A model of ionization equilibrium and Mott transition in boron doped crystalline diamond

Poklonski, N. A.; Вырко, С. А.; Poklonskaya, O. N.; Zabrodskiĭ, A. G.

doi:10.1002/pssb.200844285

Cited by 8 publications

(12 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…According to Refs. [18,21] the probability that an acceptor with energy level E > 0 above the top of the v-band (E v = 0) of an undoped crystal is ionized can be written as…”

Section: Statistics Of Hydrogen-like Impuritiesmentioning

confidence: 99%

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

Poklonski

Вырко²,

Zabrodskiĭ³

2009

Solid State Communications

View full text Add to dashboard Cite

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.

show abstract

“…According to Refs. [18,21] the probability that an acceptor with energy level E > 0 above the top of the v-band (E v = 0) of an undoped crystal is ionized can be written as…”

Section: Statistics Of Hydrogen-like Impuritiesmentioning

confidence: 99%

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

Poklonski

Вырко²,

Zabrodskiĭ³

2009

Solid State Communications

View full text Add to dashboard Cite

show abstract

“…In the thermodynamic equilibrium state for the concentration of v-band holes p averaged over the volume V of a bulk crystalline diamond sample according to [30,[35][36][37] we obtain…”

Section: Statistics Of Holes In Valence and Acceptor Bandsmentioning

confidence: 99%

“…Taking into account only Coulomb interaction between the two nearest point charges in the crystal, we find the following expression for the effective width of the acceptor band W a , which is equal to the root-mean-square fluctuation of the electrostatic energy of the ionized acceptor [35,45]:…”

Section: Statistics Of Holes In Valence and Acceptor Bandsmentioning

confidence: 99%

“…At the distances r d s  the total electrostatic potential s F of an acceptor in the charge state 1 -( ) with a screening cloud of charges is determined by the solution of the linearized Poisson equation [19,53]: ) . As a result, the total electrostatic correlation energy E cor in the system 'acceptor in the charge state 1 -( ) plus cloud of charges screening it' is [35,52,57]:…”

Section: Statistics Of Holes In Valence and Acceptor Bandsmentioning

confidence: 99%

See 1 more Smart Citation

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

et al. 2018

View full text Add to dashboard Cite

Keywords: boron-doped diamond, insulating side of the Mott transition, transition from valence-band to acceptor-band migration of holes, Nernst-Einstein-Smoluchowski relation, thermal activation energy of hopping conductivity Abstract Ionization equilibrium and dc electrical conductivity of crystalline diamond are considered, for the temperature T j in the vicinity of which valence band (v-band) conductivity is approximately equal to hopping conductivity via acceptors. For the first time, we find explicitly (in the form of definite integrals) the fundamental ratio of diffusion coefficient to drift mobility for both v-band holes and holes hopping via hydrogen-like acceptors for the temperature T j . The known ratios follow from the obtained ones as particular cases. The densities of the spatial distributions of acceptors and hydrogenlike donors as well as of holes are considered to be Poissonian and the fluctuations of electrostatic potential energy are considered to be Gaussian. The dependence of exchange energy of v-band holes on temperature is taken into account. The thermal activation energy of hopping conduction as a function of the concentration of boron atoms (as acceptors) is calculated for temperature T T 2 j 3 » . Without the use of any adjustable parameters, the results of calculations quantitatively agree with data obtained from the measurements of hopping conductivity of diamond with boron concentration from 3 10 17 to 3 10 20 cm −3 , i.e. on the insulating side of the Mott phase transition.

show abstract

“…Indeed, in Ref. 9, the model of transition of p-Dia:B from the insulating to the metallic state (Mott transition 10 ) under the increase in boron concentration is proposed in the presence of electrical conduction of v-band holes. The critical concentration of boron atoms (N M % 4 Â 10 20 cm À3 ) at which the Mott transition occurs is found experimentally in Ref.…”

Section: Introductionmentioning

confidence: 99%

Ionization equilibrium at the transition from valence-band to acceptor-band migration of holes in boron-doped diamond

Poklonski

Вырко

Poklonskaya

et al. 2016

Journal of Applied Physics

Self Cite

View full text Add to dashboard Cite

A quasi-classical model of ionization equilibrium in the p-type diamond between hydrogen-like acceptors (boron atoms which substitute carbon atoms in the crystal lattice) and holes in the valence band (v-band) is proposed. The model is applicable on the insulator side of the insulatormetal concentration phase transition (Mott transition) in p-Dia:B crystals. The densities of the spatial distributions of impurity atoms (acceptors and donors) and of holes in the crystal are considered to be Poissonian, and the fluctuations of their electrostatic potential energy are considered to be Gaussian. The model accounts for the decrease in thermal ionization energy of boron atoms with increasing concentration, as well as for electrostatic fluctuations due to the Coulomb interaction limited to two nearest point charges (impurity ions and holes). The mobility edge of holes in the v-band is assumed to be equal to the sum of the threshold energy for diffusion percolation and the exchange energy of the holes. On the basis of the virial theorem, the temperature T j is determined, in the vicinity of which the dc band-like conductivity of holes in the v-band is approximately equal to the hopping conductivity of holes via the boron atoms. For compensation ratio (hydrogen-like donor to acceptor concentration ratio) K % 0.15 and temperature T j , the concentration of "free" holes in the v-band and their jumping (turbulent) drift mobility are calculated. Dependence of the differential energy of thermal ionization of boron atoms (at the temperature 3T j /2) as a function of their concentration N is calculated. The estimates of the extrapolated into the temperature region close to T j hopping drift mobility of holes hopping from the boron atoms in the charge states (0) to the boron atoms in the charge states (À1) are given. Calculations based on the model show good agreement with electrical conductivity and Hall effect measurements for p-type diamond with boron atom concentrations in the range from 3 Â 10 17 to 3 Â 10 20 cm À3 , i.e., up to the Mott transition. The model uses no fitting parameters. Published by AIP Publishing.

show abstract

A model of ionization equilibrium and Mott transition in boron doped crystalline diamond

Cited by 8 publications

References 28 publications

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

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

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

Ionization equilibrium at the transition from valence-band to acceptor-band migration of holes in boron-doped diamond

Contact Info

Product

Resources

About