Elasto-Electrostatic Analysis of Circular Microplates Used in Capacitive Micromachined Ultrasonic Transducers

Abstract

The active structural component of a capacitive micromachined ultrasonic transducer (CMUT) is the top plate which vibrates under the influence of a time-varying electrostatic force thereby producing ultrasound waves of the desired frequency in the surrounding medium. Analysis of MEMS devices which rely on electrostatic actuation is complicated due to the fact that the structural deformations alter the electrostatic forces, which redistribute and modify the applied loads. Hence, it becomes imperative to consider the electrostatics-structure coupling aspect in the design of these devices. This paper presents an approximate analytical solution for the static deflection of a thin, clamped circular plate caused by electrostatic forces which are inherently nonlinear. Traditionally, finite element simulations using some commercial software such as ANSYS are employed to determine the structural deflections caused by electrostatic forces. Since the structural deformation alters the electrostatic field, a coupled-field simulation is required wherein the electrostatic mesh is continuously updated to coincide with the deflection of the structure. Such simulations are extremely time consuming, in addition to being nontransparent and somewhat hard to implement. We employ the classical thin-plate theory which is adequate when the ratio of the diameter to thickness of the plate is very large, a situation commonly prevalent in many MEMS devices, especially the CMUTs. We solve the thin-plate electrostatic-elastic equation using the Galerkin-weighted residual technique, under the assumption that the deflections are small in comparison to the thickness of the plate. The evaluation of the electrostatic force between the two plates is simplified due to the fact that the electrostatic gap is much smaller than the lateral dimensions of the device. The results obtained are compared to those found from ANSYS simulations and an excellent agreement is observed between the two. The pull-in voltage predicted by our model is close to the value predicted by ANSYS simulations.Index Terms-Capacitive micromachined ultrasonic transducer (CMUT), capacitive sensors, electrostatic forces, MEMS, pull-in voltage, thin plate, ultrasonic transducers.

An investigation of the static and dynamic behavior of electrically actuated rectangular microplates

“…Our choice of a constant value of Q means that we assumed negligible effect of squeeze-film damping, which reasonable assumption is assuming that the microplate is placed inside a vacuum chamber and is operated at reduced pressure. Otherwise, squeeze-film damping can have strong effect on the dynamics of microplates and needs to be modeled using Reynolds equation and a structural-fluidic model [24,26]. Figure 7 shows the maximum non-dimensional deflection max W at the center of the microplate against the non-dimensional frequency.…”

“…The axisymmetric natural frequencies of the plate were determined. Ahmad and Pratap [24] investigated the static response of a clamped circular plate under electrostatic load using the Galerkin method. Bertarelli et al [25] investigated a circular diaphragm micropump under electric actuation using a one degree-of-freedom analytical model and a finite element model.…”

A Simple Fabrication Process Based on Micro-masonry for the Realization of Nanoplate Resonators with Integrated Actuation and Detection Schemes

“…The normalized mechanical displacement and the normalized output charge for one of the cavities is shown in Figure 6 as a function of Vdc1 (empty and filled red circles, respectively). While in general, the amplitude of the circular plate capacitor is a nonlinear function of Vdc1 (Ahmad and Pratap, 2010), the displacement of the device is small enough so that the experimentally measured amplitude is observed to be linear up to a DC bias value of 3.5 V. However, the output charge is observed to vary with the square of Vdc1. Looking back into Eq.…”

Capacitive micromachined ultrasonic transducer for ultra-low pressure measurement: Theoretical study

“…Owing to the axisymmetry of the CMUT structure and the applied load, a 2D-axisymmetrical model was constructed to reduce computational time, which has the same accuracy as a full 3D model. 12,16 As shown in the 2D model (Fig. 2), the membrane of the CMUT was constructed using axisymmetric plane elements (PLANE42), and the edge of the membrane was fixed.…”