Analysis of thickness-extensional waves propagating in the lateral direction of solidly mounted piezoelectric thin film resonators

In a solidly mounted piezoelectric thin film resonator (SMR), acoustic waves propagate not only in the thickness direction but also in the lateral direction. In this study, we analyzed the acoustic wave in the SMR-type piezoelectric thin film resonator and derived the dispersion relation between the lateral wave number and frequency, considering wave propagation in the lateral direction. The lateral wave number was shown to be a complex number due to the leak of the acoustic energy to a substrate. It also was shown that the Q factor could be calculated from the complex cutoff frequency, and it becomes higher when the number of quarter-wave (lambda/4) layers increases. Using the dispersion relation, the trapped-energy resonant modes of an SMR were analyzed, considering the boundary conditions at the edge of the electrode.     

Influence of material parameters on acoustic wave propagation modes in ZnO/Si bi-layered structures

The influences of material properties on acoustic wave propagation modes in ZnO/Si bi-layered structures are studied. The transfer matrix method is used to calculate dispersion relations, wave field distributions, and electromechanical coupling coefficients of acoustic wave propagation modes in ZnO/Si bi-layered systems, in which the thickness of the substrate is of the same order of magnitude as the wavelength of the propagating wave modes. The influences of the thin film parameters on the acoustic wave propagation modes and their electromechanical coupling coefficients of the wave modes also are obtained. In addition, some experimental results for characterizing the wave propagation modes and their frequencies have also been obtained, which agree well with the theoretical predictions.     

以四面体非晶碳为布拉格反射栅高声阻抗材料的固贴式薄膜体声波谐振器性能仿真分析

为了提高固贴式薄膜体声波谐振器(SMR)的电学和声学品质,实现四面体非晶碳(ta-C)在体声波器件领域的新应用,建立了以ta-C为布拉格反射栅高声阻抗材料的SMR模型,利用MathCAD仿真研究布拉格反射栅层数对该SMR的谐振特性的影响以及ta-C中sp3杂化含量和高/低声阻抗层厚度偏差对SMR的品质因子(Q值)的影响。结果表明层数的增加提高了SMR的品质;ta-C薄膜sp3杂化含量越高,达到饱和Q值所需层数越少,当含量为80%时,至少需要6层(3对)布拉格反射层使SMR达到优异Q值;距离压电堆越近的高/低声阻抗层,其厚度偏差对Q值的影响越大,从而实现了高频率(8GHz)低损耗的SMR的设计。     

Finite element modelling of nanostructured piezoelectric resonators (NAPIERs)

A new modification to the traditional piezoelectric thin film bulk acoustic wave resonator (FBAR) and solidly mounted acoustic wave resonator (SMR) is proven to significantly improve their performances. The proposed design involves the surface micro/nano structuring of planar piezoelectric thin films to realize an array of a large number of rod-like structures. In contrast to the plate-like thickness extensional resonance in traditional FBAR and SMR devices, the rod-like structures can be excited in their length extensional resonance, yielding a higher electromechanical coupling factor and effectively eliminating the spurious resonances from lateral modes of vibration. The designs have been investigated by two and three-dimensional finite element analyses and one-dimensional transmissionline modelling. The results show that significant increases in the electromechanical coupling factor of ca. 40% can be achieved by using the rod-like length extensional resonances as compared with the plate-like thickness extensional resonances in traditional devices. Simulations show that rod width-to-thickness aspect ratios of less than 0.5 could result in an electromechanical coupling factor (k2eff) of over 10% for a zinc oxide device, compared with approximately 7% for a conventional design.     

