Multiscale roughness and modeling of MEMS interfaces

Investigation of contact and friction at multiple length scales is necessary for the design of surfaces in sliding microelectromechanical system (MEMS). A method is developed to investigate the geometry of summits at different length scales. Analysis of density, height, and curvature of summits on atomic force microscopy (AFM) images of actual silicon MEMS surfaces shows that these properties have a power law relationship with the sampling size used to define a summit, and no well-defined value for any is found, even at the smallest experimentally accessible length scale. This behavior and its similarity to results for fractal Weierstrass-Mandelbrot (W-M) function approximations indicate that a multiscale model is required to properly describe these surfaces. A multiscale contact model is developed to describe the behavior of asperities at different discrete length scales using an elastic single asperity contact description. The contact behavior is shown to be independent of the scaling constant when asperity heights and radii are scaled correctly in the model.