A scaling law approach to rate fabrication tolerances of double-sided electrostatic actuators

Abstract Symmetric double-sided electrostatic actuators in push-pull configuration are particularly suitable for linear actuation with low harmonic distortion. However, their motion still is largely determined by pull-in instabilities that are sensitive to geometry variations. A considerable simulation effort is therefore required when assessing manufacturing tolerances during the design process or determining the optimal operating point. Recently, an accurate method was demonstrated, allowing for the numerically inexpensive and experimentally non-destructive extraction of the full quasi-static performance of a clamped-free beam-like electrostatic micro-mechanical actuator with complex 3D design. The key step was to determine the voltage scaling related to the pull-in voltage based on data collected far away from pull-in conditions. This relates a dimensionless ansatz to the physical input voltages as well as the output like e.g. the actuator's tip deflection. For the chosen approach, however, the relationship between the model and the geometry parameters is unknown. In this paper we extend our method to enable quantifying the impact of geometry parameter variations. In particular, we adapt the model equation for the case of symmetry-breaking tolerances on the basis of few FEM-simulations. The quasi-static pull-in instability, as well as the nonlinear deflection, are consistently reproduced over the full range of relevant combinations of signal and bias voltages. Our analysis was developed in the context of a specific electro-acoustic transducer. However, we find indications that the underlying method is in fact applicable to a much broader range of micro-mechanical actuators.