Ionization equilibrium at the transition from valence-band to acceptor-band migration of holes in boron-doped diamond
- Physics Department, Belarusian State University, Nezavisimosti Ave. 4, 220030 Minsk (Belarus)
- Ioffe Institute, Russian Academy of Sciences, 194021 St. Petersburg (Russian Federation)
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 insulator–metal 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{sub 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{sub 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{sub j}/2) as a function of their concentration N is calculated. The estimates of the extrapolated into the temperature region close to T{sub j} hopping drift mobility of holes hopping from the boron atoms in the charge states (0) to the boron atoms in the charge states (−1) 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 × 10{sup 17} to 3 × 10{sup 20 }cm{sup −3}, i.e., up to the Mott transition. The model uses no fitting parameters.
- OSTI ID:
- 22596831
- Journal Information:
- Journal of Applied Physics, Vol. 119, Issue 24; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-8979
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ATOMS
BORON
CHARGE STATES
CONCENTRATION RATIO
CRYSTAL LATTICES
CRYSTALS
DIAMONDS
DOPED MATERIALS
ELECTRIC CONDUCTIVITY
FLUCTUATIONS
GAUSS POTENTIAL
HOLES
HYDROGEN
IONIZATION
MOBILITY
POINT CHARGE
P-TYPE CONDUCTORS
SPATIAL DISTRIBUTION
THRESHOLD ENERGY
VALENCE