamé Mode (GT-Cut)and AT-Cut Quartz Crystals [10] 3. Lamb Mode Quartz Crystal for Timing In 1976 Wagers [11] studied the spurious acoustic responses in SAW devices. Above the SAW main mode (Rayleigh Mode f o) of ST-cut quartz filter (Euler Angles (0,132.5,0 )), there exists (Fig. 8) Slow Shear Plate Modes (SSPMs 1.08f o), Fast Shear Plate Modes (FSPMs 1.6f o), Quasi-Longitudinal Plate Modes (QLPMs 1.8f o), and Surface Skimming Bulk Waves (SSBWs- FS-SSBW ~1.6f o & QL-SSBW~1.8f o). Fig. 9 Measured (with Feedthrough) and Calculated SSBWs and PMs of a ~90 MHz Rayleigh Mode ST-Cut Quartz SAW Filter [12] As the substrate gets thinner (h Quartz/λ is smaller), the intuition is that less number of PMs and no SAW are sustained. In fact in 2014 River Eletec [15] announced the world s first HF 300~1,200 MHz Lamb Mode (predominant particle motion in XY-Plane) quartz crystal product family in 5.0x3.2 (mm) size (Fig. 10 & Table 2). The exceptional cubic f-t characteristic similar to that of AT-cut quartz crystal was also achieved (Fig. 11) and was compared with the quadratic f-t characteristic of the ST-cut quartz SAW resonator. [16] However, River Eletec didn t disclose the details including the typical thickness/wavelength ratio (h Quartz/λ<5?) and the Euler Angles used for the thin quartz substrate. The authors are not aware of published papers before the product announcement like that of the HF Lamé Mode quartz crystal in Sec. 2. Fig. 8 Spurious Modes of a ~300 MHz Rayleigh Mode ST-Cut Quartz SAW Filter with Thickness/λ Ratio of ~90 The SSBWs arrive at the output IDT (Wavelength λ) before reaching the substrate s bottom. The PMs are substained by the substrate s top and bottom. These PM locations and strengths can be accurately predicted (Fig. 9). [12] When the substrate gets thicker (h Quartz/λ is larger), the number of PMs Fig. 10 HF Lamb Mode Quartz Crystals [15] 3

4 (Coined Contour Mode Resonator- CMR), f 0 α 1/W; and 3) PiezoMEMS resonator with thick piezoelectric layer (Coined Cross-Sectional Lamé Mode Resonator- CLMR), f 0 α 1/T & 1/W. f 0 is the resonant frequency. IDT fingers are in the Z-Axis direction. Table 2 Charateristics of Small Size HF Lamb Mode Quartz Crystals [15] Table 3 FBAR, CMR and CLMR [19] Fig. 11 Frequency-Temperature Charateristics of Lamb Mode Quartz Crystals and ST-Cut Quartz SAW Resonators [15] This IDT on Thin Piezoelectric Substrate/Film configuration is the basis of the development discussions of Lamé and Lamb Mode PiezoMEMS Resonators in the next few sections. The authors think, like any SAW devices, the Euler Angles information of the thin piezoelectric film (especially those of higher anisotropy) is important as they relate the orientation of the IDT (wave propagation direction) to the orientation of the thin piezoelectric film which results in specific particle motions. [17] Like in Sec. 7 the X-cut of LiNbO3 discussed and later on Olsson [18] depicted the three cases of 0, 20, and 90 (Fig. 12) which corresponded to the Euler Angles of (90,90,0 ), (90,90,-20 ) and (90,90,-90 ), respectively. IDT can be on both the top and bottom surfaces or only on the top surface (Fig. 13). [20] The Z dimension (IDT finger length, substrate dimension) sets mainly the resonator s motional and static values per the MBVD (Modified Butterworth Van Dyke) model. Fig. 13 IDT-Based Excitation: Thickness Field Excitation & Lateral Field Excitation [20] Table 4 shows the two coupling factors used in this review- 1) k 2 eff (Effective Coupling Constant) definition and its simpler forms [21] where f s is the series resonant frequency and f p is the parallel resonant frequency and 2) k 2 (Electromechanical Coupling Factor for IDT-based excitation) [22] where v o is the open circuit velocity and v m is the metallized (short) circuit velocity. Fig. 12 X-Cut LiNbO 3 [18] 4. Lamé and Lamb Mode PiezoMEMS Resonators PiezoMEMS resonators of different configurations/nomenclatures (Lamé Mode Resonator, Lamb Mode/Wave Resonator, Contour Mode Resonator, Laterally Vibrating Mode Resonator, Cross-Sectional Lamé Mode Resonator, etc.) can be confusing. Cassella et al. [19] gave a simple description (Table 3) for these three cases- 1) FBAR has top and bottom solid electrodes and f 0 α 1/T; 2) PiezoMEMS resonator with thin piezoelectric layer Table 4 k 2 eff & Its Simpler Forms Calculated from f s & f p [21] and k 2 Calculated from v o & v m [22] 4

