Elena Mayer

Precise measurements of BAW and SAW properties of Langasite in the temperature range from 25°C to 1000°C

There is a high demand for wireless sensing devices in harsh environments for industrial applications. For temperatures above 250degC, silicon-based sensors cannot be used. In contrast, bulk acoustic wave (BAW) and surface acoustic wave (SAW) devices are still suitable for this purpose. Further high-temperature applications include thermogravimetry on small volumes and gas sensing based on stoichiometry change of thin sensor films. Langasite (La3Ga5SiO14) is a piezoelectric single crystal that preserves its piezoelectric properties and is chemically stable up to its melting point at 1470degC without any phase transition and, therefore, is a promising material for high-temperature devices. Using a resonance-antiresonance method based on bulk oscillations, all components of elastic and piezoelectric tensors of langasite have been determined at temperatures up to 900deg C. Resonance spectra of several langasite samples have been measured and fitted with the impedance calculated from a one-dimensional physical model of piezoelectric bodies vibrating in several modes. In order to extract the electromechanical parameters, different resonator geometries and orientations are used. Also, the results of measurements are presented for SAW devices on langasite at temperatures from 25 to 750deg C. Two cuts with Euler angles (0deg, 138.5deg,26.6deg) and (0deg,30.1deg,26.6deg) have been studied. The devices were fabricated with a platinum (Pt) layer with different heights on a zirconium (Zr) adhesion layer. The main material parameters relevant for SAW devices such as phase velocity vp, propagation loss alpha and coupling coefficient k2 have been obtained. The measured SAW phase velocities compare well with those calculated with the elastic and piezoelectric tensors obtained by bulk-oscillation measurements.

SAW-relevant material properties of langasite in the temperature range from 25 to 750 °C: New experimental results

The aim of this work is to determine the acoustical parameters of langasite up to the highest possible point of temperature. This paper presents measurements of transfer functions for delay lines on langasite at frequencies ranging from 150 MHz to 1 GHz, at temperatures from 25 to 750degC. Two cuts with Euler angles (0deg, 138.5deg, 26.6deg) and (0deg, 30.2deg, 26.6deg) have been studied. The devices were fabricated using langasite as substrate, with two different platinum (Pt) layer heights (45 nm and 75 nm), on a zirconium (Zr) adhesion layer (4 nm). A special signal processing algorithm utilizing cross-correlation was implemented in MATLAB and used for the analysis of measured data. The material parameters relevant for SAW devices, such as phase velocity, propagation loss, and electromechanical coupling coefficient, have been determined as a function of temperature.

SAW-properties of langasite at high temperatures: Measurement and analysis

The measurement range of temperature using SAW-devices is depending on the substrate material used in the measurements. This dependence is related to the temperature point, where the substrate loses its piezoelectric properties. This occurs by the SAW-materials such as quartz and lithium niobate at about 570°C or 350°C, respectively. The piezoelectric material langasite (La3Ga5SiO14) has a thermodynamically stable phase and do not lose its piezoelectric properties up to its melting point at about 1470 °C and can be used for SAW devices at high temperatures. This paper presents the measurements of acoustical parameters of langasite up to 750°C. Langasite is used as substrate in the measurements with Euler angles (0°, 138.5°, 26.6°) and two different platinum (Pt) layer heights (45 nm and 75 nm) top of a zirconium (Zr) adhesion layer (4 nm). The investigated acoustic properties of langasite are group and phase velocity, propagation loss, and electromechanical coupling coefficient as functions of temperature. The measured data is analyzed using a special signal processing algorithm to obtain these acoustic properties of the Langasite.

Rigorous COM and P-matrix approaches to the simulation of third-order intermodulation distortion and triple beat in SAW filters

In this work a set of nonlinear coupled COM equations at interacting frequencies is derived on the basis of nonlinear electro-elasticity. The formalism is presented with the aim of describing intermodulation distortion of third-order (IMD3) and triple beat. The resulting COM equations are translated to the P-matrix formalism, where care is taken to obtain the correct frequency dependence. The scheme depends on two frequency-independent constants for an effective third-order nonlinearity. One of these two constants is negligibly small in the systems considered here. The P-matrix approach is applied to single filters and duplexers on LiTaO3 (YXl)/42° operating in different frequency ranges. Both IMD3 and triple beat show good agreement with measurement.

SAW parameters for langasite at high temperatures

For three cuts of langasite with Euler angles (0°,138.5°,27°), (0°,22°,31°), and (0°,22°,90°) the temperature dependencies of SAW parameters - velocities, reflection coefficients and propagation loss were determined experimentally up to 800°C. For this, the test structures - delay lines and resonators, operating in the frequency range from 200 MHz up to 600 MHz, were designed and fabricated using Pt metallization. The influence of a passivation layer of Al₂O₃ was investigated. The perspective for the use of the STW cut is discussed.

Application of a rigorous nonlinear P-matrix method to the simulation of third order intermodulation in test devices and duplexers

Recently a P-matrix and COM formalism was presented, which predicts third order intermodulation (IMD3) and triple beat with good accuracy and needs only a single nonlinearity constant. This formalism describes frequency dependence correctly. In this work the dependence of this nonlinearity constant on metalization ratio is investigated for aluminum metalization on LiTaO3 (YXl)/42°. By comparison to test devices the nonlinearity constant is shown to be largely independent of metalization ratio. The nonlinear effect, however, strongly depends on metalization ratio, which is well described by the model. The linearity of a duplexer is optimized by reduction of metalization ratio and redesign of Tx branch topology.

High-precision signal processing algorithm to evaluate SAW properties as a function of temperature

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.

Full 2D-FEM calculations of third-order intermodulations in SAW devices

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.

Effective nonlinear constants for SAW devices from FEM calculations

Recently we demonstrated that a single frequency-independent constant in a P-matrix approach is sufficient to describe the IMD3 of a variety of devices on LiTaO3-42YX including test devices and duplexers. In this work we investigate this effective nonlinear constant in more detail. Starting from a FEM simulation we calculate the linear fields at the frequencies of the input tones and combine them with the help of nonlinear tensors to get sources for nonlinear fields at mixing frequencies. The determination and analysis of the nonlinear shift of the resonance frequency yields an effective nonlinear coupling constant. This approach has been applied to LiNbO3-rot128YX. The value of the effective nonlinear constant calculated for this system is compared to the corresponding value extracted from nonlinear P-matrix simulations of IMD3 measurements.

Four-wave interaction in 2D periodic structures

The interaction of four SAWs is considered in a 2D periodic grating on the surface. In the isotropic case the grating reflects the incident wave with angles ±90°. Coupling-of-modes equations governing the four-wave interaction near the Bragg frequency are derived. For a rectangular shape of the area covered by the grid, they are solved analytically for zero detuning frequency and numerically for frequencies close to the Bragg frequency. The analytical solution shows resonant build-up of the amplitudes of the waves reflected in ±90° directions.