Electromechanical modelling of electrostatic actuators

Abstract

Introduction Electrostatic actuation is seemingly the most prevalent method of applying forces to deformable elements in microsystems. Two factors make electrostatic actuation appealing in systems with micron-scale dimensions. First, it is associated with the physics of the system, when practical voltages (e.g. –100 V) are applied across micron-scale gaps; the resulting electrostatic fields are sufficiently high to deform elements which, in turn, are sufficiently flexible due to their micron-scale thickness. Second, electrostatic actuation is perfectly compatible with microfabrication technology used for fabricating ICs. The same fabrication processes may be used to produce isolated conducting elements that are supported by flexible suspensions. Electrostatic actuation was introduced over four decades ago [1, 2], and has found many applications in actuation and sensing [3, 4]. Electrostatic forces are inversely proportional to the square of the distance between the electrodes and are, therefore, inherently non-linear [5, 6]. Because of this non-linearity, the electromechanical response of electrostatic actuators may become unstable. This instability, known as the pull-in phenomenon, is an unwarranted effect in applications where a large controllable dynamic range is wanted. In such cases, special designs (e.g. comb-drives [7]) or special operation modes (e.g. charge actuation [8]) may alleviate the difficulty. In other applications, the pull-in instability may be utilised to achieve a fast transition between two states of an electromechanical switch [9]. Electromechanical switches have many uses in optical MEMS [10, 11], RF MEMS [12, 13], nanoelectronics [1, 14] and nanologic [15, 16].