用neBEM求解器计算梳齿传动的三维静电特性
Use of the neBEM solver to Compute the 3D Electrostatic Properties of Comb Drives
摘要：
微机电系统（MEMS）梳状驱动器被用作传感器和致动器两者。因此，它们在MEMS技术中被认为是非常重要的，并且在过去的几年中一直处于紧张的研究之中。致动和灵敏度都主要取决于梳状结构的静电配置。因此，梳齿驱动器的静电配置的准确估计是至关重要的设计和解释阶段。近精确边界元法（neBEM）求解器是近年来发展起来的，并成功地用于解决与静电有关的难题。该求解器采用精确的解析表达式计算奇异性分布的影响，而不是采用传统的和方便的近似节点电荷浓度。由于精确的基础表达式，求解器已被发现是非常准确的完整的物理域，包括近场。在这项工作中，我们探讨了使用neBEM求解器来解决三维静电梳状驱动器相关的问题的可能性。特别是，我们调查之间的关系实现的准确性和计算费用所产生的一个现实的梳状驱动器的几何形状。在此过程中，我们估计了梳状结构的电荷密度分布、电势分布和电容。这项研究使我们得出这样的结论，即neBEM求解器可以在合理的计算开销下对所有感兴趣的属性进行非常准确的估计。
英文摘要：
Micro-Electro-Mechanical Systems (MEMS) comb drives are used for both as sensors and actuators. As a result, they have been considered to be very important in MEMS technology and has been under intense study for last few years. The actuation and the sensitivity are both dependent in a major way on the electrostatic configuration of the comb structure. As a result, accurate estimation of the electrostatic configuration of comb drives is crucial in both design and interpretation phases. The nearly exact Boundary Element Method (neBEM) solver has been developed recently and used successfully to solve difficult problems related to electrostatics. This solver uses exact analytic expression for computing the influence of singularity distributions instead of adopting the conventional and convenient approximation of nodal concentration of charges. Due to the exact foundation expressions, the solver has been found to be exceptionally accurate in the complete physical domain, including the near field. In this work, we explore the possibility of using the neBEM solver to solve 3D electrostatic problems related to comb drives. In particular, we investigate the relationship between the accuracy achieved and the computational expenses incurred for a realistic comb drive geometry. In the process, we estimate the charge density distribution, potential distribution and the capacitance of the comb structure. The study has led us to the conclusion that the neBEM solver can yield very accurate estimates of all the properties of interest at a reasonable computational expenditure.
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