基于蒙特卡罗法的MEMS测力计不确定性分析

Due to their small size, the performances of microelectromechanical systems (MEMS) are susceptible to uncertainties associated with the micro-fabrication processes; thus, it is necessary to consider these uncertainties during the design stage. By conducting an uncertainty analysis of a typical MEMS force gauge, a load-deflection model was first derived based on the comprehensive elliptic integral solution. The model showed that the force gauge exhibits a nonlinear load-deflection relationship when the deflection surpasses 30 μm. Based on the model, the uncertainty of the force gauge was analyzed using the Monte-Carlo method, by considering the variations of the material and dimensional parameters, and the contributions of the parameters to the uncertainty were analyzed using their sensitivities directly obtained from the linear regression of the Monte-Carlo samples. The results agree well with those presented in Ref.[1], indicating the correctness and effectiveness of the method. The results could be helpful for the robustness design of the force gauge, and provide guidance for improving the micro-fabrication processes. The uncertainty analysis method presented in this work is versatile, easy to use, and does not rely on analytical models; it can thus be applied to the uncertainty analysis of systems whose input-output relations cannot be explicitly formulated.