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A complete model was developed to simulate the behavior of a circular clamped axisymmetric fluid-coupled Piezoelectric Micromachined Ultrasonic Transducer (PMUT). Combining Finite Difference and Boundary Element Matrix (FD-BEM), this model is based on the discretization of the partial differential equation used to translate the mechanical behavior of a PMUT. In the model, both the axial and the transverse displacements are preserved in the equation of motion and used to properly define the neutral line position. To introduce fluid coupling, a Green's function dedicated to axisymmetric circular radiating sources is employed. The resolution of the behavioral equations is used to establish the equivalent electroacoustic circuit of a PMUT that preserves the average particular velocity, the mechanical power, and the acoustic power. Particular consideration is given to verifying the validity of certain assumptions that are usually made across various steps of previously reported analytical models. In this framework, the advantages of the membrane discretization performed in the FD-BEM model are highlighted through accurate simulations of the first vibration mode and especially the cutoff frequency that many other models do not predict. This high cutoff frequency corresponds to cases where the spatial average velocity of the plate is null and is of great importance for PMUT design because it defines the upper limit above which the device is considered to be mechanically blocked. These modeling results are compared with electrical and dynamic membrane displacement measurements of AlN-based (500 nm thick) PMUTs in air and fluid. The first resonance frequency confrontation showed a maximum relative error of 1.13% between the FD model and Finite Element Method (FEM). Moreover, the model perfectly predicts displacement amplitudes when PMUT vibrates in a fluid, with less than 5% relative error. Displacement amplitudes of 16 nm and 20 nm were measured for PMUT with 340 µm and 275 µm diameters, respectively. This complete PMUT model using the FD-BEM approach is shown to be very efficient in terms of computation time and accuracy.

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Chemically functionalized or coated sensors are by far the most employed solution in gas sensing. However, their poor long term stability represents a concern in applications dealing with hazardous gases. Uncoated sensors are durable but their selectivity is poor or non-existent. In this study, multi-parametric discrimination is used as an alternative to selectivity for uncoated capacitive micromachined ultrasonic transducers (CMUTs). This paper shows how measuring simultaneously the attenuation coefficient and the time of flight under different nitrogen mixtures allows to identify hydrogen, carbon dioxide and methane from each other and determine their concentration along with identification of temperature and humidity drifts. Theoretical comparison and specific signal processing to deal with the issue of multiple reflections are also presented. Some potential applications are monitoring of refueling stations, vehicles and nuclear waste storage facilities.

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Passive cavitation detection can be performed to monitor microbubble activity during brain therapy. Microbubbles under ultrasound exposure generate a response characterized by multiple nonlinear emissions. Here, the wide bandwidth of capacitive micromachined ultrasonic transducers (CMUTs) was exploited to monitor the microbubble signature through a rat skull and a macaque skull. The intrinsic nonlinearity of the CMUTs was characterized in receive mode. Indeed, undesirable nonlinear components generated by the CMUTs must be minimized as they can mask the microbubble harmonic response. The microbubble signature at harmonic and ultra-harmonic components (0.5-6 MHz) was successfully extracted through a rat skull using moderate bias voltage.

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This work is an extension of a model previously developed by our group to simulate the electroacoustic response of capacitive micromachined ultrasonic transducer (CMUT)-based linear arrays acoustically loaded by a fluid medium. The goal is to introduce the viscoelasticity effects of the propagation medium into the modeling. These effects are mainly due to the passivation layer used to protect the transducer, i.e., a silicon polymer, a few hundred micrometers thick. The passivation layer is also required to ensure good acoustic coupling between the transducer front face and human skin. The theoretical approach relies on the determination of a new boundary matrix to simulate the acoustic coupling between the CMUT array and the viscoelastic medium. The complete numerical implementation of a 3-D Green's function for a viscoelastic half-space is hence described. In order to reduce computing time, an optimization was carried out through vectorization and parallelization methods. A comparison is then performed with the analytical solutions, from the literature, obtained for elastic half-space. An experimental validation of shear viscosity effects is performed through electrical impedance measurements of the CMUT linear arrays loaded by oils of varying viscosity. A very good agreement is obtained, showing that the model correctly takes the shear viscosity effects on the mechanical response of the CMUT into account, i.e., a shift in the resonance frequency and a diminution in the mechanical quality factor are observed.

