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We describe a stabilized homodyne full-field interferometer capable of measuring vertical surface deformations of microstructures in the time domain. The interferometer is stabilized to a chosen operation point by obtaining a feedback signal from a non-moving, freely selectable, reference region on the sample surface. The stabilized full-field interferometer enables detection of time-dependent changes in the surface profile with nanometer scale vertical resolution, while the temporal resolution of the measurement is ultimately limited by the refresh rate of the camera only. The lateral resolution of the surface deformation is determined by the combination of the imaging optics together with the pixel size of the camera. The setup is used to measure the deformation of an Aluminum nitride membrane as a function of time-dependent pressure change. The data analysis allows for unambiguous determination of surface deformations over multiple fringes of the interferogram, hence enabling the study of a wide range of physical phenomena with varying magnitude of vertical surface movement.

The ongoing rapid development of digital camera technology together with increasing computing power enabling fast image analysis has opened up possibilities to further advance the performance of full-field interferometry. We present a software-based stabilization method for stroboscopic homodyne full-field interferometry that enables phase sensitive absolute-amplitude measurements of surface vibrations in microelectromechanical devices. The reference signal for the stabilization is obtained from a freely selectable region in the acquired interference images, resulting in a compact interferometer design without the need for additional optical components for monitoring the operation point. The proposed stabilization method is implemented in an LED-based stroboscopic Michelson-type full-field interferometer. To demonstrate the performance of the setup, an out-of-plane vibration field at 12 MHz in a square-plate silicon resonator is characterized. The data analysis reveals that a minimum detectable amplitude of less than 30 pm is achieved in the measurement. These first results already demonstrate the potential of the software-stabilization concept and serve to advance the detection of low-amplitude surface vibrations with full-field interferometry. [2014-0355]

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.

Nonlinear generation of harmonics is measured at wafer level on Temperature Compensated Surface Acoustic Wave (TC-SAW) Resonators on lithium niobate. The obtained results are different from those published for resonators on lithium tantalate. For second harmonic, strong peaks looking like multiple resonant modes are found. The frequency difference between the successive peaks increases when the substrate thickness decreases. Results also show that the level of the signal depends on the roughness of the back side of the substrate. Due to these findings, it was assumed that this signal is due to nonlinear generation of a bulk mode. This assumption is confirmed experimentally by scanning the back side with an interferometer. Possible nonlinear mechanisms explaining these results are discussed.

Paraxial coupled mode equations (paraxial COM equations or 2D COM equations) are able to characterize the transverse mode profiles in SAW grating waveguides [1], [2], [3]. The paraxial COM equations are applied to the characterization of the orthogonal transverse modes propagating in a synchronous temperature compensated SAW (TCSAW) piston mode waveguide. The solutions indicate that the number of modes bound by the waveguide changes rapidly within the grating stop band. It is also found that the transverse dependence of the modes is strongly influenced by the grating stop band.

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.

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.

This chapter introduces optical characterization of surface vibrations and wave propagation using scanning laser interferometry. The waves are excited electrically and detected utilizing optical interferometry in frequency domain. Homodyne and heterodyne optical setups and interferometric detection principle are introduced, and the capabilities and limitations of the technique are briefly discussed. Application of the frequency-domain technique into phononic crystal research is illustrated by providing examples of wave field characterization and data analysis for surface acoustic and bulk acoustic wave propagation and behavior in phononic crystals and acoustic metamaterials.

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.

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.

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.

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.

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.

We present an experimental study of the nonlinear behavior of a square-extensional (SE) mode microelectromechanicalresonator, actuated with a piezoelectricAlNthin film. The acoustic vibration fields of the device are characterized using laser probing. A nonlinear vibration behavior of the SE mode is observed above a drive power level of −10 dBm such that the vibration amplitude of the SE mode saturates and a rotational in-plane vibration mode is excited at a significantly lower frequency (0.725 MHz) than the SE mode (16.670 MHz). Interestingly, the measured∼10 nm saturation amplitude of the SE mode is more than a decade below the amplitude value at which mechanical or electromechanical nonlinearities are estimated to become significant.

