Estimation of stiction force from electrical and optical measurements on cantilever beams

In this paper, we estimate the stiction force from electrical (current-voltage) measurements on surface micromachined polysilicon cantilever beams. A bias voltage was applied between the beam and the substrate. At the pull-in voltage, the beam collapsed to the substrate and the current rose rapidly from zero. Similarlyl at the pull-out voltage during bias sweep back, the current dropped rapidly to zero when the contact between the beam and the substrate was broken. An analytic model for the stiction force was developed in terms of the pull-in and pull-out voltages and was used to estimate a stiction force of about 70 nN from the measured electrical characteristics. This method of characterization is suitable for use in packaged devices. An analytic model was developed to estimate stiction force from optical surface-profile measurements of the curvature of long collapsed cantilever beams in a cantilever-beam array, in the absence of any electrostatic actuation. The force per unit length of about 14 nN/m thus obtained was used to compare the effects of surface roughness on stiction.