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quartz layered substrates for high frequency resonators
Ultrasonics 95 (2019) 1–5
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High-velocity non-attenuated acoustic waves in LiTaO3/quartz layered substrates for high frequency resonators
T
Natalya F. Naumenko Acousto-Optical Research Center, National University of Science and Technology “MISIS”, Moscow 119049, Russia
A R T I C LE I N FO
A B S T R A C T
Keywords: Acoustic wave Layered structure Leaky wave SAW resonator
Multilayered substrates for Surface Acoustic Wave (SAW) devices are able to combine SAW characteristics that cannot coexist in a single crystal substrate and, thus, meet the strong requirements of the new class of SAW devices developed for the next generations of communication systems. Recently, high performance resonators arranged on LiTaO3/quartz bonded wafers and utilizing shear horizontally polarized acoustic waves were reported. Leaky SAWs with quasi-longitudinal polarization propagate faster and can facilitate fabrication of high frequency SAW devices but generally leak strongly into the substrate. This paper describes how the LiTaO3/ quartz structure can be optimized to allow longitudinal SAWs to propagate without attenuation. Due to the symmetry consideration, which is supplemented by a rigorous numerical simulation of the admittance functions of SAW resonators and an accurate extraction of the propagation losses, the found optimal LiTaO3 and quartz orientations with the optimized LiTaO3 thickness ensure the propagation of acoustic waves with a velocity exceeding 5400 m/s and an electromechanical coupling of 6.8% in resonators with Q factors up to 10,000. The optimal LT/quartz structures with plate thicknesses varying between 0.32 and 0.68 wavelengths can be employed in SAW resonators operating at high frequencies, up to 5 GHz. The existence of numerous orientations in quartz supporting the propagation of non-attenuated longitudinal SAWs is explained based on the concept of exceptional bulk waves, which is a part of SAW theory.
1. Introduction The next generation of mobile communication systems (5G) is characterized by very narrow gaps between the operating frequency bands and assumes the application of filters with steep bandpass edges. The surface acoustic wave (SAW) resonators and resonator filters that are required for such systems must provide very high quality (Q) factors and a low temperature dependence of the main device parameters in addition to high frequencies and low insertion losses. The regular SAW substrate materials that are used in SAW resonator filters, such as LiNbO3 (LN) or LiTaO3 (LT), cannot satisfy all these requirements. Therefore, in recent years, multilayered structures combining layers with different properties are extensively studied as alternatives to regular SAW substrates. For example, the structures using thin LN or LT plates bonded to silicon (Si) wafers were theoretically and experimentally investigated and demonstrated promising combinations of a high electromechanical coupling coefficient k2, a low temperature coefficient of frequency (TCF) and excellent Q-factors [1–3] that are limited only by the quality of the fabrication techniques, which is continuously improved. The further improvement of SAW device performances can be achieved if the Si substrate is replaced by strongly anisotropic
quartz, which is known as one of few materials with positive temperature coefficients for some elastic constants. The theoretical investigation of acoustic waves in LT/quartz [4–6] revealed that shear horizontally (SH) polarized waves can propagate in resonator structures with a high coupling k2 > 11% and a low TCF if the LT and quartz orientations and the electrode and plate thicknesses are optimized properly. Some of these results were already experimentally confirmed [7]. The velocities of SH waves propagating in LT plates bonded to a supporting substrate are limited by the waves’ nature and usually do not exceed 4200 m/s. Acoustic modes propagating faster could facilitate the fabrication of high frequency SAW devices, especially when the operating frequency exceeds 5 GHz. This paper reports on the existence of high velocity SAWs in LT/quartz with promising characteristics that are desirable for the application in high performance high frequency SAW devices. The velocities of these waves are close to those of the quasi-longitudinal bulk acoustic waves (BAW) in LT crystal. An example of low-attenuated longitudinal leaky SAW (LLSAW) propagating in LT/quartz was recently reported by Hayashi [8]. The structure combined the non-symmetric orientations of LT (X,Y + 31°cut) and quartz (X,Y + 32°-cut). Though the found LLSAW propagates
E-mail address: [email protected]. https://doi.org/10.1016/j.ultras.2019.03.001 Received 14 January 2019; Received in revised form 26 February 2019; Accepted 1 March 2019 Available online 02 March 2019 0041-624X/ © 2019 Published by Elsevier B.V.
Ultrasonics 95 (2019) 1–5
N.F. Naumenko
with very low losses, shows negligible beam steering angle and sufficient electromechanical coupling, its potential application in high-frequency resonators is limited by the requirement of a very low LT plate thickness, hLT = (0.06–0.08) λ, where λ = 2p and p is the periodicity of electrode structure, or (0.08–0.1) μm at 5 GHz frequency. In such nonsymmetric layered structures, leakage of LLSAW into the substrate is generally caused by radiation of two BAWs. Hence, suppression of propagation losses requires simultaneous optimization of three parameters, for example, substrate orientation, plate thickness and electrode thickness. As a result, fabrication of the found layered structure for its further application in high-frequency SAW devices may be a challenge if the optimized LT thickness is too small or electrodes are too thin. If one of the bulk waves in a substrate is uncoupled with the longitudinal leaky SAW, due to symmetry, zero attenuation can be achieved via variation of a plate thickness and orientation of a substrate [9,10] while the LT cut and the electrode thickness can be selected independently to provide a high electromechanical coupling and a sufficient reflectivity in a SAW resonator. An example of symmetric LT/ quartz structure supporting propagation of a low-attenuated longitudinal wave was reported in [6]. The optimal structure with LT thickness hLT = 0.28 λ, or 0.3 μm at 5 GHz frequency, is compatible with the reported experimental devices on LT/quartz [7] and can be further improved using optimization technique described hereafter and starting from the symmetry consideration of the combined materials. To find the optimal structures that allow for the propagation of the high-velocity waves with negligible leakage into quartz, first, potentially useful combinations of LT and quartz orientations were determined based on the symmetry of two crystals. Then, the range of the LT orientations with the maximum electromechanical coupling of the quasi-longitudinal wave was estimated. Finally, a rigorous numerical technique was applied to optimize the LT/quartz structures for SAW resonators via the variation of the Euler angles and LT plate thicknesses, with a finite thickness of the periodic metal grating taken into account.
