Finite element analysis of the vertical levitation force in an electrostatic MEMS comb drive actuator

A vertical levitation electrostatic comb drive actuator was manufactured for the purpose of measuring piezoelectric coefficients in small-scale materials and devices. Previous modelling work on comb drive levitation has focussed on control of the levitation in standard poly-silicon devices in order to minimize effects on lateral modes of operation required for the accelerometer and gyroscope applications. The actuator developed in this study was manufactured using a 20 μm electroplated Ni process with a 25 μm trench created beneath the released structure through chemical wet etching. A finite element analysis using ZINC was used to model electrostatic potential around a cross section of one static and one movable electrode, from which the net levitation force per unit electrode was calculated. The model was first verified using the electrode geometry from previously studied systems, and then used to study the variation of force as a function of decreasing substrate-electrode distance. With the top electrode surfaces collinear the calculated force density is 0.00651 ε₀V²_Mμm^-1, equivalent to a total force for the device of 36.4 μN at an applied voltage of V _M=100 V, just 16% larger than the observed value. The measured increase in force with distance was smaller than predicted with the FEA, due to the geometry of the device in which the electrodes at the anchored ends of the supporting spring structure displace by a smaller amount than those at the centre.