https://www.bnjohnson.webs.com/biosensing_review.pdf

Biosensing using dynamic-mode cantilever sensors: a review.

The aim of this paper is the modelling of a non-symmetric bimorph constituted by a piezoelectric material deposited on an alumina substrate and used either as an actuator or a sensor. Theoretical modelling based on the flexural modes of the structure is carried out and the influence of the electrode characteristics (geometrical dimensions and elastic parameters) is introduced in the modelling for calculating the bimorph bending displacement. In actuator mode, the electrical admittance of the cantilever non-symmetric bimorph is stated and the intrinsic electromechanical coupling factor linked to the bimorph bending motion is deduced and compared with that defined in IEEE Standards. The analytical modelling was used for characterizing a cantilever bimorph constituted by a piezoelectric thick film deposited on an alumina substrate. A trial and error fitting method is described for determining the elastic, piezoelectric and dielectric constants of the piezoelectric material. The influence of the electrode parameters is calculated and the measurement uncertainty is deduced. In sensor mode the open voltage delivered by the bent piezoelectric layer and the electrical equivalent circuit of the bimorph are given. Theoretical results are compared with those obtained by the finite element method, and discussed.

https://iopscience.iop.org/article/10.1088/0960-1317/13/6/306/pdf

Modelling of a cantilever non-symmetric piezoelectric bimorph

An optical, mirror system has been built using MEMS techniques while employing lead zirconate titanate (PZT) thin films as strong piezoelectric material. The system consists of two parallel silicon cantilever beams, on which the PZT was deposited, which were arranged to project inward from a common frame. The beams were laterally offset over a distance appropriate to fit a mirror between them. One end of each beam is fixed to the frame, while the other end is attached to a sideways projected bar, directed to the other beam. To each sideways bar a connector, parallel to the original beam, pointing toward the frame, was attached. Between both connectors a mirror was attached. The application of voltage across the electrodes on top and below the PZT causes the beams to bend as a monomorph, and the mirror between the beams to rotate around an axis through its center. A variety of thicknesses have been chosen to fabricate these devices. The mirror angle at a given voltage is inversely proportional to the square of the beam thickness, while the bandwidth is proportional to the thickness. Beams with thickness of 5 ?m were used to achieve optical angles in static mode of up to 40? using voltages up to 13 V. In that case a bandwidth of around 700 Hz was observed. In resonance optical angles of 10? with a driving voltage as low as 100 mV were achieved. For devices with 30 ?m thick beams, optical angles of up to 30? were observed in resonance at 17.4 kHz at driving voltages of around 6 V. Due to the proprietary design a figure of merit which may be defined as a product of the resonance frequency and optical angle, is much higher than one of the other PZT scanners.

https://iopscience.iop.org/article/10.1088/0960-1317/15/6/021/pdf

Microelectromechanical flexure PZT actuated optical scanner: static and resonance behavior

In this work, an analytical model, a finite element analysis and measured results for a planar, parallel and symmetrical piezoelectric bimorph structure are presented. The bimorph consists of two rectangular piezoelectric strips that are connected back-to-back on a thin metallic centre electrode. The bimorph is intended to be used as a millinewton range force sensor with dynamic excitation. The bimorph is modelled with a static, analytical expression for generated charge, voltage, displacement and force that correspond to the deflection of a freely oscillating piezoelectric bimorph. Also, a case where the movement of the bimorph is blocked is analyzed. A circuit that is used to actuate the bimorph is presented, as well as the measured results from the actuator and the sensor side of the bimorph in both free oscillation and blocked cases. The measurement results show a reasonably good agreement with the analytical model and very good agreement with the FEM model. Force sensor setup and a way to measure the force inflicted on the bimorph are also presented, as well as the force response of the bimorph against a commercial piezoresistive force sensor.

Piezoelectric bimorph charge mode force sensor

The paper deals with the mechanical behavior of a micro-beam bonded with two piezoelectric layers. The micro-beam is suspended over a fixed substrate and undergoes the both piezoelectric and electrostatic actuation. The piezoelectric layers are poled through the thickness and equipped with surface electrodes. The equation governing the micro-beam deflection under electrostatic pressure is derived according to Euler-Bernoulli beam theory and considering the voltage applied to the piezoelectric layers and Maxwell’s equations for the two dimensional electric potential distribution. The obtained nonlinear equation solved by step by step linearization method and Galerkin weighted residual method. The effects of the electric potential distribution and the ratio of the piezoelectric layer thickness respect to the elastic layer thickness on the mechanical behavior of the micro-beam are investigated. The obtained results are compared with the results of a model in which electric potential distribution is not considered. © 2012 IAU, Arak Branch. All rights reserved.

http://journals.iau.ir/article_514466_909c9b95e7de966d395527c31ab732b0.pdf

Effect of Electric Potential Distribution on Electromechanical Behavior of a Piezoelectrically Sandwiched Micro-Beam

The dynamic behavior of a bimorph clamped at one end and constrained by a linear spring at the other end was studied. The fundamental resonance frequency of the bimorph increased by an amount related to the spring stiffness when compared to the case where the end was free. Therefore, a cantilever bimorph provides a technique to assess the stiffness of a material by a simple measurement of the resonant frequency. Since the bimorph behavior is determined in part by its geometry, the device can be designed for mechanical measurement of microscopic systems such as living cells.

Determining spring stiffness by the resonance frequency of cantilevered piezoelectric bimorphs

The dynamic behavior of homogeneous, elastic piezoelectric bimorphs clamped at one end were determined in the case where the tip of the other end of the bimorph was constrained by a Hookean spring of stiffness k. It was found that the frequency at which the bimorph resonated increased by an amount related to k when compared to the case where the end was free. Therefore, a cantilever bimorph provides a technique to assess stiffness of a material by a simple measurement of the resonant frequency. Since the bimorph behavior scales with its geometry, the device can be designed specifically for mechanical measurement of microscopic systems such as living cells and molecules.

D. Stamenovic

Papers

Determining spring stiffness by the resonance frequency of cantilevered piezoelectric bimorphs

Determining material stiffness using piezoelectric bimorphs