This work experimentally investigates the effective boundary behavior of cavity-SOI piezoelectric micromachined ultrasonic transducers (PMUTs) using vibration measurements obtained by digital holographic microscopy. Measured displacement fields are projected onto analytical eigenfunctions to extract modal participations for flexural modes across multiple device sizes fabricated on the same wafer. Investigated devices are found to vibrate predominantly in their fundamental axisymmetric mode. Modal analysis consistently shows that the measured displacement profiles more closely resemble simply supported (SS) mode shapes than clamped (CL) counterparts. In contrast, the measured resonance frequencies lie between the SS and CL predictions, with their proximity to these limits depending on device size. This frequency-shape disparity, reproducible across the wafer, reflects the different sensitivities of resonance frequencies and mode shapes to boundary stiffness and is attributed to finite restraint at the PMUT edge. Specifically, resonance frequency is strongly influenced by boundary stiffness, while the displacement profile remains largely SS-like over a broad stiffness range. Higher-order resonances, including non-axisymmetric modes, are also resolved, further validating the modal participation framework. The effect of modeling diameter on modal participation is further examined, revealing that SS models achieve optimal agreement at diameters close to the nominal device size, whereas CL models require an enlarged modeling diameter. These results demonstrate that cavity-SOI PMUT boundaries are best described as elastically restrained rather than ideally CL or SS. The presented approach provides a physically transparent basis for interpreting PMUT boundary behavior and supports the development of improved analytical models incorporating elastic edge restraint.

Analytical models of piezoelectric micromachined ultrasonic transducers (PMUTs) often assume clamped edges, but this simplification causes deviations with experiments, as actual PMUTs are supported by elastic anchors and surrounded by neighboring elements in an array. This work experimentally investigates the effect of compliant support in PMUTs and proposes a model with improved accuracy in predicting the electroacoustic performance. The proposed model is based on a plate model with elastic torsional and rotational edge supports, with spring stiffness parameters determined by minimizing the deviations between the measured and modeled displacement profiles while restricting the modeled resonance frequency to within a small range of the measured value. The model was tested on an element in a 2D array of cavity SOI-based PZT PMUTs operating in air. The vibration measurements were performed using a digital holographic microscope. The proposed model based on a plate with elastic supports improves prediction accuracy of displacement by 94%, compared to the clamped plate model. Moreover, relative to the measurements, the deviation of the predicted resonance frequency using the proposed model was 4%, while this was 13% for the clamped plate model.

Wideband transducers are highly preferable for medical ultrasound imaging. Dual-frequency transducers have been developed to enlarge the operating bandwidth by separating transmission and reception. A novel dual-frequency transducer design, comprising a hybrid configuration of a partly epoxy-filled kerf piezoelectric array and a capacitive micromachined ultrasound transducer (CMUT) array, has been proposed. This work studied the fabrication feasibility such hybrid transducer, including both fabrication of the partly epoxy-filled piezoelectric array and lamination of inactive CMUTs to this array to mimic the hybrid transducer. The bonding properties of piezoelectric elements on a flexible printed circuit board were characterized through both mechanical and electrical methods. The adhesion strength of elements to the flexible printed circuit board demonstrates robustness, with a peel strength reaching up to 2.7 N/mm. Additionally, the contact resistance of an element to the board is negligibly small, approximately 0.11 Ω. Four prototype arrays, each consisting of 80 elements with air-filled kerfs, were successfully fabricated, achieving a yield ratio up to 100%. The lamination process was successfully performed, resulting in a shear strength above 4.2 MPa and maintaining an epoxy fill less than 30% in the kerfs.

Lithium niobate (LiNbO3) is a strong candidate for high-temperature ultrasonic transducers used in nondestructive testing (NDT) due to its high Curie temperature and stable piezoelectric properties. However, reliable bonding of LiNbO3 to stainless steel, used as a matching or protective layer, remains a challenge at temperatures above 300 degrees C. This work investigated five bonding methods for joining 36 degrees Y-cut LiNbO3 to stainless steel: (1) Ag paste, (2) Cu-Sn solid-liquid interdiffusion (SLID), (3) AgCu brazing, (4) Au thermocompression, and (5) glass frit. Transducer performance was assessed by electrical impedance and pulse-echo measurements using 3 MHz, 4-cycle, 4 Vpp sine wave pulses transmitted into steel. We found that only Ag paste and SLID bonding produced acoustically viable devices. Transducers bonded with Ag paste produced clear echoes up to 550 degrees C. The -6 dB BW increased from 26.5% at 25 degrees C to 31.2% at 550 degrees C, while SNR decreased from 30.8 dB to 27.1 dB. SLID bonding generated echoes at 25 degrees C but failed above 100 degrees C. This is likely due to incomplete intermetallic formation and residual Sn that re-melted during heating, creating voids and delamination. AgCu brazing, Au thermocompression, and glass frit bonding suffered from oxidation, poor wetting, or brittle fracture.

