Model for the defect-related electrical conductivity in ion-damaged diamond

Ion-damaged diamond, with a point-defect density smaller than a critical density of 10(22) cm(-3), exhibits defect-related electrical conductivity that follows an Arrhenius pattern. Subsequent to isochronal annealing, the activation energies (epsilon (A)) for this conductivity were found to increase from 0.35 to 1.15 eV as the annealing temperature (T-a) increased from 200 degreesC to 1200 degreesC. We present a quantitative explanation for this substantial increase that is based on the fact that when a vacancy in diamond is neutral, it has a deep localized state occupied by an electron with higher-lying states, which may trap an additional electron, resulting in higher-lying energy levels within the band cap. These states may form an energetically higher-lying band (the D- band) in which electrical conduction may take place. The energy gap between the Fermi level and the mobility edge of the D- band is related to the observed epsilon (A). Since both the shift of the Fermi level and the width and shape of the D- band depend on the density of defects, the observed EA depends on the defect concentration, i.e., the degree of defect annealing. This model can account for the experimentally observed variation of epsilon (A) with T-a. It can also explain some of the measured large varieties of activation energies reported for diamond ion-implanted with dopant atoms (which were previously interpreted as representing different energy states of the dopants) as attributed to unannealed residual implantation-related defects. The present model should be generally applicable for the description of electrical conduction in wide band-gap semiconductors with deep defect levels inside the forbidden energy gap.