Characterization and Modeling of Nonlinearities in In-Plane Gap Closing Electrostatic Energy Harvester

This paper investigates in detail a micro scale in-plane gap closing electrostatic energy harvester with strong nonlinearities in squeeze-film damping, electromechanical coupling, and impacts on end-stops. The device shows softening response on increasing the bias voltage and saturation behavior on impact with end-stops at high enough acceleration amplitude. We demonstrate that a lumped model can adequately describe the measured nonlinear behavior for a range of operating conditions with nonlinear fluid damping force and impact force included in the model. While modeling capacitances, a finite-element method (FEM) is used to analyze fringing field effects on the capacitance variation for gap closing electrodes. The nominal capacitance is obtained from FEM analysis, for a range of under-cut values in the fabrication process treated as a free parameter in the model. The device modeled for linear and nonlinear squeeze-film damping force highlights the importance of nonlinear damping force to understand the device behavior over the range of operating conditions. With the compliant end-stops treated as spring-dampers and with proper choice of end-stop damping-coefficient, the model successfully captures the end-stop nonlinearities for a particular operating point and reproduces the dynamic pull-in phenomena at 8 V bias, and rms acceleration 0.6 g , as observed in the experiments. Thus, the model described in this paper reproduces the subtle nonlinear effects dominating the dynamics of an in-plane gap closing electrostatic energy harvester.