Fig. 1. Slowness surfaces of (0°, 34°, 90°)-LT and (0°, 30°, 90°)-quartz and the wave vectors of three sagittally polarized modes (kLT−, kLT+ and kQ+) that are involved in the solution with a velocity of V.
(kLT+ and kLT−) and the one mode in quartz (kQ+), which contribute to the leaky SAW solution, can be geometrically determined for a wave propagating with a velocity of V. In each material, one of the BAWs (dotted lines) is not radiated due to symmetry. In LT/quartz, the coupling coefficient k2 is dominated by the LT orientation while the leakage into the substrate depends on the quartz orientation. To focus the search for the LT cuts providing the maximum coupling, the velocities of three BAWs were calculated in the YZ plane of LT with the piezoelectric effect and without it. Fig. 2 shows these velocities as functions of the propagation angle with the Y axis. The difference ΔV resulting from the piezoelectric effect may be used for the estimation of the BAW coupling as k2 ≈ 2∙ΔV/V. Fig. 3 shows the polar diagram of k2 that is obtained for the quasi-longitudinal wave propagating in the YZ cut of LT. The maximum k2 occurs when the BAW propagates along the direction Y + 30° and the normal to the LT surface is parallel to Z + 30°. Such a SAW orientation is described by the Euler angles (0°, 30°, 90°). More accurate simulations with the beam steering angle taken into account yield (0°, 35°, 90°) as the optimal LT cut for achieving the highest electromechanical coupling of the longitudinal leaky SAW. In LT/quartz structures with a fixed LT orientation (0°, 35°, 90°), the variation of the quartz cut was further used to suppress leakage into the substrate. For this purpose, longitudinal leaky waves were numerically investigated in LT plates bonded to (0°, ϴ, 90°) cuts of quartz. The minimum achievable attenuation was estimated for each ϴ via the variation of the LT thickness in the interval hLT = (0.3–0.7) λ. Computations were made for Cu electrodes that were 0.05 λ thick. The
2. Optimization of LiTaO3/quartz structure In a thin plate bonded to a half-infinite substrate, acoustic waves can be generated by using an interdigital transducer (IDT) arranged on the plate surface. Though, in general, such a wave has a complicated structure, hereafter we will call it a SAW or leaky SAW for simplicity. Such a SAW is not confined in the plate and leaks into the substrate if its velocity is higher than the cut-off BAW velocity in the specified orientation of the substrate material. If VLS, VFS and VSS are the velocities of the quasi-longitudinal, fast quasi-shear and slow quasi-shear BAWs in a substrate, respectively, then a SAW propagating with a velocity of VFS < V < VLS generally radiates into two tilted BAWs and leaks strongly into the depth of a substrate. Leakage can be reduced if one of two shear BAWs is uncoupled with the electric field, due to symmetry, and further suppressed if the contribution of the second BAW into the wave structure is minimized [9,10]. According to the symmetry of the LT and quartz crystals, one of the BAWs propagating in the YZ plane is pure shear and polarized along the X axis. This wave is uncoupled with two other BAWs (quasi-longitudinal and quasi-shear) propagating in the YZ plane and polarized in the same plane. In quartz (symmetry class 32), only pure shear BAW is coupled with the electrostatic potential. In contrast, in LT (symmetry class 3m), the pure shear BAW is uncoupled with the electric field while two BAWs that are polarized in the YZ plane are piezo-active. Hence, if a multilayered structure combines the rotated YX cuts of LT and quartz with X + 90° propagation direction (orientations defined by the Euler angles (0°, ϴ, 90°)), the sagittal plane is parallel to the YZ plane of crystal, and a sagittally polarized SAW propagating with a velocity of V < VLS couples only with the sagittally polarized quasi-shear BAW in quartz. Fig. 1 shows an example of the slowness surfaces of LT plate and quartz substrate combined in the bonded wafer with orientations defined by the specified Euler angles and explains how the wave vectors of the two modes in the LT plate
Fig. 2. Velocities of three bulk waves (VL > VF > VS) propagating in the YZ plane of LT obtained with and without piezoelectric effect. SH polarized wave (black lines) is uncoupled with the electric field. 2
Ultrasonics 95 (2019) 1–5
N.F. Naumenko
Fig. 3. Electromechanical coupling of the quasi-longitudinal BAW as a function of the propagation direction in the YZ plane of LT.
