A conformal mapping based approach for fast two-dimensional FEM electrostatic analysis of MEMS devices without re-meshing

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, 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. With the reference domain defined to be the device geometry in the absence of electrostatic actuation, we eliminate the need for repeated finite element meshing. We achieve this by mapping the deformed electrostatic domain in which the electrostatic problem must be solved to the reference undeformed domain 'conformally'. A'conformal' map preserves the form of the Laplace equation and the boundary conditions; thus, the finite element matrix for the electrostatic problem is solved only once in the reference undeformed electrostatic domain. The conformal map itself is generated through the solution of the same Laplace equation on the reference undeformed domain 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 two 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 from ANSYS.

Original languageEnglish (US)
Title of host publication2009 10th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2009
DOIs
StatePublished - Jul 21 2009
Event2009 10th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2009 - Delft, Netherlands
Duration: Apr 26 2009Apr 29 2009

Publication series

Name2009 10th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2009

Other

Other2009 10th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2009
CountryNetherlands
CityDelft
Period4/26/094/29/09

Fingerprint

Conformal mapping
MEMS
Electrostatics
Finite element method
Laplace equation
Geometry
Boundary conditions

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Control and Systems Engineering
  • Electrical and Electronic Engineering
  • Industrial and Manufacturing Engineering

Cite this

Sumant, P. S., Cangellaris, A. C., & Aluru, N. R. (2009). A conformal mapping based approach for fast two-dimensional FEM electrostatic analysis of MEMS devices without re-meshing. In 2009 10th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2009 [4938407] (2009 10th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2009). https://doi.org/10.1109/ESIME.2009.4938407

A conformal mapping based approach for fast two-dimensional FEM electrostatic analysis of MEMS devices without re-meshing. / Sumant, Prasad S.; Cangellaris, Andreas C; Aluru, Narayana R.

2009 10th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2009. 2009. 4938407 (2009 10th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2009).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Sumant, PS, Cangellaris, AC & Aluru, NR 2009, A conformal mapping based approach for fast two-dimensional FEM electrostatic analysis of MEMS devices without re-meshing. in 2009 10th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2009., 4938407, 2009 10th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2009, 2009 10th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2009, Delft, Netherlands, 4/26/09. https://doi.org/10.1109/ESIME.2009.4938407
Sumant PS, Cangellaris AC, Aluru NR. A conformal mapping based approach for fast two-dimensional FEM electrostatic analysis of MEMS devices without re-meshing. In 2009 10th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2009. 2009. 4938407. (2009 10th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2009). https://doi.org/10.1109/ESIME.2009.4938407
Sumant, Prasad S. ; Cangellaris, Andreas C ; Aluru, Narayana R. / A conformal mapping based approach for fast two-dimensional FEM electrostatic analysis of MEMS devices without re-meshing. 2009 10th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2009. 2009. (2009 10th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2009).
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