Suppression of the leaky SAW attenuation with heavy mechanical loading

We discuss effects on the propagation of surface acoustic waves (SAW) due to heavy mass loading on Y-cut lithium niobate and lithium tantalate substrates. An abrupt reduction in the leaky-SAW (LSAW) attenuation is observed in the measured admittance of a long resonator test structure on 64 degrees -YX-cut lithium niobate for aluminum electrodes of thickness h/lambda(0) beyond 9-10%. This experimental fact is explained theoretically as the slowing down of the leaky wave below the velocity of the slow shear surface-skimming bulk wave (SSBW), such that energy dissipation into bulk-wave emission becomes inhibited. An infinite transducer structure is modeled using the periodic Green's function and the boundary-element method (BEM); the computed theoretical properties well explain for the experimental findings. The model is further employed to quantify the leaky surface-wave attenuation characteristics as functions of the crystal-cut angle and the thickness of the electrodes. The resonance and antiresonance frequencies and the corresponding Q values are investigated to facilitate the selection of crystal cuts and electrode thicknesses. The transformation of the leaky SAW into a SAW-type nonleaky wave is also predicted to occur for gold electrodes, with considerably thinner finger structures.     

Optimized reflector stacks for solidly mounted bulk acoustic wave resonators

The quality factor (Q) of a solidly mounted bulk acoustic wave resonator (SMR) is limited by substrate losses, because the acoustic mirror is traditionally optimized to reflect longitudinal waves only. We propose two different design approaches derived from optics to tailor the acoustic mirror for effective reflection of both longitudinal and shear waves. The first one employs the stopband theory in optics; the second one takes advantage of the periodic nature of reflection spectra in a Bragg reflector: the diffraction grating design approach. The optimized design using stopband theory reaches a calculated minimum transmission of 25 dB and 20 dB at resonance frequency for longitudinal and shear waves, respectively, for various practical reflector material combinations. Using the diffraction grating approach, a near quarter-wave performance is maintained for longitudinal waves, whereas shear waves reach minimum transmission below 26 dB. However, this design does necessitate relatively thick layers. The experimental results show good agreement with finite element models (FEM). The extracted 1-D Q for the realized shear optimized devices was increased to around 3300.     

Light scattering described in the mode picture

A system of orthonormal functions representing the eigenmodes of an optical resonator with perfectly spherical mirror surfaces has been described in the literature. In real experiments, however, the wave front of the passing beam will be deformed by surface irregularities or index inhomogeneities inside components traversed by the beam. We describe quantitatively the relative power transferred out of the fundamental mode into higher-order modes by these irregularities.     

Dispersion and mirror transmission characteristics of bulk acoustic wave resonators

A heterodyne laser interferometer is used for a detailed study of the acoustic wave fields excited in a 932-MHz solidly mounted ZnO thin-film BAW resonator. The sample is manufactured on a glass substrate, which also allows direct measurement of the vibration fields from the bottom of the acoustic mirror. Vibration fields are measured both on top of the resonator and at the mirror-substrate interface in a frequency range of 350 to 1200 MHz. Plate wave dispersion diagrams are calculated from the experimental data in both cases and the transmission characteristics of the acoustic mirror are determined as a function of both frequency and lateral wave number. The experimental data are compared with 1-D and 2-D simulations to evaluate the validity of the modeling tools commonly used in mirror design. All the major features observed in the 1-D model are identified in the measured dispersion diagrams, and the mirror transmission characteristics predicted for the longitudinal waves, by both the 1-D and the 2-D models, match the measured values well.     

Acoustic loss mechanisms in leaky SAW resonators on lithiumtantalate

Discusses acoustic losses in synchronous leaky surface acoustic wave (LSAW) resonators on rotated Y-cut lithium tantalate (LiTaO₃ ) substrates. Laser probe measurements and theoretical models are employed to identify and characterize the radiation of leaky waves into the busbars of the resonator and the excitation of bulk acoustic waves. Escaping LSAWs lead to a significant increase in the conductance, typically occurring in the vicinity of the resonance and in the stopband, but they do not explain the experimentally observed deterioration of the electrical response at the antiresonance. At frequencies above the stopband, the generation of fast shear bulk acoustic waves is the dominant loss mechanism     

