Roughness of Deposited Carbon-Based Coatings and Its Statistical Characteristics at Nano and Microscales

Topography of surfaces may influence many processes in tribology including friction and adhesion. Its influence is usually taken into account in various statistical models of rough surfaces. Most of these models are based on an explicit or implicit assumption of normality of the asperity heights or similar assumptions that involve Gaussian distributions. Recently it has been shown that the height distribution of surfaces prepared by grinding are not Gaussian at both nano and micro-scales, while topography of epoxy resin replicas of polishing papers having nominal asperity sizes up to several micrometers, was Gaussian. Here we study roughness of carbon-based coatings deposited by direct current pulsed magnetron sputtering with and without substrate bias voltage at micro and nano-scale. Hardness measured using a Berkovich indenter tip gave 43 (biased) and 14 (non-biased) GPa, respectively. First the heights of the nano-asperities were determined by AFM (Atomic Force Microscopy). Then the heights of the micro-asperities were measured by a profilometer (a stylus). Finally the same regions measured by stylus were again studied by AFM. Standard statistical parameters of surfaces are determined at each scale. It has been also shown that the stylus measurements did not cause plastic deformations of the harder (biased) sample because the distributions of heights at nano-scale were the same. Using the experimental data obtained, the assumption of the normal distribution for the roughness heights has been studied by application of various modern tests of normality. Measurements of surfaces by stylus and by AFM with the 117 nm steps showed that the surfaces satisfy the assumption of normality of the heights. However, further studies with the 10 nm AFM steps showed that the roughness of the non-biased sample is not normal. Hence, the applicability of the standard statistical models of adhesive contact between rough solids to the non-biased sample may be questionable