Stress relaxation and thermal evolution of film properties in amorphous carbon

A model for the stress relaxation of amorphous carbon films containing high concentrations of fourfold coordinated carbon is presented. The onset of stress relaxation in these materials occurs following thermal annealing at temperatures as low as 100 degrees C, and near full stress relaxation occurs after annealing at 600 degrees C. The stress relaxation is modeled by a series of first order chemical reactions which lead to a conversion of some fourfold coordinated carbon atoms into threefold coordinated carbon atoms. The distribution of activation energies for this process is derived from the experimental measurements of stress relaxation and is found to range from 1 eV to over 3 eV. Permanent increases in the electrical conductivity of the carbon films are also found following thermal annealing. The electrical conductivity is found to be exponentially proportional to the number of additional threefold atoms which are created upon annealing, with the increase in threefold atom concentration being deduced from the stress relaxation model. This indicates that the increase in electrical conductivity and the stress relaxation originate from the same fourfold to threefold conversion process and that electrical transport through these films is dominated by a hopping conduction process.