Relation between charge on free electrodes and the response of electrostatic MEMS actuators and sensors

Stability is an important factor in the study of electrostatic MEMS switches and sensors. Their response is significantly improved by either applying a large dc bias or by depositing a prescribed value of charge on the oating electrodes. This charge is related to the pull-in voltages. Measurement of charge without causing loading is recommended; so instead of incorporating any field operated transistor circuitry for this purpose, methods are developed to relate the charge magnitude to the dynamical response of the actuators. Elata et al. developed eficient and reliable ways of charge monitoring without causing loading to the device. These methods rely on energy of the system instead of performing integration in the time domain. Based on their work, this paper examines the alterations in the dynamic response of actuators. The positive and negative pull-in voltages in the voltage displacement plane are symmetrically located with respect to charge on the oating electrode. This fact is exploited to carry out indirect charge measurement from the average of the two pull-in values. A regression scheme is proposed that predicts the charge from the voltage shift based on limited measurements of capacitance of the actuator.