Electrical conduction of ion tracks in tetrahedral amorphous carbon: temperature, field and doping dependence and comparison with matrix data

This paper gives an extended overview of the electrical properties of ion tracks in hydrogen-free tetrahedral amorphous carbon (ta-C) with a sp³ bond fraction of about 80%. The films were grown by mass selected ion beam deposition of 100 eV ¹²C⁺ ions. The ion tracks are generated by irradiation of ta-C films with uranium ions of 1 GeV kinetic energy. Along the ion path a conversion from diamond-like (sp³) carbon to graphite-like (sp²) carbon takes place. Topography and current measurements of individual ion tracks were performed by atomic force microscopy at ambient temperature. The temperature dependence of the electric conductivity was studied between 15 and 390 K by means of 0.28 mm² large contact pads averaging over about 10⁷ tracks. For each sample and at each temperature the conductivity as a function of the applied electrical field (non-ohmic behaviour) was measured separately and the data were extrapolated to field zero. In this way, the zero-field conductivity was determined independent from the field dependence. In spite of large differences in the absolute values, the temperature dependence of the zero-field conductivities is found to be very similar in shape for all samples. The conductivities follow a T-1/4 law up to temperatures slightly below room temperature. At higher temperatures a transport mechanism based on over-barrier hopping dominates with an activation energy of about 220 meV for tracks and 260 meV for the ta-C matrix. The field dependence measurements show that the deviation of the I–V characteristics from ohmic behaviour decreases with increasing zero-field conductivity. We also tested Cu-doped ta-C samples and found that they conduct significantly better than pure ta-C. However, the doping also increases the zero-field conductivity resulting in a weaker contrast between the track and matrix. The data are interpreted within the so-called ‘barrier model’ where the electrons are assumed to move fairly freely in well-conducting sp² regions but encounter barriers in track sections consisting of more sp³-like bonds.