Self and Mutual Radiation Impedances for Modeling of Multi-Frequency CMUT Arrays

Radiation Impedance of Rectangular CMUTs

Recently, capacitive micromachined ultrasound transducers (CMUTs) with long rectangular membranes have demonstrated performance advantages over conventional piezoelectric transducers; however, modeling these CMUT geometries has been limited to computationally burdensome numerical methods. Improved fast modeling methods, such as equivalent circuit models, could help achieve designs with even better performance. The primary obstacle in developing such methods is the lack of tractable methods for computing the radiation impedance of clamped rectangular radiators. This paper presents a method that approximates the velocity profile using a polynomial shape model to rapidly and accurately estimate radiation impedance. The validity of the approximate velocity profile and corresponding radiation impedance calculation was assessed using finite element simulations for a variety of membrane aspect ratios and bias voltages. Our method was evaluated for rectangular radiators with width:length ratios from 1:1 up to 1:25. At all aspect ratios, the radiation resistance was closely modeled. However, when calculating the radiation reactance, our initial approach was only accurate for low aspect ratios. This motivated us to consider an alternative shape model for high aspect ratios, which was more accurate when compared with FEM. To facilitate the development of future rectangular CMUTs, we provide a MATLAB script that quickly calculates radiation impedance using both methods.

Transparent Dual-Frequency CMUT Arrays for Photoacoustic Imaging

The opaque ultrasound transducers used in conventional photoacoustic imaging systems necessitate oblique light delivery, which gives rise to some disadvantages such as inefficient target illumination and bulky system size. This work proposes a transparent capacitive micromachined ultrasound transducer (CMUT) linear array with dual-band operation for through-illumination photoacoustic imaging. Fabricated using an adhesive wafer bonding method, the array consists of optically transparent conductors [indium tin oxide (ITO)] as both top and bottom electrodes, a transparent polymer [bisbenzocyclobutene (BCB)] as the sidewall and adhesive material, and largely transparent silicon nitride as the membrane. The fabricated device had a maximum optical transparency of 76.8% in the visible range. Furthermore, to simultaneously maintain higher spatial resolution and deeper imaging depth, this dual-frequency array consists of low- and high-frequency channels with 4.2- and 9.3-MHz center frequencies, respectively, which are configured in an interlaced architecture to minimize the grating lobes in the receive point spread function (PSF). With a wider bandwidth compared to the single-frequency case, the fabricated transparent dual-frequency CMUT array was used in through-illumination photoacoustic imaging of wire targets demonstrating an improved spatial resolution and imaging depth.

Modeling a Fluid-Coupled Single Piezoelectric Micromachined Ultrasonic Transducer Using the Finite Difference Method

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.

High-Performance Electrode-Post CMUTs: Fabrication Details and Best Practices

Capacitive micromachined ultrasound transducers (CMUTs) have been investigated for over 25 years due to their promise for mass manufacturing and electronic co-integration. Previously, CMUTs were fabricated with many small membranes comprising a single transducer element. This, however, resulted in suboptimal electromechanical efficiency and transmit performance, such that resulting devices were not necessarily competitive with piezoelectric transducers. Moreover, many previous CMUT devices were subject to dielectric charging and operational hysteresis that limited long-term reliability. Recently, we demonstrated a CMUT architecture using a single long rectangular membrane per transducer element and novel electrode-post (EP) structures. This architecture not only offers long-term reliability, but also provides performance advantages over previously published CMUT and piezoelectric arrays. The purpose of this article is to highlight these performance advantages and provide details of the fabrication process, including the best practices to avoid common pitfalls. The objective is to provide sufficient detail to inspire a new generation of microfabricated transducers, which could lead to performance gains of future ultrasound systems.

cMUT technology developments

Capacitive micromachined ultrasonic transducer (cMUT) technology has steadily advanced since its advent in the mid-1990's. Though cMUTs have not supplanted piezoelectric transducers for medical ultrasound imaging to date, researchers and engineers are continuing to improve cMUTs and leverage unique cMUT characteristics toward new applications. While not intended to be an exhaustive review of every aspect of cMUT state-of-the-art, this article provides a brief overview of cMUT benefits, challenges, and opportunities, as well as recent progress in cMUT research and translation.

