Modelling considerations for electrostatic forces in electrostatic microactuators

Electrostatic force generation may offer distinct advantages over more familiar magnetostatics at size scales approaching microns. The fabrication of very small electrostatic actuators is becoming technologically feasible, but is extremely difficult, so that mathematical modelling of actuator designs is likely to be very important in the advancement of this technology. Modelling involves difficulties not only in finding solution (typically numerical) to a mathematical problem, but more important, it requires that the mathematical problem be well formulated. This in turn requires an understanding of, and intuition for, what electrostatic effects are likely to be revelant, as well as an appreciation for the behavior of materials in electrostatic interactions and for the impact on other machine components (bearing, loads, etc). The well-established lore of magnetostatics is not of much use as a guide in this task for several reasons: magnetic materials tend to be either highly permeable (i.e. ferromagnetic) or to have no magnetic effect. By contrast, there are no electrostatically inert materials; the relative dielectric constant ε of any solid (of normal density) is of order two or greater, and thus any solid element of an electrostatic configuration has a significant influence on the field. Also, the sources of magnetic fields, currents or magnetization, can be specified with some confidence, while the sources of the electrostatic field, electric charge and polarization, are much more elusive and subject to change. It is the purpose of this paper to point out some of the effects that must be taken into account if a mathematical model is to give an adequate representation of the behavior of an actualy system. To do this we sketch a brief list of the types of electrostatic elements and interactions (conductors, dielectrics, compensated and uncompensated electrets, ferroelectrics, image forces, dielectrophretic forces, etc.) and use this list as background for discussing some electrostatic effects that may be important in the design or modelling of microactuators. For some of these effects, applicable results are reported from experimental investigations carried out with both a small (several hundred micron scale) electrostatically actuated device (‘SCOFSS’) built to study aspects of microelectromechanical design and of control via electrostatic actuation, and the ‘Wobble Motor’, a successful electrostatic microactuator.