Mechanics of microcantilever beams subject to combined electrostatic and adhesive forces

One of the most important issues facing the continued development and application of microelectromechanical systems (MEMS) is that of adhesion and friction between microstructures intended to transfer force. In this work, we develop modeling approaches for studying adhesion (i.e., stiction) using the observed shape of microcantilevers under electrostatic loading. Analytical models for an idealized configuration are presented first. The solutions reveal the regimes over which the cantilever deflections are sensitive to adhesion versus applied loading. Also, the energy release rate and hence the cantilever adhesion value is shown to be independent of the curvature of the initially freestanding beam. Second, with a finite-element modeling approach, we quantify the slight sensitivity of the cantilever deflections to the surface force law assumed and show that with Angstrom scale resolution of beam deflections, cohesive zone law information can in principle be deduced. We also use this approach to model the nonuniform electrostatic loading force used in our experiments and the effect of support post compliance. We then demonstrate how adhesion values are obtained along the length of a microcantilever.