Outperforming piezoelectric ultrasonics with high-reliability single-membrane CMUT array elements

It has long been hypothesized that capacitive micromachined ultrasound transducers (CMUTs) could potentially outperform piezoelectric technologies. However, challenges with dielectric charging, operational hysteresis, and transmit sensitivity have stood as obstacles to these performance outcomes. In this paper, we introduce key architectural features to enable high-reliability CMUTs with enhanced performance. Typically, a CMUT element in an array is designed with an ensemble of smaller membranes oscillating together to transmit or detect ultrasound waves. However, this approach can lead to unreliable behavior and suboptimal transmit performance if these smaller membranes oscillate out of phase or collapse at different voltages. In this work, we designed CMUT array elements composed of a single long rectangular membrane, with the aim of improving the output pressure and electromechanical efficiency. We compare the performance of three different modifications of this architecture: traditional contiguous dielectric, isolated isolation post (IIP), and insulated electrode-post (EP) CMUTs. EPs were designed to improve performance while also imparting robustness to charging and minimization of hysteresis. To fabricate these devices, a wafer-bonding process was developed with near-100% bonding yield. EP CMUT elements achieved electromechanical efficiency values as high as 0.95, higher than values reported with either piezoelectric transducers or previous CMUT architectures. Moreover, all investigated CMUT architectures exhibited transmit efficiency 2-3 times greater than published CMUT or piezoelectric transducer elements in the 1.5-2.0 MHz range. The EP and IIP CMUTs demonstrated considerable charging robustness, demonstrating minimal charging over 500,000 collapse-snap-back actuation cycles while also mitigating hysteresis. Our proposed approach offers significant promise for future ultrasonic applications.

Dual-Frequency CMUT Arrays for Multiband Ultrasound Imaging Applications

Dual-frequency capacitive micromachined ultrasonic transducers (CMUTs) are introduced for multiscale imaging applications, where a single array transducer can be used for both deep low-resolution imaging and shallow high-resolution imaging. These transducers consist of low- and high-frequency membranes interlaced within each subarray element. They are fabricated using a modified sacrificial release process. Successful performance is demonstrated using wafer-level vibrometer testing, as well as acoustic testing on wirebonded dies consisting of arrays of 2- and 9-MHz elements of up to 64 elements for each subarray. The arrays are demonstrated to provide multiscale, multiresolution imaging using wire phantoms and can span frequencies from 2 MHz up to as high as 17 MHz. Peak transmit sensitivities of 27 and 7.5 kPa/V are achieved with the low- and high-frequency subarrays, respectively. At 16-mm imaging depth, lateral spatial resolution achieved is 0.84 and 0.33 mm for low- and high-frequency subarrays, respectively. The signal-to-noise ratio of the low-frequency subarray is significantly higher for deep targets compared to the high-frequency subarray. The array achieves multiband imaging capabilities difficult to achieve with current transducer technologies and may have applications to multipurpose probes and novel contrast agent imaging schemes.

The Effects of Manufacturing Inaccuracies in an Underwater Acoustic Projector Array on the Acoustic Interactions

We report on the importance of considering manufacturing inaccuracies in underwater acoustic projectors by elucidating how small variations affect the response characteristics of a projector array in the presence of mutual-loading effects. A wave-based distributed mechanical model accurately calculates the changes arising from small variations, so rapid changes occurring in the vicinity of the transducer resonance can be simulated. The results showed the effects of mutual loading between projector units and confirmed that the changes can be drastically intensified in the presence of manufacturing inaccuracies. A voltage adjustment method to compensate for these changes is also demonstrated as a solution. This framework could guide the design of projector arrays in sound navigation and ranging (SONAR) systems for a variety of applications and, in particular, may contribute significantly to determining manufacturing tolerances.

