Lumped comb drive models found in the literature ignore the electrostatic levitation effect, which decreases their accuracy. The levitation effect occurs when the substrate is within close proximity to the comb drive.
Previously, modeling the levitation effect on a large number of comb drive fingers was limited to finite element analysis (FEA)^1^ and boundary element analysis (BEA)^2^. We use Schwarz-Christoffel mapping (SCM)^3^ based algorithm to quickly and precisely model the levitation effect.
Compared to FEA and BEA, our speed improvement is because the SCM solver does not discretize the boundaries and subdomains into a large number of coupled equations, and our precision improvement is due to SCM’s ability to treat electrostatic forces at vertices exactly.
In current v1.0 simulation tool, we provide a plot showing the relationship between net electrostatic force on the rotor finger versus different levitation positions. The equilibrium levitation position is the intersection between the curve and the levitation position axis (horizontal axis).
(1) W. Tang, M. Lim, and R. Howe, "Electrostatic Comb Drive Levitation And Control Method," ''Journal of Microelectromechanical Systems'', vol. 1, 1992, pp. 170-178.
(2) S. Chyuan, Y. Liao, and J. Chen, "Computational study of the effect of finger width and aspect ratios for the electrostatic levitating force of MEMS combdrive," ''Journal of Microelectromechanical Systems'', vol. 14, 2005, pp. 305-312.
(3)T. A. Driscoll and L. N. Trefethen, Schwarz-Christoffel Mapping, Cambridge University Press, 2002.
We use the MATLAB-based SC Toolbox developed by Prof. Toby Driscoll to solve for the potential distribution in our tool. The toolbox can be downloaded from http://www.math.udel.edu/~driscoll/software/index.html.
F. Li, J. V. Clark, "Improved Modeling of the Comb Drive Levitation Effect", Nanotech 2010, International Conference on Modeling and Simulation of Microsystems, Anaheim CA, June 21-25, 2010
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