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A Nonlinear FEM Model to Calculate Third-Order Harmonic and Intermodulation in TC-SAW Devices
(2018)
Nonlinearities in Temperature Compensated SAW (TC-SAW) devices in the 2 GHz range are investigated using a nonlinear finite element model by simultaneously considering both third-order intermodulation distortion (IMD3)and third harmonic (H3). In the employed perturbation approach, different contributions to the total H3, the direct and indirect contribution, are discussed. H3 and IMD3 measurements were fitted simultaneously using scaling factors for SiO 2 film and Cu electrode nonlinear material tensors in TC-SAW devices. We employ a P-Matrix simulation as intermediate step: Firstly, measurement and nonlinear P-Matrix calculations for finite devices are compared and coefficients of the P-Matrix simulation are determined. The nonlinear tensor data of the different materials involved in periodic nonlinear finite element method (FEM) computations are optimized to fit periodic P-Matrix calculations by introducing scaling factors. Thus, the contribution of different materials to the nonlinear behavior of TC-SAW devices is obtained and the role of materials is discussed.
The growing complexity in RF front-ends, which support carrier aggregation and a growing number of frequency bands, leads to tightened nonlinearity requirements in all sub-components. The generation of third order intermodulation products (IMD3) are typical problems caused by the non-linearity of SAW devices. In the present work, we investigate temperature compensating (TC) SAW devices on Lithium Niobate-rot128YX. An accurate FEM simulation model [1] is employed, which allows to better understand the origin of nonlinearities in such acoustic devices.
Nonlinearity can give rise to intermodulation distortions in surface acoustic wave (SAW) devices operating at high input power levels. To understand such undesired effects, a finite element method (FEM) simulation model in combination with a perturbation theory is applied to find out the role of different materials and higher order nonlinear tensor data for the nonlinearities in such acoustic devices. At high power, the SAW devices containing metal, piezoelectric substrate, and temperature compensating (TC) layers are subject to complicated geometrical, material, and other nonlinearities. In this paper, third-order nonlinearities in TC-SAW devices are investigated. The materials used are LiNbO 3 -rot128YX as the substrate and copper electrodes covered with a SiO 2 film as the TC layer. An effective nonlinearity constant for a given system is determined by comparison of nonlinear P-matrix simulations to third-order intermodulation measurements of test filters in a first step. By employing these constants from different systems, i.e., different metallization ratios, in nonlinear periodic P-matrix simulations, a direct comparison to nonlinear periodic FEM-simulations yields scaling factors for the materials used. Thus, the contribution of the different materials to the nonlinear behavior of TC-SAW devices is obtained and the role of metal electrodes, substrate, and TC film are discussed in detail.
In the present work, nonlinearities in temperature compensating (TC) SAW devices are investigated. The materials used are LiNbO₃-rot128YX as the substrate and Copper electrodes covered with a SiO₂-layer as the compensating layer. In order to understand the role of these materials for the nonlinearities in such acoustic devices, a FEM simulation model in combination with a perturbation approach is applied. The nonlinear tensor data of the different materials involved in TC-SAW devices have been taken from literature, but were partially modified to fit experimental data by introducing scaling factors. An effective nonlinearity constant is determined by comparison of nonlinear P-matrix simulations to IMD3 measurements of test filters. By employing these constants in nonlinear periodic P-matrix simulations a direct comparison to nonlinear periodic FEM-simulations yields the scaling factors for the material used. Thus, the contribution of different materials to the nonlinear behavior of TC-SAW devices is obtained and the role of metal electrodes is discussed in detail.
This work focuses on the dependencies between typical design parameters of surface acoustic wave (SAW) resonators and the nonlinear emitted signals of second and third order. The parameters metalization ratio and pitch are used as examples, but the approach can be extended to other design parameters as well. It is shown, that the interaction between the nonlinear current generation and the linear admittance is defining the measured nonlinear power signals. It is also discussed, that changes in linear properties get more pronounced in nonlinear responses. Therefore, slight effects on linear parameters will have significant influence on the observed nonlinearity.
