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Capacitance Modeling Tool Using Schwarz-Christoffel Mapping

By Fengyuan (Thomas) Li1, jason clark1

1. Purdue University

Calculate the capacitance between two conductors that may be represented as simply-connected polygonal geometries in 2.5D with Dirichlet boundary conditions

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Version 0.2 - published on 20 Aug 2014

doi:10.4231/D3FX73Z79 cite this

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Abstract

Electrostatic actuation and sensing mechanisms are widely used in various micro-electro-mechanical systems (MEMS) devices. This tool can quickly and accurately calculates the capacitance between two conductors that may be represented as simply-connected polygonal geometries in 2.5D with Dirichlet boundary conditions.

Previously, both analytical and numerical methods are widely used to calculate capacitances for MEMS devices. The accuracy of the analytical methods, such as parallel-plate methods, is not always good. The requirement of the computational time and memory of the numerical methods, such as finite element analysis (FEA), is usually high. We use Schwarz-Christoffel mapping (SCM)-based1 algorithm to quickly and accurately find the capacitance.

In current v0.1, users can define the vertices position of the polygon and two prevertices at Infinite in the ideal parallel-plate domain. The equipotential and electric field lines are shown after the simulation.

(1)T. A. Driscoll and L. N. Trefethen, Schwarz-Christoffel Mapping, Cambridge University Press, 2002.

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We use the MATLAB-based SC Toolbox developed by Prof. Toby Driscoll in our tool. The toolbox can be downloaded from http://www.math.udel.edu/~driscoll/software/index.html.

Publications

F. Li, J. V. Clark, "An Online Electrostatics Modeling Tool for Microdevices with Dirichlet Boundary Conditions by Schwarz-Christoffel Mapping", Nanotech 2010, International Conference on Modeling and Simulation of Microsystems, Anaheim CA, June 21-25, 2010

Cite this work

Researchers should cite this work as follows:

  • Fengyuan (Thomas) Li; jason clark (2014), "Capacitance Modeling Tool Using Schwarz-Christoffel Mapping," http://nanohub.org/resources/capacitancescm. (DOI: 10.4231/D3FX73Z79).

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