A fractal analysis of stiction in microelectromechanical systems

The strong adherence (stiction) of adjacent surfaces is a major design concern in microelectromechanical systems (MEMS). Advances in micromachine technology greatly depend on basic understanding of microscale stiction phenomena. An analysis of the different stiction micromechanisms and the elastic deformation of asperities at MEMS interfaces is developed using a two-dimensional fractal description of the surface topography. The fractal contact model is scale independent since it is based on parameters invariant of the sample area size and resolution of measuring instrument. The influence of surface roughness, relative humidity, applied voltage, and material properties on the contributions of the van der Waals, electrostatic, and capillary forces to the total stiction force is analyzed in eight of simulation results. It is shown that the effects of surface roughness and applied voltage on the maximum stiction force are significantly more pronounced than that of material properties. Results for the critical pull-off stiffness versus surface roughness are presented for different material properties and microstructure stand-free surface spacings. The present analysis can be used to determine the minimum stiffness of microdevices required to prevent stiction in terms of surface roughness, apparent contact area, relative humidity, applied voltage, and material properties.