5 f s and f p can be extracted from measurements or numerical simulations. v o and v m can be extracted from analytical calculations or numerical simulations. The Electromechanical Coupling Coefficient k 2 t is not used here as it s more related to the thickness-longitudinal vibration mode in BAW devices. This review covers the following cases (TC is for Temperature-Compensated)- AlN S 0 and S 1 Mode ScAlN S 0 Mode LiNbO 3 S 0/A 1/SH 0 Mode LiTaO 3 S 0/A 1/TC-A 1 and AlN TC-S 0 Mode 5. AlN S0 and S1 Mode PMR As in FBAR, the CMR and CLMR (Fig. 14- Red is largest displacement and blue is smallest/zero displacement) in general use C-Axis polycrystal AlN (// to Y-Axis). When the film is thin (say h AlN/λ=0.1), the S 0 mode with predominant particle motion in X-Axis (width extensional vibration) got excited (called CMR). When the film is thick (say h AlN/λ=0.5), the S 0 mode with predominant particle motion in XY-Plane got excited (called CLMR). The CLMR is actually similar to the Lamb Mode quartz crystal discussed in Sec. 3. The easy explanation is that for CLMR if we view it at the XY-Plane, it s like the Lamé Mode quartz/linbo 3 resonator discussed in Sec. 2 (Fig. 3). The authors will use the term PiezoMEMS Resonator (PMR) to cover both and also the SH one (similar to the FSPM in Sec. 3) in the rest of this paper for simplicity purpose. Fig. 16 ~500 MHz AlN Thin Film S 0 Mode PMR [24] Fig & 950 MHz AlN Thin Film S 0 Mode PMR [25] In 2016 Zhu et al. [26] and Cassella et al. [19] studied the 2.25 GHz and the 2.8 GHz thick film AlN S 0 Mode PMRs, respectively (Figs. 18 & 19). Fig. 14 AlN S 0 Mode CMR & CLMR Fig GHz AlN Thick Film S 0 Mode PMR [26] Fig. 15 Calculated k 2 eff vs h AlN/λ of Different IDT Electrode Materials of AlN S 0 Mode PMR [23] Fig. 15 shows the calculated k 2 eff vs h AlN/λ for different IDT electrode materials and for the top electrode only case and for the top and bottom electrode case of AlN S 0 Mode PMR. [23] Lin et al. [24] in 2011 and Gao et al. [25] in 2017 and studied the ~500 MHz and the 220 & 950 MHz thin film AlN S 0 Mode PMRs, respectively (Figs. 16 & 17). Spurious mode suppression techniques like apodization, mode conversion, etc. were proposed and successfully implemented. Fig GHz AlN Thick Film S 0 Mode PMR [19] 5

6 Many researchers have studied thin/thick film AlN S 0 PMR. The authors summarize their assessment of the current known performances of AlN thin/thick film S 0 Mode PMR in Table 5. They have slightly-dispersive velocity and are suitable for high frequency operation (λ=2μm equivalent to ~4.5 GHz). The highest k 2 eff reported approaches that of FBAR. Table 5 Current Known Performances of AlN Thin/Thick Film S 0 Mode PMR Fig GHz AlN S 1 Mode PMR [27] Higher order S 1 Mode exists with dispersive phase velocity above that of the S 0 Mode. Fig. 20 shows the mode shape (predominant particle motion in XY-Plane), the calculated phase velocity, and the k 2 vs h AlN/λ. Fig GHz AlN S 1 Mode PMR [28] Table 6 Current Known Performances of AlN S 1 Mode PMR Fig. 20 Mode Shape, Phase Velocity and k 2 vs h AlN/λ of AlN S 1 Mode PMR Gao et al. [25] in 2017 and Zuo et al. [27] in 2011 studied the 3.5 GHz and the 1.96 GHz AlN S 1 Mode PMRs, respectively (Figs. 21 & 22). Zou et al. [28] reported