numerical technique SDA-FEM-SDA combining the finite element modeling (FEM) analysis of electrodes with the spectral-domain analysis (SDA) of a multilayered substrate [11] was used to compute the admittance functions of SAW resonators built on LT/quartz and extract the complex SAW velocities VR = 2pfR·(1 + jδR) and VA = 2pfA·(1 + jδA) from the admittance functions at the resonant fR and anti-resonant fA frequencies, respectively. The found attenuation (propagation loss) at the resonance (δR) or the anti-resonance (δA) determine the Q-factors of the SAW resonators, QR,A ∼ (δR,A)−1. The estimated losses are associated only with leakage into bulk waves. Other loss mechanisms (electrode resistance, viscous losses, etc.) were ignored. Fig. 4 shows the minimum attenuation δR as a function of the Euler angle ϴ. With the LT thickness changing continuously within four different ranges, δR < 0.001 dB/λ was found in each range. Such low δR values were obtained for quartz orientations of (0°, 38°, 90°), (0°, 75°, 90°), (0°, 110°, 90°) and (0°, 125°, 90°). The existence of multiple orientations in quartz, which allow for the propagation of longitudinal leaky SAWs with negligible attenuation when the quartz substrate is combined with the LT plate, can be explained by the existence of quasilongitudinal exceptional bulk waves in quartz cuts of (0°, 48°, 90°), (0°, 70°, 90°), (0°, 105°, 90°) and (0°, 145°, 90°) [12]. The exceptional bulk wave [13] satisfies the stress-free mechanical boundary conditions on the selected crystal surface and breaks the sufficiency condition for the existence of Rayleigh SAW, according to Lothe-Barnett theorem [14,15]. Such waves exist in any crystal. Usually, they are (quasi)shear, but in some crystals with strong acoustic anisotropy, for example quartz, quasi-longitudinal exceptional waves were also found [12].
Fig. 5. Contour plot of attenuation δR in dB/λ as a function of the plate thickness h/λ and Euler angle ϴ in (0°, 35°, 90°)-LT bonded to (0°, ϴ, 90°)quartz calculated around the optimal point: ϴ = 38°, h/λ = 0.36.
When a thin LT plate is loaded on a quartz substrate, the boundary condition at the LT/quartz interface continuously deviates from the stress-free state as the plate thickness increases. As a result, the optimal quartz orientations providing propagation of non-attenuated waves change. An additional shift arises from the mass load imposed by the electrodes of the grating. It should be mentioned that in LT/quartz with the quartz orientation of (0°, ϴ, 90°), the optimal angle ϴ, which allow for the propagation of the non-attenuated longitudinal leaky SAW, does not continuously move as the LT thickness increases. In each of the analyzed intervals of the LT thickness, the minimum leakage occurs at a certain point in the two-dimensional space (hLT, ϴ) when the electrode thickness hEl is fixed (as shown in Fig. 5) or at a certain point in the space (hEl, ϴ) when the LT thickness is fixed. Such behavior is typical for the high-velocity leaky waves and was previously observed in diamond and sapphire with zinc oxide films [9] and in LT substrates with a thick gold film or a periodic gold grating [16]. It is different from the behavior of the SH-type leaky waves, for example in ϴ-rotated YX cuts of LT with metal film or periodic grating, where negligible attenuation was observed along the line in the 2D space (hEl, ϴ) when ϴ varies between 36° and 54° [17]. The LT thicknesses that are required to achieve the maximum Qfactors QR and QA in SAW resonators using LT/quartz do not coincide. Moreover, the simulations reveal that it is easier to obtain high Q-factors at the resonance than at the anti-resonance. Fig. 6 shows two examples of the simulated admittance functions of SAW resonators using LT plates with Euler angles (0°, 35°, 90°) bonded to quartz orientations of (0°, 40°, 90°) and (0°, 120°, 90°) with Cu grating on top. The optimal LT plate thicknesses of 0.36 λ and 0.41 λ, respectively, provide theoretical values of QR > 104 in these structures, but the QA values are much lower. Though the analyzed quartz orientations differ by 80°, the velocity (VR ≈ 5435 m/s) and coupling (k2 ≈ 6.8%) are almost the same for both structures. It can be explained by the dominant influence of the LT orientation on the main wave characteristics. The displacement fields following the wave propagation at the resonant frequency are illustrated by the colored diagrams of the longitudinal (u1) and shear vertical (u3) components (insets to Fig. 6). The shear horizontal component (u2) is negligible due to the symmetry of the analyzed LT and quartz orientations. In both structures, the longitudinal motions are almost totally confined in the LT plate. The vertical motions penetrate deeper into the quartz substrate but do not increase with the depth. A typical ladder filter design includes series and shunt SAW resonators and requires a high Q-factor at the resonance or at the anti-
Fig. 4. Minimum achievable attenuation δR as a function of the Euler angle ϴ in (0°, 35°, 90°)-LT bonded to (0°, ϴ, 90°)-quartz, which were obtained for Cu electrode thickness hCu = 0.05λ via the optimization of the LT thickness for each ϴ. 3
Ultrasonics 95 (2019) 1–5
N.F. Naumenko
resonance. To fabricate resonators with high QR and high QA on the same layered structure with a fixed LT thickness, varying the duty factor a/p (the electrode width to the period ratio) can be applied instead of varying the LT thickness. Fig. 7 shows VR, VA, QR and QA as functions of the duty factor in (0°, 34°, 90°) LT bonded to (0°, 30°, 90°) quartz with hLT = 0.32λ. When a/p < 0.3 or a/p > 0.65, the Q-factor exceeds 5000 at the anti-resonance or at the resonance, respectively. Three examples of the simulated admittances with high QR, high QA and QR ≈ QA are shown in Fig. 8. In a wide range of frequencies, two modes with velocities 2700–2800 m/s and 5300–5700 m/s are generated by the IDT. For comparison, the simulated admittance is shown for the non-symmetric LLSAW structure suggested by Hayashi, with hLT = 0.0625 λ and hAl = 0.005 λ . In (0°, 34°, 90°)-LT/(0°, 30°, 90°)quartz, higher reflectivity can be achieved in SAW resonators due to heavier Cu electrodes but the velocity decreases with metal thickness. In non-symmetric structures, low reflectivity in conjunction with the complex reflection coefficient manifests itself by a spurious mode at the resonator stopband edge. In the analyzed LLSAW-Hayashi structure, perturbation occurs between the resonant and anti-resonant frequencies. These simulations agree with reported in [8] and confirm the advantages of symmetric layered structures over non-symmetric.
