Hanno Hammer
Analytical Model for Comb Capacitance Fringe Fields
(581K, pdf)
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.