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

Abstract

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