The TDK model for micromachined capacitive Lamb wave transducers

Underwater target acoustic scattering is an important aspect of underwater acoustic research. Research on the elastic scattering wave is related to the wave dispersion curves and the exit angle, but the excited condition of a Lamb wave is rarely discussed in the context of elastic plates. The energy distribution for the reflected Lamb waves of several modes when Lamb waves of other anti-symmetric modes are formed by reflection at the end face of an elastic plate is also rarely discussed. However, the research concentrating on the excitation condition of Lamb waves and mode conversion at the end face of a submerged elastic plate can be the basis for target recognition. Based on R.D. Mindlin Hamilton's principle and using an orthogonal complete feature, the frequency dispersion equation of a Lamb wave is derived for an elastic plate in a vacuum; and water, phase velocity, attenuation coefficients and group velocity dispersion curves are obtained. Analysis of the energy ratio between each of two anti-symmetric mode backward Lamb waves resulting from mode conversion when an anti-symmetric Lamb wave is incident at the end face of the plate in single mode is derived. The scattering wave of a submerged elastic plate is measured experimentally, which shows that only the incident anti-symmetric Lamb wave at the critical angle of one mode can directly excite a Lamb wave of this mode in the elastic plate, Lamb waves of other anti-symmetric modes are formed by reflection at the end face of the elastic plate. There is also no energy change between a symmetric Lamb wave and an anti-symmetric Lamb wave, even with mode conversion, if the waves are reflected at the end of the elastic plate. Combined with radiation efficiency of submerged elastic plate energy ratio between each two anti-symmetric mode backward lamb waves resulted from mode conversion when anti-symmetric lamb wave incident at the end face of plate in single mode confirmed validity of the analysis results.

Symmetry properties of second harmonics generated by antisymmetric primary Lamb waves are systematically studied in this work. In theory, the acoustic field of second harmonic Lamb waves is obtained by using the perturbation approximation and normal modal method, and the energy flux transfer from the primary Lamb waves to second harmonics is mainly explored. Symmetry analyses indicate that either the symmetric or antisymmetric Lamb waves can merely generate the symmetric second harmonics. Finite element simulations are performed on the nonlinear Lamb wave propagation of the antisymmetric A0 mode in the low frequency region. The signals of the second harmonics and the symmetric second harmonic s0 mode are found to be exactly equivalent in the time domain. The relative acoustic nonlinearity parameter A2/A12 oscillates with the propagation distance, and the oscillation amplitude and spatial period are well consistent with the theoretical prediction of the A0-s0 mode pair, which means that only the second harmonic s0 mode is generated by the antisymmetric primary A0 mode. Experiments are further conducted to examine the cumulative generation of symmetric second harmonics for the antisymmetric-symmetric mode pair A3-s6. Results show that A2/A12 increases linearly with the propagation distance, which means that the symmetric second harmonic s6 mode is generated cumulatively by the antisymmetric primary A3 mode. The present investigation systematically corroborates the proposed theory that only symmetric second harmonics can be generated accompanying the propagation of antisymmetric primary Lamb waves in a plate.

Major steps used in fabricating surface micromachined capacitive ultrasonic immersion transducers are investigated. Such steps include membrane formation and cavity sealing under vacuum. Three transducer membrane structures are evaluated: a nitride membrane with an LTO sacrificial layer; a polysilicon membrane with an LTO sacrificial layer; and a nitride membrane with a polysilicon sacrificial layer. The major differences in the three processes are the conductivity, dielectric constant and residual stress of the membrane. Three vacuum sealing mechanisms are compared, each of which requires a different degree of lithographic sophistication, and results in a sealed cavity. Submicron via sealing requires sophisticated lithography, but is amenable to LPCVD nitride, LTO and other sealing procedures. Standard g-line lithography results in vias which seal only with high sticking coefficient species, such as LTO. A novel etch channel structure, which results in lateral sealing and requires neither sophisticated lithography nor a particular sealing is demonstrated. The experiments in the paper are guided by theoretical analysis and computer simulations when applicable. The optimized process based on a nitride membrane with a polysilicon sacrificial layer results in devices which have a broad band 50 /spl Omega/ real part impedance in the megahertz range. In addition, a transducer dynamic range in excess of 100 dB is achieved with an untuned bandwidth of 50%. The fabrication techniques and results herein reported indicate that surface micromachined capacitive ultrasonic transducers are an alternative to piezoelectric transducers in immersion applications.

