Out-of-plane deformation and pull-in voltage of cantilevers with residual stress gradient: experiment and modelling

The out-of-plane deformation and the pull-in voltage of electrostatically actuated cantilevers with a residual stress gradient, is investigated in the length range 100–300 µm. Measured pull-in voltages are compared with calculations, which are obtained using previously proposed analytical expressions and a finite element method (FEM) modelling. In particular, a simplified model of the residual stress distribution inside cantilevers is formulated that enables FEM simulation of measured out-of-plane deformations and pull-in voltages for all lengths of fabricated cantilevers. The presented experimental results and FEM model are exploitable in the design of cantilever-based microelectromechanical systems, in order to provide a reliable prediction of the influence of residual stress gradient on device shape and pull-in voltage.