Model of hopping dc conductivity via nearest neighbor boron atoms in moderately compensated diamond crystals
Expressions for dependences of the pre-exponential factor σ3 and the thermal activation energy ɛ3 of hopping electric conductivity of holes via boron atoms on the boron atom concentration N and the compensation ratio K 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) form a nonstoichiometric simple cubic lattice with translational period R=[ within the crystalline matrix. A hopping event occurs only over the distance R at a thermally activated accidental coincidence of the acceptor levels in charge states (0) and (-1). Donors block the fraction 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 R. The shift of the acceptor band towards the top of the valence band with increasing N 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) and ɛ3(N) for K≈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 v-band of diamond to hopping conductance via boron atoms.