Multiscale Roughness of MEMS Surfaces

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 asperities at different length scales. Analysis of density, height, and curvature of asperities on atomic force microscopy (AFM) images of actual silicon MEMS surfaces show these properties have a power law relationship with the sampling size used to define an asperity. 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 the surfaces.