Process variation analysis for MEMS design
Luca Schenato, Wei‐Chung Wu, Laurent El Ghaoui, Kristofer S. J. Pister · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2001
Process variations, incurred during the fabrication stage of MEMS structures, may lead to substantially different performance than the nominal one. This is mainly due to the small variation of the geometry of the structure with respect to the ideal design. In this paper we propose an approach to estimate performance variations for general planar suspended MEMS structure for low frequency applications. This approach is based on two complementary techniques, one probabilistic and the other deterministic. The former technique, based on the Monte-Carlo method, defines a random distribution on the geometric variables and evaluates the possible outcome performance by sampling that distribution. The latter technique, based on robust optimization and semidefinite programming (SDP) approximations \cite{EOL:98}, finds bounds on performance parameters given the bounds on the geometric variables, i.e. it considers the worst case scenario. Both techniques have been integrated with SUGAR, a simulation tool for MEMS devices available to the public \cite{Zhou98} \cite{Sito}, and tested on different types of folded springs.