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In the framework of electro-elasticity theory and the finite element method (FEM), a model is set up for the computation of quantities in surface acoustic wave (SAW) devices accounting for nonlinear effects. These include second-order and third-order intermodulations, second and third harmonic generation and the influence of electro-acoustic nonlinearity on the frequency characteristics of SAW resonators. The model is based on perturbation theory, and requires input material constants, e.g., the elastic moduli up to fourth order for all materials involved. The model is two-dimensional, corresponding to an infinite aperture, but all three Cartesian components of the displacement and electrical fields are accounted for. The first version of the model pertains to an infinite periodic arrangement of electrodes. It is subsequently generalized to systems with a finite number of electrodes. For the latter version, a recursive algorithm is presented which is related to the cascading scheme of Plessky and Koskela and strongly reduces computation time and memory requirements. The model is applied to TC-SAW systems with copper electrodes buried in an oxide film on a LiNbO3 substrate. Results of computations are presented for the electrical current due to third-order intermodulations and the displacement field associated with the second harmonic and second-order intermodulations, generated by monochromatic input tones. The scope of this review is limited to methodological aspects with the goal to enable calculations of nonlinear quantities in SAW devices on inexpensive and easily accessible computing platforms.
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.
The laser ultrasound (LU) technique has been used to determine dispersion curves for surface acoustic waves (SAW) propagating in AlScN/Al2O3 systems. Polar and non-polar Al0.77Sc0.23N thin films were prepared by magnetron sputter epitaxy on Al2O3 substrates and coated with a metal layer. SAW dispersion curves have been measured for various propagation directions on the surface. This is easily achieved in LU measurements since no additional surface structures need to be fabricated, which would be required if elastic properties are determined with the help of SAW resonators. Variation of the propagation direction allows for efficient use of the system’s anisotropy when extracting information on elastic properties. This helps to overcome the complexity caused by a large number of elastic constants in the film material. An analysis of the sensitivity of the SAW phase velocities (with respect to the elastic moduli and their dependence on SAW propagation direction) reveals that the non-polar AlScN films are particularly well suited for the extraction of elastic film properties. Good agreement is found between experiment and theoretical predictions, validating LU as a non-destructive and fast technique for the determination of elastic constants of piezoelectric thin films.
A laser-operated, angle-tunable transducer was employed to excite selectively elastic waves guided along the apex of a solid wedge. The propagation of wedge waves at anisotropic monocrystalline silicon edges with different symmetry properties was studied by optical detection. The reduced symmetry in crystals, as compared to isotropic media, causes a number of new features, such as the existence of supersonic leaky wedge waves, tilted spatial pulse profiles, and other peculiarities of their localization. Experimental and theoretical results are presented for three different types of symmetry configurations: the wedge symmetric about its midplane, the wedge symmetric about the plane normal to its apex line, and the wedge symmetric about one of its faces. The experiments include accurate measurements of the phase velocity and the wave field distribution, providing information on localization and coupling of wedge waves with other waves. Theoretically, the wedge waves were treated by the Laguerre function method, extended to modes that are not localized at the tip of the wedge. This approach allowed an accurate description of the observed localized and leaky wedge waves in anisotropic wedges.
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.
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.