The constituent equations of piezoelectric heterogeneous bimorphs

Abstract

The electromechanical characteristics of a heterogeneous piezoelectric bender subjected to various electrical and mechanical boundary conditions are discussed based on the results of the free bender analysis. The mechanical boundary conditions considered are: a mechanical moment at the end of the bender, a force applied perpendicularly to the tip of the bender, and a uniform load applied over the entire length of the bender. The constituent equations of the bender under these electromechanical influences are derived by calculating the internal energy assuming thermodynamic equilibrium.

Piezoelectric nanoelectromechanical resonators based on aluminum nitride thin films

“…2͑d͒, the displacement on resonance is 0.54 nm at 2 mV drive. Following a detailed numerical analysis of piezoelectrically deflected multilayer cantilevers, 20 we determine the piezoelectric coefficient of the 100 nm AlN layer to be d 31 = 2.4 pm/ V. To complement these measurements, we have also fabricated centimeterscale samples from the same wafer, and independently measured the piezoelectric constant of the AlN layer by means of a setup detailed elsewhere. 21 Such measurements yield d 31 = 2.6 pm/ V, a value consistent with that determined by the NEMS resonance measurements.…”

Study of a piezoelectric multimorph based micro-scanner

“…The following section concerns the calculation of this force. Smits and Choi [3] have presented the constituent equations of piezoelectric heterogeneous bimorphs. These equations, derived from thermodynamic principles, describe the static and dynamic behavior of bimorph structures.…”

“…Several works have been published on modeling of bimorphs or multimorphs, as a device is named when it consists of more than two layers. Smits and Choi [3] presented the constituent equations of piezoelectric heterogeneous bimorphs, deriving the static behavior of bimorph structures from basic thermodynamic principles.…”

Electromechanical theory of microelectromechanical devices

“…Although detailed analyses have been given in literature, we briefly touch on the modeling of a unimorph piezo vibrator, which is often utilized for a micro vibration power generator [18,19]. Fig.…”