Tapani Makkonen

Finite element simulations of thin-film composite BAW resonators

A finite element method (FEM) formulation is presented for the numerical solution of the electroelastic equations that govern the linear forced vibrations of piezoelectric media. A harmonic time dependence is assumed. Both of the approaches, that of solving the field problem (harmonic analysis) and that of solving the corresponding eigenvalue problem (modal analysis), are described. A FEM software package has been created from scratch. Important aspects central to the efficient implementation of FEM are explained, such as memory management and solving the generalized piezoelectric eigenvalue problem. Algorithms for reducing the required computer memory through optimization of the matrix profile, as well as Lanczos algorithm for the solution of the eigenvalue problem are linked into the software from external numerical libraries. Our FEM software is applied to detailed numerical modeling of thin-film bulk acoustic wave (BAW) composite resonators. Comparison of results from 2D and full 3D simulations of a resonator are presented. In particular, 3D simulations are used to investigate the effect of the top electrode shape on the resonator electrical response. The validity of the modeling technique is demonstrated by comparing the simulated and measured displacement profiles at several frequencies. The results show that useful information on the performance of the thin-film resonators can be obtained even with relatively coarse meshes and, consequently, moderate computational resources.

Estimating materials parameters in thin-film BAW resonators using measured dispersion curves

The dispersion curves of Lamb-wave modes propagating along a multilayer structure are important for the operation of thin-film bulk acoustic wave (BAW) devices. For instance, the behavior of the side resonances that may contaminate the electrical response of a thin-film BAW resonator depends on the dispersion relation of the layer stack. Because the dispersion behavior depends on the materials parameters (and thicknesses) of the layers in the structure, measurement of the dispersion curves provides a tool for determining the materials parameters of thin films. We have determined the dispersion curves for a multilayer structure through measuring the mechanical displacement profiles over the top electrode of a thin-film BAW resonator at several frequencies using a homodyne Michelson laser interferometer. The layer thicknesses are obtained using scanning electron microscope (SEM) measurements. In the numerical computation of the dispersion curves, the piezoelectricity and full anisotropy of the materials are taken into account. The materials parameters of the piezoelectric layer are determined through fitting the measured and computed dispersion curves.

Surface-acoustic-wave devices for the 2.5–5 GHz frequency range based on longitudinal leaky waves

The recently discovered “longitudinal leaky” surface acoustic wave on YZ-cut lithium niobate has been used to implement low-loss bandpass filters operating in the 2.5-GHz Bluetooth frequency range. The filter is of the ladder type, employing synchronous resonators as building blocks. Resonator Q-values above 300 have been measured. The filter features a center frequency of 2491 MHz, a minimum insertion loss of 3.5 dB, and a fractional 3-dB bandwidth as wide as 6.2%.

ZnO based thin film bulk acoustic wave filters for EGSM band

We present results for a ZnO based filters for the mobile Extended GSM (EGSM) Rx band centered at 942.5 MHz. Our devices are of the SMR type. The acoustical isolation from the glass substrate is achieved by a tungsten-silicon dioxide quarter wavelength mirror. Resonators with an effective coupling coefficient of 0.236 and Q/spl sim/800 have been achieved. The filters are realized as either 3-section ladder or 2-section lattice connected FBARs without any external components. The ladder filters achieve a 3.5 dB absolute bandwidth of 39 MHz with minimum insertion loss of 1.3 dB, stop band rejection at 23 dB and VSWR of 2.2 in the pass band. The balanced filter design has a slightly larger bandwidth of 46 MHz and improved stop band behavior characteristic for this type of device.

Acoustic loss mechanisms in leaky SAW resonators on lithium tantalate

We discuss acoustic losses in synchronous leaky surface-acoustic wave resonators on rotated Y-cut lithium tantalate substrates. Laser probe measurements and theoretical methods are employed to estimate the radiation of leaky waves into the busbars of the resonator and the excitation of bulk-acoustic waves. We find that the escaping waves lead to a significant increase in the conductance, typically in the vicinity of the resonance and in the stopband, but that they do not explain the experimentally observed deterioration of the electric response at the antiresonance. At frequencies above the stopband the generation of fast shear bulk-acoustic waves is the dominant loss mechanism.Discusses acoustic losses in synchronous leaky surface acoustic wave (LSAW) resonators on rotated Y-cut lithium tantalate (LiTaO/sub 3/) substrates. Laser probe measurements and theoretical models are employed to identify and characterize the radiation of leaky waves into the busbars of the resonator and the excitation of bulk acoustic waves. Escaping LSAWs lead to a significant increase in the conductance, typically occurring in the vicinity of the resonance and in the stopband, but they do not explain the experimentally observed deterioration of the electrical response at the antiresonance. At frequencies above the stopband, the generation of fast shear bulk acoustic waves is the dominant loss mechanism.

