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

TL;DR

This paper develops a theoretical model describing how hopping electric conductivity in boron-doped diamond depends on impurity concentration and compensation ratio, aligning well with experimental data near the insulator-metal transition.

Contribution

It introduces a quasiclassical approximation model for hopping conductivity in boron-doped diamond, accounting for impurity lattice structure, Coulomb interactions, and screening effects, providing new quantitative insights.

Findings

Calculated conductivity and activation energy match experimental data.

Model predicts dependence of conductivity on boron concentration and compensation ratio.

Agreement observed near the insulator-metal phase transition.

Abstract

Expressions for dependences of the pre-exponential factor \sigma_3 and the thermal activation energy \epsilon_3 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_h = [(1 + K)N]^{-1/3} within the crystalline matrix. A hopping event occurs only over the distance R_h 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_h. The shift of the acceptor band towards the top of the valence band with increasing N due to screening (in the Debye--H\"uckel approximation) of the impurity ions by holes hopping via acceptor states was taken into account. The calculated values of \sigma_3(N) and \epsilon_3(N) for K \approx 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.