Nonlinear effects have become an important issue in microacoustic component development to improve performance. In addition to the modeling, simulations and electrical characterization tools, a direct method for observing the nonlinear vibration fields in these components would be beneficial in the device design. We use laser probing for studying the nonlinear acoustic behavior in two square-extensional (SE) mode MEMS resonators, whose electrically measured SE-resonances compress above a certain, unexpectedly low, input drive power level. In the laser probe measurements, the vibration amplitude of the SE mode is observed to nearly saturate above this drive power level, and simultaneously another mode at a different frequency is excited. It is also observed that the nonlinearly excited modes are different in the two resonators, and each resonator has a distinct nonlinear behavior.

Acoustic wave fields both within the active electrode area of a solidly mounted 1.8 GHz bulk acoustic wave resonator, and around it, are measured using a heterodyne laser interferometer. Plate wave dispersion diagrams for both regions are extracted from the measurement data. The waves leaking from the resonator area enable the determination of the dispersion properties of the sourceless outside region. The experimental dispersion data reveal the cutoff frequencies of the acoustic vibration modes in the region surrounding the resonator, and therefore, the lateral energy trapping range of the resonator can be directly determined from the measurements. The onset of the acoustic leakage from the resonator is signalled on one hand by propagating wave modes appearing in the dispersion diagram of the surrounding region, and on the other hand by the abruptly diminishing amplitude of curves in the resonator dispersion diagram. This information is important for verifying and further developing the simulation tools used for the design of the resonators. Experimental wave field images, dispersion diagrams for both regions, and the threshold for energy leakage are discussed

International audience; We consider launching a monochromatic surface acoustic wave packet on a large set of random scatterers. The interference of the multiple scattered waves creates a random pattern of ripples on the crystal surface that is recorded by optical interferometry. The Fourier transform of the amplitude and phase data of the measured wave field unveils the complete slowness curve, i.e., the wave-vector as a function of the propagation angle. A simple acoustic speckle model is proposed to explain this observation.

Acoustic wave fields both within the active electrode area of a solidly mounted 1.8 GHz bulk acoustic waveresonator, and around it in the surrounding region, are measured using a heterodyne laser interferometer. Plate-wave dispersion diagrams for both regions are extracted from the measurement data. The experimental dispersion data reveal the cutoff frequencies of the acoustic vibration modes in the region surrounding the resonator, and, therefore, the energy trapping range of the resonator can readily be determined. The measureddispersionproperties of the surrounding region, together with the abruptly diminishing amplitude of the dispersion curves in the resonator, signal the onset of acoustic leakage from the resonator. This information is important for verifying and further developing the simulation tools used for the design of the resonators. Experimental wave field images, dispersion diagrams for both regions, and the threshold for energy leakage are discussed.

A heterodyne laser interferometer is used to study acoustic wave fields excited in a 1.8 GHz AlN thin film bulk acoustic waveresonator. The electrical response of the resonator exhibits a strong thickness resonance onto which spurious modes, caused by lateral standing plate waves, are superposed. Optical interferometermeasurements are used to extract dispersion curves of the laterally propagating waves responsible for the spurious responses. A discrete eigenmode spectrum due to the finite lateral dimensions of the resonator is observed. An equivalent circuit model for a multimode resonator is fitted to the mechanical resonator response extracted along a single curve in the dispersion diagram, and is used to determine properties, such as Q-values, of the individual lateral eigenmodes.Measuredwave field images, extracted dispersion curves, and the eigenmode spectrum with the model fitting results are presented.

We report laser probing results on a set of piezo-electrically actuated square plate MEMS resonators. The plate size of the resonators is systematically varied in order to study the frequency scaling of the main, square-extensional resonance mode in the range between 13–30 MHz. In electrical impedance measurements, an unexpected splitting of the main mode branch into two separate mode branches is observed at intermediate plate size dimensions. To get further insight of the origin of the splitting phenomenon, the two observed mode branches are directly measured by laser probing. The laser probe measurements confirmed that the vibration modes on both branches had a lateral vibration field characteristic for a square-extensional mode. Furthermore, the results indicate that the square-extensional mode may couple to other resonance modes occurring around 20–22 MHz, hence causing the splitting of the mode branch.

