A Two-Dimensional Electrostatic Model of Interdigitated Comb Drive in Longitudinal Mode

A periodic homogenization model of the electrostatic equation is constructed for a comb drive with a large number of fingers and whose mode of operation is in-plane and longitudinal. The model is obtained in the case where the distance between the rotor and the stator is of an order $\varepsilon ^{α}$, $α\geq 2$, where $\varepsilon$ denotes the period of distribution of the fingers. The model derivation uses the two-scale convergence technique.\ Strong convergences are also established. This allows us to find, after a proper scaling, the limit of the electrostatic force applied to the rotor in the longitudinal direction.