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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.
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.
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.
Properties of higher-order surface acoustic wave modes in Al(1-x)Sc(x)N / sapphire structures
(2021)
In this work, surface acoustic wave (SAW) modes and their dependence on propagation directions in epitaxial Al0.68Sc0.32N(0001) films on Al2O3(0001) substrates were studied using numerical and experimental methods. In order to find optimal propagation directions for higher-order SAW modes, phase velocity dispersion branches of Al0.68Sc0.32N on Al2O3 with Pt mass loading were computed for the propagation directions <11-20> and <1-100> with respect to the substrate. Experimental investigations of phase velocities and electromechanical coupling were performed for comparison with the numerical results. Simulations carried out with the finite element method (FEM) and with a Green function approach allowed identification of each wave type, including Rayleigh, Sezawa and shear horizontal wave modes. For the propagation direction <1-100>, significantly increased wave guidance of the Sezawa mode compared to other directions was observed, resulting in enhanced electromechanical coupling (k2eff = 1.6 %) and phase velocity (vphase = 6 km/s). We demonstrated, that selecting wave propagation in <1-100> with high mass density electrodes results in increased electromechanical coupling without significant reduction in phase velocities for the Sezawa wave mode. An improved combination of metallization, Sc concentration x, and SAW propagation direction is suggested which exhibits both high electromechanical coupling (k2eff > 6 %) and high velocity (vphase = 5.5 km/s) for the Sezawa mode.
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.
High-precision signal processing algorithm to evaluate SAW properties as a function of temperature
(2013)
This paper presents a signal processing algorithm which accurately evaluates the SAW properties of a substrate as functions of temperature. The investigated acoustic properties are group velocity, phase velocity, propagation loss, and coupling coefficient. With several measurements carried out at different temperatures, we obtain the temperature dependency of the SAW properties. The analysis algorithm starts by reading the transfer functions of short and long delay lines. The analysis algorithm determines the center frequency of the delay lines and obtains the delay time difference between the short and long delay lines. The extracted parameters are then used to calculate the acoustic properties of the SAW material. To validate the algorithm, its accuracy is studied by determining the error in the calculating delay time difference, center frequency, and group velocity.