As semiconductor device geometries shrink, the need for silicon wafers with smaller surface micro-roughness is critical. In advanced device fabrication processes, rinse and ion implantation steps also can cause small but unacceptable roughnesses in oxide films and silicon-base materials, and the high-resolution measurements of the surface roughness using an atomic force microscope (AFM) have been performed. In this paper it has been shown that the measured micro-roughness of the polished silicon wafers using an AFM strongly depends on the sampling area size and must be treated with caution. When the micro-roughness shows a fractal nature, it can be analyzed by its power spectrum. An equation relating the fractal dimension to the micro-roughness (Root Mean Square) has been introduced and proved to be a powerful tool for the analysis of the surface roughness of various materials.