Patterning the piezoelectric layer of a piezoelectric micromachined ultrasonic transducer (PMUT) plate usually leads to improved performance; however, modeling of such PMUT is not as straightforward as its conventional counterpart. This article presents an electroacoustic model for conventional as well as patterned PMUTs with square shaped membranes. Hamilton's principle is utilized to formulate the dynamics of the patterned PMUT. The derived mode shape is used to obtain the electrical, mechanical, and acoustic parameters to arrive at the complete electroacoustic model. The model is applied to eight different designs, where four are of conventional type with different electrode configurations and the other four are patterned designs with different patterning configurations. Using the proposed model, the electrode and patterning geometry for each PMUT design is optimized. Natural frequency, mode shape, the input impedance at the electrical port, and the transfer function from the electrical to the acoustic port calculated from this model are shown to be in good agreement with those obtained from finite-element analysis for all the studied designs. Moreover, the patterned PMUTs are shown to have superior performance, in terms of volume velocity per unit voltage, over conventional PMUTs operating at a given resonance frequency.

Tissue harmonic imaging requires good control of the nonlinearity in the ultrasound probe, as transmitted second harmonics from the probe may interfere with tissue harmonics and degrade image quality. We have studied the nonlinearity in four different medical ultrasound probes by measuring the capacitive part of their electrical impedances under varying electric fields, at frequencies well below and above the resonances. The probes were made with two different piezoelectric materials, piezoceramic PZT and single-crystal PMN-PT, with either soft backing operating at half-wavelength resonance or hard backing operating at quarter-wavelength resonance. When the applied electric field amplitude E was increased from 0.05V/mu m to 0.5V/mu m, we observed an increase in both the capacitance at high frequency, interpreted as clamped conditions, and at low frequency, interpreted as free conditions. This is a nonlinear phenomenon as these capacitances will not change in the linear regime. The increase in free capacitance was from 4 to 10 times larger than the increase in clamped capacitance for all the investigated probes. This indicates a stronger nonlinearity for the free capacitance. At the low-frequency excitation, we observed distortion in the current passing through the acoustic stack corresponding to a relative second harmonic level of -20 dB. We conclude that the nonlinear impedance of the acoustic stack in the investigated probes was primarily caused by nonlinearities in the mechanical coefficients, while contributions from dielectric nonlinearity were negligible.

Development of ultrasound transducers for operation in high pressure and high temperature environments is still a challenge. This paper presents an evaluation of different bonding techniques for ultrasound transducers intended for harsh environments. Performance at temperature 180 degrees C was investigated at atmospheric pressure, and performance under hydrostatic pressure 1000 bar was investigated at temperature 15 degrees C. Five different bonding configurations were tested, two polymer adhesives and three metallurgical bonding methods. One of the polymer adhesives is a standard epoxy-adhesive, the other is an adhesive intended for operation at high tem-peratures. Two of the metallurgical bonding configurations studied are Solid-liquid Interdiffusion (SLID) bonds. The third metallurgical bonding method introduces preform soldering as a new bonding technique for ultrasound transducers. All the metallurgical bonding methods outperform polymer adhesives in shear strength and tem-perature stability. Compared to the SLID-methods, preform-soldering offers a faster and cheaper bonding process without the need for electroplating, making it an attractive metallurgical bonding technique for ultrasound transducers.

Harmonic imaging plays a crucial role in medical ultrasound imaging, where the transducer probes are required to emit low-frequency ultrasonic waves into the tissues, and receive reflected signals at the higher, typically the second harmonic of the transmitted wave. We have designed a unique probe with a high-frequency capacitive micromachined ultrasonic transducer (CMUT) on top of a low-frequency piezoelectric array for harmonic imaging. This paper presents a lamination process between CMUT and piezoelectric array using epoxy. The bond-line between the two components was thoroughly investigated using mechanical and electrical methods. The resulting bond-line thickness was less than 2 μm, and shear strength fell within the range 4.8 – 5.1 MPa. Additionally, electrical impedance measurement of all elements in the low-frequency array exhibited resonance shifts before and after bonding, providing further insight into the bonding process.