Fig. 6. Admittances of two SAW resonators using (0°, 35°, 90°)-LT/(0°, 40°, 90°)-quartz and (0°, 35°, 90°)-LT/(0°, 120°, 90°)–quartz structures with LT thicknesses that are optimized for the maximum QR. The acoustic wave structure is shown at the resonant frequency as colored diagrams of the tangential (u1) and vertical (u3) motions.
3. Conclusions Longitudinal high-velocity leaky SAWs were theoretically investigated in layered structures combining a thin LT plate with an anisotropic quartz substrate and a Cu grating on top with respect to their potential application in high performance, high frequency SAW resonators. The selection of the proper LT and quartz orientations based on the symmetry of two crystals, along with the further optimization of the cut angle of the quartz substrate and the LT plate thickness, revealed that longitudinal SAWs can propagate with velocities of V > 5400 m/s, electrochemical coupling of k2 > 6.8% and a negligible attenuation required to design high-Q resonators. Due to strong acoustic anisotropy of quartz, multiple orientations exist that allow for the propagation of non-attenuated high-velocity SAWs when an LT plate is loaded on a quartz substrate. The thicknesses of Cu electrodes (hCu = 0.05 λ ) and LT plates (hLT = (0.32–0.65)λ) in the found optimal structures stay sufficiently large (550 Å and 0.35–0.7 μm, respectively) and compatible with the existing fabrication technologies for SAW devices on bonded wafers when the operating frequency grows up to 5 GHz.
Fig. 7. Velocities at the resonance (VR) and the anti-resonance (VA) and the Qfactors (QR, QA) as functions of the duty factor for (0°, 34°, 90°)-LT/(0°, 30°, 90°)-quartz with an LT thickness of hLT/λ = 0.32 and a Cu electrode thickness of hCu/λ = 0.05.
Acknowledgements The research was partly supported by the Ministry of Education and Science of the Russian Federation (Project 02.A03.21.0004). References [1] M. Kadota, S. Tanaka, Wideband acoustic wave resonators composed of hetero acoustic layer structure, Jpn. J. Appl. Phys. 57 (2018) 07LD12, https://doi.org/10. 7567/JJAP.57.07LD12. [2] M. Kadota, S. Tanaka, Solidly mounted resonator using shear horizontal mode plate wave in LiNbO3 plate, in: 2016 IFCS Proceedings, New Orleans, LA, USA, 9–12 May 2016. https://doi.org/10.1109/FCS.2016.7546795. [3] N.F. Naumenko, Multilayered structures using thin plates of LiTaO3 for acoustic wave resonators with high quality factor, Ultrasonics 88C (2018) 115, https://doi. org/10.1016/j.ultras.2018.03.014. [4] M. Kadota, S. Tanaka, Improved quality factor of Hetero Acoustic Layer (HAL) SAW resonator combining LiTaO3 thin plate and quartz substrate, in: 2017 IUS Proceedings, Washington, DC, USA, 6–9 Sept 2017; https://doi.org/10.1109/ ULTSYM.2017.8092963. [5] M. Gomi, T. Kataoka, J. Hayashi, S. Kakio, High-coupling leaky surface acoustic waves on LiNbO3 or LiTaO3 thin plate bonded to high-velocity substrate, Jpn. J. Appl. Phys. 56 (2017) 07JD13, https://doi.org/10.7567/JJAP.56.07JD13. [6] N. Naumenko, Suppression of propagation losses in TC SAW resonators using thin plates of LiTaO3 bonded to quartz substrates, in: 2018 IUS Proceedings, Kobe, Japan, 22–25 Oct 2018; https://doi.org/10.1109/ULTSYM.2018.8579813. [7] M. Kadota, Y. Ishii, T. Shimatsu, M. Uomoto, S. Tanaka, Spurious-free, near-zero-
Fig. 8. Admittances and estimated Q-factors of SAW resonators using (0°, 34°, 90°)-LT/(0°, 30°, 90°)-quartz with an LT thickness of hLT/λ = 0.32, a Cu thickness of hCu/λ = 0.05 and three duty factors: a/p = 0.3, 0.37 and 0.7, compared to the admittance of a resonator using LLSAW-Hayashi structure [8].
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[8]
[9]
[10]
[11]
[12] N.F. Naumenko, Application of exceptional wave theory to materials used in surface acoustic wave devices, J. Appl. Phys. 79 (1996) 8936, https://doi.org/10.1063/1. 362624. [13] P. Chadwick, G.D. Smith, Foundations of the theory of surface waves in anisotropic elastic materials, Adv. Appl. Mech. 17 (1977) 303. [14] D.M. Barnett, J. Lothe, Consideration of the existence of surface wave (Rayleigh wave) solutions in anisotropic elastic crystals, J. Phys. F4 (1974) 671–686. [15] V.I. Alshits, A.N. Darinskii, A.L. Shuvalov, Elastic waves in infinite and semi-infinite anisotropic media, Physica Scripta T44 (1992) 85–93. [16] N.F. Naumenko, A numerical investigation of HVPSAW in LiTaO3 with uniform gold film and periodic gold grating, in: 2001 IUS Proceedings, Atlanta, GA, USA, 7–10 Oct. 2001; https://doi.org/10.1109/ULTSYM.2001.991602. [17] N. Naumenko, B. Abbott, Optimized cut of LiTaO3 for resonator SAW filters with improved performance, in: 2002 IUS Proceedings. Munich, Germany, 8–11 Oct 2002. https://doi.org/10.1109/ULTSYM.2002.1193426.