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The stress state is a crucial parameter for the design of innovative microelectromechanical systems based on silicon carbide (SiC) material. Hence, mechanical properties of such structures highly depend on the fabrication process. Despite significant progresses in thin-film growth and fabrication process, monitoring the strain of the suspended SiC thin-films is still challenging. However, 3C-SiC membranes on silicon (Si) substrates have been demonstrated, but due to the low quality of the SiC/Si heteroepitaxy, high levels of residual strains were always observed. In order to achieve promising self-standing films with low residual stress, an alternative micromachining technique based on electrochemical etching of high quality homoepitaxy 4H-SiC layers was evaluated. This work is dedicated to the determination of their mechanical properties and more specifically, to the characterization of a 4H-SiC freestanding film with a circular shape. An inverse problem method was implemented, where experimental results obtained from bulge test are fitted with theoretical static load-deflection curves of the stressed membrane. To assess data validity, the dynamic behavior of the membrane was also investigated: Experimentally, by means of laser Doppler vibrometry (LDV) and theoretically, by means of finite element computations. The two methods provided very similar results since one obtained a Young's modulus of 410 GPa and a residual stress value of 41 MPa from bulge test against 400 GPa and 30 MPa for the LDV analysis. The determined Young's modulus is in good agreement with literature values. Moreover, residual stress values demonstrate that the fabrication of low-stressed SiC films is achievable thanks to the micromachining process developed.

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This paper presents the development of a novel acoustic transformer with high galvanic isolation dedicated to power switch triggering. The transformer is based on two capacitive micromachined ultrasonic transducers layered on each side of a silicon substrate; one is the primary circuit, and the other is the secondary circuit. The thickness mode resonance of the substrate is leveraged to transmit the triggering signal. The fabrication and characterization of an initial prototype is presented in this paper. All experimental results are discussed, from the electrical impedance measurements to the power efficiency measurements, for different electrical load conditions. A comparison with a specifically developed finite-element method model is done. Simulations are finally used to identify the optimization rules of this initial prototype. It is shown that the power efficiency can be increased from 35% to 60%, and the transmitted power can be increased from 1.6 to 45 mW/Volt.

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Multielement transducers enabling novel cost-effective fabrication of imaging arrays for medical applications have been presented earlier. Due to the favorable low lateral coupling of the screen-printed PZT, the elements can be defined by the top electrode pattern only, leading to a kerfless design with low crosstalk between the elements. The thick-film-based linear arrays have proved to be compatible with a commercial ultrasonic scanner and to support linear array beamforming as well as phased array beamforming. The main objective of the presented work is to investigate the performance of the devices at the transducer level by extensive measurements of the test structures. The arrays have been characterized by several different measurement techniques. First, electrical impedance measurements on several elements in air and liquid have been conducted in order to support material parameter identification using the Krimholtz-Leedom-Matthaei model. It has been found that electromechanical coupling is at the level of 35%. The arrays have also been characterized by a pulse-echo system. The measured sensitivity is around -60 dB, and the fractional bandwidth is close to 60%, while the center frequency is about 12 MHz over the whole array. Finally, laser interferometry measurements have been conducted indicating very good displacement level as well as pressure. The in-depth characterization of the array structure has given insight into the performance parameters for the array based on PZT thick film, and the obtained information will be used to optimize the key parameters for the next generation of cost-effective arrays based on piezoelectric thick film.

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In view of the maturity of fabrication processes for capacitive micromachined ultrasonic transducers (cMUTs), engineers and researchers now need efficient and accurate modeling tools to design linear arrays according to a set of technological specifications, such as sensitivity, bandwidth, and directivity pattern. A simplified modeling tool was developed to meet this requirement. It consists of modeling one element as a set of cMUT columns, each being a 1-D periodic array of cMUTs. Model description and assessment of simulation results are given in the first part of the paper. The approach is based on the theory of linear systems so the output data are linked to input data through a large matrix, known as an admittance matrix. In the second part of the paper, we propose reorganization of matrix equations by applying the normal mode theory. From the modal decomposition, two categories of eigenmodes are highlighted, one for which all cMUTs vibrate in phase (the fundamental mode) and the others, which correspond to localized subwavelength resonances, known as baffle modes. The last part of the paper focuses mainly on the fundamental mode and gives several design strategies to optimize the frequency response of an element.

