Ingo Bleyl

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.

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.

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.

Accurate determination of thin film properties using SAW differential delay lines

We have investigated a method to accurately determine elastic properties of thin films. For this purpose the phase velocity of a layered system is calculated using surface acoustic wave (SAW) differential delay lines on LiNbO₃ substrates. The phase velocity can be calculated with an accuracy of Δv_ph = ±0.5m/s. The material parameters density, elastic constant (c₁₁ and c₄₄) and their temperature coefficients TC(c₁₁) and TC(c₄₄) of Si₃N₄ thin film have been determined. They could be extracted by fitting them to the calculated phase velocity of the layered system Si₃N₄/LiNbO₃. Furthermore, the influence of deposition conditions on the material tensor data has been studied.

Accurate characterization of SiO 2 thin films using surface acoustic waves

We have investigated the acoustic properties of silicon dioxide thin films. Therefore, we determined the phase velocity dispersion of LiNbO3 substrate covered with SiO2 deposited by a plasma enhanced chemical vapor deposition and a physical vapor deposition (PVD) process using differential delay lines and laser ultrasonic method. The density p and the elastic constants (c11 and c44) can be extracted by fitting corresponding finite element simulations to the phase velocities within an accuracy of at least ±4%. Additionally, we propose two methods to improve the accuracy of the phase velocity determination by dealing with film thickness variation of the PVD process.

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.

Estimation of temperature dependence of C 44 elastic constant in LiTaO 3 single crystals

In this work, electromechanical coupling factor, K2, and Temperature Coefficient of Frequency (TCF) of Bulk Acoustic Wave (BAW) resonators based on high aspect ratio ridge structures in 42°Y-X LiTaO3 (LT) and Z-cut LT single crystals with different Li stoichiometries were studied experimentally, analytically and by combined finite element / boundary element analysis. Initially, analytical analysis was carried out to determine the contribution of different elastic constants in thickness field excitation of shear modes in high aspect ratio ridge structures. The analysis shows shear modes that are dependent on C44 in ridge resonators based on 42°Y-X and Z-cut LT crystals. However, the measured frequency response of such structures exhibited many spurious resonances, making difficult the direct extraction of acoustical parameters. A fitting procedure that allows taking into account several resonances occurring simultaneously in a restricted frequency range was used. Higher K2 and more positive temperature dependence of frequency were determined for ridge structures in nearly stoichiometric crystals compared to those of equivalent structures in congruent ones.

A refined method to determine the elastic constants of SiO 2 thin films

We use differential delay lines to extract the phase velocity of a SAW on a LiNbO₃ substrate covered with thin SiO₂ films which have been deposited by a plasma enhanced chemical vapour deposition (PECVD) and a physical vapour deposition (PVD) process. The variation in film thickness of the PVD process between the differential delay lines has to be corrected to a reference thickness which is done by signal processing. The accuracy of the results allows the determination of the elastic constants (c₁₁ and c₄₄) and the density ρ of the PECVD thin film within an accuracy of ±2.4% and of the PVD SiO₂ process within an accuracy of ±4.1% by fitting corresponding simulations.

Second harmonic generation and detection in a Rayleigh-type SAW structure

With ever increasing requirements on the linearity of SAW signal processing devices in mobile communication, nonlinear effects like harmonic generation and intermodulations have gained renewed interest and have become an active field of research with the aim of identifying their origin, analyzing and counteracting them. In this contribution we focus on second-harmonic generation in SAW resonators. Like counter-propagating surface waves in SAW-type convolvers [1,2], part of the second-harmonic is a bulk wave propagating from the surface into the substrate [3,4]. In SAW resonators, this bulk wave has recently been investigated experimentally in detail [4]. Its reflections from the bottom of the substrate were found to give rise to Fabry-Perot-type resonances which were measured electrically at the output port. An open question remained: Why is the second harmonic visible in electrical measurements in a device with symmetrically arranged electrodes on the surface, since the nonlinear driving terms resulting from the fundamental via second-order nonlinearity of the materials contain equal charges on adjacent electrodes. This suggests that an electrical output signal at the second harmonic is not visible unless symmetry-breaking deviations from a perfect system are present.

The study of the anomalous thermomechanical effect of fluorine-doped silicon dioxide (FSG) films using temperature dependent FTIR measurements

Fluorine-doped silicon dioxide (FSG) is a material of interest in surface acoustic wave (SAW) technology due to its anomalous thermomechanical behavior. Therefore, it can be used in SAW devices for improved temperature compensation compared to undoped SiO2. However, up to now there is still no generally accepted theory, which explains this phenomenon. We investigate the reason for its anomalous thermomechanical behavior using Fourier transform infrared spectroscopy (FTIR) measurements of a fluorine-doped silicon dioxide thin films with about 3.4 at.% of fluorine at different temperatures. Geometrical interpretations of the FTIR measurements reveal that the decreasing intertetrahedral Si-O-Si bond angle θ with increasing temperature overcompensates the increasing Si-O bond length, which results in a very low thermal expansion coefficient. The fluorine doping of SiO2 leads to an increase in the bond angle and therefore a less dense network.