TCF Hetero Acoustic Layer (HAL) SAW resonators using LiTaO3 thin plate on quartz, in: 2018 IUS Proceedings, Kobe, Japan, 22–25 Oct 2018; https://doi.org/10. 1109/ULTSYM.2018.8580111. J. Hayashi, K. Yamaya, S. Asakawa, M. Suzuki, S. Kakio, H. Kuwae, T. Yonai, K. Kishida, J. Mizuno, Longitudinal leaky SAW with low attenuation on LiTaO3 thin plate bonded to quartz substrate, in: 2018 IUS Proceedings, Kobe, Japan, 22–25 Oct 2018; https://doi.org/10.1109/ULTSYM.2018.8579715. N. Naumenko, I. Didenko, High-velocity surface acoustic waves in diamond and sapphire with zinc oxide film, Appl. Phys. Lett. 75 (1999) 3029, https://doi.org/10. 1063/1.125223. A.N. Darinskii, I.S. Didenko, N.F. Naumenko, Fast quasi-longitudinal sagittally polarized surface waves in layer-substrate structures, J. Acoust. Soc. Amer. 107 (5 Pt 1) (2000) 2351–2359, https://doi.org/10.1121/1.428621. N.F. Naumenko, Advanced numerical technique for analysis of surface and bulk acoustic waves in resonators using periodic metal gratings, J. Appl. Phys. 116 (2014) 104503, https://doi.org/10.1063/1.4895140.
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Contents lists available at ScienceDirect
Ultrasonics journal homepage: www.elsevier.com/locate/ultras
Short communication
High-velocity non-attenuated acoustic waves in LiTaO3/quartz layered substrates for high frequency resonators
T
Natalya F. Naumenko Acousto-Optical Research Center, National University of Science and Technology “MISIS”, Moscow 119049, Russia
A R T I C LE I N FO
A B S T R A C T
Keywords: Acoustic wave Layered structure Leaky wave SAW resonator
Multilayered substrates for Surface Acoustic Wave (SAW) devices are able to combine SAW characteristics that cannot coexist in a single crystal substrate and, thus, meet the strong requirements of the new class of SAW devices developed for the next generations of communication systems. Recently, high performance resonators arranged on LiTaO3/quartz bonded wafers and utilizing shear horizontally polarized acoustic waves were reported. Leaky SAWs with quasi-longitudinal polarization propagate faster and can facilitate fabrication of high frequency SAW devices but generally leak strongly into the substrate. This paper describes how the LiTaO3/ quartz structure can be optimized to allow longitudinal SAWs to propagate without attenuation. Due to the symmetry consideration, which is supplemented by a rigorous numerical simulation of the admittance functions of SAW resonators and an accurate extraction of the propagation losses, the found optimal LiTaO3 and quartz orientations with the optimized LiTaO3 thickness ensure the propagation of acoustic waves with a velocity exceeding 5400 m/s and an electromechanical coupling of 6.8% in resonators with Q factors up to 10,000. The optimal LT/quartz structures with plate thicknesses varying between 0.32 and 0.68 wavelengths can be employed in SAW resonators operating at high frequencies, up to 5 GHz. The existence of numerous orientations in quartz supporting the propagation of non-attenuated longitudinal SAWs is explained based on the concept of exceptional bulk waves, which is a part of SAW theory.
1. Introduction The next generation of mobile communication systems (5G) is characterized by very narrow gaps between the operating frequency bands and assumes the application of filters with steep bandpass edges. The surface acoustic wave (SAW) resonators and resonator filters that are required for such systems must provide very high quality (Q) factors and a low temperature dependence of the main device parameters in addition to high frequencies and low insertion losses. The regular SAW substrate materials that are used in SAW resonator filters, such as LiNbO3 (LN) or LiTaO3 (LT), cannot satisfy all these requirements. Therefore, in recent years, multilayered structures combining layers with different properties are extensively studied as alternatives to regular SAW substrates. For example, the structures using thin LN or LT plates bonded to silicon (Si) wafers were theoretically and experimentally investigated and demonstrated promising combinations of a high electromechanical coupling coefficient k2, a low temperature coefficient of frequency (TCF) and excellent Q-factors [1–3] that are limited only by the quality of the fabrication techniques, which is continuously improved. The further improvement of SAW device performances can be achieved if the Si substrate is replaced by strongly anisotropic
quartz, which is known as one of few materials with positive temperature coefficients for some elastic constants. The theoretical investigation of acoustic waves in LT/quartz [4–6] revealed that shear horizontally (SH) polarized waves can propagate in resonator structures with a high coupling k2 > 11% and a low TCF if the LT and quartz orientations and the electrode and plate thicknesses are optimized properly. Some of these results were already experimentally confirmed [7]. The velocities of SH waves propagating in LT plates bonded to a supporting substrate are limited by the waves’ nature and usually do not exceed 4200 m/s. Acoustic modes propagating faster could facilitate the fabrication of high frequency SAW devices, especially when the operating frequency exceeds 5 GHz. This paper reports on the existence of high velocity SAWs in LT/quartz with promising characteristics that are desirable for the application in high performance high frequency SAW devices. The velocities of these waves are close to those of the quasi-longitudinal bulk acoustic waves (BAW) in LT crystal. An example of low-attenuated longitudinal leaky SAW (LLSAW) propagating in LT/quartz was recently reported by Hayashi [8]. The structure combined the non-symmetric orientations of LT (X,Y + 31°cut) and quartz (X,Y + 32°-cut). Though the found LLSAW propagates
E-mail address: [email protected]. https://doi.org/10.1016/j.ultras.2019.03.001 Received 14 January 2019; Received in revised form 26 February 2019; Accepted 1 March 2019 Available online 02 March 2019 0041-624X/ © 2019 Published by Elsevier B.V.