Q of 1,837 for a 1.34 GHz part in the highest Q for a AlN S 1 Mode PMR known so far (Fig. 23). k 2 eff though was only 0.42%. The authors summarize their assessment of the current known performances of AlN S 1 Mode PMR in Table ScAlN S0 Mode PMR ScAlN (Scandium-doped AlN) is being used in FBAR/SMR to increase the k 2 eff. In 2013 Konno et al. [29] studied the 2.7 GHz ScAlN S 0 Mode PMR (Figs. 24 & 25, Table 7). k 2 eff of 7.4% was reported but unfortunately the Q was very low (Qs 117 and Qp 129). Q degradation is also observed for FBAR when the AlN is Sc-doped. Fig. 24 Phase Velcoity & k 2 eff of AlN/ScAlN S 0 Mode PMR [29] Fig GHz AlN S 1 mode PMR [25] Fig GHz ScAlN S 0 Mode PMR [29] 6

7 Table 7 Current Known Performances of ScAlN S 0 Mode PMR 7. LiNbO3 S0/A1/SH0 Mode PMR In RF SAW filter applications, it s known some LSAW cuts of LiNbO 3 offer k 2 as high as 38%. [30] In 2013 Gong et al. [31] studied Rotated X/Y/Z-cut LiNbO 3 S 0 Mode PMR (h LiNbO3/λ<0.2). Fig MHz LiNbO 3 S 0 Mode PMR [32] Table 8 Current Known Performances of LiNbO 3 S 0 Mode PMR Higher order A 1 Mode (Fig. 29) exists with higher phase velocity above that of the S 0 Mode. Fig. 29 Mode Shape of LiNbO 3 A 1 Mode PMR Fig. 26 S 0 Mode Shape, Calculated Phase Velocity and k 2 vs Cut Angle (Rotated About X-Axis) for Different h LiNbO3/λ of X-Cut LiNbO 3 S 0 PMR [31] As in the case of AlN/ScAlN S 0 Mode PMR, the predominant particle motion of the LiNbO 3 S 0 Mode PMR is in the X-Axis. Calculations indicated the phase velocity could reach >7,000m/s and the k 2 could be as high as 25% (Fig. 26) when the angle was close to 30 to the Y-Axis for Rotated X-cut. Gong et al. [31] reported a 517 MHz LiNbO 3 S 0 Mode PMR with k 2 eff of 11.5% but unfortunately Q of only 352 was achieved. Excessive spurious modes were also observed (Fig. 27). Fig. 30 Calculated Phase Velocity and k 2 vs h LiNbO3/λ of Different Modes of ZX LiNbO 3 PMR [33] In 2011 Kadota et al. [33] calculated the phase velocity and the k 2 vs h LiNbO3/λ of different modes ZX LiNbO 3 PMR (Fig. 30). They also reported their 5.4 GHz ZX LiNbO 3 A 1 Mode PMR with 20.3% k 2 eff. The phase velocity was 15,200m/s. Q though was only at 560. Some spurious modes were also observed (Fig. 31). Fig MHz LiNbO 3 S 0 Mode PMR [31] In 2012 Wang et al. [32] reported their 463 MHz Y136 LiNbO 3 (Euler Angles (0,136,0 )?) S 0 Mode PMR with a k 2 eff of 7%. A Q of 1,500 was achieved- the highest for a LiNbO 3 S 0 Mode PMR known so far. Excessive spurious modes were also observed (Fig. 28). The authors summarize their assessment of the current known performances LiNbO3 S 0 Mode PMR in Table 8. Fig GHz ZX LiNbO 3 A 1 Mode PMR [33] 7

8 In 2017 Yang et al. [34] reported similar ZX LiNbO 3 A 1 Mode PMR at 5.25 and 4.35 GHz. k 2 eff extracted was 26.6% and 29%. Q though was only at 112 and 537. Some spurious modes were also observed (Fig. 32). The authors summarize their assessment of the current known performances ZX LiNbO3 A 1 Mode PMR in Table 9. Fig. 34 SH 0 Mode Shape and k 2 of Different Modes vs h LiNbO3/λ of 30 YX LiNbO 3 PMR [35] In 2013 Kadota et al. [36] reported their 430~560 MHz 30 YX LiNbO 3 SH 0 Mode PMR using very thin LiNbO3 (0.06~0.08 h LiNbO3/λ) with ~23% k 2 eff and improved spurious mode suppression (Fig. 35). Q though was still only at 290. Fig & 4.35 GHz ZX LiNbO 3 A 1 Mode PMR [34] Fig ~560 MHz 30 YX LiNbO 3 SH 0 Mode PMR [36] Table 9 Current Known Performances of ZX LiNbO 3 A 1 Mode PMR In 2012 Kadota et al. [35] calculated the phase velocity of different modes of 30 YX LiNbO 3 vs h LiNbO3/λ and noted the SH 0 Mode (Shear Horizontal Mode) was non-dispersive (Fig. 33). Then k 2 vs the θ of the Euler Angles (0,θ,0) under different h LiNbO3/λ was calculated for the SH 0 Mode. In 2016 Song et al. [37] reported similar SH 0 Mode PMR using 80 YX LiNbO 