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Full-Lagrangian Based Newton Scheme for Dynamic Analysis of Electrostatic MEMS

S.K. De and N.R. Aluru
Beckman Institute for Advanced Science and Technoloy, US

Keywords: MEMS-dynamics, full-Lagrangian analysis, Newton-scheme, comb-drives, second-superharmonic-resonance

A novel physical level simulation method for the dynamic analysis of MEMS based on a full Lagrangian description of both the mechanical and electrical domains and a Newton scheme to obtain a self-consistent solution at any given time instant has been developed. The major advantage of this method is that it allows accurate computation of the inter-domain coupling term (mechanical to electrical) for the Jacobian-matrix of the Newton method which, otherwise, is a very difficult task for the conventional FEM/BEM methods, as both the mechanical and the electrical analysis are done on the un-deformed geometry for this method, making it more robust and efficient. The strong non-linear coupling between the mechanical and the electrical domains often reduces the convergence rate significantly (or even failure of convergence) of the relaxation scheme thereby indicating the need for Newton based methods. The full-Lagrangian approach also eliminates surface re-meshings and surface interpolation function re-computations needed before each electrostatic analysis in the FEM/BEM methods. Un-damped dynamic simulations of several MEMS (comb-drives) have been performed using the method and good experimental agreement observed. Resonant frequency, frequency response curves and sensitivity analysis of these devices is done. Second super harmonic resonance is observed.

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