This research presents the development and characterization of a high temperature ultrasound transducer for non-destructive testing (NDT) applications, specifically designed to operate in harsh environments up to 550 °C. The transducer is based on a 36° Y-cut lithium niobate (LiNbO 3 ) crystal, chosen for its superior thermal stability compared to traditional PZTs. The transducer consists of a lithium niobate crystal bonded to a steel cylinder. The transducer's electrical impedance and pulse-echo performance were evaluated during heating cycles from room temperature to 550 °C. Experimental results demonstrated that the transducer continues to operate at high temperature, showing its potential for high temperature NDT application. The electrical impedance magnitude stabilized after several heating cycles, and the electromechanical coupling coefficient remained consistent. The pulse-echo response at 550 °C exhibited a SNR of 23 dB, despite a shift in the echo position caused by thermal expansion and changes in the speed of sound in steel under high temperatures. The findings indicate that LiNbO 3 holds promise as a temperature-resistant ultrasound transducer for high-temperature NDT, without the issue of depoling.

Second harmonic imaging is established in medical ultrasound and handled by conventional transducers. However, certain applications greatly benefit from receiving even higher harmonics. Notable examples are microbubble detection for perfusion studies and cavitation detection in drug delivery applications. This study presents a novel dual-frequency transducer design that transmits high intensity pulses at a low frequency and receives over a wide bandwidth around the higher harmonics of the transmitted frequency. The key to this design is the incorporation of a mass–spring structure, which effectively isolates the HF receiver from the LF structure and increase the receiving bandwidth. A prototype was fabricated and characterized. The transmit at 2 MHz with 54% bandwidth is done by a PZT element, while the receive in range 5 – 11 MHz is done by a PVDF film.

Piezoelectric micromachined ultrasonic transducers (PMUTs) with multiple electrodes can be utilized as multi-frequency transducers by exciting selected vibration modes of the diaphragm providing configurability that may be beneficial in modern ultrasound imaging and therapeutic techniques. This requires judicious arrangement of the electrode configuration to excite the desired modes or combination of modes. Optimization of the electrode pattern can be done using full electroacoustic Finite Element Method (FEM) simulations, but this is computationally intensive and gives limited insight into the underlying physics. This paper presents a simple and efficient approach based on the in-vacuum strain mode shapes of the PMUT diaphragm to optimize the electrode configurations for an arbitrary PMUT cell resonating at any flexural mode. Strain mode shapes are obtained both from an analytical model as well as FEM. The proposed method is compared to and verified by full electroacoustic FEM simulations of PMUTs radiating into water. The optimal electrode patterns for the first few flexural modes are found for rectangular PMUTs with three different length-to-width aspect ratios, and examples of configurable PMUTs are given by combining the optimal electrodes at two different modes.

This study presents a novel and simple approach to form metallurgical bonds between layers of the acoustic stack in an ultrasound transducer using a eutectic AuSn preform, which is a pre-shaped thin sheet of solder. The bonding takes 10 minutes and yields uniform bondlines of 10 μm with a melting temperature of 280 °C. The resulting bonds are electrically conductive, mechanically robust and have a characteristic acoustic impedance of 29 Mrayls. AuSn bonding was demonstrated by successfully bonding two equally thick layers of PZT. The bonded PZT-stacks were polarized and sub-diced into a 2-dimensional array. Characterization was performed by optical microscopy, scanning acoustic microscopy and electrical impedance measurements. Combining scanning acoustic microscopy and electrical impedance measurements proved to be a useful approach to experimentally study inter-element variations induced by varying concentrations of voids in a metallurgical bondline.

