基于力学描述的MEMS器件行为模拟方法

The Method of Behavioral Simulation Based on Mechanical Description for MEMS Devices

将MEMS悬臂梁在静电驱动下的受力过程映射为悬臂梁自由端(即其纵向最大位移点)的力学描述,从而实现对悬臂梁的直流稳态分析。其基本原理是基于结构的受力分析,以位移为共同变量,引入反馈机制描述耦合过程。首先引入一个合适的挠度形函数,它包含一个表示悬臂梁自由端位移值的参变量,而后以此形函数为基础利用能量原理,推导出悬臂梁自由端所受到的静电吸引力和弹性回复力的解析表达式,运用MATLAB编程的方法计算出悬臂梁在直流电压驱动下的稳态工作点。分析结果与CoventorWare软件模拟结果相比较,证明了该方法的有效性。

The dynamic process of a MEMS cantilever beam is mapped to the mechanical description for the free end, i.e. the point with the maximum longitudinal displacement, and then the DC steady-state analysis for the beam can be carried out. The main idea of the method is to take the displacement for the common variable and implement the coupling process by feedback mechanism, which is based on the mechanical analysis of the MEMS structure. Firstly a proper tentative function of flexibility which contains a parameter representing the free-end displacement is introduced. So the analytical expressions for the electrostatic force and the elastic force of the free end can be obtained by using the energy principle. The steadystate point can be calculated by programming in MATLAB. Simulation from CoventorWare has confirmed the validity of the method.