Fabrication uncertainties and yield optimization in MEMS tunable capacitors

Intrinsic uncertainties of MEMS fabrication processes can severely affect the performance of devices because the tolerance ranges of these processes are relatively large and improvement of process accuracy is very expensive. Therefore, the analysis of fabrication uncertainties and their outcome on a device performance is a vital task before finalizing the design. In this paper, the effects of process inaccuracy on the performance of MEMS tunable capacitors are studied. Design parameters such as dimensions of electrodes and the initial gap between them and the stiffness of supporting beams are considered as random variables. The variation of these parameters within tolerance ranges drastically alters the capacitor's actual response from the desired one and results in low yield. Hence, design optimization with the objective of maximizing yield in early steps becomes very important. An effective method for yield optimization of MEMS capacitors under given fabrication uncertainties is introduced. The method utilizes aspects of the advanced first-order second-moment (AFOSM) reliability method to find a linearized feasible region to estimate the yield. The yield is calculated directly using the joint cumulative distribution function (CDF) over the tolerance box requiring no numerical integration and avoiding computational complexity. The optimal design verified by Monte-Carlo (M-C) simulation exhibits a significant increase in the yield. The main advantage of this method comparing to other design optimization methods is that the proposed method does not change the design topology or fabrication accuracy. It increases the yield by finding the optimum design variables as demonstrated in this paper.