Growth Randomness, Porosity, and Surface Coverage of Carbon Films

Mathematical models that describe the static growth processes of sputtered and ion-beam deposited amorphous carbon films are established. Two important factors are considered in deriving the models: the film porosity and the growth randomness. The growth randomness for both hydrogenated sputter carbon and hydrogenated ion-beam carbon films are deduced from the film roughness vs. film thickness data obtained from X-ray reflectometry. The porosities of the two types of films are estimated from the experimentally determined values of film densities and sp³/sp² C–C bonding ratios. The derived film growth models, which find support from a surface coverage experiment, have allowed us to predict the surface coverage of the two types of carbon films in the thickness range of interest. We find that, neglecting intermixing at the substrate/carbon interface, the denser ion-beam carbon films are nearly as effective at achieving a similar level of surface coverage as the less dense sputter carbon films at twice the thicknesses. Our surface coverage model points to further increasing the carbon film density as the most effective approach for the continued reduction in the carbon overcoat thickness while maintaining adequate surface coverage.