09-108 Hanno Hammer

Analytical Model for Comb Capacitance Fringe Fields (581K, pdf) Jul 7, 09

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Abstract. Analytical expressions for electric potential and electric fringe fields in regions above the fingers of MEMS (Micro-Electro-Mechanical-System) comb capacitances are derived using potential-theoretic methods. The formulae are valid for 1) a comb geometry exhibiting a large number of identical fingers and 2) a finger geometry where the gap between fingers is small compared to height of fingers and finger overlap. For these conditions, symmetries inherent to the comb geometry can be exploited fruitfully to set up a properly defined Dirichlet problem formulation for the potential which can be solved for explicitly, yielding a series expansion for electrostatic potential and electric field components. The accuracy of approximated analytical solutions, obtained by truncating the series expansions to contain only a finite number of terms, is compared with results obtained from Finite Element simulations of electrostatic potential and electric field. From the analytic result, an approximation to the levitation force acting on the upper finger surfaces is derived. A formula expressing the mean length of fringe electric field lines emanating from upper finger surfaces into the ambient space is presented.

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