Efficient Reliability-Based Design Optimization for Microelectromechanical Systems

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The miniaturization of microelectromechanical systems (MEMS) makes cheaper products (due to less chip size consumption) and new applications, e.g., in chip cards, possible. With further miniaturization, however, the influence of manufacturing variances increases: hence it is more and more important to consider them already in the design optimization phase. The widely used Monte Carlo (MC) simulation is not suitable for the implementation in optimization algorithms, as a large number of required samples result in long simulation times. Instead we apply the Sigma-Point approach which enables the accurate calculation of the output variances, even for nonlinear functions with only few sample calculations. In conjunction with a MEMS resonator model the Sigma-Point approach turns out to be four orders of magnitude faster than an equivalent MC calculation. Therefore, it is optimally suited for an efficient reliability-based design optimization (RBDO). Furthermore, the Sigma-Point approach is simple to implement and matrix notation enables fast calculation, even for large models. A versatile analysis of the interaction between <emphasis emphasistype="boldital">optimized sensor design</emphasis>, <emphasis emphasistype="boldital">yield requirements</emphasis>, and <emphasis emphasistype="boldital">manufacturing tolerances</emphasis> is feasible with the suggested RBDO methodology. </para>