Increasing power density causes increased self-generation of harmonics and intermodulation. As this leads to violations of the strict linearity requirements, especially for carrier aggregation (CA), the nonlinearity must be considered in the design process of RF devices. This raises the demand of accurate simulation models. Linear and nonlinear P-Matrix/COM models are used during the design due to their fast simulation times and accurate results. However, the finite element method (FEM) is useful to get a deeper insight in the device's nonlinearities, as the total field distributions can be visualized. The FE method requires complete sets of material tensors, which are unknown for most relevant materials in nonlinear micro-acoustics. In this work, we perform nonlinear FEM simulations, which allow the calculation of nonlinear field distributions of a lithium tantalate based layered SAW system up to third order. We aim at achieving good correspondence to measured data and determine the contributions of each material layer to the nonlinear signals. Therefore, we use approximations circumventing the issue of limited higher order tensor data. Experimental data for the third order nonlinearity is shown to validate the presented approach.
In this work the nonlinear behavior of layered surface acoustic wave (SAW) resonators is studied with the help of finite element (FE) computations. The full calculations depend strongly on the availability of accurate tensor data. While there are accurate material data for linear computations, the complete sets of higher-order material constants, needed for nonlinear simulations, are still not available for relevant materials. To overcome this problem, scaling factors were used for each available nonlinear tensor. The approach here considers piezoelectricity, dielectricity, electrostriction, and elasticity constants up to the fourth order. These factors act as a phenomenological estimate for incomplete tensor data. Since no set of fourth-order material constants for LiTaO3 is available, an isotropic approximation for the fourth-order elastic constants was applied. As a result, it was found that the fourth-order elastic tensor is dominated by one-fourth order Lamé constant. With the help of the FE model, derived in two different, but equivalent ways, we investigate the nonlinear behavior of a SAW resonator with a layered material stack. The focus was set to third-order nonlinearity. Accordingly, the modeling approach is validated using measurements of third-order effects in test resonators. In addition, the acoustic field distribution is analyzed.
Existing ultrasonic stress evaluation methods utilize the acoustoelastic effect for bulk waves propagating in volume, which is unsuitable for a surface treated material, possessing a significant variation in material properties with depth. With knowledge of nonlinear elastic parameters – third-order elastic constants (TOEC) close to the surface of the sample, the acoustoelastic effect might be used with surface acoustic waves. This work is focused on the development of an independent method of TOEC measurement using the effect of nonlinear surface acoustic waves scattering – i.e. the effect of elastic waves interaction in a nonlinear medium.
In this paper, the possible three wave interactions of surface guided waves and bulk waves are described and formulae for the efficiency of harmonic generation and mode mixing are derived. A comparison of the efficiency of surface waves scattering in an isotropic medium for different interaction types is carried out with the help of nonlinear perturbation theory. First results for surface and bulk wave mixing with known second- and third-order elastic constants are shown.
Surface treatment intensity monitoring is still an open and challenging nondestructive testing problem. For the estimation of residual stress with ultrasonic measurements, local linear and nonlinear elastic constants are needed as input. In this paper, nonlinear elastic-wave interactions (also called wave mixing or scattering) — namely, the generation of secondary ultrasonic waves in a nonlinear medium — are considered as a prospective means for near-surface nonlinear elastic parameter evaluation. The allowed interactions between bulk and surface waves, as well as the dependence of the scattering efficiency on the frequency and angle between source waves, were investigated through an analytical model, then compared with FEM simulations and experimental results. Finally, possible future steps for the development of the applied methods for the determination of near-surface higher-order elastic constants are discussed. In addition, several problem-relevant data processing procedures are presented.
The characteristic features and applications of linear and nonlinear guided elastic waves propagating along surfaces (2D) and wedges (1D) are discussed. Laser-based excitation, detection, or contact-free analysis of these guided waves with pump–probe methods are reviewed. Determination of material parameters by broadband surface acoustic waves (SAWs) and other applications in nondestructive evaluation (NDE) are considered. The realization of nonlinear SAWs in the form of solitary waves and as shock waves, used for the determination of the fracture strength, is described. The unique properties of dispersion-free wedge waves (WWs) propagating along homogeneous wedges and of dispersive wedge waves observed in the presence of wedge modifications such as tip truncation or coatings are outlined. Theoretical and experimental results on nonlinear wedge waves in isotropic and anisotropic solids are presented.
Silicon edges as one-dimensional waveguides for dispersion-free and supersonic leaky wedge waves
(2012)
Acoustic waves guided by the cleaved edge of a Si(111) crystal were studied using a laser-based angle-tunable transducer for selectively launching isolated wedge or surface modes. A supersonic leaky wedge wave and the fundamental wedge wave were observed experimentally and confirmed theoretically. Coupling of the supersonic wave to shear waves is discussed, and its leakage into the surface acoustic wave was observed directly. The velocity and penetration depth of the wedge waves were determined by contact-free optical probing. Thus, a detailed experimental and theoretical study of linear one-dimensional guided modes in silicon is presented.