When a tilted circular plate is illuminated with high-frequency sound in water, significant enhancements occur when the angle of incidence corresponds to a Lamb wave coupling angle. Previously, scattering associated with the lowest-order symmetric Lamb wave, s0, was studied using acoustic holography and modeled using quantitative ray methods [B. T. Hefner and P. L. Marston, J. Acoust. Soc. Am. 107, 2847 (2000)]. The present investigation focuses on backscattering associated with the antisymmetric Lamb waves. Above the cutoff frequency of the first-order antisymmetric wave, a1, enhancements are observed which are associated with both the a1 wave and the a0 wave. For these enhancements, however, mode conversion between these modes plays a significant role. To examine the mode conversion and to identify the scattering mechanisms, acoustic holography was used to image the plate surface when the plate is ensonified at the a1 wave coupling angle. From the imaged wave field, the enhancement at this angle involves a wave which moves around the circumference of the plate: a ‘‘whispering gallery’’ mode involving the a1 wave or a flexural edge wave. Both of these possibilities are considered as well as a possible scattering mechanism at the a0 wave coupling angle. [Work supported by the Office of Naval Research.]

Since the proposing of capacitive micromachined ultrasonic transducer by Khuri Yakub group in 1994 that this kind of transducer occupying the advantages of wide bandwidth, impedance matching well with the propagation medium especially in fluid and air and high sensitivity, has shown a great potential for wide ranges of applications. This Letter reports kind of micro‐electro‐mechanical systems (MEMS) capacitive ultrasonic transducer with the novel cavities embedded in the device layer of silicon on insulator wafer bonded with a glass substrate. The optimum geometric dimensions are confirmed by both mechanical vibrating of the membrane and the electrical characteristics analysis. Finite‐element analysis is adopted to determine the operation mode. The safety and reliability of the proposed device is ensured by the obtained deflections and equivalent stress under operation/collapse voltage. The bottom electrodes of the proposed transducer are fabricated on the top surface of the glass substrate. The parallel parasitic capacitance is reduced, thus improving the electromechanical coupling coefficient. The test results show that the electromechanical coupling coefficient is 69.65%, which demonstrates that this proposed MEMS capacitive ultrasonic transducer structure can enhance the performance significantly.

Capacitive micro-fabricated ultrasonic transducers for biometric applications

Capacitive micromachined ultrasonic transducers ~CMUTs!, introduced about a decade ago, have been shown to be a good alternative to conventional piezoelectric transducers in various aspects, such as sensitivity, transduction efficiency, and bandwidth. In this paper, we discuss the principles of capacitive transducer operation that underlie these aspects. Many of the key features of capacitive ultrasonic transducers are enabled with micromachining technology. Micromachining allows us to miniaturize device dimensions and produce capacitive transducers that perform comparably to their piezoelectric counterparts. The fabrication process is described briefly, and the performance of the CMUT transducers is evaluated by demonstrating characterization results. It is shown that the transduction efficiency as defined by the electromechanical coupling coefficient can be close to unity with proper device design and operating voltage. It is also shown that CMUTs provide large bandwidth ~123% fractional bandwidth! in immersion applications which translate into high temporal and axial resolution. Finally, the feasibility of using CMUTs is demonstrated by showing imaging examples in air and in immersion.

Parametric equalization is often used to achieve a desired response from an audio transmitter, but is rarely applied to ultrasonic transducer systems. The ability of a broadband ultrasonic transmission and reception system to adapt its frequency and time domain response to changing acoustic conditions would be a distinct advantage in certain applications. Ultrasonic remote monitoring systems would benefit significantly from this ability, as signal levels could be minimized and consequentially the transmitter power consumption decreased. This work presents a real-time adaptive ultrasonic parametric equalizer using optimization driven Matlab code to control the coefficients of a switched capacitor filter network implemented in a Cypress PSOC (Programmable System On a Chip). In this work, adaptive parametric magnitude equalization of a through-transmission ultrasonic system using CUTs (Capacitive Ultrasonic Transducers) has been achieved in real time by tracking a desired SNR (signal to noise ratio) across the operational frequency spectrum. A Matlab general radial basis function (GRBF) artificial neural network (ANN) was developed to control the equalization filter coefficients based on the received frequency response data. The adaptive parametric equaliser adjusts the magnitude of the driving signal to maintain the desired SNR as closely as possible. The neural network was trained using PSO (Particle Swarm Optimization) back-propagation, based on a state space model of the system developed from frequency response data. The developed equalization circuitry, which is switched capacitor based and was fully implemented on the PSOC, is also described.

