Online Capacitance Modeling Tool for Conductors Represented as Simply-Connected Polygonal Geometries in 2D


We present an online tool for calculating the capacitance between two conductors represented as simply-connected polygonal geometries in 2D with Dirichlet boundaries and homogeneous dielectric. Our tool can be used to model the so-called 2.5D geometries, where the 3rd dimension can be extruded out of plane. Micro-electro-mechanical systems (MEMS) with significant facing surfaces may be approximated with 2.5D geometry. Our tool compares favorably in accuracy and speed to the finite element method (FEM). We achieve modeling accuracy by treating the corners exactly with a Schwarz-Christoffel mapping. And we achieve fast results by not needing to discretize boundaries and subdomains. As a test case, we model a MEMS torsional actuator. Our tool computes capacitance about 1000 times faster than FEM with 4.7% relative error.

Share and Cite:

F. Li and J. V. Clark, "Online Capacitance Modeling Tool for Conductors Represented as Simply-Connected Polygonal Geometries in 2D," Journal of Sensor Technology, Vol. 2 No. 3, 2012, pp. 155-163. doi: 10.4236/jst.2012.23022.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] V. Kempe, “Inertial MEMS: Principles and Practice,” Cambridge University Press, Cambridge, 2011. doi:10.1017/CBO9780511933899
[2] V. Kaajakari, “Practical MEMS: Analysis and Design of Microsystems, MEMS Sensors, Electronics, Actuators, RF MEMS, Optical MEMS, and Microfluidic Systems,” Small Gear Publishing, Las Vegas, 2009.
[3] J. Cheng, J. Zhe and X. Wu, “Analytical and Finite Element Model Pull-In Study of Rigid and Deformable Electrostatic Microactuators,” Journal of Micromechanics and Microengineering, Vol. 14, No. 1, 2004, pp. 57-68. doi:10.1088/0960-1317/14/1/308
[4] P. S. Sumant, A. C. Cangellaris and N. R. Aluru, “A Conformal Mapping-Based Approach for Fast Two-Dimensional FEM Electrostatic Analysis of MEMS Devices,” International Journal of Numerical Modeling: Electronic Networks, Devices and Fields, Vol. 24, No. 2, 2011, pp. 194-206.
[5] K. Nabors and J. White, “FastCap: A Multipole Accelerated 3-D Capacitance Extraction Program,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 10, No. 11, 1991, pp. 1447-1459. doi:10.1109/43.97624
[6] G. Li and N. Aluru, “A Lagrangian Approach for Quantum-Mechanical Electrostatic Analysis of Deformable Silicon Nanostructures,” Engineering Analysis with Boundary Elements, Vol. 30, No. 11, 2006, pp. 925-939. doi:10.1016/j.enganabound.2006.03.012
[7] P. Bruschi, A. Nannini, F. Pieri, G. Raffa, B. Vigna and S. Zerbini, “Electrostatic Analysis of a Comb-Finger Actuator with Schwarz–Christoffel Conformal Mapping,” Sensors and Actuators A: Physical, Vol. 113, No. 1, 2004, pp. 106-117. doi:10.1016/j.sna.2004.02.038
[8] S. He and R. B. Mrad, “Design, Modeling, and Demonstration of a MEMS Repulsive-Force Out-Of-Plane Electrostatic Micro Actuator,” Journal of Microelectromechanical Systems, Vol. 17, No. 3, 2008, pp. 532-547. doi:10.1109/JMEMS.2008.921710
[9] W. A. Johnson and L. K. Warne, “Electrophysics of Micromechanical Comb Actuators,” Journal of Microelectromechanical Systems, Vol. 4, No. 1, 1995, pp. 49-59. doi:10.1109/84.365370
[10] J.-L. A. Yeh, C.-Y. Hui and N. C. Tien, “Electrostatic Model for an Asymmetric Combdrive,” Journal of Microelectromechanical System, Vol. 9, No. 1, 2000, pp. 126-135. doi:10.1109/84.825787
[11] J. V. Clark, “Electro Micro Metrology,” Ph. D. Thesis, University of California, Berkeley, 2005.
[12] T. A. Driscoll and L. N. Trefethen, “Schwarz-Christoffel Mapping,” Cambridge University Press, Cambridge, 2002. doi:10.1017/CBO9780511546808
[13] F. Li and J. V. Clark, “An Online Capacitance Modeling Tool for Conductors that May Be Represented as Simply-Connected Polygonal Geometries in 2.5D,” Nanotech Conference & Exposition, Anaheim, 21-24 June 2010, pp. 557-600.
[14] A. Jeffrey, “Complex Analysis and Applications,” 2nd Edition, Chapman & Hall, Boca Raton, 2006.
[15] D. James, “Chipworks inside TI’s DLP Chip,” EE Times Asia, 2006.
[16] J. Kim, H. Choo, L. Lin and R. S. Muller, “Microfabricated Torsional Actuators Using Self-Aligned Plastic Deformation of Silicon,” Journal of Microelectromechanical Systems, Vol. 15, No. 3, 2006, pp. 553-562. doi:10.1109/JMEMS.2006.876789
[17] D. Hah, E. Yoon and S. Hong, “A Low-Voltage Actuated Micromachined Microwave Switch Using Torsion Springs and Leverage,” IEEE Transactions on Microwave Theory and Techniques, Vol. 48, No. 12, 2000, pp. 2540-2545. doi:10.1109/22.899010
[18] V. P. Jaecklin, C. Linder, N. F. de Rooij, J.-M. Moret and R. Vuilleumier, “Line-Addressable Torsional Micromirrors for Light Modulator Arrays,” Sensors and Actuators A: Physical, Vol. 41, No. 1-3, 1994, pp. 324-329. doi:10.1016/0924-4247(94)80131-2

Copyright © 2022 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.