Computation of capacitance and electrostatic forces for the electrostatically driving actuators considering fringe effects

Many micro-electro-mechanical systems sensors and actuators adopted electrostatically driving structures, whose electrostatic forces or driving voltages should be considered and evaluated based on calculating the capacitance and electrostatic forces of the structures, such as parallel plate capacitors, plate combs and sector combs. Generally, calculation of the capacitance and electrostatic forces are neglecting the fringe effects which would be resulted in the estimation errors of electrostatic forces even the driving voltages, and this could bring forth the failure of the device design. So in this paper, we considered the fringe effects and modified the conventional equations to better estimate the capacitances and the electrostatic forces of the electrostatically driving structures. Through computing and simulation, the results show that the fringe effects could have great effects on the capacitances and electrostatic forces or driving voltages in most situations.