Spurious Modes in Laterally Excited Bulk Acoustic Resonators (XBARs): Analysis and Suppression.

Laterally excited bulk acoustic resonators (XBARs) are plate mode resonators in which one of the higher-order plate modes transforms into the bulk acoustic wave (BAW) due to the very thin plates used in these devices. The propagation of the primary mode is usually accompanied by numerous spurious modes, which deteriorate resonator performances and restrict potential XBARs' applications. This article suggests a combination of different methods for insight into the nature of the spurious modes and their suppression. Analysis of the BAW slowness surface provides optimization of XBARs for single-mode performance in the filter passband and around it. The rigorous simulation of admittance functions in the optimal structures allows for further optimization of electrode thickness and duty factor. Finally, the nature of different plate modes generated in a wide frequency range is clarified via simulation of dispersion curves, which characterize acoustic mode propagation in a thin plate under the periodic metal grating, and visualization of displacements accompanying wave propagation. Application of this analysis to lithium niobate (LN)-based XBARs demonstrated that in LN cuts with Euler angles (0°, 4°-15°, 90°) and plate thickness dependent on orientation and varying between 0.05 and 0.1 wavelengths, the spurious-free response could be achieved. Due to tangential velocities of 18-37 km/s combined with the coupling of 15%-17% and feasible duty factor a/p = 0.5, the found XBAR structures can be applied in high-performance 3-6 GHz filters.

Analysis of Acousto-Optic Figure of Merit in KGW and KYW Crystals.

Monoclinic potassium rare-earth crystals are known as efficient materials for solid-state lasers and acousto-optic modulators. A number of specific configurations for acousto-optic devices based on those crystals have recently been proposed, but the acousto-optic effect of those crystals has only been analyzed fragmentarily for some interaction directions. In this work, we numerically searched for the global maxima of an acousto-optic figure of merit for isotropic diffraction in KGd(WO4)2 and KY(WO4)2 crystals. It was demonstrated that the global maxima of the acousto-optic figure of merit in those crystals occur in the slow optical mode propagating along the crystal's twofold symmetry axis and in the acoustic wave propagating orthogonally, both for quasi-longitudinal and quasi-shear acoustic modes. The proposed calculation method can be readily used for the optimization of the acousto-optic interaction geometry in crystals with arbitrary symmetry.

Symmetry Aspects in the Use of Multilayered Substrates for SAW Devices.

Multilayered structures extensively studied as a novel type of substrates for surface acoustic wave (SAW) devices are characterized by an asymmetry of wave propagation: acoustic wave characteristics generally change with inversion of propagation direction or interchange of top/bottom surfaces in one of the layers, though separately each material is symmetric for such inversions. In this article, the matrix formalism known as an effective tool for theoretical and numerical investigation of acoustic wave propagation in multilayered structures is applied to explain the existence of asymmetry and analyze its relation to the symmetry and orientations of combined materials. This phenomenon is illustrated by the examples of layered structures combining LiTaO3 (LT) plate with quartz or Si, previously reported as potential substrates for SAW devices with improved performance. Asymmetry arises from anisotropy of combined materials and occurs even when one of these materials is non-piezoelectric. It was estimated numerically as a variation of SAW resonator characteristics with substrate or plate inversion and was analyzed as a function of plate or substrate orientation. In particular, it was shown that "polarity inverted" structure enabling alternative resonator performance for the same material layers can be obtained either by an interchange of top/bottom surfaces of a piezoelectric plate or by inversion of propagation direction in a substrate. Asymmetry decreases with the introduction of an isotropic layer at the plate-substrate interface.

High-efficiency KYW acousto-optic Q-switch for a Ho:YAG laser.

A new, to the best of our knowledge, type of acousto-optic Q-switch was developed using slow shear acoustic mode in potassium yttrium tungstate (KYW) crystal. Two Q-switch configurations were created: one for vertical and one for horizontal light polarization, both providing over 50% diffraction efficiency at a wavelength of 2.1 µm and an RF driving power below 8 W. The laser-induced damage threshold of the KYW crystal was found to equal 650 MW/cm2. Operation of a nanosecond periodically pulsed Ho:YAG laser emitting 15 mJ pulses at 2.1 µm with the KYW Q-switch is reported.

Temperature Behavior of SAW Resonators Based on LiNbO3/Quartz and LiTaO3/Quartz Substrates.