3 at ~100 MHz. k 2 eff extracted was 16.1%. Q was 952. Some spurious modes existed but could be suppressed to some extent (Fig. 36). Fig MHz 80 YX LiNbO 3 SH 0 Mode PMR [37] The authors summarize their assessment of the current known performances YX LiNbO3 SH 0 Mode PMR in Table 10. Fig. 33 Phase Velocity of Different Modes of 30 YX LiNbO 3 PMR and k 2 vs θ of the Euler Angles (0,θ,0) of Different h LiNbO3/λ of LiNbO 3 SH 0 PMR [35] Very high k 2 was obtained for 30 YX LiNbO 3 (Euler Angles (0,120,0)) when h LiNbO3/λ became small (Fig. 34). Table 10 Current Known Performances of YX LiNbO 3 SH 0 Mode PMR 8. LiTaO3 S0/A1/TC-A1 and AlN TC-S0 Mode PMR In 2010 Kando et al. [38] calculated the spurious mode strength vs θ of the Euler Angles (0,θ,0 ) of different LiTaO 3 LMR Modes (Fig. 37). They also reported the phase velocity, k 2 8

9 and TCF vs θ of the Euler Angles (0,θ,0 ) of LiTaO 3 A 1 Mode LMR (Fig. 38). In 2011 Kando et al. [40] reported the TC version of 3.5 GHz 121 YX LiTaO 3 A 1 Mode PMR with k 2 eff of 7% (Fig. 41). Again Q value was not reported as in their 2010 paper. [38] Fig. 37 Spurious Mode Strength vs θ of the Euler Angles (0,θ,0 ) of Different LiTaO 3 PMR Modes [38] Fig GHz LiTaO 3 TC-A 1 Mode PMR [40] A year earlier in 2010 Lin et al. [41] reported the TC version of a 711 MHz AlN S 0 Mode PMR with Q of 1,000, k 2 eff of 0.56%, and 1 st TCF of zero at room temperature (Fig. 42). Fig. 38 Phase Velocity, k 2 and TCF vs θ of the Euler Angles (0,θ,0 ) of LiTaO 3 A 1 Mode PMR [38] In 2014 Wang et al. [39] reported their 870 MHz LiTaO 3 S 0 Mode PMR. Q of 2,000 and low TCF of -20ppm/ C were recorded. However, k 2 eff of only 0.9% was recorded (Fig. 39). In their 2010 paper Kando et al. [38] also presented the results of a 3.38 GHz 121 YX LiTaO 3 A 1 Mode PMR (Fig. 40). Good k 2 eff of 8% and modest -38ppm/ C TCF were recorded. Q value was not reported. No strong spurious modes were observed. Fig & 711 MHz TC-AlN S 0 Mode PMR [41] The authors summarize their assessment of the current known performances of YX LiTaO 3 S 0/A 1/TC-A 1 Mode PMR in Table 11. Table 11 Current Known Performances of YX LiTaO 3 S 0/A 1/TC-A 1 Mode PMR 9. Prospects of PMR for RF Filtering Fig MHz LiTaO 3 S 0 Mode PMR [39] Fig GHz LiTaO 3 A 1 Mode PMR [38] The development of AlN PMR, AlN FBAR/SMR, capacitive MR and piezoresistive MR to support MEMS oscillator for timing applications [42] was started more than a decade ago to compete with the entrenched crystal oscillator which uses high Q, low impedance, and low TCF quartz crystal as the resonant element. High Q means the oscillator is more stable; low impedance means the resonant element damps slower such that less energy is needed to sustain vibration; and low TCF means the oscillator drifts less over temperature. It seems though the now surviving MEMS oscillator in the competitive timing market is the one which uses capacitive MR. [43] With the continuous increase of RF filter usage in the RFFE [44,45] of smartphones, it s encouraging to see more research effort is being put into PMR development for 9

10 filtering applications. In 2012 IWPC Mobile RF Filter Group [46] released a comprehensive report on RF filter technology to encourage the FCC to consider the present limits of RF filtering technology when establishing spectrum rules & regulations. The impact of Q (series resonant Q s and parallel resonant Q p), k 2 eff, and TCF of the then available SAW/FBAR/SMR resonator technologies on insertion loss, bandwidth, transition bandwidth, attenuation, etc. in covering the key RF bands was well discussed. Today there are still no other technologies which can compete with SAW/FBAR/SMR in terms of performance, cost and size which customers care most. In the meantime, more bands are being added. [45,47] In addition, multiplexing, carrier