Onset of hopping conduction in carbon-ion-implanted diamond

The conduction of diamond implanted with carbon ions, at a target temperature of 250 °C, was studied as a function of ion energy using the electrical sheet resistance of these implanted layers as a probe. It was found that ion doses at which the onset of hopping conduction occurs increases with range straggling Δ$R_p$ as (Δ$R_p$ ${)}^{3/2}$. This result may be explained by a simple model if it is assumed that the interstitial atoms formed in the collision cascades are mobile, but not the vacancies. Accordingly, those interstitials which do not recombine with vacancies diffuse out of the implanted layer leaving behind a surplus of vacancies. When a certain critical vacancy density is reached, this layer relaxes to a state in which hopping conduction is possible. At implantation energies below about 100 keV, the results seem to indicate that a force exists which attracts the mobile interstitials to the surface.