×

A conformal mapping-based approach for fast two-dimensional FEM electrostatic analysis of MEMS devices. (English) Zbl 1211.78031

Summary: A methodology is proposed for expediting the coupled electro-mechanical two-dimensional finite element modeling of electrostatically actuated MEMS. The proposed methodology eliminates the need for repeated finite element meshing and subsequent electrostatic modeling of the device during mechanical deformation. We achieve this by mapping the deformed electrostatic domain to the reference undeformed domain ‘conformally’. A ‘conformal’ map preserves the form of the Laplace equation and the boundary conditions; thus the electrostatic problem is solved only once in the undeformed electrostatic domain. The conformal map itself is generated through the solution of the same Laplace equation on the undeformed geometry and with displacement boundary conditions dictated by the movement of the mechanical domain. The proposed methodology is demonstrated through its application to the modeling of three MEMS devices with varying length-to-gap ratios, multiple dielectrics and complicated geometries. The accuracy of the proposed methodology is confirmed through comparisons of its results with results obtained using the conventional finite element solution.

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
78A30 Electro- and magnetostatics
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Yao, RF MEMS from a device perspective, Journal of Micromechanics and Microengineering 10 pp 9– (2000)
[2] Tillmans, MEMS for wireless communications: ’from RF-MEMS components to RF-MEMS-SIP’, Journal of Micromechanics and Microengineering 13 pp 139– (2003)
[3] Varadan, RF MEMS and Their Applications (2003)
[4] van Spengen, A comprehensive model to predict the charging and reliability of capacitive RF MEMS switches, Journal of Micromechanics and Microengineering 14 pp 514– (2004)
[5] Senturia, A computer-aided design system for microelectromechanical systems (MEMCAD), Journal of Microelectromechanical systems 1 pp 3– (1992)
[6] Nabors, FastCap: a multi-pole accelerated 3-D capacitance extraction program, IEEE Transactions on Computer-Aided Design 10 pp 1447– (1991) · Zbl 05449149
[7] Jin, The Finite Element Method in Electromagnetics (2002) · Zbl 1001.78001
[8] Li, Hybrid techniques for electrostatic analysis of nanoelectromechanical systems, Journal of Applied Physics 96 pp 2221– (2004)
[9] De, Full-Lagrangian schemes for dynamic analysis of electrostatic MEMS, Journal of Microelectromechanical Systems 13 pp 737– (2004)
[10] Li, A Lagrangian approach for electrostatic analysis of deformable conductors, Journal of Microelectromechanical systems 11 pp 245– (2002)
[11] Soma, Meshing approach in non-linear FEM analysis of microstructures under electrostatic loads, Proceedings of SPIE 4408 pp 216– (2001)
[12] Chiandussi, A simple method for automatic update of finite element meshes, Communications in Numerical Methods in Engineering 16 pp 1– (2000) · Zbl 0960.74060
[13] Zhulin V Owen S Ostergaard D Finite element based electrostatic-structural coupled analysis with automated mesh morphing 501 504
[14] Fusco, FDTD algorithm in curvilinear coordinates, IEEE Transactions on Antennas and Propagation 38 (1) pp 76– (1990)
[15] Jurgens, Finite-difference time-domain modeling of curved surfaces, IEEE Transactions on Antennas and Propagation 40 (4) pp 357– (1992)
[16] Pan, 2D FDTD modelling of objects with curved boundaries, using embedded boundary orthogonal grids, IEE Proceedings on Microwaves, Antennas and Propagation 147 (5) pp 399– (2000)
[17] Jeffrey, Complex Analysis and Applications (2006)
[18] Hamad, An improved two-dimensional coupled electrostatic-mechanical model for RF MEMS switches, Journal of Micromechanics and Microengineering 16 pp 1424– (2006)
[19] Zhang, A study of the static characteristics of a torsion micromirror, Sensors and Actuators A 90 pp 73– (2001)
[20] Buhler, Electrostatic Aluminum micromirrors using double-pass metallization, Journal of Microelectromechanical systems 6 (2) pp 126– (1997)
[21] Degani, Pull-in study of an electrostatic torsion microactuator, Journal of Microelectromechanical systems 7 (4) pp 373– (1998)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.