Robust design and model validation of nonlinear compliant micromechanisms

Although the use of compliance or elastic flexibility in microelectromechanical systems (MEMS) helps eliminate friction, wear, and backlash, compliant MEMS are known to be sensitive to variations in material properties and feature geometry, resulting in large uncertainties in performance. This paper proposes an approach for design stage uncertainty analysis, model validation, and robust optimization of nonlinear MEMS to account for critical process uncertainties including residual stress, layer thicknesses, edge bias, and material stiffness. A fully compliant bistable micromechanism (FCBM) is used as an example, demonstrating that the approach can be used to handle complex devices involving nonlinear finite element models. The general shape of the force-displacement curve is validated by comparing the uncertainty predictions to measurements obtained from in situ force gauges. A robust design is presented, where simulations show that the estimated force variation at the point of interest may be reduced from ±47 μN to ±3 μN. The reduced sensitivity to process variations is experimentally validated by measuring the second stable position at multiple locations on a wafer.