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

N A Poklonski, S A Vyrko, A I Kovalev, A N Dzeraviaha

https://zenodo.org/record/3694005#.XnIRbXIzbIU

ABSTRACT

Ionization equilibrium and dc electrical conductivity of crystalline diamond are considered, for the temperature  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 . The known ratios follow from the obtained ones as particular cases. The densities of the spatial distributions of acceptors and hydrogen-like 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 . 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  to  cm−3, i.e. on the insulating side of the Mott phase transition..

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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

 

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