Screening of the Coulomb interaction in two-dimensional variable-range hopping

Keuls, F. W. Van; Hu, Xiao-Long; Jiang, Hongda; Dahm, A. J.

doi:10.1103/physrevb.56.1161

Cited by 92 publications

(84 citation statements)

References 35 publications

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“…A similar hopping exponent has been reported by other authors [5,10,13,14], but has rarely been discussed per se. Since there is no theory which predicts this value of the hopping exponent, its origin has been left an open question.…”

Section: Introductionsupporting

confidence: 55%

“…In the analysis of their data, Van Keuls et al [5] assumed that the number of configurations of occupied states reached by the correlated hopping of a number of electrons is proportional to the single-particle density of states. In that case, the qualitative behavior of the resistance remains unchanged, and the effects of correlations enter through the constants which determine the parameter T 0 in different regimes.…”

Section: Survey Of Hopping Modelsmentioning

confidence: 99%

“…1 is independent of temperature. Van Keuls et al [5] studied the resistivity in a gated GaAs/Al x Ga 1−x As heterostructures as a function of temperature, electron density and magnetic field. Assuming the prefactor of the form:…”

Section: Survey Of Hopping Modelsmentioning

confidence: 99%

“…Efros and Shklovskii (ES) showed that including Coulomb interactions between electrons results in a soft gap in the density of states at the Fermi energy, which changes the variable range hopping exponent to x = 1/2 in all dimensions [2]. Hopping conduction has been investigated in a wide variety of materials, such as doped semiconductors [3,4], semiconducting heterostructures [5], amorphous metals [6][7][8][9][10], magnetic materials [11] and superconductors [12]. Both the Mott and the ES forms of variable range hopping have been observed, as well as a crossover between the two regimes [5,6].…”

Section: Introductionmentioning

confidence: 99%

“…Hopping conduction has been investigated in a wide variety of materials, such as doped semiconductors [3,4], semiconducting heterostructures [5], amorphous metals [6][7][8][9][10], magnetic materials [11] and superconductors [12]. Both the Mott and the ES forms of variable range hopping have been observed, as well as a crossover between the two regimes [5,6]. It should be emphasized, however, that it is often hard to distinguish between Mott and ES hopping, particularly in experiments in which the resistance changes only by one or two orders of magnitude.…”

Section: Introductionmentioning

confidence: 99%

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Anomalous hopping exponents of ultrathin metal films

et al. 2000

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The temperature dependence of the resistance R(T ) of ultrathin quench-condensed films of Ag, Bi, Pb and Pd has been investigated. In the most resistive films films, R(T ) = R0 exp (T0/T ) x , where x = 0.75 ± 0.05. Surprisingly, the exponent x was found to be constant for a wide range of R0 and T0 in all four materials, possibly implying a consistent underlying conduction mechanism. The results are discussed in terms of several different models of hopping conduction.

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Section: Introductionsupporting

confidence: 55%

Section: Survey Of Hopping Modelsmentioning

confidence: 99%

Section: Survey Of Hopping Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Anomalous hopping exponents of ultrathin metal films

et al. 2000

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Experimental Evidence for Correlated Hopping in Two Dimensions

Keuls

Dahm

1998

phys. stat. sol. (b)

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Hopping Transport through an Ensemble of Ge Self-Assembled Quantum Dots

Yakimov

Двуреченский

Никифоров

et al. 2000

phys. stat. sol. (b)

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We report investigations of the hole transport in arrays of Ge quantum dots buried in Si. Based on measurements of the temperature dependence of the conductance, the charge-transfer mechanism is proposed to be due to variable-range hopping between the dots with the typical hopping energy determined by inter-dot Coulomb interaction. We find that putting a metal plane close to the dot layer causes a crossover from Efros-Shklovskii variable-range hopping conductance to two-dimensional Mott behavior as the temperature is reduced. At the crossover temperature the hopping activation energy is observed to fall off. The experimental results are explained by screening of long-range Coulomb potentials and give evidence for strong electrostatic interaction between dots in the absence of screening. Conductance oscillations with gate voltage resulting from successive loading of holes into the dots are observed in the field-effect structures.Introduction Variable-range hopping (VRH) is a general conduction mechanism in systems with strongly localized carriers at sufficiently low temperatures. In a regime of VRH, the hopping distance increases as temperature is lowered and the temperature dependence of conductivity is given by sT s 0 exp ÀT 0 aT x , where, in the twodimensional case in the absence of long-range Coulomb interaction, the exponent x 1a3 and T 0 T M G gE F x 3 À1 (Mott VRH), gE F being the density of states in the vicinity of the Fermi level E F and x is the localization radius. If the interaction energy of a displaced electron and the hole it leaves behind is large compared with disorder energies, the conductivity is decribed by the Efros-Shklovskii (ES) law with x 1a2 and T 0 T ES G e 2 aE r x, where E r is the relative permittivity. In this paper, we describe a set of experiments in which we have studied hopping transport in Si metal-oxide±semiconductor field effect structures containing a two-dimensional array of Ge self-assembled quantum dots (QDs) as a conductive channel. The dots are separated from each other by silicon, and the only conduction mechanism at low temperatures is tunnelling of holes between them. The pseudomorphic Ge islands grown epitaxially on a Si (001) surface exhibit a large band discontinuity in the valence band and can be viewed as doping`artificial atoms'. They provide a system in which the number of holes confined in three dimensions, the structure of the hole energy levels, the shape of wavefunctions, and the strength of Coulomb interaction can be controlled. First, we discuss samples in which the holes on the dots are supplied by a

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Screening of the Coulomb interaction in two-dimensional variable-range hopping

Cited by 92 publications

References 35 publications

Anomalous hopping exponents of ultrathin metal films

Anomalous hopping exponents of ultrathin metal films

Experimental Evidence for Correlated Hopping in Two Dimensions

Hopping Transport through an Ensemble of Ge Self-Assembled Quantum Dots

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