Ultrasonics 95 (2019) 1–5
N.F. Naumenko
with very low losses, shows negligible beam steering angle and sufficient electromechanical coupling, its potential application in high-frequency resonators is limited by the requirement of a very low LT plate thickness, hLT = (0.06–0.08) λ, where λ = 2p and p is the periodicity of electrode structure, or (0.08–0.1) μm at 5 GHz frequency. In such nonsymmetric layered structures, leakage of LLSAW into the substrate is generally caused by radiation of two BAWs. Hence, suppression of propagation losses requires simultaneous optimization of three parameters, for example, substrate orientation, plate thickness and electrode thickness. As a result, fabrication of the found layered structure for its further application in high-frequency SAW devices may be a challenge if the optimized LT thickness is too small or electrodes are too thin. If one of the bulk waves in a substrate is uncoupled with the longitudinal leaky SAW, due to symmetry, zero attenuation can be achieved via variation of a plate thickness and orientation of a substrate [9,10] while the LT cut and the electrode thickness can be selected independently to provide a high electromechanical coupling and a sufficient reflectivity in a SAW resonator. An example of symmetric LT/ quartz structure supporting propagation of a low-attenuated longitudinal wave was reported in [6]. The optimal structure with LT thickness hLT = 0.28 λ, or 0.3 μm at 5 GHz frequency, is compatible with the reported experimental devices on LT/quartz [7] and can be further improved using optimization technique described hereafter and starting from the symmetry consideration of the combined materials. To find the optimal structures that allow for the propagation of the high-velocity waves with negligible leakage into quartz, first, potentially useful combinations of LT and quartz orientations were determined based on the symmetry of two crystals. Then, the range of the LT orientations with the maximum electromechanical coupling of the quasi-longitudinal wave was estimated. Finally, a rigorous numerical technique was applied to optimize the LT/quartz structures for SAW resonators via the variation of the Euler angles and LT plate thicknesses, with a finite thickness of the periodic metal grating taken into account.
Fig. 1. Slowness surfaces of (0°, 34°, 90°)-LT and (0°, 30°, 90°)-quartz and the wave vectors of three sagittally polarized modes (kLT−, kLT+ and kQ+) that are involved in the solution with a velocity of V.
(kLT+ and kLT−) and the one mode in quartz (kQ+), which contribute to the leaky SAW solution, can be geometrically determined for a wave propagating with a velocity of V. In each material, one of the BAWs (dotted lines) is not radiated due to symmetry. In LT/quartz, the coupling coefficient k2 is dominated by the LT orientation while the leakage into the substrate depends on the quartz orientation. To focus the search for the LT cuts providing the maximum coupling, the velocities of three BAWs were calculated in the YZ plane of LT with the piezoelectric effect and without it. Fig. 2 shows these velocities as functions of the propagation angle with the Y axis. The difference ΔV resulting from the piezoelectric effect may be used for the estimation of the BAW coupling as k2 ≈ 2∙ΔV/V. Fig. 3 shows the polar diagram of k2 that is obtained for the quasi-longitudinal wave propagating in the YZ cut of LT. The maximum k2 occurs when the BAW propagates along the direction Y + 30° and the normal to the LT surface is parallel to Z + 30°. Such a SAW orientation is described by the Euler angles (0°, 30°, 90°). More accurate simulations with the beam steering angle taken into account yield (0°, 35°, 90°) as the optimal LT cut for achieving the highest electromechanical coupling of the longitudinal leaky SAW. In LT/quartz structures with a fixed LT orientation (0°, 35°, 90°), the variation of the quartz cut was further used to suppress leakage into the substrate. For this purpose, longitudinal leaky waves were numerically investigated in LT plates bonded to (0°, ϴ, 90°) cuts of quartz. The minimum achievable attenuation was estimated for each ϴ via the variation of the LT thickness in the interval hLT = (0.3–0.7) λ. Computations were made for Cu electrodes that were 0.05 λ thick. The
2. Optimization of LiTaO3/quartz structure In a thin plate bonded to a half-infinite substrate, acoustic waves can be generated by using an interdigital transducer (IDT) arranged on the plate surface. Though, in general, such a wave has a complicated structure, hereafter we will call it a SAW or leaky SAW for simplicity. Such a SAW is not confined in the plate and leaks into the substrate if its velocity is higher than the cut-off BAW velocity in the specified orientation of the substrate material. If VLS, VFS and VSS are the velocities of the quasi-longitudinal, fast quasi-shear and slow quasi-shear BAWs in a substrate, respectively, then a SAW propagating with a velocity of VFS < V < VLS generally radiates into two tilted BAWs and leaks strongly into the depth of a substrate. Leakage can be reduced if one of two shear BAWs is uncoupled with the electric field, due to symmetry, and further suppressed if the contribution of the second BAW into the wave structure is minimized [9,10]. According to the symmetry of the LT and quartz crystals, one of the BAWs propagating in the YZ plane is pure shear and polarized along the X axis. This wave is uncoupled with two other BAWs (quasi-longitudinal and quasi-shear) propagating in the YZ plane and polarized in the same plane. In quartz (symmetry class 32), only pure shear BAW is coupled with the electrostatic potential. In contrast, in LT (symmetry class 3m), the pure shear BAW is uncoupled with the electric field while two BAWs that are polarized in the YZ plane are piezo-active. Hence, if a multilayered structure combines the rotated YX cuts of LT and quartz with X + 90° propagation direction (orientations defined by the Euler angles (0°, ϴ, 90°)), the sagittal plane is parallel to the YZ plane of crystal, and a sagittally polarized SAW propagating with a velocity of V < VLS couples only with the sagittally polarized quasi-shear BAW in quartz. Fig. 1 shows an example of the slowness surfaces of LT plate and quartz substrate combined in the bonded wafer with orientations defined by the specified Euler angles and explains how the wave vectors of the two modes in the LT plate
Fig. 2. Velocities of three bulk waves (VL > VF > VS) propagating in the YZ plane of LT obtained with and without piezoelectric effect. SH polarized wave (black lines) is uncoupled with the electric field. 2
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Fig. 3. Electromechanical coupling of the quasi-longitudinal BAW as a function of the propagation direction in the YZ plane of LT.
