Recent developments in miniaturized sensors, digital processors and wireless communication systems have many desirable applications. The realization of these applications however, is limited by the lack of a similarly sized power source. Micro-scale concepts to generate electrical power include devices which use the stored energy in fuels to those which harvest energy from the environment. Many proposed power generation systems employ a piezoelectric component to convert the mechanical energy to electrical energy. Of primary importance is the efficiency of power conversion. In this paper, an exact formula is developed that predicts the power conversion efficiency for a device that contains a piezoelectric component. This formula transparently and quantitatively reveals a trade-off effect on efficiency caused by the quality factor and electromechanical coupling factor of the device. In particular, decreasing the structural stiffness leads to the largest gains in efficiency, followed by decreasing the mechanical damping and increasing the effective mass.

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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.