Analytical model for MEMS electret energy harvester with long-stroke tip-sliding electrodes

Abstract

We develop an equivalent circuit model for a MEMS vibrational energy harvester that uses electrets or permanent electrical charges to generate electrostatic induction currents from mechanical vibrations. An electrode pair of periodically arranged comblike fingers is electrically biased by the built-in potential of an electret, and the distribution of electrostatically induced charges is altered by the relative mechanical motion of the electrodes. The electrostatic force as well as the induction charges are described as a function of the boundary condition and implemented into a multiphysics equivalent-circuit model by using the nonlinear current sources of the simulation software LTspice. As a practical solution for avoiding computational error, we have eliminated the use of polygonal approximations for the conditional analytical model and newly introduced a geometrical modulation function based on sigmoidal functions, by which the analytical model has become mathematically smooth and twice-differentiable with respect to the displacement. The short-circuit waveforms of vibrational energy harvesting are reproduced by simulation and are in good agreement with the experimental results.