In anisotropic media, the existence of leaky surface acoustic waves is a well-known phenomenon. Very recently, their analogs at the apex of an elastic silicon wedge have been found in experiments using laser-ultrasonics. In addition to a wedge-wave (WW) pulse with low speed, a pseudo-wedge wave (p-WW) pulse was found with a velocity higher than the velocity of shear bulk waves, propagating in the same direction. With a probe-beam-deflection technique, the propagation of the WW pulses was monitored on one of the faces of the wedge at variable distance from the apex. In this way, their depth structure and the leakage of the p-WW could be visualized directly. Calculations were carried out using a method based on a representation of the displacement field in Laguerre functions. This method has been validated by calculating the surface density of states in anisotropic media and comparing the results with those obtained from the surface Green's tensor. The approach has then been extended to the continuum of acoustic modes in infinite wedges with fixed wave-vector along the apex. These calculations confirmed the measured speeds of the WW and p-WW pulses.
A theoretical description is given for the propagation of surface acoustic wave pulses in anisotropic elastic media subject to the influence of nonlinearity. On the basis of nonlinear elasticity theory, an evolution equation is presented for the surface slope or the longitudinal surface velocity associated with an acoustic pulse. It contains a non-local nonlinearity, characterized by a kernel that strongly varies from one propagation geometry to another due to the anisotropy of the substrate. It governs pulse shape evolution in homogeneous halfspaces and the shapes of solitary surface pulses that exist in coated substrates. The theory describing nonlinear Rayleigh-type surface acoustic waves is extended in a straightforward way to surface waves that are localized at a one-dimensional acoustic waveguide like elastic wedges.
Surface and interface acoustic waves are two-dimensionally guided waves, as their displacement field is plane-wave like regarding its dependence on the spatial coordinates parallel to the guiding plane, while it decays exponentially along the axis normal to that plane. When propagating at the planar surface or interface of homogeneous media, they are non-dispersive. Another type of non-dispersive acoustic waves which is, however, one-dimensionally guided, has displacement fields localized near the apex of a wedge made of an elastic material. In this short review, their propagation properties are described as well as theoretical and experimental methods which have been used for their analysis. Experimental findings are discussed in comparison with corresponding theoretical work and potential applications of this fascinating type of acoustic waves are presented.
Anisotropy has been found to play an important role for the existence of edge-localized acoustic modes as well as for nonlinear effects in rectangular edges. For a certain propagation geometry in silicon, the effective second-order nonlinearity for wedge waves was determined numerically from second-order and third-order elastic moduli and compared with the nonlinearity for Rayleigh waves propagating in the direction of the apex on one of the two surfaces forming the edge. In the presence of weak dispersion resulting from modifications of the wedge tip or coating of the adjacent surfaces, solitary pulses are predicted to exist and their shape was calculated.
In a recent paper it has been shown that the effective nonlinear constant which is used in a P-Matrix approach to describe third-order intermodulation (IMD3) in surface acoustic wave (SAW) devices can be obtained from finite element (FEM) calculations of a periodic cell using nonlinear tensor data [1]. In this paper we extend this FEM calculation and show that the IMD3 of an infinite periodic array of electrodes on a piezoelectric substrate can be directly simulated in the sagittal plane. This direct approach opens the way for a FEM based simulation of nonlinearities for finite and generalized structures avoiding the simplifications of phenomenological approaches.
In einer SAW-Vorrichtung, welche einen SAW-Chip umfasst, der einen SAW-Wandler aufweist, welcher innerhalb einer ersten Signalleitung angeordnet ist, werden Parasitärsignale infolge höherer Harmonischer der Betriebsfrequenz der SAW-Vorrichtungen durch Kompensationsmittel elektrisch beseitigt, welche zumindest eine zweite Signalleitung mit Mitteln zum Erzeugen eines Aufhebungssignals, das im Vorzeichen oder in der Phase vom Parasitärsignal verschieden ist, oder eine Nebenschlussleitung zum elektrischen Verbinden des SAW-Wandlers mit einer rückseitigen Metallisierung des SAW-Chips umfassen.