A probabilistic design optimization for MEMS tunable capacitors

作者：Shavezipur M^*; Ponnambalam K; Hashemi S M; Khajepour A

来源：Microelectronics Journal, 2008, 39(12): 1528-1533.

DOI：10.1016/j.mejo.2008.03.008

• MEMS capacitors
• Probabilistic design
• Yield optimization
• Fabrication uncertainties

This paper presents a design optimization method for MEMS parallel-plate capacitors under fabrication uncertainties. The objective of the optimization problem is to maximize the production yield considering the fabrication tolerances. The method utilizes aspects of the advanced first-order second-moment (AFOSM) reliability method in probabilistic design to find a linearized feasible region for performance functions and uses an analytical double-bounded-probability distribution DB-PDF) to approximate the distribution of random variables. Then, it attempts to place the tolerance box in such a way that the portions of the box with higher yield lies in the feasible region. The yield is directly estimated using the joint cumulative distribution CDF) over the tolerance box requiring no numerical integration and saving considerable computational complexity for multidimensional problems. For this reason, any arbitrary distribution can be considered for random parameters and the problem is not restricted to normality assumptions. Numerical examples, verified by Monte-Carlo simulations, demonstrate that optimal designs significantly increase the yield. The advantage of the proposed design optimization method is that the yield can be maximized in early design stages without tightening tolerances or increasing the fabrication cost and complexity. The application of the presented method is not limited to tunable capacitors and can be extended to other MEMS devices.

• 出版日期2008-12