A MEMS Transducer for Ultrasonic Flaw Detection A. Jain, D. Greve, J. Oppenheim Pages 375-381 (2002 Proceedings of the 19th ISARC, Washington, USA, ISSN 2413-5844) Abstract: Metal structures can fail because of fatigue crack propagation or because of section loss from corrosion. Regular inspection is required to intercept such failures, and in situ sensors would be a superior technology for that purpose. We have designed and fabricated arrays of MEMS capacitive diaphragm transducers and we report on their performance as pulse-echo detectors in direct contact with solids. Our chip is approximately 1-cm square and features nine detectors in a linear array, each detector containing 180 hexagonal diaphragms. Performance of the detector array was studied by bonding the chip to test specimens and applying an ultrasonic pulse using a commercial ultrasonic transducer. One experiment recreates an on-axis excitation in which the pulse arrives uniformly at all detectors, and another experiment recreates an off-axis excitation in which the pulse arrival is delayed from one detector to the next along the length of the array, permitting accurate localization of the source using phased array signal processing. The results establish that MEMS transducers can function successfully as phased array detectors of ultrasonic signals in solids. Keywords: Diaphragm; flaw detection; MEMS; phased array; ultrasonics DOI: https://doi.org/10.22260/ISARC2002/0059 Download fulltext Download BibTex Download Endnote (RIS) TeX Import to Mendeley

The multimode and dispersion characteristics of Lamb waves make them difficult to apply to nondestructive evaluation. This paper presents a paired configuration of a meander-line coil electromagnetic acoustic transducer (EMAT) to generate a single-mode symmetric and antisymmetric Lamb wave in aluminum plates. In the paired structure, the bias magnetic field of the EMAT that generates symmetric mode Lamb waves is perpendicular to the plate surface, while the bias magnetic field of the EMAT that generates antisymmetric Lamb waves is parallel to the plate surface. The symmetric and antisymmetric exciting forces generated by these two EMATs are consistent with the dispersion equations of single symmetric and antisymmetric Lamb wave modes, respectively. The numerical simulations and experiments verified that the presented paired configurations of meander-line coil EMATs can effectively control the generation of single-mode Lamb waves at low frequencies.

The reflection and transmission of Lamb waves at an imperfect joint of plates are analyzed numerically by the modal decomposition method and the hybrid finite element method. The joint is modeled as a spring-type interface characterized by distributed normal and tangential stiffnesses. The analysis is focused on a low-frequency range where the lowest-order symmetric and antisymmetric Lamb waves are the only propagating modes. The frequency-dependent reflection and transmission characteristics of these Lamb modes are computed for different interfacial stiffnesses, together with the generation behavior of localized, non-propagating higher-order Lamb modes. As a result, S0-mode Lamb wave is shown to exhibit the reflection and transmission characteristics which are monotonically frequency-dependent. On the other hand, A0-mode Lamb wave shows complicated and non-monotonic frequency dependence in the reflection and transmission characteristics. The obtained Lamb wave characteristics are discussed in the light of approximate one-dimensional models constructed based on classical plate theories. As a result, the reflection and transmission coefficients of S0-mode Lamb wave are accurately reproduced by a simple model of longitudinal wave in thin plates, while those of A0-mode Lamb wave are well described by the Mindlin plate model of flexural wave. It is also shown that stiffness reduction at the corners of the contacting edges of plates has only minor influence on the reflection and transmission characteristics.

Capacitive Micromachined Ultrasonic Transducers (CMUTs), introduced about few decades ago, have been shown to be a good alternative to conventional piezoelectric transducers in various aspects, such as sensitivity, transduction efficiency, and bandwidth. It is used in a wide range of applications including Non destructive testing applications, medical imaging, flow metering, micro/nanoelectronics and industrial cleaning etc. The advent of MEMS technology has lead to intensive study of micro machined ultrasonic transducers. They are similar to other capacitance transducers as they employ a vibrating membrane to send and receive ultrasound in air and in water. The advantage of hexagonal Capacitance micro machined ultrasonic transducers (CMUTs) is that they can be operated in the high temperature range and the transducer array can be fabricated at a lower cost. Presented in this paper is a study on some aspects of the design of a modified CMUT, which the authors believe would lead to a CMUT with many advantages, including less loading effect and higher packing density. The focus of discussion in the paper is FEM simulation of a single cell hexagonal CMUT using polysilicon as membrane material. Also discussed is the simulation study of the critical parameters which influence the operation of the CMUTs. The simulations were carried out using MATLAB and IntelliSuite 8.0. The study indicates that in the range of study, the best performance is achieved at the natural resonance frequency, which is very desirable.

