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Nonlinear generation of harmonics is measured on the wafer level on temperature compensated surface-acoustic-wave resonators on lithium niobate. The second-harmonic response features strong peaks looking like multiple resonant modes. The product of the frequency difference between the successive peaks to the substrate thickness is found to remain almost constant. The results also show that the level of the harmonic signal strongly depends on the roughness of the back side of the substrate. Due to these findings, it was assumed that the signal is due to nonlinear generation of a bulk mode. This assumption is confirmed experimentally by measuring the second-harmonic wave field on the back side of the substrate with an interferometer. Possible nonlinear mechanisms explaining these results are discussed.

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We present phase-sensitive absolute amplitude measurements of surface acoustic wave fields obtained using a stroboscopic white-light interferometer. The data analysis makes use of the high resolution available in the measured interferometric phase data, enabling the characterization of the out-of-plane surface vibration fields in electrically excited microstructures with better than 100 pm amplitude resolution. The setup uses a supercontinuum light source with tailored spectral properties for obtaining the high amplitude resolution. The duration of the light pulses is less than 300 ps to allow the detection of high frequencies. These capabilities enabled a detailed measurement of the focusing of surface acoustic waves by an annular interdigital transducer structure operating at 74 MHz, featuring a maximum vibration amplitude of 3 nm.

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We present a picosecond supercontinuum light source designed for stroboscopic white-light interferometry. This source offers a potential for high-resolution characterization of vibrational fields in electromechanical components with frequencies up to the GHz range. The light source concept combines a gain-switched laser diode, the output of which is amplified in a two-stage fiber amplifier, with supercontinuum generation in a microstructured optical fiber. Implemented in our white-light interferometer setup, optical pulses with optimized spectral properties and below 310 ps duration are used for stroboscopic illumination at freely adjustable repetition rates. The performance of the source is demonstrated by characterizing the surface vibration field of a square-plate silicon MEMS resonator at 3.37 MHz. A minimum detectable vibration amplitude of less than 100 pm is reached.

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We describe a LED-based stroboscopic white-light interferometer and a data analysis method that allow mapping out-of-plane surface vibration fields in electrically excited microstructures with sub-nm amplitude resolution for vibration frequencies ranging up to tens of MHz. The data analysis, which is performed entirely in the frequency domain, makes use of the high resolution available in the measured interferometric phase data. For demonstration, we image the surface vibration fields in a square-plate silicon MEMS resonator for three vibration modes ranging in frequency between 3 and 14 MHz. The minimum detectable vibration amplitude in this case was less than 100 pm.

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RESUMEN

Acoustically coupled thin-film bulk acoustic wave resonator filters, in which the coupling takes place mechanically in the lateral direction between closely-spaced narrow resonators, are a promising approach to passband filtering at gigahertz frequencies. In this paper, filters with interdigital electrode structures are studied. Electrode number, electrode width, and coupling gap width are varied. The resonators are solidly mounted, having an acoustic mirror isolating the resonator from a Si substrate and providing the means to engineer the acoustic dispersion properties of the resonators. The center frequency of the filters is around 2 GHz. Electrical frequency responses of the filters are measured and the strength of the lateral acoustic coupling is calculated from the measurements. The effects of device parameters on the acoustic coupling and the obtainable filter bandwidth are analyzed in detail. A bandpass filter with 4.9% bandwidth, minimum insertion loss of 2 dB and sharp transition from passband to suppression band, is presented.

RESUMEN

Acoustic wave fields in a thin-film bulk acoustic wave resonator are studied using a heterodyne laser interferometer. The measurement area is extended outside the active electrode region of the resonator, so that wave fields in both the active and surrounding regions can be characterized. At frequencies at which the region surrounding the resonator does not support laterally propagating acoustic waves, the analysis of the measurement data shows exponentially decaying amplitude fields outside the active resonator area, as suggested by theory. The magnitude of the imaginary wave vectors is determined by fitting an exponential function to the measured amplitude data, and thereby the experimentally determined dispersion diagram is extended into the region of imaginary wave numbers.

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A heterodyne laser interferometer is used for a detailed study of the acoustic wave fields excited in a 932-MHz solidly mounted ZnO thin-film BAW resonator. The sample is manufactured on a glass substrate, which also allows direct measurement of the vibration fields from the bottom of the acoustic mirror. Vibration fields are measured both on top of the resonator and at the mirror-substrate interface in a frequency range of 350 to 1200 MHz. Plate wave dispersion diagrams are calculated from the experimental data in both cases and the transmission characteristics of the acoustic mirror are determined as a function of both frequency and lateral wave number. The experimental data are compared with 1-D and 2-D simulations to evaluate the validity of the modeling tools commonly used in mirror design. All the major features observed in the 1-D model are identified in the measured dispersion diagrams, and the mirror transmission characteristics predicted for the longitudinal waves, by both the 1-D and the 2-D models, match the measured values well.

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A 2-D model is developed for calculating lateral acoustical coupling between adjacent thin film BAW resonators forming an electrical N-port. The model is based on solution and superposition of lateral eigenmodes and eigenfrequencies in a structure consisting of adjacent regions with known plate wave dispersion properties. Mechanical and electrical response of the device are calculated as a superposition of eigenmodes according to voltage drive at one electrical port at a time while extracting current induced in the other ports, leading to a full Y-parameter description of the device. Exemplary cases are simulated to show the usefulness of the model in the study of the basic design rules of laterally coupled thin film BAW resonator filters. Model predictions are compared to an experimental 1.9-GHz band-pass filter based on aluminum nitride thin film technology and lateral acoustical coupling. Good agreement is obtained in prediction of passband behavior. The eigenmode-based model forms a useful tool for fast simulation of laterally coupled acoustic devices. It allows one to gain insight into basic device physics in a very intuitive fashion compared with more detailed but heavier finite element method. Shortcomings of this model and possible improvements are discussed.

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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.

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This correspondence presents an estimator for reflective delay line-type surface acoustic wave (SAW) sensors. The estimator is derived from an analytical model and its range of validity is discussed. The proposed estimator enables simultaneous access to several SAW sensors with time-orthogonal responses and it can be implemented in a computationally efficient way utilizing the fast Fourier transform algorithm. The estimator is experimentally verified and its performance is compared with that of a reference estimator.

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This correspondence presents an optimized frequency modulated continuous-wave (FMCW) interrogation procedure for reflective delay line-type SAW sensors. In this method, the time delays between reflections are obtained with Fourier transform from optimally windowed frequency response. Optimal window functions maximize the signal-tointerference ratio at chosen temporal points of interest. The method is experimentally verified and its accuracy is compared with that of a Fourier transform from Hamming-windowed frequency response.

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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/kappa where K2 is the coupling coefficient of the substrate material and kappa 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 42 degrees-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 and the phase imbalance from 1 degrees to 4.5 degrees. 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.

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