Continuation-Based Pull-In and Lift-Off Simulation Algorithms for Microelectromechanical Devices

Abstract

The voltages at which microelectromechanical actuators and sensors become unstable, known as pull-in and lift-off voltages, are critical parameters in microelectromechanical systems (MEMS) design. The state-of-the-art MEMS simulators compute these parameters by simply sweeping the voltage, leading to either excessively large computational cost or to convergence failure near the pull-in or lift-off points. This paper proposes to simulate the behavior at pull-in and lift-off employing two continuation-based algorithms. The first algorithm appropriately adapts standard continuation methods, providing a complete set of static solutions. The second algorithm uses continuation to trace two kinds of curves and generates the sweep-up or sweep-down curves, which can provide more intuition for MEMS designers. The algorithms presented in this paper are robust and suitable for general-purpose industrial MEMS designs. Our algorithms have been implemented in a commercial MEMS/integrated circuits codesign tool, and their effectiveness is validated by comparisons against measurement data and the commercial finite-element/boundary-element (FEM/BEM) solver CoventorWare.