The ongoing robotic revolution in oceanic science puts new requirements on sonar technology. Small platforms require compact multi-purpose transducers, with strict requirements on power consumption and heat dissipation. Introducing single-crystal ferroelectrics as the active material of the transmitter can be one way of meeting the new requirements. The large electromechanical coupling coefficient of single crystals can enable an extension of the usable frequency band compared to conventional PZT. For the applications considered in this work, the usable frequency band is restricted by both the transmitted acoustic power and the reactive electrical power. Single crystals as the active materials can double the usable band, but the acoustic matching required for this can be difficult to obtain in practice. We investigated an air-backed, plane 1–3 composite transducer, matched to water by acoustic matching layers. For many applications, the diversity provided by a large usable frequency range is more important than a flat acoustic power response, and the transducer can be used far beyond the −3-dB limit. We defined the usable band by requiring maximum −12-dB ripple in transmitted acoustic power and maximum 50% reactive power. The matching layers were optimized to maximize the usable band according to this definition, in contrast to the conventional approach where matching layers are optimized for maximally flat response. Under the chosen definitions, our modeling showed that with a single crystal as the active material we could achieve 188% usable frequency band relative to the resonance frequency, compared to 121% for a PZT.

This study presents a finite element method (FEM) approach to estimate the effective medium parameters of 2-D and 3-D layers of arbitrary composition. The resonance frequency of a layer to be investigated is found by exciting the layer with plane waves and studying the reflected sound pressure from the layer as a function of frequency and incidence angle. This allowed for the calculation of compressional and shear wave velocities. The method was validated by applying the method to layers with known acoustic parameters and by comparing with results from the established analytical models. Composite layers with 1-3 and 2-2 connectivity are well described by established effective-medium theories, but these require the composite structures to be small compared to the acoustic wavelength. This limitation was overcome by the described FEM-based model, which could also capture deviations occurring in coarser composites. Conventional analytical models predict wave velocities as a function of void concentration, not considering positions of the voids. The described FEM approach predicted up to 5% variation in wave velocities for gold layers with identical volume fraction of voids, depending on the void distribution. This demonstrates that void positions influence wave velocity. The influence of connectivity between inclusions was studied by modeling tungsten inclusions in an epoxy matrix. It was found that composites with inclusions connected in a preferred direction had higher wave velocity in the direction of connectivity compared to randomly oriented inclusions. It is concluded that the presented FEM model reproduces the literature values for homogeneous materials and agrees with effective medium theories for fine-pitched composites. However, the strength of the model is its ability to go beyond this and model phenomena in real finite-size composites not captured by the classic effective medium models.

This paper presents a simple and efficient electrode optimization method, which is applicable to any flat PMUT diaphragm shape resonating at any flexural mode. The method exploits the fact that the sensitivity of a PMUT stack is proportional to the sum of in-plane strains of the PMUT diaphragm. The in-vacuo strain mode shapes is obtained from the eigenfrequency finite element method (FEM). The method is applied to elliptical PMUTs with two different aspect ratios having single electrodes and the optimal electrode parameters for the maximum performance at the first three odd flexural modes are obtained. The results show good agreement with those acquired from three-dimensional fully coupled FEM simulations in water.

This study presents a finite element approach to estimate acoustic parameters of layers of arbitrary compositions using 2D and 3D models. In this approach the resonance frequency of a layer to be investigated is found by exciting the layer with plane waves and studying the reflected and transmitted sound pressure from the layer. Compressional and shear modes can be excited separately by varying the angle of incidence. A script for generating inhomogeneous layers with randomly distributed inclusions of arbitrary shape and size was developed for this study. A Matlab application was built for processing the result and comparison with analytical calculations. The 2D and 3D models were validated by comparing derived acoustic parameters of known materials with no more than 0.06% deviation from expected values. Estimated parameters for a layer of gold with 10.6% volume fraction of spherical inclusions of voids of 3 µm and 5 µm diameter was found to range from 2540 m/s to 2652 m/s for compressional sound speed and from 1039 m/s to 1067 for shear speed of sound.