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Ultrasound-mediated targeted therapy represents a promising strategy in the arsenal of modern therapy. Capacitive micromachined ultrasonic transducer (cMUT) technology could overcome some difficulties encountered by traditional piezoelectric transducers. In this study, we report on the design, fabrication, and characterization of an ultrasound-guided focused ultrasound (USgFUS) cMUT probe dedicated to preclinical evaluation of targeted therapy (hyperthermia, thermosensitive liposomes activation, and sonoporation) at low frequency (1 MHz) with simultaneous ultrasonic imaging and guidance (15 to 20 MHz). The probe embeds two types of cMUT arrays to perform the modalities of targeted therapy and imaging respectively. The wafer-bonding process flow employed for the manufacturing of the cMUTs is reported. One of its main features is the possibility of implementing two different gap heights on the same wafer. All the design and characterization steps of the devices are described and discussed, starting from the array design up to the first in vitro measurements: optical (microscopy) and electrical (impedance) measurements, arrays' electroacoustic responses, focused pressure field mapping (maximum peak-to-peak pressure = 2.5 MPa), and the first B-scan image of a wire-target phantom.

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Capacitive micromachined ultrasonic transducers (cMUTs) are a promising alternative to the piezoelectric transducer. However, their native nonlinear behavior is a limitation for their use in medical ultrasound applications. Several methods based on the pre-compensation of a preselected input voltage have been proposed to cancel out the harmonic components generated. Unfortunately, these existing pre-compensation methods have two major flaws. The first is that the pre-compensation procedure is not generally automatic, and the second is that they can only reduce the second harmonic component. This can, therefore, limit their use for some imaging methods, which require a broader bandwidth, e.g., to receive the third harmonic component. In this study, we generalized the presetting methods to reduce all nonlinearities in the cMUT output. Our automatic pre-compensation method can work whatever the excitation waveform. The precompensation method is based on the nonlinear modeling of harmonic components from a Volterra decomposition in which the parameters are evaluated by using a Nelder-Mead algorithm. To validate the feasibility of this approach, the method was applied to an element of a linear array with several types of excitation often encountered in encoded ultrasound imaging. The results showed that the nonlinear components were reduced by up to 21.2 dB.

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We report a fast time-domain model of fluid-coupled cMUTs developed to predict the transient response-i.e., the impulse pressure response--of an element of a linear 1-D array. Mechanical equations of the cMUT diaphragm are solved with 2-D finite-difference schemes. The time-domain solving method is a fourth--order Runge-Kutta algorithm. The model takes into account the electrostatic nonlinearity and the contact with the bottom electrode when the membrane is collapsed. Mutual acoustic coupling between cells is introduced through the numerical implementation of analytical solutions of the impulse diffraction theory established in the case of acoustic sources with rectangular geometry. Processing times are very short: they vary from a few minutes for a single cell to a maximum of 30 min for one element of an array. After a description of the model, the impact of the nonlinearity and the pull-in/pull-out phenomena on the dynamic behavior of the cMUT diaphragm is discussed. Experimental results of mechanical displacements obtained by interferometric measurements and the acoustic pressure field are compared with simulations. Different excitation signals-high-frequency bandwidth pulses and toneburst excitations of varying central frequency-were chosen to compare theory with experimental results.

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A model is developed for studying the acoustic behavior of a cMUT array. This model is based on separate calculations of the terms describing the behavior of a single cMUT on one hand, and those corresponding to acoustic mutual coupling on the other hand. The terms are combined into an equivalent circuit with matrix terms which displays only one degree of freedom per cell. This approach allows the simulation of several dozen cMUTs considered individually with a very short computer time. A Finite Difference model is used for the simulation of an isolated cell radiating acoustic energy and the determination of its equivalent electromechanical circuit. It is shown for various mutual coupling situations that the coupling between cells can be correctly approximated using a very simple mutual impedance term. The model is compared with experimental results, using a set of different cMUT configurations. Experimental results were obtained with electrical impedancemetry and laser interferometry techniques performed in fluid immersion.