LiNbO3 (LN) or LiTaO3 (LT) thin plates bonded to quartz are novel types of layered substrates for temperature-compensated surface acoustic wave (TCSAW) devices. In SAW resonators with Al electrodes arranged on LT/quartz and LN/quartz substrates, improved temperature behavior due to opposite signs of temperature coefficients of frequency (TCF) in quartz substrates and LT or LN plates can be combined with high Q -factors if the quartz orientation is optimized. The quartz orientation areas that enabled high Q -factors were deduced from analyzing the quartz anisotropy and the characteristics of shear horizontally (SH) polarized waves were calculated in the optimal orientations as functions of the quartz cut angle and plate thickness. The simulation results illustrated by contour plots of the wave characteristics revealed the presence of zero lines on the plots demonstrating TCFs at resonant (TCFR) and antiresonant (TCFA) frequencies in both layered structures. The strong quartz anisotropy explained anomalous temperature behavior of SAW resonators and the existence of LT/quartz structures with TCFA = TCFR facilitating the design of SAW devices with improved thermal stability in the passband. In the LT/quartz structures, two TCFs vanished simultaneously at certain plate thickness and quartz orientation, while in the LN/quartz zero lines did not intersect but low TCF = -(10-20) ppm/°C combined with electromechanical coupling exceeding 18% were obtained numerically in some structures. The effect of inverting the propagation direction or cut angle in one of the combined materials on the wave characteristics was discussed and numerically estimated.

Advanced Substrate Material for SAW Devices Combining LiNbO3 and Langasite.

A layered structure combining a thin plate of lithium niobate (LN) with a langasite (LGS) substrate was numerically investigated as an advanced substrate material for surface acoustic wave (SAW) devices with improved characteristics, including capability of operating at high temperatures. The longitudinal leaky SAWs (LLSAWs) propagating with negligible attenuation and high velocities up to 6400 m/s were found in LN/LGS using an optimization technique previously applied to the LN/quartz structure. Compared with quartz, the use of LGS as a substrate imposes less constrains on bonding at elevated temperatures for fabrication of a layered structure. Due to the specific acoustic anisotropy of LGS crystals, low-attenuated high-velocity waves exist in a wide range of LGS orientations, including the commercially available SAW cut, when LGS substrate is combined with an LN plate. In the found optimal structures, the electromechanical coupling increased from 5.5% to 14.5%, with increasing LN thickness, making LN/LGS substrate suitable for application in SAW devices with a widely varying bandwidth. In addition, low shear bulk wave velocities in LGS provide a wide spurious-free frequency range in resonators using LLSAW.

Optimization of LiNbO3/Quartz Substrate for High-Frequency Wideband SAW Devices Using Longitudinal Leaky Waves.

Multilayered structures can successfully replace single crystal substrates in high-performance surface acoustic wave (SAW) devices. A combination of high propagation velocity and strong piezoelectric coupling is required for acoustic modes used in wideband high-frequency SAW devices. These characteristics can be achieved simultaneously in SAW devices arranged on a lithium niobate (LN) thin plate bonded to quartz and using longitudinal leaky SAW (LLSAW) if the orientations of both the crystals and the plate thickness are optimized. This article describes an optimization procedure developed to find low-attenuated LLSAWs in layered structures that can be used in LN/quartz applications. The symmetry consideration of two crystals was followed by the optimization of the LN orientation to achieve the largest electromechanical coupling and by an analysis of quartz anisotropy as a crucial factor of the existence of nonattenuated LLSAWs. Finally, the quartz orientation and LN thickness were optimized by a rigorous numerical simulation of resonator admittances and by the extraction of LLSAW attenuation at resonant and antiresonant frequencies. The discovered structures enable the propagation of LLSAWs with velocities in the range of 5400-6000 m/s, electromechanical coupling up to 18%, and negligible attenuation. High Q -factors can be achieved at resonance and antiresonance by the variation of the duty factor in the same layered structure. The specific behavior of the LLSAW attenuation with a variation of the LN thickness and quartz cut angle is illustrated by contour plots for each of the optimal structures discovered.

High-velocity non-attenuated acoustic waves in LiTaO3/quartz layered substrates for high frequency resonators.

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.

Multilayered structures using thin plates of LiTaO3 for acoustic wave resonators with high quality factor.

Multilayered substrates, including thin plates of LiTaO3 (LT) bonded to silicon (Si) or glass wafers either directly or via intermediate layers, were numerically investigated as potential materials for surface acoustic wave (SAW) resonators with high quality (Q)-factor required for the next generation of mobile communication systems. The propagation velocities and electromechanical coupling coefficients of shear horizontally (SH) polarized acoustic waves were estimated as functions of LT orientation and thicknesses of all layers in LT/Si, LT/SiO2/Si, LT/glass, LT/AlN/glass and structures with several pairs of SiO2/AlN layers between LT and the glass wafer. Optimal combinations of cut angle, LT and electrode thicknesses, as well as the number and thicknesses of intermediate layers, required for the construction of resonators with improved performance were observed for each analyzed structure. In the resonators employing LT/Si and LT/SiO2/Si structures with 30°YX - 48°YX LT cuts, high electromechanical coupling k2, reaching 11.6%, can be combined with high velocities up to 4000 m/s, zero TCF at the resonant frequency and Q-factors that are considerably higher than in the LSAW filters using regular LT substrates. To understand the loss mechanisms that limit resonator Q-factors in LT/glass, mechanical displacements that accompany wave propagation in multilayered structures were visualized. Investigation of the nature of acoustic modes and their transformations with number and thicknesses of the layers revealed that the low-velocity glass wafer can be used as a supporting substrate if an intermediate AlN layer or alternating pairs of low- and high-velocity layers, for example SiO2/AlN, are introduced between LT and the glass wafer.

