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

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.

Design and Fabrication of 1-D CMUT Arrays for Dual-Mode Dual-Frequency Acoustic Angiography Applications

When microbubble contrast agents are excited at low frequencies (less than 5 MHz), they resonate and produce higher-order harmonics due to their nonlinear behavior. We propose a novel scheme with a capacitive micromachined ultrasonic transducer (CMUT) array to receive high-frequency microbubble harmonics in collapse mode and to transmit a low-frequency high-pressure pulse by releasing the CMUT plate from collapse and pull it back to collapse again in the same transmit-receive cycle. By patterning and etching the substrate to create glass spacers in the device cavity we can reliably operate the CMUT in collapse mode and receive high-frequency signals. Previously, we demonstrated a single-element CMUT with spacers operating in the described fashion. In this article, we present the design and fabrication of a dual-mode, dual-frequency 1-D CMUT array with 256 elements. We present two different insulating glass spacer designs in rectangular cells for the collapse mode. For the device with torus-shaped spacers, the 3 dB receive bandwidth is from 8 to 17 MHz, and the transmitted maximum peak-to-peak pressure from 32 elements at 4 mm focal depth was 2.12 MPa with a 1.21 MPa peak negative pressure, which corresponds to a mechanical index (MI) of 0.58 at 4.3 MHz. For the device with line-shaped spacers, the 3-dB receive bandwidth at 150 V dc bias extends from 10.9 to 19.2 MHz. By increasing the bias voltage to 180 V, the 3 dB bandwidth shifts, and extends from 11.7 to 20.4 MHz. The transmitting maximum peak-to-peak pressure with 32 elements at 4 mm was 2.06 MPa with a peak negative pressure of 1.19 MPa, which corresponds to an MI of 0.62 at 3.7 MHz.

Squeeze Film Effect in Surface Micromachined Nano Ultrasonic Sensor for Different Diaphragm Displacement Profiles

In the present paper, we have analytically explored the small variations of the local pressure in the trapped air film of both sides of the clamped circular capacitive micromachined ultrasonic transducer (CMUT), which consists of a thin movable membrane of silicon nitride (Si₃N₄). This time-independent pressure profile has been investigated thoroughly by solving the associated linear Reynold's equation in the framework of three analytical models, viz. membrane model, plate model, and non-local plate model. The solution involves Bessel functions of the first kind. The Landau-Lifschitz fringing technique has been assimilated to engrave the edge effects in estimation of the capacitance of CMUT, which should be considered in the micrometer or lesser dimension. To divulge the dimension-based efficacy of the considered analytical models, various statistical methods have been employed. Our use of contour plots of absolute quadratic deviation revealed a very satisfactory solution in this direction. Though the analytical expression of the pressure profile is very cumbersome in various models, the analysis of these outputs exhibits that the pressure profile follows the displacement profile in all the cases indicating no viscous damping. A finite element model (FEM) has been used to validate the systematic analyses of displacement profiles for several radii and thicknesses of the CMUT's diaphragm. The FEM result is further corroborated by published experimental results bearing excellent outcome.

Investigation on Design Theory and Performance Analysis of Vacuum Capacitive Micromachined Ultrasonic Transducer

The capacitive micromachined ultrasonic transducer (CMUT), as a new acoustic-electric conversion element, has a promising application prospect. In this paper, the structure of the vacuum capacitive micromachined ultrasonic transducer is presented, and its performance-influencing factors are investigated. Firstly, the influencing factors of the performance parameters of the vacuum CMUT are analyzed theoretically based on the circular plate model and flat plate capacitance model, and the design principles of the structural parameters of the CMUT cell are proposed. Then, the finite element simulation software COMSOL Multiphysics is used to construct CMUT cell models with different membrane materials, membrane shapes, membrane radius thicknesses, and cavity heights for simulation verification. The results show that both the membrane parameters and the cavity heights affect the performance parameters of the Vacuum CMUT. In order to improve the efficiency of the CMUT, materials with low bending stiffness should be selected, and the filling factor of the membrane should be increased. In order to achieve high-transmission sound pressure, a smaller radius thickness and a larger cavity height should be selected. To achieve high reception sensitivity, a larger membrane radius thickness and a smaller cavity height should be selected. In order to obtain high fractional bandwidth, a larger membrane radius thickness should be selected. The results of this paper provide a basis for the design of Vacuum CMUT cell structure.

