Stiction of Flexural MEMS Structures

A variational method using the principle of virtual work (PVW) is presented to formulate the problem of the microcantilever stiction. Compared with the Rayleigh–Ritz method using the arc-shaped or S-shaped deflection, which prescribes the boundary conditions and thus the deflection shape of a stuck cantilever beam, the new method uses the matching conditions and constraint condition derived from PVW and minimization of the system free energy to describe the boundary conditions at the contact separation point. The transition of the beam deflection from an arc-shape-like one to an S-shape-like one with the increase of the beam length is shown by the new model. The (real) beam deflection given by this new model deviates more or less from either an arc-shape or an S-shape, which has significant impact on the interpretation of experimental data. The arc-shaped or S-shaped deflection assumption ignores the beam bending energy inside the contact area and the elastic energy due to the beam/substrate contact, which is inappropriate as shown by this study. Furthermore, the arc-shaped or S-shaped deflection only approximately describes the deflection shape of a stuck beam with zero external load and obviously, the external load changes the beam deflection. The Rayleigh–Ritz method using the arc-shaped or S-shaped deflection assumption in essence can only be used to tell approximately whether stiction occurs or not. Rather than assuming a certain deflection shape and by incorporating the external load, the new method offers a more general and accurate study not only on the microcantilever beam stiction but also on its de-adherence.