Olli Holmgren

Piezoelectrically transduced single-crystal-silicon plate resonators

We report on the design, fabrication and characterization of piezoelectrically actuated single-crystal silicon plate resonators vibrating mainly in their bulk acoustic wave modes. Two resonator types are presented: one operates in the square extensional mode at 26 MHz with Q~18000 and motional resistance Rm~0.240 kOmega, while the other resonator features a resonance at 22 MHz with Q~51000 and Rm~1.5 kOmega. The resonators are characterized electrically and by scanning laser interferometry. Measured vibration fields are compared to simulated eigenmodes.

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

Imaging surface-acoustic fields in a longitudinal leaky wave resonator

Acoustic wave fields in a surface-acoustic-wave resonator employing the longitudinal leaky wave mode have been imaged using a scanning Michelson laser interferometer. The synchronous one-port resonator is fabricated on YZ-cut lithium niobate. The vibration amplitude component perpendicular to the surface has been measured at several frequencies around the fundamental-mode resonance frequency of 1.54 GHz and around the Rayleigh-wave resonance frequency of 0.82 GHz. The longitudinal beating pattern, typically observed in the resonators utilizing Rayleigh waves, is not observed in the longitudinal leaky surface acoustic-wave resonator within the measured frequency range.

Laser interferometric measurement of Lamb wave dispersion and extraction of material parameters in FBARs

Laser interferometric measurement and Fourier transformation techniques have been used to extract the dispersion characteristics of a mirror (SMR) type thin film bulk acoustic wave resonator (FBAR). A numerically robust matrix method incorporating anisotropic materials and piezoelectricity has been used to calculate the dispersion curves based on information of the layer thicknesses and material parameters of individual layers. A fit has been performed between the measured and simulated curves thereby allowing the extraction of the material parameters of the ZnO piezolayer. We present the set of material parameters resulting from the fitting.

Direct optical measurement of the Q values of RF-MEMS resonators

Q values of a RF MEMS square-plate resonator are determined using a scanning Michelson laser interferometer. In- and out-of-plane vibration components have been measured as a function of frequency under ambient air pressure and in vacuum for both the main square-extensional (SE) mode and the Lam´ e mode. From the data collected with the interferometer, amplitude responses of the modes are determined as a function of frequency. Theoretical response is fitted to the experimental data and the Q value is determined from the fit. The Q values for SE mode are 9,000 and 87,000 and for Lam´ e mode 6,000 and 37,000 (air pressure and vacuum, respectively). The results agree with the Q values determined from the electrical measurements.

Design, simulation, and visualization of R-SPUDT devices with transverse mode suppression

When designing narrow band resonant SPUDT devices, the excitation of undesired transverse modes may result both in extra ripple in the passband and in spurious response in the stop band. To avoid these issues, it was proposed to use an approach similar to the one used for bulk-acoustic-wave devices. The principle is to add a low-velocity region at the edge of the transducer. If this edge region is properly designed, the transducer supports a so-called piston mode, i.e., a mode having a flat transverse amplitude profile across the aperture. A P-matrix model is extended to account for transverse modes in SPUDTs. The model is used to analyze both regular and piston-mode devices. Different physical possibilities to implement the low-velocity region are investigated and compared. In particular, it was found important to design the transducer so that the acoustical sources and reflectors extend into the edge region to minimize the coupling to higher order modes. From these considerations, a new implementation for piston-mode devices is proposed and demonstrated on a GSM base station 199-MHz filter. Electrical measurements as well as acoustical wave fields measured with an optical interferometer are analyzed and compared with simulations.

P3J-2 Laser-Interferometric Analysis of Rayleigh Wave Radiation from a LLSAW Resonator

Rayleigh wave side radiation from a synchronous 1.6 GHz longitudinal leaky SAW (LLSAW) resonator on YZ-LiNbO3 substrate is studied in this paper. Acoustic wave fields measured from the LLSAW resonator using a scanning laser interferometer are presented. The radiation angles extracted from the interferometric measurements are compared to theoretical calculations in a wide frequency range. Furthermore, the relative strength of the escaping Rayleigh wave beams evaluated from the interferometric measurements as a function of frequency is compared to the calculated coupling strength. These measurements reveal interesting effects not observed earlier. While the number of beams, the angles of radiation and their dependence on frequency can be reasonably explained, there are other effects whose explanation remains uncertain.

Double-resonance SAW filters

A novel surface acoustic wave filter on a leaky-wave substrate is studied. It features a hiccup-type resonance occurring around a distributed gap between two long interdigital transducers. Compared to a classical coupled resonator filter, it enables a relatively narrow passband (1% to 2% of center frequency) with low insertion loss, steep skirts, and improved suppression levels. The structure consists of long transducers having the number of fingers greater than 1/K2 and 1/K, where K2 is the coupling coefficient of the substrate material and K is the reflectivity per wavelength, separated with short transducer sections constituting a distributed gap. A strong, localized resonance is formed in the gap region, in addition to the resonance arising in the long structures - hence, the name double-resonance filter. The substrate studied here is 42deg-rotated lithium tantalite. We show experimental results for both single-ended and unbalanced-to-balanced filters at 1.6 GHz, having a minimum insertion loss of 1.07 dB, suppressions of 30 dB, and absolute -3-dB bandwidth of 29 MHz (1.9% of the center frequency). For the balanced device, the amplitude imbalance over the passband ranges from -0.6 dB to 2 dB arid the phase imbalance from 1deg to 4.5deg. Furthermore, we have measured the acoustical power distributions using a scanning laser interferometer, and we compare these results with the profiles simulated using a coupling-of-modes model

Imaging of acoustic fields generated in a longitudinal leaky SAW resonator

We utilize a sensitive scanning laser-interferometric probe to map the spatial distribution of the acoustic field within a one-port synchronous leaky longitudinal SAW (LLSAW) resonator. This marks the first visualization of LLSAWs within such a structure. Interest in these waves exists since LLSAWs feature high velocities (>6100 m/s) on the YZ-LiNbO/sub 3/ substrate and hence enable the fabrication of bandpass filters operating in the 2.5-5 GHz range with conventional optical lithography. Measurements at frequencies below and above the resonance for a 1.6 GHz LLSAW resonator fabricated on YZ-cut LiNbO/sub 3/ are performed. We find that below the resonance frequency the longitudinal profile does not feature a beating pattern typically observed for leaky SAW resonators. The transversal profile within the IDT features 2, 3, 4, 5, ... maxima as the drive frequency is increased. Furthermore, oblique Rayleigh-wave beams are observed to radiate from the sides of the resonator.

Method for phase sensitive measurements of surface vibrations using homodyne interferometry without stabilization

A method for detecting phase and absolute amplitude of surface vibrations with homodyne laser interferometry is presented. An advantage of this detection scheme is that no stabilization of the optical path is required, hence allowing for a simple homodyne interferometer design. The principle of the detection concept is described and the method is implemented to an existing homodyne scanning laser interferometer, originally developed for measuring relative amplitude data of surface vibrations in microacoustic devices. Selected measurements from two different piezo-actuated micromechanical resonators are presented to demonstrate the detection method. With current electronics, the interferometer is capable of detecting out-of-plane vibrations up to 2.5 GHz with lateral resolution of < 1 ¿m and with minimum detectable amplitudes of ~ 1 pm.