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

We present a method to calculate macroscopic bulk stresses in tetrahedral amorphous carbon (ta-C) films grown by a realistic atomic scale simulation of ion-beam deposition. Similar to real as-deposited films, the simulated films have a high content of sp3 bonded atoms and large intrinsic compressive stresses. Deriving atomic stresses from an interatomic potential and averaging them over slices inside the film, we show that the average stresses in the inner film region converge to realistic values (∼10 GPa) as the thickness of the slices exceeds 1 nm. The analysis of stress variation with depth reveals that in amorphous films deposited with low energy (20–30 eV) ions the highest compressive stress is attained in the region of steady-state growth, while in films grown with 80 eV ions it reaches a maximum in an intermediate layer adjacent to the crystalline substrate. The transition from graphitic carbon to ta-C is found to occur at a threshold stress of about 13 GPa.