Reliability-based analysis and design optimization of electrostatically actuated MEMS

This paper studies the feasibility, potential, and limitations of using high fidelity electromechanical simulation for the reliability-based analysis and design optimization of electrostatically actuated Micro-ElectroMechanical Systems (MEMS). A reliability-based analysis and design optimization framework is presented that accounts for stochastic variations in structural parameters and operating conditions. A First-Order Reliability Method (FORM) is embedded into a design optimization procedure by a modular nested loop approach. The steady-state electromechanical problem is described by a three-field formulation and solved by a staggered procedure, coupling a structural finite element model and a finite element discretization of the electrostatic field. The motion of the electrostatic mesh is described by a fictitious elastic structure. The coupled electromechanical design sensitivities and imperfection sensitivities are efficiently evaluated by direct and adjoint approaches. The computational framework is verified by the analysis and optimization of a three-dimensional MEMS device. The appropriateness of the FORM approximation on the non-linear problem is investigated by a comparison with Monte Carlo simulation results. While computationally significantly more expensive than deterministic electromechanical optimization, the example illustrates the importance of accounting for uncertainties and the need for reliability-based optimization methods in the design of MEMS.