Calculation of intrinsic stresses in amorphous carbon films grown by molecular dynamics simulation: from the atomic to the macroscopic scale

We present a method of calculation and an estimate for the bulk intrinsic stress in nonequilibrium tetrahedral amorphous carbon (ta-C) films grown by a realistic atomic scale simulation of ion-beam deposition. The simulated films have a thickness of a few nanometers and reproduce the important features of the real as grown nonequilibrium (not annealed) structures such as the presence of a steady-state growth region with uniform properties, the large content of sp3 bonded atoms, and the high intrinsic compressive stress, which seriously limits the maximum thickness of films that can be deposited. Using slices from the nearly structurally uniform film region, a 3D periodic model was constructed for the bulk intrinsic stress calculation. Employing empirical interatomic potentials for carbon, atomic stresses as well as the bulk stresses were computed. The obtained value of the compressive stress for the transition from the graphitic-like carbon to ta-C is in a good agreement with experimental data for the stress threshold.