Effects of layer thickness for SAW, PSAW, and HVPSAW devices

Considerable efforts in recent SAW device design and development have been aimed at obtaining high frequency, low loss, and high performance. A large number of applications relate to cellular and mobile telephony, pagers, local area networks, cordless phones, global positioning systems (GPS), and security systems. Pseudo-SAW (PSAW) and high velocity PSAW (HVPSAW) have received great attention because of their high phase velocities and, therefore, the high frequencies of operation that these modes provide. In addition to high phase velocities, the pseudomodes must also present low propagation losses and considerably high electromechanical coupling coefficients to be considered for surface acoustic wave (SAW) devices. This paper verifies that the metallic layer thickness is a relevant SAW device parameter, which must be considered to achieve lower losses for high frequency, low loss SAW devices. Popular PSAW and HVPSAW material orientations, such as 64 degrees YX LiNbO3 (0 degree -26 degrees 0 degree), 36 degrees YX LiTaO3 (0 degree -54 degrees 0 degree), LiNbO3 (90 degrees 90 degrees 36 degrees), LiTaO3 (90 degrees 90 degrees 31 degrees), and Li2B4O7 (0 degree 47.3 degrees 90 degrees), are considered as examples. In addition to the reduced loss analysis and the dispersion analysis for the pseudo modes, the present work discusses the transitions with respect to the layer thickness from the PSAWs and HVPSAWs to the generalized SAWs (GSAWs) and Rayleigh (sagittal particle motion) modes. In addition to contributing to the knowledge of the pseudomodes behavior with layer thickness, this mode transition analysis enlightens the situation in which the losses in the pseudo modes go to zero because of the merging of the pseudo modes into the SAWs (GSAWs and Rayleigh). The fact that the SAWs are a continuation as a function of thickness for the pseudo modes may be conveniently used in the fabrication of low loss devices. In addition, the effects of heavy layer metals, such as gold, in reducing the layer thickness at which the pseudo modes merge to the SAWs are discussed. Numerical results are compared with experimental data available in the literature, and the present analysis elucidates experimentally observed higher order pseudo modes and values of layer thickness for which lower losses are achieved.     

Longitudinal leaky SAW resonators and filters on YZ-LiNbO3.

The high-phase velocity (above 6100 m/s in an aluminum (Al) grating on lithium niobate (LiNbOs)) of the longitudinal leaky surface acoustic wave (SAW) (LLSAW) mode makes it attractive for application in high-frequency SAW ladder filters in the 2-5 GHz range. We investigate the dependence of one-port synchronous LLSAW resonator performance on YZ-LiNbO3 on the metallization thickness and metallization ratio, both experimentally and theoretically. Our results indicate a strong dependence of the Q factor and resonance frequency on the aluminum thickness, with the optimal thickness that produces the highest Q values being about 8%. The optimal thickness increases with the metallization ratio. The observed behavior is interpreted with the help of simulations using a combined finite element method (FEM)/boundary element method (BEM) technique. As an application, bandpass filters have been fabricated in the 2.8 GHz frequency regime, based on LLSAWs. The synchronous resonators constituting the ladder filters operate in the fundamental mode. The filters feature low insertion losses below 3 dB and wide relative passbands of 4.5-5%.     

Longitudinal leaky SAW resonators and filters on YZ-LiNbO/sub 3/

The high-phase velocity (above 6100 m/s in and aluminum (Al) grating on lithium niobate (LiNbO/sub 3/)) of the longitudinal leaky surface acoustic wave (SAW) (LLSAW) mode makes it attractive for application in high-frequency SAW ladder filters in the 2-5 GHz range. We investigate the dependence of one-port synchronous LLSAW resonator performance or YZ-LiNbO/sub 3/ on the metallization thickness and metallization ratio, both experimentally and theoretically. Our results indicate a strong dependence of the Q factor and resonance frequency on the aluminum thickness, with the optimal thickness that produces the highest Q values being about 8%. The optimal thickness increases with the metallization ratio. The observed behavior is interpreted with the help of simulations using a combined finite element method (FEM)/boundary element method (BEM) technique. As an application, bandpass filters have been fabricated in the 2.8 GHz frequency regime, based on LL-SAWs. The synchronous resonators constituting the ladder filters operate in the fundamental mode. The filters feature low insertion losses below 3 dB and wide relative passbands of 4.5-5%.     

