Optimization of electromechanical coupling for a thin-film PZT membrane: I. Modeling

Abstract

In this two-part paper, the optimization of the electromechanical coupling coefficient for thin-film piezoelectric devices is investigated both analytically and experimentally. The electromechanical coupling coefficient is crucial to the performance of piezoelectric energy conversion devices. A membrane-type geometry is chosen for the study. In part I a one-dimensional model is developed for a membrane composed of two layers, a passive elastic material and a piezoelectric material. The lumped-parameter model is then used to explore the effect of design and process parameters, such as residual stress, substrate thickness, piezoelectric thickness and electrode coverage, on the electromechanical coupling coefficient. The model shows that the residual stress has the most substantial effect on the electromechanical coupling coefficient. For a given substrate material and thickness an optimum piezoelectric thickness can be found to achieve the maximum coupling coefficient. The substrate stiffness affects the magnitude of the maximum coupling coefficient that can be obtained. Electrode coverage was found to be important to electromechanical coupling. The model predicts an optimum electrode coverage of 42% of the membrane area. The model developed in part I formed the basis for the parameters studied experimentally in part II.

Efficiency of energy conversion for a piezoelectric power harvesting system

“…It is shown that the efficiency depends on the normalized resistance r, the frequency ratio and, in particular, the relative magnitudes of the electromechanical coupling coefficient k 2 e and the mechanical damping ratio ζ m . In general, high energy conversion efficiency can be achieved with large k 2 e ζm ; the improvement of the coupling coefficient k 2 e for micromachined piezoelectric membrane harvesters has been recently investigated by Cho et al [35,36]. The induced damping added to the system due to the removal of mechanical energy from the vibrating structure is obtained based on the derived formula of conversion efficiency.…”

“…In general, the conversion efficiency can be improved with a larger coupling coefficient and smaller damping. Recently, Cho et al [35,36] performed a series of experiments and proposed a set of design guidelines for the performance optimization of micromachined piezoelectric membrane generators by enhancing the electromechanical coupling coefficient.…”

Experiment and simulation validated analytical equivalent circuit model for piezoelectric micromachined ultrasonic transducers

“…Some work has begun to address the analytical model gap by focusing on the development of plate theory based electromechanical models [1], [3], [13], [22]- [28]. In [3], [22], explicit analytical equations for effective electromechanical coupling k 2 ef f are defined based on material constants and geometric parameters enabling optimized design for high k 2 ef f .…”

“…In [3], [22], explicit analytical equations for effective electromechanical coupling k 2 ef f are defined based on material constants and geometric parameters enabling optimized design for high k 2 ef f . More comprehensive approaches [1], [13], [23]- [27] expand model capabilities to include definitions of lumped mechanical and electrical impedance parameters of the Mason equivalent circuit.…”

MEMS Technologies for Energy Harvesting

“…The interdigitated electrode, IDE, configuration presented by Jeon et al at [66] and Park et al at [87] enables to employ the 33 mode and discards the bottom electrode layer, Figure 30. Therefore, the electrode lengths and shapes are important parameters that affect the output voltage due to the non uniformity of the strain along the beam [88]. Kim et al have fabricated and compared piezoelectric energy harvesters based on d 31 and d 33 modes [89].…”