A Hybrid Boundary Element Model for Simulation and Optimization of Large Piezoelectric Micromachined Ultrasonic Transducer Arrays

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.

A Fluidics-Based Double Flexural Membrane Piezoelectric Micromachined Ultrasonic Transducer (PMUT) for Wide-Bandwidth Underwater Acoustic Applications

In acoustic receiver design, the receiving sensitivity and bandwidth are two primary parameters that determine the performance of a device. The trade-off between sensitivity and bandwidth makes the design very challenging, meaning it needs to be fine-tuned to suit specific applications. The ability to design a PMUT with high receiving sensitivity and a wide bandwidth is crucial to allow a wide spectrum of transmitted frequencies to be efficiently received. This paper presents a novel structure involving a double flexural membrane with a fluidic backing layer based on an in-plane polarization mode to optimize both the receiving sensitivity and frequency bandwidth for medium-range underwater acoustic applications. In this structure, the membrane material and electrode configuration are optimized to produce good receiving sensitivity. Simultaneously, a fluidic backing layer is introduced into the double flexural membrane to increase the bandwidth. Several piezoelectric membrane materials and various electrode dimensions were simulated using finite element analysis (FEA) techniques to study the receiving performance of the proposed structure. The final structure was then fabricated based on the findings from the simulation work. The pulse-echo experimental method was used to characterize and verify the performance of the proposed device. The proposed structure was found to have an improved bandwidth of 56.6% with a receiving sensitivity of -1.8864 dB rel 1 V µPa. For the proposed device, the resonance frequency and center frequency were 600 and 662.5 kHz, respectively, indicating its suitability for the targeted frequency range.

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.

3D FEM Analysis of High-Frequency AlN-Based PMUT Arrays on Cavity SOI

This paper presents three-dimensional (3D) models of high-frequency piezoelectric micromachined ultrasonic transducers (PMUTs) based on the finite element method (FEM). These models are verified with fabricated aluminum nitride (AlN)-based PMUT arrays. The 3D numerical model consists of a sandwiched piezoelectric structure, a silicon passive layer, and a silicon substrate with a cavity. Two types of parameters are simulated with periodic boundary conditions: (1) the resonant frequencies and mode shapes of PMUT, and (2) the electrical impedance and acoustic field of PMUT loaded with air and water. The resonant frequencies and mode shapes of an electrically connected PMUT array are obtained with a laser Doppler vibrometer (LDV). The first resonant frequency difference between 3D FEM simulation and the measurement for a 16-MHz PMUT is reasonably within 6%, which is just one-third of that between the analytical method and the measurement. The electrical impedance of the PMUT array measured in air and water is consistent with the simulation results. The 3D model is suitable for predicting electrical and acoustic performance and, thus, optimizing the structure of high-frequency PMUTs. It also has good potential to analyze the transmission and reception performances of a PMUT array for future compact ultrasonic systems.

Analysis and Design of High-Frequency 1-D CMUT Imaging Arrays in Noncollapsed Mode

High-frequency ultrasound imaging arrays are important for a broad range of applications, from small animal imaging to photoacoustics. Capacitive micromachined ultrasonic transducer (CMUT) arrays are particularly attractive for these applications as low noise receiver electronics can be integrated for an overall improved performance. In this paper, we present a comprehensive analysis of high-frequency CMUT arrays based on an experimentally verified CMUT array simulation tool. The results obtained on an example, a 40-MHz 1-D CMUT array for intravascular imaging, are used to obtain key design insights and tradeoffs for receive only and pulse-echo imaging. For the receiver side, thermal mechanical current noise, plane wave pressure sensitivity, and pressure noise spectrum are extracted from simulations. Using these parameters, we find that the receiver performance of CMUT arrays can be close to an ideal piston, independent of gap thickness, and applied dc bias, when coupled to low noise electronics with arrays utilizing smaller membranes performing better. For pulse-echo imaging, thermal mechanical current noise limited signal-to-noise ratio is observed to be dependent on the maximum available voltage and gap thickness. In terms of bandwidth, we find that the Bragg resonance of the array, related to the fill factor, is a significant determinant of the high frequency limit and the fluid loaded single membrane resonance determines the lower limit. Based on these results, we present design guidelines requiring only fluid loaded single membrane simulations and membrane pitch to achieve a desired pulse-echo response. We also provide a design example and discuss limitations of the approach.