Static response of microbeams due to capillary and electrostatic forces

Micro-sensors or micro-switches usually operate under the effect of electrostatic force and could face some environmental effects like humidity, which may lead to condensation underneath the beams and create strong capillary forces. Those tiny structures are principally made of microbeams that can undergo instabilities under the effect of those created huge capillary forces. In fact, during the fabrication of microbeams, there is an important step to separate the beam from its substrate (wet etching). After this step, the microstructure is dried, which may causes the onset of some droplets of water trapped underneath the beam that could bring about a huge capillary force pulling it toward its substrate. If this force is bigger than the microbeam's restoring force, it will become stuck to the substrate. This paper investigates the instability scenarios of both clamped-clamped (straight and curved) and cantilever (straight and curled) microbeams under the effect of capillary and/or electrostatic forces. The reduced order modeling (ROM) based on the Galerkin procedure is used to solve the nonlinear beam equations. The non-ideal boundaries are modeled by adding springs. The volume of the fluid between the beam and the substrate underneath it is varied and the relation between the volume of the water and the stability of the beam is shown. An analysis for the factors of which should be taken in to consideration in the fabrication processes to overcome the instability due to huge capillary forces is done. Also the size of the electrode for the electrostatic force is varied to show the effect on the micro-switch stability. A variation of the pull-in voltage with some specific beam parameters and with more than one case of electrode size is shown. It is found that capillary forces have a pronounced effect on the stability of microbeams. It is also found that the pull-in length decreases as the electrode size increases. It is also shown that the pull-in voltage decreases as the amount of fluid underneath the beam increases.