Screening of the Coulomb gap

Hu, Xiao-Long; Keuls, F. W. Van; Carmi, Y.; Jiang, H. W.; Dahm, A. J.

doi:10.1016/0038-1098(95)00401-7

Cited by 14 publications

(10 citation statements)

References 9 publications

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“…For the

t ≲ 6.3

nm films the two‐dimensional (2D) Mott variable‐range hopping (VRH) mechanism governs the low temperature charge transport process from

\sim

80 K down to

\sim

20 K, while a crossover from Mott VRH to 2D Efros–Shklovskii (ES) VRH is observed. This observation is quantitatively consistent with the predication of 2D Mott and ES VRH theories , .…”

Section: Introductionsupporting

confidence: 90%

“…However, the crossover from Mott‐type to ES‐type VRH conducting processes has been seldom observed in 2D system. To our knowledge, the Mott‐type to ES‐type VRH conducting transition had been only reported in ultrathin Mo‐C film and GaAs/AlGaAs heterojunction , . To realize 2D VRH conduction, the mean hopping distance of electrons should be greater than film thickness and the localization length.…”

Section: Resultsmentioning

confidence: 98%

“…is expressed as

ρ false(T false) = ρ_{{italicES}_{0}} exp {((), T_{ES} / T)}^{1 / 2},

with

T_{ES} = \frac{β e^{2}}{k_{B} ε ξ},

where

β

is a constant with the value 2.8, and

ε

is the static dielectric constant. The Coulomb gap induced by the Coulomb interaction between charge carriers is given by

Δ_{CG} = (27 / π β^{2}) k_{B} (T_{italicES}^{2} / T_{M}),

For the ES‐VRH, the mean hopping distance

{\overline{R}}_{ES}

and the average hopping energy

{\overline{E}}_{ES}

can be expressed as

{\overline{R}}_{ES} / ξ = \frac{1}{4} {((), T_{ES} / T)}^{1 / 2}

and

{\overline{E}}_{ES} = \frac{1}{2} k_{B} T^{1 / 2} T_{ES}^{1 / 2} .

…”

Section: Resultsmentioning

confidence: 99%

See 2 more Smart Citations

The variation of electrical transport properties with thickness for ultrathin indium oxide films

Jiang

Yang

Zhang

et al. 2017

Physica Status Solidi (b)

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We have systematically investigated the electrical transport properties of a series of In2O3 films (with thickness t ranging from ∼4 to ∼45 nm) grown on yttrium stabilized ZrO2 single crystal substrates. Those tthinmathspace≳thinmathspace11.5nm films reveal metallic characteristics in electrical transport properties, and electron–electron interaction effects govern the low temperature behaviors of the resistivity. For the 6.3 and 3.7 nm thick films, the resistivities variation with temperature [ρfalse(Tfalse)] curves show insulator behaviors in the whole measured temperature range (2–300K). In addition, the two‐dimensional (2D) Mott type variable‐range‐hopping (VRH) dominates the temperature behavior of resistivity in the temperature range Tcross≲thinmathspaceTthinmathspace≲thinmathspace80thinmathspacenormalK, and a crossover to the 2D Efros–Shklovskii (ES) VRH occurs below Tcross. Our results are quantitatively consistent with the theoretical predications of the 2D Mott‐VRH and 2D ES‐VRH theories in the corresponding temperature regions.

show abstract

“…For the

t ≲ 6.3

nm films the two‐dimensional (2D) Mott variable‐range hopping (VRH) mechanism governs the low temperature charge transport process from

\sim

80 K down to

\sim

20 K, while a crossover from Mott VRH to 2D Efros–Shklovskii (ES) VRH is observed. This observation is quantitatively consistent with the predication of 2D Mott and ES VRH theories , .…”

Section: Introductionsupporting

confidence: 90%

Section: Resultsmentioning

confidence: 98%

“…is expressed as

ρ false(T false) = ρ_{{italicES}_{0}} exp {((), T_{ES} / T)}^{1 / 2},

with

T_{ES} = \frac{β e^{2}}{k_{B} ε ξ},

where

β

is a constant with the value 2.8, and

ε

is the static dielectric constant. The Coulomb gap induced by the Coulomb interaction between charge carriers is given by

Δ_{CG} = (27 / π β^{2}) k_{B} (T_{italicES}^{2} / T_{M}),

For the ES‐VRH, the mean hopping distance

{\overline{R}}_{ES}

and the average hopping energy

{\overline{E}}_{ES}

can be expressed as

{\overline{R}}_{ES} / ξ = \frac{1}{4} {((), T_{ES} / T)}^{1 / 2}

and

{\overline{E}}_{ES} = \frac{1}{2} k_{B} T^{1 / 2} T_{ES}^{1 / 2} .