Finite element simulation and visualization of leaky Rayleigh wavesfor ultrasonic NDE

The generation and propagation properties of transient leaky Rayleigh waves are characterized by a two-dimensional finite element model. The displacement vector is used as the primary variable for the solid medium and a potential scalar, which is a replacement for the pressure, is taken as the fundamental variable for the fluid medium. The coupled system of finite element equations are solved in the time domain by direct integration through the central difference scheme. Three configurations are considered: the conversion of a Rayleigh surface wave into a leaky Rayleigh wave, a focused beam probing a fluid/solid interface at the Rayleigh angle, and the interaction of a defocused wave with the interface. The wave velocity in the fluid (water) is lower than the Rayleigh wave velocity in the solid (aluminum). The wave propagation profile in each case is predicted by the model. The finite element model proves to be an effective tool for surface acoustic device design and ultrasonic NDE     

A few-mode optical fiber retaining optical vortices

The ability of an optical fiber with axial losses to selectively suppress the fundamental HE ₁₁ mode, as well as the TE and TM waveguide modes, and, simultaneously, to transmit optical vortices with almost zero energy losses is considered. The attenuation coefficients for the corresponding eigenmodes and vortices are determined. It is shown that such a fiber operates as a mode filter for the feeding beam.     

Optimal cut for leaky SAW on LiTaO3 for high performance resonators and filters

The paper describes how the characteristics of leaky surface acoustic wave (LSAW) propagation depend on the thickness of Al grating electrodes on rotated Y-X LiTaO3. It is shown that the propagation loss arising from leaky nature changes parabolically with both the grating electrode thickness and rotation angle and becomes zero when electrode thickness and rotation angle are properly determined. This means that even when thick grating electrodes are needed in device design, zero propagation loss is always realized by properly determining the rotation angle. When the grating electrode thickness is 0.07 to 0.1 in wavelength for example, LSAWs on 40-42 degrees Y-X LiTaO3 give zero propagation loss without deteriorating other characteristics. Ladder-type filters for the 800-MHz range were fabricated, which essentially need thick Al grating electrodes of about 0.1 wavelength thickness. As predicted by theoretical calculation, experimental results showed that if the rotation angle is increased to circa 420 from a conventional value of 36 degrees, the insertion loss and shape factor are markedly improved compared with devices based on 36 degrees Y-X LiTaO3. This is essentially a result of the minimized propagation loss.     

Electromagnetic theory of an open resonator.

Particular higher-order sources give rise to electromagnetic Gaussian beams, which are linearly polarized and have their maximum in the propagation direction. For this dipolar beam the cross-sectional shape changes in the propagation direction. Nodal surfaces exist on which the tangential component of the electric field vanishes in the standing wave that is formed by the two oppositely directed dipolar, electromagnetic Gaussian beams. These surfaces are identified as the mirror shapes for an open resonator that supports this standing wave. For standing waves that have a particular cross-sectional shape at the waist the cross section of the beam near the mirror surfaces is circular. The resonant frequencies for the fundamental transverse mode of such a resonator have been determined as a function of the geometry and the axial mode number. By a perturbation technique the resonant frequency of an open resonator with spherical mirrors has been obtained. This result is valid in only the paraxial approximation. Illustrative numerical results are included.     