Structural design of an acoustic planar array transducer by using the equivalent circuit method

Underwater acoustic transducers are used to detect and track targets by using sound waves in underwater environments. To enhance the performance, they can be arranged in various formations to create arrays. However, acoustic interaction between the constituent channels of array transducers is inevitable, and it distorts their characteristics. In this study, the transmitting voltage response (TVR) spectrum of an acoustic planar array transducer is analyzed by considering the crosstalk between channels. The transmitting performance of an array transducer is frequently analyzed using the conventional finite element method (FEM). However, when the size of the array is large, the time and cost of computation using the FEM increase to almost prohibitive levels. To overcome this problem, a new equivalent circuit method (ECM) is developed to analyze the acoustic characteristics of an underwater array transducer. The ECM is validated by comparing its TVR spectrum with that analyzed using the FEM. After validation, the ECM is utilized to design the optimal structure of a planar array transducer having the broadest bandwidth. The sample analysis conducted using the ECM was approximately 1780 times faster than that by the FEM. Therefore the ECM developed in this work can facilitate the design of an underwater planar array transducer with a superior speed and efficiency compared with those achievable with the conventional numerical analysis methods such as the FEM.

A Boundary Element Model for CMUT-Arrays Loaded by a Viscoelastic Medium

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.

A Nonlinear Lumped Equivalent Circuit Model for a Single Uncollapsed Square CMUT Cell

An accurate nonlinear lumped equivalent circuit model is used for modeling of capacitive micromachined ultrasonic transducers (CMUTs). Finite-element analysis (FEA) is a powerful tool for the analysis of CMUT arrays with a small number of cells while with the harmonic balance (HB) analysis of the lumped equivalent circuit model, the entire behavior of a large-scale arbitrary CMUT array can be modeled in a very short time. Recently, an accurate nonlinear equivalent circuit model for uncollapsed single circular CMUT cells has been developed. However, the need for an accurate large-signal circuit model for CMUT cells with square membranes motivated us to produce a new nonlinear large-signal equivalent circuit model for uncollapsed CMUT cells. In this paper, using analytical calculations and FEA as the tuning tool, a precise large signal equivalent circuit model of square CMUT dynamics was developed and showed excellent agreement with finite-element modeling (FEM) results. Then, different CMUT single cells with square and circular membranes were fabricated using a standard sacrificial release process. Model predictions of resonance frequencies and displacements closely matched experimental vibrometer measurements. The framework presented here may prove valuable for future design and modeling of CMUT arrays with square membranes for ultrasound imaging and therapy applications.

Multifrequency Interlaced CMUTs for Photoacoustic Imaging

Multifrequency capacitive micromachined ultrasound transducers (CMUTs) are introduced consisting of interlaced 82- [Formula: see text] (low frequency) and 36- [Formula: see text] (high frequency) membranes. The membranes have been interlaced on a scale smaller than the shortest wavelength of operation allowing several advantages over other multifrequency transducer designs including aligned beam profiles, optimal imaging resolution, and minimal grating lobes. The low- and high-frequency CMUTs operate at 1.74 and 5.04 MHz in immersion, respectively. Multifrequency transducers have applications in wideband photoacoustic (PA) imaging where multifrequency transducers are better able to detect both high- and low-frequency PA frequency content. The PA frequency content is target size dependent, which means traditional high-frequency transducers have less sensitivity to larger objects such as diffuse contrast agents. We demonstrate that the low-frequency subarrays are able to better visualize diffuse agent distributions, while the high-frequency subarrays offer fine-resolution imaging important for microvascular imaging and structural navigation. Spectroscopically unmixed images superimpose high sensitivity images of agent concentrations (acquired using low-frequency subarrays) onto high-resolution images of microvessel-mimicking phantoms (acquired using high-frequency subarrays).