静电致动硅膜板的宏模型建立方法

器件宏模型技术是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，在模态有限元分析的基础上，利用多维非线性函数拟合方法，将由数值计算得到的板的动能、弹性能和电容写成以模态广义坐标表示的解析式。导出双模态坐标下的静电微板的动力学特性方程，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比较。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。

Compact modeling method for the electrostatically actuated silicon diaphragm

The compact modeling (or macromodeling) method for the MEMS devices is the key issues in MEMS system design and system level simulations. For constructing the compact modeling of the nonlinear silicon diaphragm actuated by a distributed electrostatic force, a nonlinear function fitting scheme is used after several finite element analysis running, where the energy date are calculated for constructing an analytical model of kinetic energy, strain energy and electrostatic co-energy of the system. Then all theses energy function is represented in the term of general mode coordinates and subjected into the Lagrange Equation to deduce the motion equations of the silicon diaphragm. Thus the macromodel was obtained. After that the macromodel was used to simulate the device’s quasi-static and dynamic characteristics. The simulation results were compared with the results calculated by finite element method. All results show that the compact model can capture the quasi-state and dynamic behaviors of the electrostatically actuated silicon diaphragm quite well. This compact modeling method can consider the effect of residual stress and geometry nonlinear and has a low computational cost.