Model of hopping dc conductivity via nearest neighbor boron atoms in moderately compensated diamond crystals

Expressions for dependences of the pre-exponential factor σ3σ3 and the thermal activation energy ε3ε3 of hopping electric conductivity of holes via boron atoms on the boron atom concentration NN and the compensation ratio KK are obtained in the quasiclassical approximation. It is assumed that the acceptors (boron atoms) in charge states (0) and (−1) and the donors that compensate them in the charge state (+1+1) form a nonstoichiometric simple cubic lattice with translational period Rh=[(1+K)N]−1/3 within the crystalline matrix. A hopping event occurs only over the distance Rh at a thermally activated accidental coincidence of the acceptor levels in charge states (0) and (−1). Donors block the fraction K/(1−K)K/(1−K) of impurity lattice sites. The hole hopping conductivity is averaged over all possible orientations of the lattice with respect to the external electric field direction. It is supposed that an acceptor band is formed by Gaussian fluctuations of the potential energy of boron atoms in charge state (−1) due to Coulomb interaction only between the ions at distance Rh. The shift of the acceptor band towards the top of the valence band with increasing NN due to screening (in the Debye–Hückel approximation) of the impurity ions by holes hopping via acceptor states was taken into account. The calculated values of σ3(N)σ3(N) and ε3(N)ε3(N) for K≈0.25K≈0.25 agree well with known experimental data at the insulator side of the insulator–metal phase transition. The calculation is carried out at a temperature two times lower than the transition temperature from hole transport in vv-band of diamond to hopping conductance via boron atoms.