For underwater transducers mounted on small platforms, reactive electrical power can constitute a main restriction on the usable frequency range. The frequency range in which the amount of reactive power is acceptable can be increased by increasing the electromechanical coupling coefficient of the active material. However, to avoid large electrical power factor ripple, the transducer design must also have a low mechanical quality factor, $Q_{m}$ . A ferroelectric single crystal can have electromechanical coupling coefficient $k=0.9$ . The optimum $Q_{m}$ is then as low as 0.6, which is challenging to achieve. We investigated this challenge for a tonpilz design, by calculating $Q_{m}$ for different combinations of head masses and tonpilz stiffnesses, and by calculating the stiffness to density ratio required in the head material to avoid flexural resonances. The effective coupling coefficient of a real transducer is reduced compared to the material coupling coefficient, and in many applications some power factor ripple can be accepted. Both factors relax the $Q_{m}$ requirement. We calculated the power factor of a tonpilz design with $k=0.82$ and $Q_{m}=1.9$ , and showed that the power factor ripple is smaller than 0.2 in a frequency band that is 150 % wide relative to the resonance frequency. The frequency independent matching inherent in the tonpilz gives this design an advantage regarding power factor ripple, and this can weigh up for a large $Q_{m}$ . We showed this by comparing the tonpilz to an air-backed composite plate. Like the tonpilz, the composite plate had $k=0.82$ , but it was matched to water by two conventional acoustic matching layers. Compared to the tonpilz, the composite design had a larger distance between the −3dB points of the acoustic power. Beyond these points, the acoustic power was however falling off more rapidly, resulting in an electrical power factor ripple of nearly 0.5.

Tissue harmonic imaging is often the preferred ultrasound imaging modality due to its ability to suppress reverberations. The method requires good control of the transmit stage of the ultrasound scanner, as harmonics in the transmitted ultrasound pulses will interfere with the harmonics generated in the tissue during nonlinear propagation, degrading image quality. In this study, a medical ultrasound probe used in tissue harmonic imaging was experimentally characterized for transmitted second-harmonic distortion to identify and compare the sources of nonlinear distortion in the probe and transmit electronics. The system was tested up to amplitudes above what is found during conventional operation, pushing the system to the limits in order to investigate the phenomenon. Under these conditions, second-harmonic levels up to -20 dB relative to the fundamental frequency were found in the ultrasound pulses transmitted from the probe. The transmit stage consists of high-voltage transmit electronics, cable, tuning inductors, and the acoustic stack. The contribution from the different stages in the ultrasound transmit chain was quantified by separating and measuring at different positions. Nonlinearities in the acoustic transducer stack were identified as the dominating source for second harmonics in the transmitted ultrasound pulses. Contribution from other components, e.g., transmit electronics and cable and tuning circuitry, were found to be negligible compared with that from the acoustic stack. Investigation of the stack's electrical impedance at different driving voltages revealed that the impedance changes significantly as a function of excitation voltage. The second-harmonic peak in the transmitted pulses can be explained by this nonlinear electrical impedance distorting the driving voltage and current.

This study describes results from an experimental ultrasound system with miniature transducers sutured directly onto the epicardial surface and used to measure heart contractions continuously. This system was used to find velocity distributions through the myocardium. The resulting velocities were used to track the motion of four layers at different depths through the myocardium and to find the regional strain in each of the four layers. Velocities inside the myocardium vary from the epicardial to the endocardial borders. Conventional velocity estimators based on Doppler and on time delay estimation were modified to better handle these variations. Results from four different velocity estimators were tested against a simulation model for ultrasound echoes from moving tissue and on ultrasound recordings from five animals. We observed that the tested velocity estimators were able to reproduce the myocardial velocity distributions, track the myocardial layer motion and estimate strain at different positions inside the myocardium for both simulated and real ultrasound recordings. The most accurate results were obtained when the digitized ultrasound scanlines were upsampled by a factor of 10 before applying cross-correlation to estimate time delays. A modified Doppler algorithm allowing the velocity to vary linearly with time throughout the duration of the pulse packet (constant acceleration Doppler) was found to be better at capturing rapidly changing velocities compared with conventional Doppler processing. The best results were obtained using upsamling and time delay estimation, but the long computation time required by this method may make it best suited in a laboratory setting. In a real-time system, the computationally quicker constant acceleration Doppler may be preferred.

This paper investigates the influence of high pressure on Au-Sn solid-liquid interdiffusion (SLID) bonds formed by bonding Si substrates to dies of either lead-zirconate titanate (PZT) with high surface roughness or Si with low surface roughness. Bonded samples were exposed to 1000 bar pressure in a silicone oil filled pressure vessel. Samples were characterized before and after exposure by means of scanning acoustic microscopy, optical microscopy and scanning electron microscopy with energy dispersive x-ray spectroscopy. All but one sample successfully passed the pressure exposure. This failed sample had a delamination in the proximity of a large void in the intermetallic layer.