critical relative indentation depth in carbon based thin films

The thin film hardness estimation by nanoindentation is influenced by substrate beyond a critical relative indentation depth (CRID). In this study we developed a methodology to identify the CRID in amorphous carbon film. Three types of amorphous carbon film deposited on silicon have been studied. The nanoindentation tests were carried out applying a 0.1–10 mN load range on a Berkovich diamond tip, leading to penetration depth-to-film thickness ratios of 8–100%. The work regained during unloading (We) and the work performed during loading (Wt) was estimated for each indentation. The trend of unload-to-load ratio (We/Wt) data as a function of depth has been studied. We/Wt depth profiles showed a sigmoid trend and the data were fitted by means of a Hill sigmoid equation. Using Hill sigmoid fit and a simple analytical method it is possible to estimate CRID of carbon based films.