A large-signal model for CMUT arrays with arbitrary membrane geometry operating in non-collapsed mode

Abstract

A large signal, transient model has been developed to predict the output characteristics of a CMUT array operated in the non-collapse mode. The model is based on separation of the nonlinear electrostatic voltage-to-force relation and the linear acoustic array response. For linear acoustic radiation and crosstalk effects, the boundary element method is used. The stiffness matrix in the vibroacoustics calculations is obtained using static finite element analysis of a single membrane which can have arbitrary geometry and boundary conditions. A lumped modeling approach is used to reduce the order of the system for modeling the transient nonlinear electrostatic actuation. To accurately capture the dynamics of the non-uniform electrostatic force distribution over the CMUT electrode during large deflections, the membrane electrode is divided into patches shaped to match higher order membrane modes, each introducing a variable to the system model. This reduced order nonlinear lumped model is solved in the time domain using Simulink. The model has two linear blocks to calculate the displacement profile of the electrode patches and the output pressure for a given force distribution over the array, respectively. The force to array displacement block uses the linear acoustic model, and the Rayleigh integral is evaluated to calculate the pressure at any field point. Using the model, the transient transmitted pressure can be simulated for different large signal drive signal configurations. The acoustic model is verified by comparison to harmonic FEA in vacuum and fluid for high and low aspect ratio membranes as well as mass-loaded membranes. The overall Simulink model is verified by comparison to transient 3D FEA and experimental results for different large drive signals; and an example for a phased array simulation is given.

CMUTs with high-K atomic layer deposition dielectric material insulation layer

“…To determine the range of acceptable insulation layer thicknesses that are feasible for a particular gap design, the collapse voltage is calculated either with (8) or with the large-signal model used in [2] for higher accuracy to match the breakdown voltage at a particular thickness. As an example, this calculation is performed for HfO layer CMUTs for a 35 μm × 35 μm square membrane.…”

“…The spectra of the received signals were also monitored to make sure that the devices operated in the non-collapsed mode. No DC bias was applied with this short pulse to achieve maximum output pressure with full-gap swing [2]. Pulse amplitudes of 32 V and 60 V were found to reach maximum output pressure for HfO and SiN insulation devices respectively.…”

“…In the transmit mode, where large voltage signals are applied to obtain large membrane displacement swings, the electrostatic force applied to the CMUT membrane is a quadratic function of the ratio between the applied voltage to the instantaneous gap [2]. Therefore, one should reduce the gap between the top and bottom electrodes of the CMUT for efficient operation with reduced voltage levels.…”

Investigation and analysis of the influence of excitation signal on radiation characteristics of capacitive micromachined ultrasonic transducer

“…The finite element analysis model can create 2D or 3D finite element models for vibrating films of any complex shape to obtain optimized design parameters by analysis and calculation, which is usually through ANSYS, COMSOL and other professional finite element analysis software. When the CMUT that contains many micro-units takes the finite element analysis model, the calculation process will be very time-consuming, which makes the simulation analysis and optimization design cycle longer (Satir et al 2013). The finite difference model reduces the analysis time through thin plate theory and boundary element method.…”

“…However, the current finite difference model cannot analyze the nonlinearity of CMUT micro-units, and not for large signals as well. Only the small signal linear model can be accurately analyzed (Satir et al 2013).…”