影响三维MEMS结构静电计算精度的因素
Factors Affecting the Precision of Electrostatic Computation of 3D MEMS Structures
摘要：
微机电系统（MEMS）通常具有固定或移动的结构（薄梁的板或阵列），其横截面为微米量级，长度为数十或数百微米量级。静电力在操纵这些器件中起着非常重要的作用，因此，彻底了解这些结构的静电特性是至关重要的。最近，一个接近精确的边界元法（neBEM）求解器已经开发出来，并用于解决各种设备的静电相关的困难问题。由于精确的基础表达式，这个求解器被发现是非常准确的，而解决关键问题，通常需要特殊的配方涉及优雅，但困难的数学。在这项工作中，我们调查的各种可能的近似的效果上获得的MEMS结构的三维静电解决方案。特别是，我们调查的离散化，遗漏的表面上的最终结果，如在不同的表面上的电荷分布或电容的一个给定的MEMS结构的少量的电荷积累的影响。
英文摘要：
Micro-Electro-Mechanical Systems (MEMS) normally have fixed or moving structures (plates or array of thin beams) with cross-sections of the order of microns and lengths of the order of tens or hundreds of microns. Electrostatic forces play a very major role in maneuvering these devices, and hence, a thorough understanding of the electrostatic properties of these structures is of critical importance. Recently, a nearly exact boundary element method (neBEM) solver has been developed and used to solve difficult problems related to electrostatics of various devices. Because of the exact foundation expressions, this solver has been found to be very accurate while solving critical problems which normally necessitate special formulations involving elegant, but difficult mathematics. In this work, we investigate the effects of various possible approximations on the 3D electrostatic solutions obtained for MEMS structures. In particular, we investigate the effects of discretization, omission of surfaces with small amount of charge accumulation on the final results such as the charge distribution on various surfaces or capacitance of a given MEMS structure.
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