Stiction force estimation from attachment length and electrostatic measurements on cantilever beams

An estimate of stiction force, rather than the more commonly reported surface energy, helps design reliable structures. Stiction is a major cause of failure in surface micromachined structures. We report on the modeling and estimation of the stiction force from simple I-V curves on cantilever beams which can be measured even on packaged devices. We have fabricated oxide anchored cantilever beams of polysilicon by surface micromachining. Current is measured for an applied bias between the beam and the substrate. Pull-in and pull-out voltages are determined as the points of maximum slope calculated by differentiating a cubic spline fit to the measured I-V data. The commercial package CoventorWare was used to develop an empirical model for estimating the pull-out voltage for the cases when there is no stiction and in the presence of stiction. A model is developed for finding the stiction force from the simulated and the experimental pull-out voltages. The method uses only measured values of pull-in and pull-out voltages and the beam length and does not require the value of Young's modulus. We also discuss an independent visual method to estimate the process stiction force from the cantilever beam array that is normally used to estimate the surface adhesive energy. An analytical model is developed to calculate the stiction force from the attachment length of long stuck cantilever beams that are released in the same process.