Modeling is an important step of the MEMS design. The simulation of MEMS components consist of several iteration levels. The physical behavior of 3D continuums is described by partial differential equations which are typically solved by the finite element (FE) method. The FE method allows for interactions among different physical domains to obtain static, modal, frequency and transient responses. From a large-scale 3D multi-physics simulation to reduced order modeling (ROM), one is interested to obtain the model response with respect to design parameters. Such simulations provide full information of the device behavior and lead to MEMS components with optimized performance parameters at system-level. Currently, the parametric model is extracted by series of discrete FE solutions and subsequent interpolation procedures (multivariate polynomial and rational fitting, Gaussian process regression). Especially for a large set of design variables, data sampling and fit become time consuming and prone to errors. In contrast to the data sampling technique, the paper deals with some aspects of the high order derivatives (HOD) analysis for determining the model response. The application of HOD analysis to FE equations as a way to increase the efficiency and robustness was started in the middle of the 1990s [1]. The model response can be expanded in the vicinity of the initial position with regard to dimensional and physical parameters in a single FE run as multivariate Taylor series or its Pade equivalent. The objective of this paper is to demonstrate the implementation process and performance of the HOD FE analysis to parametric simulation of MEMS in the different response domains on the basis of the structural analysis and ROM.
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