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

Abstract

Expressions for dependences of the pre-exponential factor σ3 and the thermal activation energy ε3 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 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) 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 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 ε3(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.

Drift-diffusion model of hole migration in diamond crystals via states of valence and acceptor bands

“…In this work in the weak electric field limit (e d k T B E  , where d is the mean hop length of electron via localized states) and when the thermal energy is greater than the fluctuation dispersion of energy levels of localized states it is shown that the ratio of the diffusion coefficient to the drift mobility is equal to k T e B . Finally, the values of effective hole or electron concentrations involved in hopping migration via hydrogenlike impurities in crystalline semiconductors are determined in [13,16,17,[28][29][30]. [31][32][33][34] used particular forms of the expressions for N hp and N hn that are only suitable for limiting values of the compensation ratio (K 1  or K 1 1 - ) of the majority impurity by the minority impurity.…”

“…As the concentration of v-band holes increases, their exchange interaction becomes significant [52,57,60]. As a result, the energy of the top of the v-band (E v = 0 for an undoped crystal) shifts deeper into the band gap, decreasing the energy level E per for hole percolation, equation (29), by the value of the exchange energy E exc for a single v-band hole. That is equivalent to the top of the v-band approaching the center of the acceptor band E a and is taken into account in equation (24).…”

“…According to [46,57] only the linear approximation of the screening charge density  . Taking into account equations (3) and (7), the radius of static screening of the Coulomb field of the impurity ion by v-band holes and holes of the acceptor band migrating over the crystal is determined by the following expression (see also [26,28,29,46]): = ---( ) according to equations (1) and (6) is the effective concentration of holes hopping via acceptors in the vicinity of the screening ion; p…”

“…for hopping via acceptors holes D M k with equation (4) for ideal nondegenerate gas of v-band holes. For the wide acceptor band (W k T a B ), from equation(21)it follows that[29]…”

The method for calculation of carrier concentration in narrow-gap n-type doped Hg1−xCdxTe structures

“…where Poklonski et al (2009) developed a model of hopping dc conductivity via the nearest boron atoms in moderately compensated diamond crystals. They have assumed that the energy of acceptor levels exhibits the Gaussian distribution due to the fluctuations of the electrostatic interaction of ionized acceptors with other ionized atoms, both acceptors and donors.…”