…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

The variation of electrical transport properties with thickness for ultrathin indium oxide films

Jiang

Yang

Zhang

et al. 2017

Physica Status Solidi (b)

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“…More recently, Coulomb gap behavior has been observed in relatively low-mobility GaAs/AlGaAs heterostructures 4,5]. In this paper, we report experimental studies of the temperature dependence of resistivity of high-mobility silicon MOSFET's.…”

mentioning

confidence: 95%

Experimental evidence for a Coulomb gap in two dimensions

et al. 1995

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We have studied the resistivity of a two-dimensional electron system in silicon in the temperature range 200 mK < T < 7.5 K at zero magnetic eld at low electron densities, when the electron system is in the insulating regime. Our results show that at an intermediate temperature range, = 0 exp (T0=T) 1 2 ] for at least four orders of magnitude up to 3 10 9 . This behavior is consistent with the existence of a Coulomb gap. Near the metal/insulator transition, the prefactor was found to be 0 h=e 2 , and resistivity scales with temperature. For very low electron densities, ns, the prefactor diminishes with diminishing ns. A comparison with the theory shows that a speci c set of conditions are necessary to observe the behavior of resistivity consistent with the existence of the Coulomb gap.At su ciently low temperatures (T), in disordered systems such as semiconductors, transport occurs by phonon-assisted tunneling to states nearby in energy. The tunneling distance to a state within k B T of the Fermi energy (E F ) increases with decreasing temperature (here k B is the Boltzmann constant). This transport process has been labeled variable-range hopping (VRH) and is characterized by resistivity of the form (T ) = 0 exp (T 0 =T ) x ;(1) where T 0 is some characteristic temperature. Mott 1] derived this law by assuming a constant density of states (DOS) at the Fermi energy and found in two dimensions that x = 1 3 . This is a single-particle picture which ignores the Coulomb interaction. Efros and Shklovskii 2] have argued that the Coulomb interaction between localized electrons creates a gap, the so-called \Coulomb gap", in the density of states near the Fermi energy. This is manifested by a resistivity of the form of Eq. (1) with x = 1 2 , which is universal for both two-and three-dimensional (2D and 3D) electronic systems.In 1986, Timp, Fowler, Hartstein, and Butcher (TFHB) 3] examined the conductivity as a function of temperature and electric eld in sodium-doped silicon metal-oxide-semiconductor eld-e ect transistors (MOSFET's) and found no evidence of the Coulomb gap. More recently, Coulomb gap behavior has been observed in relatively low-mobility GaAs/AlGaAs heterostructures 4,5]. In this paper, we report experimental studies of the temperature dependence of resistivity of high-mobility silicon MOSFET's. Our experimental data follows the form of Eq. (1) with x = 1 2 for a range of parameters such as temperature and 2D electron density n s . This behavior is consistent with the existence of the Coulomb gap. We believe di erences between our results and those of TFHB are due to di erences between parameter spaces examined in each case.

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“…Another important evidence of the Coulomb glass are the experiments on variable-range hopping conduction near a metallic electrode which screens the interactions at lengths larger than the distance between the electrode and the sample (Hu et al 1995, Van Keuls et al 1997, Yakimov et al 2000. This results in a crossover from T ¡1=2 to Mott behaviour as the temperature is decreased and so the relevant length scale becomes larger than the screening length.…”

Section: Variable-range Hoppingmentioning

confidence: 99%

Coulomb interactions in Anderson insulators

Ortuño¹

2001

Philosophical Magazine B

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We review the main theoretical aspects concerning Coulomb glasses, that is systems with states localized by disorder and long-range interactions between their particles. The numerical algorithms available for their simulations are explained. We analyse tunnelling experiments and the role of screening by metallic electrodes. We study the mechanism for variable-range hopping conductance in these systems and in particular the role of many-electron correlations. Recent relaxation experiments and the possible glass transitions are reviewed. Finally, we describe diOE erent approaches to incorporate quantum eOE ects in the study of Coulomb glasses.

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Screening of the Coulomb gap

Cited by 14 publications

References 9 publications

The variation of electrical transport properties with thickness for ultrathin indium oxide films

The variation of electrical transport properties with thickness for ultrathin indium oxide films

Experimental evidence for a Coulomb gap in two dimensions

Coulomb interactions in Anderson insulators

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