静电致动硅膜板的宏模型建立方法

Macro modeling method for electrostatical drive silicon diaphragm

器件宏模型技术是微机电(MEMS)系统设计和系统级仿真的关键技术。为了建立静电致动硅膜板的宏模型,在运用有限元进行模态分析的基础上,利用多变量非线性函数拟合方法,将由数值计算得到的静电器件系统的动能、弹性能和电容写成模态广义坐标表示的解析式,导出以模态坐标表达的器件系统动力学方程,即宏模型。利用该宏模型研究了器件的静态、动态特性,并与有限元计算结果进行比较。结果表明:用模态坐标表达的动态宏模型能够考虑残余应力、大变形、静电力等非线性因素的影响,大大地减少了计算费用,而且具有足够的仿真精度。

The macro modeling method for Micro-electro-mechanical System（MEMS） devices is a key issue in the design and simulation of MEMS system. For establishing the macro model of the nonlinear silicon diaphragm drived by a distributed electrostatic force, a nonlinear function fitting scheme was used to calculate the energy data after finite element analysis for establishing an analytical model of kinetic energy, strain energy and electrostatic co-energy of the system. Then, all these energy functions were represented in the term of general mode coordinates and were subjected into the Lagrange equation to deduce the motion equations of the silicon diaphragm. Thus a macro model was obtained to simulate the quasi-static and dynamic characteristics of the device. By comparing the macro model and the finite element calculating, it concludes that the macro model can capture the quasi-state and dynamic behaviors of the electrostatical drive device quite well. And this modeling method can consider the effects of residual stress and nonlinear geometry and can reduce lots of computational Cost.