numerical technique SDA-FEM-SDA combining the finite element modeling (FEM) analysis of electrodes with the spectral-domain analysis (SDA) of a multilayered substrate [11] was used to compute the admittance functions of SAW resonators built on LT/quartz and extract the complex SAW velocities VR = 2pfR·(1 + jδR) and VA = 2pfA·(1 + jδA) from the admittance functions at the resonant fR and anti-resonant fA frequencies, respectively. The found attenuation (propagation loss) at the resonance (δR) or the anti-resonance (δA) determine the Q-factors of the SAW resonators, QR,A ∼ (δR,A)−1. The estimated losses are associated only with leakage into bulk waves. Other loss mechanisms (electrode resistance, viscous losses, etc.) were ignored. Fig. 4 shows the minimum attenuation δR as a function of the Euler angle ϴ. With the LT thickness changing continuously within four different ranges, δR < 0.001 dB/λ was found in each range. Such low δR values were obtained for quartz orientations of (0°, 38°, 90°), (0°, 75°, 90°), (0°, 110°, 90°) and (0°, 125°, 90°). The existence of multiple orientations in quartz, which allow for the propagation of longitudinal leaky SAWs with negligible attenuation when the quartz substrate is combined with the LT plate, can be explained by the existence of quasilongitudinal exceptional bulk waves in quartz cuts of (0°, 48°, 90°), (0°, 70°, 90°), (0°, 105°, 90°) and (0°, 145°, 90°) [12]. The exceptional bulk wave [13] satisfies the stress-free mechanical boundary conditions on the selected crystal surface and breaks the sufficiency condition for the existence of Rayleigh SAW, according to Lothe-Barnett theorem [14,15]. Such waves exist in any crystal. Usually, they are (quasi)shear, but in some crystals with strong acoustic anisotropy, for example quartz, quasi-longitudinal exceptional waves were also found [12].
Fig. 5. Contour plot of attenuation δR in dB/λ as a function of the plate thickness h/λ and Euler angle ϴ in (0°, 35°, 90°)-LT bonded to (0°, ϴ, 90°)quartz calculated around the optimal point: ϴ = 38°, h/λ = 0.36.
When a thin LT plate is loaded on a quartz substrate, the boundary condition at the LT/quartz interface continuously deviates from the stress-free state as the plate thickness increases. As a result, the optimal quartz orientations providing propagation of non-attenuated waves change. An additional shift arises from the mass load imposed by the electrodes of the grating. It should be mentioned that in LT/quartz with the quartz orientation of (0°, ϴ, 90°), the optimal angle ϴ, which allow for the propagation of the non-attenuated longitudinal leaky SAW, does not continuously move as the LT thickness increases. In each of the analyzed intervals of the LT thickness, the minimum leakage occurs at a certain point in the two-dimensional space (hLT, ϴ) when the electrode thickness hEl is fixed (as shown in Fig. 5) or at a certain point in the space (hEl, ϴ) when the LT thickness is fixed. Such behavior is typical for the high-velocity leaky waves and was previously observed in diamond and sapphire with zinc oxide films [9] and in LT substrates with a thick gold film or a periodic gold grating [16]. It is different from the behavior of the SH-type leaky waves, for example in ϴ-rotated YX cuts of LT with metal film or periodic grating, where negligible attenuation was observed along the line in the 2D space (hEl, ϴ) when ϴ varies between 36° and 54° [17]. The LT thicknesses that are required to achieve the maximum Qfactors QR and QA in SAW resonators using LT/quartz do not coincide. Moreover, the simulations reveal that it is easier to obtain high Q-factors at the resonance than at the anti-resonance. Fig. 6 shows two examples of the simulated admittance functions of SAW resonators using LT plates with Euler angles (0°, 35°, 90°) bonded to quartz orientations of (0°, 40°, 90°) and (0°, 120°, 90°) with Cu grating on top. The optimal LT plate thicknesses of 0.36 λ and 0.41 λ, respectively, provide theoretical values of QR > 104 in these structures, but the QA values are much lower. Though the analyzed quartz orientations differ by 80°, the velocity (VR ≈ 5435 m/s) and coupling (k2 ≈ 6.8%) are almost the same for both structures. It can be explained by the dominant influence of the LT orientation on the main wave characteristics. The displacement fields following the wave propagation at the resonant frequency are illustrated by the colored diagrams of the longitudinal (u1) and shear vertical (u3) components (insets to Fig. 6). The shear horizontal component (u2) is negligible due to the symmetry of the analyzed LT and quartz orientations. In both structures, the longitudinal motions are almost totally confined in the LT plate. The vertical motions penetrate deeper into the quartz substrate but do not increase with the depth. A typical ladder filter design includes series and shunt SAW resonators and requires a high Q-factor at the resonance or at the anti-
Fig. 4. Minimum achievable attenuation δR as a function of the Euler angle ϴ in (0°, 35°, 90°)-LT bonded to (0°, ϴ, 90°)-quartz, which were obtained for Cu electrode thickness hCu = 0.05λ via the optimization of the LT thickness for each ϴ. 3
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resonance. To fabricate resonators with high QR and high QA on the same layered structure with a fixed LT thickness, varying the duty factor a/p (the electrode width to the period ratio) can be applied instead of varying the LT thickness. Fig. 7 shows VR, VA, QR and QA as functions of the duty factor in (0°, 34°, 90°) LT bonded to (0°, 30°, 90°) quartz with hLT = 0.32λ. When a/p < 0.3 or a/p > 0.65, the Q-factor exceeds 5000 at the anti-resonance or at the resonance, respectively. Three examples of the simulated admittances with high QR, high QA and QR ≈ QA are shown in Fig. 8. In a wide range of frequencies, two modes with velocities 2700–2800 m/s and 5300–5700 m/s are generated by the IDT. For comparison, the simulated admittance is shown for the non-symmetric LLSAW structure suggested by Hayashi, with hLT = 0.0625 λ and hAl = 0.005 λ . In (0°, 34°, 90°)-LT/(0°, 30°, 90°)quartz, higher reflectivity can be achieved in SAW resonators due to heavier Cu electrodes but the velocity decreases with metal thickness. In non-symmetric structures, low reflectivity in conjunction with the complex reflection coefficient manifests itself by a spurious mode at the resonator stopband edge. In the analyzed LLSAW-Hayashi structure, perturbation occurs between the resonant and anti-resonant frequencies. These simulations agree with reported in [8] and confirm the advantages of symmetric layered structures over non-symmetric.
