The Dual BEM and Its Applications to the Simulation and Modeling of Electronic Devices and MEMS
Date Issued
2004
Date
2004
Author(s)
Chyuan, Shiang-Woei
DOI
zh-TW
Abstract
For electronic devices and MEMS, the calculations of surface charge density and electrostatic force due to electric field are very important, and an accurate electrostatic analysis is essential. For variable designs of electronic devices and MEMS, the BEM has become a better method than the domain-type FEM because BEM can provide a complete solution in terms of boundary values only, with substantial saving in modeling effort. Although the BEM is a widely used computational technique nowadays because of the superiority for infinite boundary and unbounded domain, the influence matrix is rank deficient or ill-conditioned and numerical results become unstable when the degenerate problems with singularity caused by a degenerate scale or a degenerate boundary are encountered. In this dissertation, the dual BEM and some regularization techniques were used to obtain rapid, precise, and efficient solutions for simulating and modeling of electronic devices and MEMS.
In addition to degenerate problem, engineers usually adopt multilayered design for semiconductor and electronic devices, the dual BEM accompanied by subregion technology, instead of tedious calculation of Fourier-Bessel transforms for the spatial Green’s functions, could be used to efficiently simulate the electric effect of diverse ratios of permittivity between arbitrarily multilayered domain and the fringing field around the edge of conductors. Results show that different ratios of permittivity will affect the electric field seriously, and the values of surface charge density on the edge of conductors are much higher than those on the middle part because of fringing effect. In addition, if using the dual BEM to model the fringing field around the edge of conductors, the minimum allowable data of dielectric strength for keeping off dielectric breakdown can be obtained very efficiently.
Since the gap size between combdrive fingers and ground plane or movable finger and fixed finger, the width ratio between movable and fixed fingers, and the aspect ratio between the height and width of fingers, can play very important roles for MEMS performance, the studies of the variations in gap, finger ratio and aspect ratio are indispensable. By way of dual BEM, the less the gaps between combdrive fingers and ground plane are, the larger the levitating force acting on the movable finger is, and the levitating force becomes more predominant as the gaps between movable finger and fixed finger decrease. Besides levitating force, the results from dual BEM also show that the driving force is obviously dependent on traveled distance, and the approximate method can’t work well for all traveled positions because there is an apparent error, especially at the beginning and ends of the range of travel. In addition, the smaller the gap between movable and fixed fingers is, the larger the driving force is, and the error of approximate method also becomes more and more predominant as the gap decreases.
Subjects
對偶邊界元素法
微機電
電子元件
電磁
dual BEM
electromagnetics
MEMS
electronic device
Type
thesis
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