Surface roughness affects the functional properties of surfaces, including adhesion, friction, hydrophobicity, biological response, and electrical and thermal transport properties. However, experimental investigations to quantify these links are often inconclusive because surfaces are fractal-like, and the values of measured roughness parameters depend on measurement size. Here, we demonstrate the characterization of topography of an ultrananocrystalline diamond (UNCD) surface at the angstrom scale using transmission electron microscopy (TEM), as well as its combination with conventional techniques to achieve a comprehensive surface description spanning 8 orders of magnitude in size. We performed more than 100 individual measurements of the nanodiamond film using both TEM and conventional techniques (stylus profilometry and atomic force microscopy). While individual measurements of root-mean-square (RMS) height, RMS slope, and RMS curvature vary by orders of magnitude, we combine the various techniques using the power spectral density and use this to compute scale-independent parameters. This analysis reveals that "smooth" UNCD surfaces have an RMS slope greater than 1, even larger than the slope of the Austrian Alps when measured on the scale of a human step. This approach of comprehensive multiscale roughness characterization, measured with angstrom-scale detail, will enable the systematic evaluation and optimization of other technologically relevant surfaces, as well as systematic testing of the many analytical and numerical models for the behavior of rough surfaces.
Keywords: atomic force microscopy (AFM); hurst exponent; power spectral density (PSD); self-affinity; surface roughness parameters; surface topography; transmission electron microscopy (TEM); ultrananocrystalline diamond (UNCD).