Fig. 6. Admittances of two SAW resonators using (0°, 35°, 90°)-LT/(0°, 40°, 90°)-quartz and (0°, 35°, 90°)-LT/(0°, 120°, 90°)–quartz structures with LT thicknesses that are optimized for the maximum QR. The acoustic wave structure is shown at the resonant frequency as colored diagrams of the tangential (u1) and vertical (u3) motions.
3. Conclusions Longitudinal high-velocity leaky SAWs were theoretically investigated in layered structures combining a thin LT plate with an anisotropic quartz substrate and a Cu grating on top with respect to their potential application in high performance, high frequency SAW resonators. The selection of the proper LT and quartz orientations based on the symmetry of two crystals, along with the further optimization of the cut angle of the quartz substrate and the LT plate thickness, revealed that longitudinal SAWs can propagate with velocities of V > 5400 m/s, electrochemical coupling of k2 > 6.8% and a negligible attenuation required to design high-Q resonators. Due to strong acoustic anisotropy of quartz, multiple orientations exist that allow for the propagation of non-attenuated high-velocity SAWs when an LT plate is loaded on a quartz substrate. The thicknesses of Cu electrodes (hCu = 0.05 λ ) and LT plates (hLT = (0.32–0.65)λ) in the found optimal structures stay sufficiently large (550 Å and 0.35–0.7 μm, respectively) and compatible with the existing fabrication technologies for SAW devices on bonded wafers when the operating frequency grows up to 5 GHz.
Fig. 7. Velocities at the resonance (VR) and the anti-resonance (VA) and the Qfactors (QR, QA) as functions of the duty factor for (0°, 34°, 90°)-LT/(0°, 30°, 90°)-quartz with an LT thickness of hLT/λ = 0.32 and a Cu electrode thickness of hCu/λ = 0.05.
Acknowledgements The research was partly supported by the Ministry of Education and Science of the Russian Federation (Project 02.A03.21.0004). References [1] M. Kadota, S. Tanaka, Wideband acoustic wave resonators composed of hetero acoustic layer structure, Jpn. J. Appl. Phys. 57 (2018) 07LD12, https://doi.org/10. 7567/JJAP.57.07LD12. [2] M. Kadota, S. Tanaka, Solidly mounted resonator using shear horizontal mode plate wave in LiNbO3 plate, in: 2016 IFCS Proceedings, New Orleans, LA, USA, 9–12 May 2016. https://doi.org/10.1109/FCS.2016.7546795. [3] N.F. Naumenko, Multilayered structures using thin plates of LiTaO3 for acoustic wave resonators with high quality factor, Ultrasonics 88C (2018) 115, https://doi. org/10.1016/j.ultras.2018.03.014. [4] M. Kadota, S. Tanaka, Improved quality factor of Hetero Acoustic Layer (HAL) SAW resonator combining LiTaO3 thin plate and quartz substrate, in: 2017 IUS Proceedings, Washington, DC, USA, 6–9 Sept 2017; https://doi.org/10.1109/ ULTSYM.2017.8092963. [5] M. Gomi, T. Kataoka, J. Hayashi, S. Kakio, High-coupling leaky surface acoustic waves on LiNbO3 or LiTaO3 thin plate bonded to high-velocity substrate, Jpn. J. Appl. Phys. 56 (2017) 07JD13, https://doi.org/10.7567/JJAP.56.07JD13. [6] N. Naumenko, Suppression of propagation losses in TC SAW resonators using thin plates of LiTaO3 bonded to quartz substrates, in: 2018 IUS Proceedings, Kobe, Japan, 22–25 Oct 2018; https://doi.org/10.1109/ULTSYM.2018.8579813. [7] M. Kadota, Y. Ishii, T. Shimatsu, M. Uomoto, S. Tanaka, Spurious-free, near-zero-
Fig. 8. Admittances and estimated Q-factors of SAW resonators using (0°, 34°, 90°)-LT/(0°, 30°, 90°)-quartz with an LT thickness of hLT/λ = 0.32, a Cu thickness of hCu/λ = 0.05 and three duty factors: a/p = 0.3, 0.37 and 0.7, compared to the admittance of a resonator using LLSAW-Hayashi structure [8].
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