The acoustic wave fields excited in a 1.8 GHz AlN thin film bulk acoustic wave resonator are measured in detail with a heterodyne laser interferometer. The electrical response of the resonator exhibits a strong thickness resonance onto which spurious modes, caused by lateral standing plate waves, are superposed. The acoustic wave fields are measured with a heterodyne interferometer and are used to calculate dispersion diagram of the laterally propagating waves responsible for the spurious electrical responses. The dispersion diagram features a discrete eigenmode spectrum due to the finite lateral dimensions of the resonator. An equivalent circuit model for a multi-mode resonator is fitted to the mechanical resonator response extracted along a single curve in the dispersion diagram, and is used to determine properties, such as Q-values, of the individual lateral eigenmodes. Measured wave field images, extracted dispersion curves, and the eigenmode spectrum with the model fitting results are presented.

We report results of a parametric study on a set of single-crystal-silicon plate resonators, whose lateral dimensions are varied so that the main resonance mode occurs at a range of f = 13...30 MHz. The resonator transduction is based on a piezoelectric AlN thin film. Measurements spanning >1000 devices and two wafers indicate that with certain device dimensions the square extensional resonance mode and a higher-order extensional mode are excited with a relatively low frequency scatter of Δf ~ 2 000 ppm (full range). Other resonance modes typically have a frequency scatter larger than 15 000 ppm, which we interpret to be an indication of their flexural character. Additionally, we observe a splitting of the main resonance mode branch at intermediate device dimensions.

International audience; Surface acoustic wave propagation within a two-dimensional phononic band gap structure has been studied using a heterodyne laser interferometer. Acoustic waves are launched by interdigital transducers towards a square lattice of holes etched in a piezoelectric medium. Interferometer measurements performed at frequencies lying below, within, and above the expected band gap frequency range provide direct information of the wave interaction with the phononic crystal, revealing anisotropic scattering into higher diffraction orders depending on the apparent grating pitch at the boundary between the phononic crystal and free surface. Furthermore, the measurements also confirm the existence of an elastic band gap, in accordance with previous electrical measurements and theoretical predictions.

Vibrations in a micromechanical 13.1 MHz bulk acoustic mode silicon resonator are imaged utilizing a scanning Michelson laser interferometer. A novel detection scheme for our interferometer is discovered, enabling imaging of the in-plane vibrations in addition to the out-of-plane component of the vibrations. We are able to measure the in- and out-of-plane oscillations of the silicon resonator at the resonance frequencies of the square-extensional and Lame/spl acute/ modes. The measured results are compared with FEM simulations. In addition, undesirable parasitic vibrations in the electrode regions are observed.

International audience; We report on the direct observation of trapping and guiding of surface-guided elastic waves in a linear defect introduced into a micron-scale phononic crystal. Elastic field amplitude detection using laser scanning interferometry was used to characterize the different transmission regimes of the one-period wide line defect in a phononic crystal structure as a function of frequency and to discriminate phononic waveguiding from transmission outside the band gap. Surface density-of-states computations support the experimental observations.

We present an experimental study of the frequency scaling of the main, square-extensional mode in a piezoelectrically actuated plate resonator. The studied set consists of resonators of different plate sizes with identical anchors. The behavior of the square-extensional mode is analyzed using electrical impedancemeasurements and optical characterization of the mechanical vibration fields. The results reveal a detrimental anchor effect, where for certain plate sizes the square-extensional mode branch is split into two due to a coupled oscillation of the resonator plate and the anchors.

We describe a scanning heterodyneinterferometer for imaging surface vibrations with a wide frequency range, with current electronics, up to 6GHz. The heterodyne operation facilitates measurement of absolute amplitude and phase of the surface vibration without calibration. Currently, the setup allows detection of vibration amplitudes down to ∼1pm with a lateral resolution of