三维MEMS结构静电特性的计算
Computation of Electrostatic Properties of 3D MEMS Structures
摘要：
微机电系统（MEMS）通常具有固定或移动结构，其横截面为微米（$μm$）量级，长度为数十或数百微米量级。这些结构通常是薄梁的板或阵列，由于它们的小，可以通过施加低电压容易地移动或偏转。由于静电力在操纵这些器件中起着非常重要的作用，因此对这些结构的静电特性的透彻理解是至关重要的，特别是在MEMS的设计阶段。在许多情况下，MEMS的静电分析使用边界元法（BEM）进行，而结构分析使用有限元法（FEM）进行。在本文中，我们专注于精确的静电分析的MEMS使用边界元法。特别是，我们考虑的问题，计算的电荷分布和电容的薄导电板相关的MEMS的数值模拟。求解器的准确性背后的原因是它使用了在整个物理域中无缝有效的封闭形式的解析表达式来计算影响系数。因此，它是可能的，以避免边界元法的最严重的近似之一，即，假设分布在一个边界元素的电荷的效果可以近似的电荷位于该元素的质心。与文献中其他结果的比较似乎表明，目前的结果比现有的更准确。
英文摘要：
Micro-Electro-Mechanical Systems (MEMS) normally have fixed or moving structures with cross-sections of the order of microns ($μm$) and lengths of the order of tens or hundreds of microns. These structures are often plates or array of thin beams which, owing to their smallness, can be moved or deflected easily through the application of low voltages. Since electrostatic forces play a very major role in maneuvering these devices, a thorough understanding of the electrostatic properties of these structures is of critical importance, especially in the design phase of MEMS. In many cases, the electrostatic analysis of MEMS is carried out using boundary element method (BEM), while the structural analysis is carried out using finite element method (FEM). In this paper, we focus on accurate electrostatic analysis of MEMS using BEM. In particular, we consider the problem of computing the charge distribution and capacitance of thin conducting plates relevant to the numerical simulation of MEMS. The reason behind the accuracy of the solver is the fact that it uses closed-form analytic expressions that are valid seamlessly throughout the physical domain for computing the influence coefficients. Thus, it is possible to avoid one of the most serious approximations of the BEM, namely, the assumption that the effect of a charge distributed over a boundary element can be approximated by charge located at the centroid of the element. Comparison with other results available in the literature seems to indicate that the present results are more accurate than the existing ones.
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