Electromechanical instability of microscale structures

Electrical pull-in instability of microscale structures is an important failure mechanism in microelectromechanical systems (MEMS), in which there is no equilibrium state for the MEMS structures. Using the elastic membrane theory, the electromechanical interaction of a suspended MEMS structure in an electric field is presented. The statically mechanical deformation of the microscale membrane under electrostatic loading is examined. The critical value of electric voltage needed to pull the membrane into the contact with the substrate is determined analytically. The critical pull-in electric voltage is proportional to the square root of the residual tensile force and inversely proportional to the length of the membrane if the residual line tensile force is much larger than the line force due to the stretch of the membrane, while it is inversely proportional to the square of the membrane length if the membrane is initially stress free. The contact problem after the occurrence of the pull-in collapse phenomenon is studied. It turns out that the contact length between the membrane and the substrate increases with the increase of the membrane length and the electric voltage, and decreases with the tensile force in the membrane. A closed-form solution on the release-electric voltage is obtained, which depends on the membrane length and the tensile force.