13 research outputs found
Model of hopping dc conductivity via nearest neighbor boron atoms in moderately compensated diamond crystals
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.Comment: 6 pages, 2 figure