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In a recent publication [E. Filoux, S. Callé, D. Certon, M. Lethiecq, F. Levassort, Modeling of piezoelectric transducers with combined pseudospectral and finite-difference methods, J. Acoust. Soc. Am. 123 (6) (2008) 4165-4173], a new finite-difference/pseudospectral time-domain (FD-PSTD) algorithm was presented and used to model the generation of acoustic waves by a piezoelectric resonator and their propagation in the structure and the surrounding water. In this paper, the model has been extended to simulate the two-dimensional behaviour of a complete single-element transducer, composed of the resonator, a backing and a front matching layer. This further version of the model takes into account the mechanical loss in materials, and enables the calculation of electrical impedance, which is a characteristic of high interest to optimize the performance of ultrasonic transducers. The impedance curves of a PZT [URL: http://www.ferroperm-piezo.com (last viewed 04/2008); B. Jaffe, R.S. Roth, S. Marzullo, Piezoelectric properties of lead zirconate-lead titanate solid-solution ceramics, J. Appl. Phys. 25 (1954) 809-810] plate-based high-frequency transducer, with a 50 MHz thickness resonant frequency, were compared to those of a KLM model [R. Krimholtz, D.A. Leedom, G.L. Matthei, New equivalent circuit for elementary piezoelectric transducers, Electron. Lett. 6 (1970) 398-399] in the one-dimensional case. The acoustical properties were also found to be in good agreement with those obtained using the finite element (FE) method of ATILA software in two-dimensional configuration.

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An analytical model is presented to achieve simultaneous prediction of the elementary electroacoustic response and directivity pattern of a one-dimensional (1-D) piezocomposite array. The theoretical approach was based on guided wave theory in a multilayered structure in which the 1-3 piezocomposite material is considered as a homogeneous piezoelectric plate. A matrix method was applied to simulate the displacement fields generated at the surface of the array when one element was excited with an electrical pulse. A test device was manufactured, then characterized through measurements of displacement performed with an interferometric laser probe when the array vibrated in air and in water. The experimental results are presented and compared with theory.

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We report the development of two methods for determining the effective electroacoustic tensor of 1-3 piezocomposite material, one experimental and one theoretical based on homogenization techniques. The main aim was to compare and validate the results provided by these approaches. The slowness surfaces of bulk wave were computed in the large wavelength domain and were fitted to obtain the effective properties of the composite. Model predictions are discussed and compared with the Smith's model. The experimental method is an inversion technique comparing measurement of transmission coefficient through the piezocomposite plate with the simulated coefficient. The accuracy and stability of the minimization procedure is discussed. Experimental results obtained from two piezocomposite test plates are presented and compared with theory.

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The theoretical response of a 1-3 piezocomposite plate submitted to localized electrical excitation was studied with the theory of guided waves. The theoretical modeling was based on the global matrix method, and the piezocomposite material was considered as a homogeneous medium. To validate the theoretical results, experimental displacement measurements were performed with an interferometric probe on two piezocomposite plates, one with a single element and one with an array of electrodes. The measured response on the single-element plate was mainly supported by the S0 and S3 modes of the plate. Homogenization limits of the composite in terms of frequency and wave number are defined on the basis of data from this sample. Within these limits, the piezocomposite material operates as a homogeneous medium, and comparison between theoretical and experimental results allows the equivalent electroacoustic parameters to be evaluated. A second sample was measured to study the effects of the electrode array on the electroacoustic response of the plate. Two kinds of electrical excitation were studied.

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A finite difference method was implemented to simulate capacitive micromachined ultrasonic transducers (cMUTs) and compared to models described in the literature such as finite element methods. Similar results were obtained. It was found that one master curve described the clamped capacitance. We introduced normalized capacitance versus normalized bias voltage and metallization rate, independent of layer thickness, gap height, and size membrane, leading to the determination of a coupling factor master curve. We present here calculations and measurements of electrical impedance for cMUTs. An electromechanical equivalent circuit was used to perform simulations. Our experimental measurements confirmed the theoretical results in terms of resonance, anti-resonance frequencies, clamped capacitance, and electromechanical coupling factor. Due to inhomogeneity of the tested element array and strong parasitic capacitance between cells, the maximum coupling coefficient value achieved was 0.27. Good agreement with theory was obtained for all findings.

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