Effects of mass density on the microhardness and modulus of tetrahedral amorphous carbon films

Tetrahedral amorphous carbon (ta-C) films were deposited by filtered cathodic vacuum arc technique with substrate negative bias setting in the range of 0–200 V. The film density, hardness and Young's modulus were respectively obtained from the X-ray reflectivity and nanoindentation measurements. A maximum value of density was identified in the middle range of incident ion energy. Correlations between the density and elastic behavior of the films were then discussed theoretically based on the constraint-counting model of Philips and Thorpe. The measured Young's modulus and hardness almost vary linearly with the increasing density which agrees quite well with the theoretic predictions.