In this work, we present a newly proposed concept of engineering the anchor fins in a suspended Lamb wave resonator and using it as an important design parameter to optimize the resonator performance. The exploration was conducted on antisymmetric Lamb wave resonators based on 128° Y-cut lithium niobate (LN or LiNbO<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${}_{\mathbf {3}}$</tex-math> </inline-formula>) and the deformation was adjusted by introducing different anchor fin designs that mount the suspended structure to the supporting substrate. The proposed design methodology was validated by the demonstration of first-order antisymmetric Lamb wave (A1-mode) resonators operating at 12GHz, and also third-order antisymmetric Lamb wave (A3-mode) resonators operating at 36GHz. It has been proved that special anchor fin design serves as an effective means to improve the power handling or linearity of Lamb wave resonators. Therefore, this work opens up a brand new design space for acoustic resonators based on a suspended thin-film structure, which makes it possible to realize further performance enhancement and optimization for Lamb wave resonators especially at centimeter wave (cmWave) and millimeter wave (mmWave) frequencies. [2025-0117]

Ultrasound transducer is a crucial component for several imaging modalities, where acoustic sensing is utilized as a part of hybrid or combination of pure optical and ultrasound imaging. However, conventional ultrasound transducers are opaque, and the optical components in the system require a different pathway to avoid any interference. The absence of coaxial integration limits the optical illumination area, adds complexity, and makes the system bulky. Moreover, the system performance is deteriorated due to the unoptimized illumination in hybrid imaging and the lack of correlation between the data acquired through the combined modalities. To overcome these drawbacks, different approaches to realize optically transparent ultrasound transducers have been explored that includes piezoelectric-based and microelectromechanical system-based capacitive and piezoelectric ultrasonic transducers. Unlike conventional opaque transducers, each component of transparent ultrasound transducers requires specific materials and a certain recipe which all together determine the overall performance of the transducer. In this article, we have performed a comparative analysis on the materials and the fabrication process used to make different types of transparent ultrasound transducer.

Frequency-modulated ultrasound signals like chirp-signals show variations in phase at the different transmission angles. Analyzing the phase of ultrasound chirp-echoes enables to accurately determine distance and polar angle to the point of reflection. Though single piezoceramic ultrasound transducers have a small bandwidth, an ultrasound transducer made of a combination of piezoceramic elements with different resonance frequencies as presented in this work enables transmission of broadband chirp- signals and shows the required rotational symmetry. Frequency-modulated chirp-signals transmitted by ultrasound sensors with broad bandwidth show different variations in phase at different directions of the radiated sound pattern. With the phase information of the echo signal it is possible to determine the angle of the point of reflection with respect to the main transmission direction of the ultrasound transducer, representing the polar angle in a spherical coordinate system with the main transmission direction being the z axis. Processing the frequency-modulated chirp-signal by use of a correlation algorithm delivers high accuracy of the distance measurement. Using only one ultrasound transducer transmitting a broadband signal and assuming rotational symmetry, we get the distance and one of the two angles needed to exactly determine the 3D coordinates of the reflection point, instead of getting only the distance like in other known systems. Off the shelf ultrasound transducers for air applications are based on different technologies, like electrostatic transducers, PVDF (Polyvinylidene fluoride) transducers, piezoceramic and piezocomposite transducers. Although typical constructions of electrostatic transducers are not well suited for industrial environment, many air ultrasound applications are based on this transducer type producing high sound pressure amplitudes by simultaneous small power consumption. Though electrostatic transducers have also an advantageous broad bandwidth, they are not appropriate to be used for polar angle measurements, because they still cannot be produced with a good rotational symmetry. The only air ultrasound transducers that show appropriate rotational symmetry are piezoceramic transducers. Piezoceramic transducers have a narrow bandwidth and are driven most effectively at their geometry-dependent resonance frequencies.