aggregation (CA), diversity, increased power handling, etc. create further demand for even better filter performance. This paper doesn t and can t cover all types of PMR researchers have worked on and with great progress. The authors summarize in Table 12 the known performances of different PMRs reported in the previous sections. materials of different kind, different modes, different configurations, etc. It s probably the time to try outside the box also in order to break out from the current struggle of achieving better Q, k 2 eff and TCF at the same time. May thicker PMR with interfacial-layers be able to offer something unexpected? One of the authors wrote in 2004 [17] - In the earlier days of SAW filter development, electrode finger reflection was to be suppressed to reduce passband ripples. Finger reflection today instead is the corner stone allowing us to realize low-loss SAW filters. As in other sciences, SAW researchers sometimes need to slow down and look back what we missed in the past. What was bad in the past may now be important. With persistent study of this material, we shall see more surprises in the future The authors look forward to great surprises from the PMR researchers with performance, cost and size in mind so the RF filter industry has additional technology to support its growth. It s known though that not all LTE bands always needs high Q, high k 2 eff, and low TCF. [46,47] Combinations of optimized Q, k 2 eff, and TCF need to be examined based on Tx and Rx separation (in the case of duplexer), transition bandwidth requirements, out of band reflectivity, attenuation level requirements for nearby bands, etc. It s possible certain PMRs can support some filter bands now. However, it may be difficult for filter suppliers to support SAW, FBAR/SMR, and PMR productions at the same time. Table 12 Summary of Performances of Different PMRs References From Table 12 it s clear PMR is still struggling with what SAW/FBAR/SMR have been struggling all along- for the 3 key parameters (Q, k 2 eff and TCF), how to improve on one without degrading too much the other two? The announcement of IHP SAW by MuRata in 2016 [48] was a great encouragement for the filter industry especially the SAW one. For the first time, the SAW industry showed that it s POSSIBLE to have it all- better Q, better k 2 eff and better TCF. The study of thin LiTaO 3 on Silicon, Sapphire, Spinel, etc. isn t new (Fig. 43). [49,50] Takai et al. chose to try ( outside the box ) using ultrathin LiTaO 3 (<1μm? and with some interfacial-layers) which resulted in minimizing the LSAW leakage and in achieving dramatic (or incredible as coined) improvement of Q p. Fig. 43 LiTaO 3 on Low Temperature Coefficient of Expansion Material [49] As seen in this review, PMR researchers for many years have done great work on using thin/ultrathin piezoelectric 1. C.S. Lam, A Review of the Timing and Filtering Technologies in Smartphones, Proc. IEEE Int l Ultrasonics Symposium, C.S. Lam et al., Aging Performance of Small Size MHz Quartz Crystal Under High Drive, Proc. Symposium on Piezoelectricity, Acoustic Waves, and Device Applications, Shenzhen, China, S.Y. Pao et al., Beveling AT-cut Quartz Resonator Design by an Efficient Numerical Method, Proc. IEEE Int l Ultrasonics Symposium, H. Kawashima et al., Lamé-Mode Quartz Crystal Resonators, Proc. IEEE Int l Frequency Control Symposium, James Ransley, 2014, nderstanding-standards. 6. P. C. Y. Lee et al., Extensional Vibrations of Rectangular Crystal Plates, Journal of Applied Physics 53, 4081, khz GT-Cut, 2018, GLASS-ENVELOPE-RESONATOR-FREQUENCY-10 0-kHz-HUGE-BLANK-GT-cut-/ K. Nakamura et al., Lamé-Mode Piezoelectric Resonators Using LiNbO 3 Crystals, Electronics and Communications in Japan, Part 2, Vol. 79, No. 2,

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