Anisotropic diffraction of bulk acoustic wave beams in lithium niobate.

The formalism of planar diffraction tensor was applied to the analysis of anisotropy of bulk acoustic wave diffraction and to build a full map of anisotropic diffractional coefficients for three bulk acoustic wave modes propagating in lithium niobate. For arbitrary propagation direction the diffractional coefficients derived allow estimation of ultrasonic beam divergence in far-field. Analysis of obtained data revealed that the maxima of acousto-optic figure of merit for anisotropic diffraction in the YZ plane correspond to moderate diffractional spreading of the beams exceeding isotropic diffraction 2-3 times.

Dispersion of Lamb waves under a periodic metal grating in aluminum nitride plates.

Dispersion of Lamb waves propagating in AlN plates with a periodic Al grating on the top surface and an Al electrode on the bottom surface is investigated using the numerical technique SDA-FEM-SDA, which combines finite element modeling (FEM) analysis of the electrode region with spectral-domain analysis (SDA) of the adjacent multi-layered half-spaces. Characteristics of zero-order and higher-order Lamb waves are presented as functions of plate thickness and spectral frequency, which varies in the first Brillouin zone. The structures of typical Lamb waves are examined via visualization of the instantaneous displacement fields in the AlN plate confined between the grating and the bottom electrode. The mechanism of building hybrid modes, which arise from intermode coupling between the counter-propagating Lamb waves of different symmetry and order, is illustrated by two examples of modes propagating with wavelengths λ = 3p and λ = 4p, where p is the pitch of the grating.

Effect of anisotropy on characteristics and behavior of shear horizontal SAWs in resonators using langasite.

Orientations of langasite (LGS) with Euler angles (0°, µ, 90°) are potentially useful for applications in wireless SAW sensors because of wide variation of their temperature coefficient of frequency (TCF), between -50 and +50 ppm/°C, combined with high values of electromechanical coupling coefficient, especially if thick electrodes are utilized. The nature and characteristics of shear-horizontally polarized SAWs (SHSAWs) propagating in these orientations are investigated using a combination of numerical techniques: analysis of the BAW slowness surface and its effect on the SH-SAW structure; visualization of displacements that follow wave propagation in the grating; calculation of admittance of infinite periodic gratings; and analysis of SAW dispersion in the gratings, including possible interaction between SH-SAWs and parasitic Rayleigh SAWs. The characteristics of SH-SAWs propagating in symmetric cuts (velocities, localization depth, electromechanical coupling, etc.) are supplemented by analysis of propagation directions deviating from the YZ-plane toward the x-axis of LGS, for the temperature compensated cut with Euler angles (0°, 22°, 90°) and one more orientation for comparison. This extended analysis reveals that in actual devices, the anisotropy may be a reason for strong interaction between SH-SAWs and parasitic Rayleigh SAWs and cause degradation of the device's performance.

Analysis of interaction between two SAW modes in Pt grating on langasite cut (0°, 138.5°, 26.6°).

The numerical technique based on a previously developed rational approximation of harmonic admittance of a periodic grating was applied to analysis of SAW behavior in platinum grating on langasite cut with Euler angles (0°, 138.5°, 26.6°). The approximation is able to take into account interaction between surface and bulk waves or between two SAW modes. SAW dispersion was calculated at different values of electrode thickness varying between 1% and 4% of wavelength. It was found that with increasing Pt thickness, SAW behavior in the grating is strongly affected by interaction between two SAW modes propagating in the same orientation. An additional stopband, which results from this interaction, occurs at certain detuning from synchronous reflection condition and can cause spurious resonances of the admittance function. Interaction between two SAW modes is also responsible for anomalously slow growth of reflectivity with increasing platinum thickness.

Transformation of acoustic waves in periodic metal grating sandwiched between piezoelectric and dielectric.

The mechanism of SAW transformation with variation of film thickness is investigated in a piezoelectric substrate with a metal grating overlaid by a dielectric film, via simulation and visualization of the acoustic fields. By way of example, two orientations of lithium niobate substrates are analyzed, YX-LN and 128°YX-LN, with a Cu grating and an isotropic silica glass overlay. The motions, which follow the wave propagation in the sagittal plane, are visualized within two periods of the grating, with added contour plots showing the shear horizontal displacements. The continuous transformation of the wave's nature is investigated for each wave propagating in the analyzed material structures when the film thickness is increased from zero to a few wavelengths. The examples of the SAW transformation into boundary waves and into plate modes of different polarization have been found and investigated. The behavior of the SAW characteristics in the grating is correlated with transformation of the wave structure with increasing overlay thickness.