Kimmo Kokkonen

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.

Phase-sensitive absolute-amplitude measurements of surface waves using heterodyne interferometry

Phase-sensitive absolute-amplitude measurements of surface waves using heterodyne interferometry. We describe a novel heterodyne interferometer for scanning surface-acoustic waves at high frequencies, up to 6 GHz. The heterodyne operation facilitates the measurement of the absolute amplitude of the surface waves without calibration. It simultaneously also enables measuring the phase. The amplitude and phase information allows a precise characterization of the surface acoustic waves. Moreover, the wave motion can be visualized in the form of animations to gain insight. The interferometer has been tested by measuring a 167 MHz SPUDT device and a 374 MHz fan-shaped SAW filter.

Laterally coupled solidly mounted BAW resonators at 1.9 GHz

Laterally coupled bulk acoustic wave resonators fabricated onto an acoustic mirror are studied. The acoustic mirror comprises two W-SiO2 pairs. Thin-film AlN is used as the piezoelectric material with a Mo bottom electrode and an Al top electrode. Structures consist of laterally acoustically coupled electrodes 2.5 µm wide and 300 µm long, with gaps of 4 µm in-between. Acoustical coupling between the electrodes results in two resonances forming an electrical bandpass response at 1.9 GHz. A device with two coupled electrodes features a 1.5% relative to center frequency bandwidth, 10 dB insertion loss in 50-Ω environment and 3.9 dB insertion loss after matching. Electrical frequency responses are presented and compared to simulations. Mechanical vibration fields in the devices are studied with a laser interferometer.

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 interferometers in physical acoustics

The paper gives a brief introduction to laser interferometry used in device characterization in physical acoustics. Principal interferometric concepts (homodyne and heterodyne detection) are discussed, and some general capabilities and limitations of the concepts and current setups are presented. Data processing possibilities via Fourier methods are discussed. Application examples and recent results are reviewed briefly.

Modelling of 2-D lateral modes in solidly-mounted BAW resonators

Lateral resonances occurring in bulk acoustic wave resonators contribute to the device operation, e.g., by creating spurious electrical responses. Predicting lateral effects in two dimensions typically requires computationally heavy 3-D finite element modelling. Here, dispersion characteristics calculated using a 1-D transfer matrix model are used in a finite-element software to model lateral resonance modes of solidly-mounted bulk acoustic wave resonators. Based on the resulting spectrum of 2-D eigenmodes, electrical frequency response as well as mechanical displacement is then calculated using mode superposition. Resonators with elliptic and rectangular shapes are studied. Simulated results for ellipses are compared to measured electrical frequency response and mechanical displacement. Simulations are found to agree with measured data. Dependence of electrical spurious responses on resonator shape and eigenmode spectrum is studied.

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.

Interferometric Measurements of Dispersion Curves and Transmission Characteristics of the Acoustic Mirror in Thin Film BAW Resonator

A heterodyne laser interferometer is used for a detailed study of acoustic wave fields excited in a 932 MHz ZnO solidly mounted BAW resonator. The sample is manufactured onto a glass substrate, which allows for direct measurement of the vibration fields from the bottom of the mirror stack. The vibration fields are measured both on top of the resonator and at the bottom of the mirror stack. Dispersion curves are calculated from the experimental data in both cases. This enables comparison between the vibration amplitudes on top of the resonator with those at the bottom of the mirror stack, and hence allows to determine the transmission characteristics of the acoustic mirror within the measured wave-vector, frequency space. The experimental dispersion curves and mirror transmission are compared with simulations.

Characterization of surface acoustic wave focusing by an annular interdigital transducer

The annular interdigital transducer (AIDT) is an IDT whose electrodes are shaped to follow the wave surface for surface acoustic waves propagating on an anisotropic piezoelectric material. At the resonance frequency, waves emitted in all directions are in phase at the center of the device and create an intense acoustic spot. We use a phase sensitive heterodyne interferometer to characterize the formation of the focal spot at the center of the AIDT as a function of frequency. It is found that the displacement distribution is characterized by an angular spectrum restricted in Fourier space to the slowness curve for the SAW on the free surface. The transduction of waves is dictated by an emission factor that depends both on frequency and emission angle. The shift of the focus with frequency - which is predicted by the model because of a combination of anisotropy and dispersion in the electrode grating - is analyzed and verified experimentally.