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.

A MEMS Ultra-Wideband (UWB) Power Sensor with a Fe-Co-B Core Planar Inductor and a Vibrating Diaphragm Capacitor

The design of a microelectromechanical systems (MEMS) ultra-wideband (UWB) RMS power sensor is presented. The sensor incorporates a microfabricated Fe-Co-B core planar inductor and a microfabricated vibrating diaphragm variable capacitor on adhesively bonded glass wafers in a footprint area of 970 × 970 µm² to operate in the 3.1–10.6 GHz UWB frequency range. When exposed to a far-field UWB electromagnetic radiation, the planar inductor acts as a loop antenna to generate a frequency-independent voltage across the MEMS capacitor. The voltage generates a coulombic attraction force between the diaphragm and backplate that deforms the diaphragm to change the capacitance. The frequency-independent capacitance change is sensed using a transimpedance amplifier to generate an output voltage. The sensor exhibits a linear capacitance change induced voltage relation and a calculated sensitivity of 4.5 aF/0.8 µA/m. The sensor can be used as a standalone UWB power sensor or as a 2D array for microwave-based biomedical diagnostic imaging applications or for non-contact material characterization. The device can easily be tailored for power sensing in other application areas such as, 5G, WiFi, and Internet-of-Things (IoT). The foreseen fabrication technique can rely on standard readily available microfabrication techniques.

Closed-Form Expressions on CMUTs With Layered Anisotropic Microplates Under Residual Stress and Pressure

Capacitive micromachined ultrasonic transducers (CMUTs) are promising in the emerging fields of personalized ultrasonic diagnostics, therapy, and noninvasive 3-D biometric. However, previous theories describing their mechanical behavior rarely consider multilayer and anisotropic material properties, resulting in limited application and significant analysis errors. This article proposes closed-form expressions for the static deflection, collapse voltage, and resonant frequency of circular-microplate-based CMUTs, which consider both the aforementioned properties as well as the effects of residual stress and hydrostatic pressure. These expressions are established by combining the classical laminated thin plate (CLTP) theory, Galerkin method, a partial expansion approach for electrostatic force, and an energy equivalent method. A parametric study based on finite-element method simulations shows that considering the material anisotropy can significantly improve analysis accuracy (~25 times higher than the theories neglecting the material anisotropy). These expressions maintain accuracy across almost the whole working voltage range (up to 96% of collapse voltages) and a wide dimension range (diameter-to-thickness ratios of 20-80 with gap-to-thickness ratios of ≤2). Furthermore, their utility in practical applications is well verified using numerical results based on more realistic boundary conditions and experimental results of CMUT chips. Finally, we demonstrate that the high accuracy of these expressions at thickness-comparable deflection results from the extended applicable deflection range of the CLTP theory when it is used for electrostatically actuated microplates.

A novelly universal theory: Toward accurately evaluating radial vibration characteristics for radially sandwiched spherical piezoelectric transducer

With the development of ultrasonic technology, some ultrasonic processing technologies require a wide processing range. In this paper, a radially sandwiched spherical piezoelectric transducer is proposed and analyzed, which is composed of a spherical piezoelectric ceramic sandwiched by two concentric spherical metal shells. The electromechanical equivalent circuits of the spherically isotropic spherical shell and the spherical piezoelectric ceramic with arbitrary wall thickness are derived from their motion equations. According to the mechanical boundary conditions, the electromechanical equivalent circuits and frequency equation of various piezoelectric composite vibration systems can be obtained, including the radially sandwiched spherical piezoelectric transducer. The correctness of the proposed theory is verified via comparison with the finite element method and the previous theoretical model. In addition, the 2nd-order effective mechanical coupling coefficient for the radially sandwiched spherical piezoelectric transducer is higher than that of 1st-order within a specific range of wall thickness, which can be designed as the high-frequency transducer. The radially sandwiched spherical piezoelectric transducer is expected to be used in underwater sound, structural health monitoring, and high-frequency ultrasound.