Electrophysics of micromechanical comb actuators

A simple approximate theory is developed for the electrostatic forces operating in a micromechanical comb actuator. The comb drive is considered both without (for simplicity) and with an underlying ground plane. The forces are partitioned into local forces (electric fields confined to the cross-sections of the individual comb fingers) and global force corrections (electric fields resulting from effective equipotential sheets representing the engaged and unengaged comb finger regions). The local forces are obtained by applying the principle of virtual work (both engaged and unengaged regions are involved when a ground plane is present beneath the comb fingers). The global forces are obtained from the force between magnetic current filaments introduced to model the electric-potential discontinuities in the effective equipotential sheets of the engaged and unengaged finger regions. Conformal mapping, in addition to a static mode decay approximation, is used to obtain simple and accurate formulas for the local charge per unit length (local forces) and, when a ground plane is present, for the effective sheet potentials (magnetic currents and global forces). The forces in the separated case (which are also global in nature) are also obtained by the principle of virtual work. The results of the paper show that the attractive local forces are independent of engagement distance and the smaller repulsive global forces are inversely proportional to engagement distance. The attractive separated forces are inversely proportional to the separation distance without the ground plane and inversely proportional to the square of the separation distance with the ground plane