The experimental and theoretical characterization of the SAW propagation properties for zinc oxide films on silicon carbide

The surface acoustic wave (SAW) propagation properties of zinc oxide (ZnO) films on silicon carbide (SiC) have been theoretically and experimentally characterized in the film thickness-to-acoustic wavelength ratio range up to 0.12. The experimental characterization of the SAW propagation properties was performed with a linear array of interdigital transducer (IDT) structures. The measurements characterized the velocity and propagation loss of two surface modes, a generalized SAW (GSAW) mode with velocities between 6000 and 7000 m/s, and a high velocity Pseudo-SAW (HVPSAW) mode with velocities between 8500 and 12 500 m/s. The experimentally determined characteristics of the two waves have been compared with the results of calculations based on published data for SiC and ZnO. Simulation of wave characteristics was performed with various values of the elastic constant C(13), which is absent in the published set of material constants for SiC, within the interval permitted by the requirement of positive elastic energy in a hexagonal crystal. The best agreement between the measured and calculated propagation losses of the HVPSAW has been obtained for C(13) near zero. Although for the GSAW mode the calculated velocity dispersion has been found nearly insensitive to the value of C (13) and consistent with the experimental data, for the HVPSAW, some disagreement between measured and calculated velocities, which increased with ZnO film thickness, has been observed for any C(13 ) value. Theoretical analysis of HVPSAW has revealed the existence of a previously unknown high velocity SAW (HVSAW). The displacement components of this wave have been analyzed as functions of depth and confirmed its pure surface, one-partial character.     

Analysis of temperature compensation in a plate thickness mode bulk acoustic wave resonator

We analyze temperature-induced frequency shift in a thickness mode bulk acoustic wave resonator with a layer of another material for temperature compensation. The perturbation integral by Tiersten is used to calculate frequency shifts in the resonator under a temperature change. It is shown that, with a proper design of the compensation layer, temperature sensitivity of the resonator can be reduced or made zero.     

Experimental investigation of acoustic substrate losses in 1850-MHz thin film BAW resonators

After optimizing for electromechanical coupling coefficient K², the main performance improvement in the thin film bulk acoustic wave resonators and filters can be achieved by improving the Q value, i.e., minimizing the losses. In Braggreflector- based solidly mounted resonator technology, a significant improvement of Q has been achieved by optimizing the reflector not only for longitudinal wave, the intended operation mode, but also for shear waves. We have investigated the remaining acoustic radiation losses to the substrate in so-optimized 1850-MHz AlN resonators by removing the substrate underneath the resonators and comparing the devices with and without substrate by electrical characterization before and after the substrate removal. Several methods to extract Q-values of the resonators are compared. Changes caused by substrate removal are observed in resonator behavior, but no significant improvement in Q-values can be confirmed. Loss mechanisms other than substrate leakage are concluded to dominate the resonator Q-value. Difficulties of detecting small changes in the Q-values of the resonators are also discussed.     

Theoretical study of surface acoustic waves in (n11) GaAs-cuts

The propagation characteristics of true and leaky or pseudo surface acoustic waves (TSAW and PSAW=LSAW) on (n11) GaAs-cuts, n=1, 2, 3 and 4, are theoretically calculated as a function of propagation direction. They include phase velocity (V), electromechanical coupling constant (K(2)), and attenuation factor (alpha) of wave propagation on a metallized surface. The results show that PSAW mode velocities are significantly higher than corresponding TSAW velocities, and for certain propagation directions the attenuation factor is extremely small (10(-5) dB/lambda). Highly coupled PSAW modes exist for propagation directions where the TSAW are very poorly coupled. For certain isolated directions, attenuation of the wave is null (alpha=0), PSAW becoming a non-leaky SAW with partial polarization. And in this case the corresponding TSAW are decoupled from the surface electric excitation. Analysis of relations between various modes (TSAW, PSAW and SSBW, surface skimming bulk wave) is made with the help of the effective surface permittivity function and the generalized slowness diagram. A coupling constant definition different from the usual 2DeltaV/V is used, its validity and application conditions are discussed.