Computational approaches, opportunities and challenges in reduced order modelling based on mode superposition method of the coupled electrostaticstructural domains, including effective model generation and geometrical parameterization, as well as physical and system design of MEMS component are presented and discussed.
IntroductionThe growth in the MEMS industry in the past ten years has led to the necessity of standardization of the MEMS models and design tools. The goal of MEMS compact modeling is to create a black-box model with interface input/output ports and internal state variables what can be analyzed within reasonable time and almost the same accuracy as obtained from full finite element (FE) models. In the year 2002, ANSYS, Inc. shipped the ANSYS Multiphysics software product (Release 7.0) with first version of the reduced order modeling (ROM) tool for the coupled electrostaticstructural domains. The ANSYS ROM [1] tool has been developed as an extension of mode superposition method to the coupled electrostatic-structural domains. It describes the dynamic behaviour of electomechanical flexible component as a system of second order ordinary differential equations (ODE). The number of degrees of freedom of this system is equal to the number of chosen modes. Nowadays, the ANSYS ROM tool has become the industry standard for macromodels extracting of MEMS components [2-4]. The MEMS suppliers like IC ones can provide model libraries for their electromechanical components.The ROM macromodels capture the complex nonlinear dynamics inherent in MEMS due to highly nonlinear electrostatic forces, residual stresses, stress stiffening and supports multiple electrode systems and mechanical contact phenomena. Geometrical nonlinearities, such as stress stiffening, can be taken into account if the modal stiffness is computed from the second derivatives of the strain energy with respect to modal coordinates. The ROM technology based on mode superposition method is very effective technique for fast transient simulation of MEMS component and for export macromodels to external system simulators. The most common simulation tools at system level are signal flow graphs system Simulink ® ; PSPICE circuit simulators and VHDL-AMS, VERILOG-AMS simulators. The extracted macromodel can be automatically export to VHDL-AMS language. The description of ROM macromodels in PSPICE is presented in [5].