Side radiation of Rayleigh waves from synchronous SAW resonators

Surface acoustic wave (SAW) resonators on lithium tantalate (LiTaOa) and lithium niobate (LiNbO3) are investigated. The amplitude of the acoustic fields in the resonators are measured using a scanning laser interferometer. The amplitude profiles of the surface vibrations reveal the presence of distinct acoustic beams radiated from the transducer region of the SAW resonators and propagating with low attenuation. We suggest that this radiation is generated by the charges accumulating at the tips of the finger electrodes. The periodic system of sources, namely oscillating charges at the fingertips, generates Rayleigh-wave beams in the perpendicular and oblique directions. Greens function theory is used to calculate the coupling strength and slowness of the Rayleigh waves on 42degY-cut LiTaO3 and Y-cut LiNbO 3 substrates as a function of the propagation direction. Furthermore, the propagation angles of the Rayleigh-wave beams as a function of frequency are calculated. The computed angles are compared with the measured ones for both the LiTaO3 and LiNbO3 substrates

Fundamental mode 5 GHz surface-acoustic-wave filters using optical lithography

Resonators and bandpass filters have been implemented in the 5 GHz frequency range, based on “longitudinal leaky” surface-acoustic waves on standard YZ-cut lithium niobate substrate. The synchronous one-port resonators constituting a ladder filter operate in the fundamental mode. The electrode width in the resonators is above 0.25 μm, thus making them readily accessible for fabrication with optical lithography. Test resonators are fabricated to study the effects of the metallization ratio and aperture on the resonator behavior. For the prototype filter, a center frequency of 5.20 GHz, a wide fractional 3 dB bandwidth of 6.3%, a minimum insertion loss of 3.3 dB and a high stopband suppression of 25 dB have been achieved.

Electromagnetic modeling of package parasitics in SAW-duplexer

We model the inductive and capacitive parasitic electromagnetic couplings in a packaged surface-acoustic wave (SAW) antenna duplexer. Theoretical estimates for self- and mutual inductances of the bond wires are computed in the presence of two ground planes. An equivalent circuit for the duplexer including the parasitic elements is presented. The frequency response of the duplexer is predicted with the help of circuit simulation. The modeling is further refined with optimization of the model parameters to improve the fit between the measured and simulated responses.

FEM/BEM simulation and experimental study of LLSAW resonator characteristics on YZ-LiNbO/sub 3/

The high velocity (above 6000 m/s in LiNbO/sub 3/) of the longitudinal leaky SAW (LLSAW) mode makes it attractive for use in high frequency SAW devices in the 2-3 GHz range. We have investigated, both experimentally and theoretically, the dependence of one-port LLSAW resonator performance on YZ-LiNbO/sub 3/ on the metallization thickness and metallization ratio. The results indicate a strong dependence of the Q factor and resonance frequency on the aluminum thickness. The observed behaviour is addressed with the help of simulations using a combined FEM-Greens function method. Based on the simulated and experimental data, the optimal aluminum thickness is found to be approximately 8%.

Longitudinal leaky SAW resonators and filters on YZ-LiNbO/sub 3/

The high-phase velocity (above 6100 m/s in and aluminum (Al) grating on lithium niobate (LiNbO/sub 3/)) of the longitudinal leaky surface acoustic wave (SAW) (LLSAW) mode makes it attractive for application in high-frequency SAW ladder filters in the 2-5 GHz range. We investigate the dependence of one-port synchronous LLSAW resonator performance or YZ-LiNbO/sub 3/ on the metallization thickness and metallization ratio, both experimentally and theoretically. Our results indicate a strong dependence of the Q factor and resonance frequency on the aluminum thickness, with the optimal thickness that produces the highest Q values being about 8%. The optimal thickness increases with the metallization ratio. The observed behavior is interpreted with the help of simulations using a combined finite element method (FEM)/boundary element method (BEM) technique. As an application, bandpass filters have been fabricated in the 2.8 GHz frequency regime, based on LL-SAWs. The synchronous resonators constituting the ladder filters operate in the fundamental mode. The filters feature low insertion losses below 3 dB and wide relative passbands of 4.5-5%.