Role of electrostatic fluctuations in doped semiconductors upon the transition from band to hopping conduction (by the example of p-Ge:Ga)

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

doi:10.1134/s1063782616060191

Cited by 16 publications

(30 citation statements)

References 42 publications

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“…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.…”

Section: At Temperatures T T Jmentioning

confidence: 99%

“…The average concentration of the acceptors in the charge state (−1), taking into account deviations of their energy levels E a from the average value E 0 a > , can be written as [30]:…”

Section: Statistics Of Holes In Valence and Acceptor Bandsmentioning

confidence: 99%

“…The parameter h x enters the expression for the coefficient of the differential thermo-emf for hopping migration of holes via acceptors [51]. To calculate p x and h x using equations (20) and (21) we need to establish the dependence of the energy of the acceptor band center E a on the acceptor concentration N, the compensation ratio K, and the temperature T. According to [13,30] and figure 1 the center of the acceptor band E 0 a > (relative to the top of the v-band in the ideal crystal E v =0) is given by the following expression where I a is the energy level of a solitary acceptor in the ideal crystal, E 0 v d < is the shift of the top of the v-band into the band gap due to the doping of crystal by impurity atoms, E 0 cor < is the energy of the correlative reduction of the affinity of an acceptor in the charge state 1 -( ) to a v-band hole due to the screening of the Coulomb field of the ionized acceptor by a cloud of charges surrounding it (with total charge e + ), E 0 per < is the percolation threshold for v-band holes, i.e. the minimum energy needed for v-band holes to migrate within the entire crystalline sample [13,52], E 0 exc < is the shift of the top of the v-band into the band gap due to the exchange interaction of holes in the v-band.…”

Section: Statistics Of Holes In Valence and Acceptor Bandsmentioning

confidence: 99%

“…The algorithm for solving of the system of equations (1), (8)-(30) numerically consists of four steps (see also [13,30]):…”

Section: Algorithm Of Numerical Calculationsmentioning

confidence: 99%

“…into account equations(27),(29) and(30). In equation(32) the density of states of holes in the v-band g E v p p -D ( )is given by equation (10) with the energy of the hole E p replaced by E ; v p -D the Fermi-Dirac distribution function for v-band holes f is written taking into account the shift of the reference point for the total energy E p of a hole (see inset in figure 1) from E v =0 by 0 v D < deep into the band gap.…”

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

et al. 2018

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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 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.

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Section: At Temperatures T T Jmentioning

confidence: 99%

“…The average concentration of the acceptors in the charge state (−1), taking into account deviations of their energy levels E a from the average value E 0 a > , can be written as [30]:…”

Section: Statistics Of Holes In Valence and Acceptor Bandsmentioning

confidence: 99%

Section: Statistics Of Holes In Valence and Acceptor Bandsmentioning

confidence: 99%

“…The algorithm for solving of the system of equations (1), (8)-(30) numerically consists of four steps (see also [13,30]):…”

Section: Algorithm Of Numerical Calculationsmentioning

confidence: 99%

mentioning

confidence: 99%

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

et al. 2018

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Model of DC Tunneling Conductivity via Hydrogen‐Like Impurities in Heavily Doped Compensated Semiconductors

Poklonski

Anikeev

Вырко

et al. 2023

Physica Status Solidi (b)

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Activation Energy of DC Hopping Conductivity of Lightly Doped Weakly Compensated Crystalline Semiconductors

Poklonski,

Anikeev,

Vyrko

et al. 2024

Physica Status Solidi (b)

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A model is proposed for calculating the thermal activation energy of direct current hopping conductivity via nearest neighbors in lightly doped and weakly compensated crystalline semiconductors with hydrogen‐like impurities. The temperature region is considered in which hops of single holes occur only between acceptors randomly distributed over the crystal (or hops of single electrons only between donors). The model is based on the idea of the Coulomb blockade of charge carriers by the field of compensating impurities (trap impurities). The hopping length of a hole between acceptors (or an electron between donors) is assumed to be equal to the critical (percolation) radius of the spherical region per a majority (doping) impurity atom. At a critical radius, an infinite cluster connecting ohmic contacts is formed in the crystal, along which charge carriers move in a hopping manner via majority impurities. The value of is defined as average work on overcoming the electrostatic Coulomb blockade by a charge carrier and its hopping via the electrically conducting cluster to “infinity”. The results of calculating by the proposed model of the Coulomb blockade for the most well‐studied bulk germanium and silicon p‐ and n‐type crystals are consistent with known experimental data.

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Role of electrostatic fluctuations in doped semiconductors upon the transition from band to hopping conduction (by the example of p-Ge:Ga)

Cited by 16 publications

References 42 publications

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

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

Model of DC Tunneling Conductivity via Hydrogen‐Like Impurities in Heavily Doped Compensated Semiconductors

Activation Energy of DC Hopping Conductivity of Lightly Doped Weakly Compensated Crystalline Semiconductors

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