RESUMEN
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.
RESUMEN
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.
RESUMEN
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.
RESUMEN
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.