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Showing papers on "Variable-range hopping published in 1986"


Journal ArticleDOI
TL;DR: A simple two-dimensional hopping model for independent electrons which has strictly localized states in addition to the extended states is presented and the effect is shown to hold for a much more general class of systems.
Abstract: We present a simple two-dimensional hopping model for independent electrons which has strictly localized states in addition to the extended states. These localized states can exist either in a band gap or within the continuum. The localized states persist if the lattice periodicity is destroyed. Finally, the effect is shown to hold for a much more general class of systems.

318 citations


Journal ArticleDOI
TL;DR: In this article, a charge transport in amorphous silicon (aSi) doped with ion implantation of Mn+, Ni+, Fe+, and Cu+ ions is studied using ESR technique, temperature dependence of conductivity σ(T), and thermopower α(T) measurements with increasing of impurity (Mn, Ni, Fe, Fe) concentration (from 1018to 1019 cm−3), the localized state density and σ decrease owing to the passivation of silicon dangling bonds with impurity atoms.
Abstract: Charge transport in amorphous silicon (aSi) doped with ion implantation of Mn+, Ni+, Fe+, and Cu+ ions is studied using ESR technique, temperature dependence of conductivity σ(T), and thermopower α(T) measurements With increasing of impurity (Mn, Ni, Fe) concentration (from 1018to 1019 cm−3) the localized state density and σ decrease owing to the passivation of silicon dangling bonds with impurity atoms An analysis of conductivity and thermopower data allows to reveal three temperature regions 1) At 250 500 K electron transport dominates 3) At T < 250 K hopping conductivity with variable range hopping near Fermi level prevails For a-Si:Mn in the region of 4 < T < 80 K Coulomb correlations are detected in the behaviour of σ(T) The Coulomb gap is foundto reach a maximum value 25 meV which appears to be one order of value larger than the known (one) in semiconductors doped with shallow impurity levels [Russian Text Ignored]

143 citations



Journal ArticleDOI
TL;DR: In this paper, the Coulomb gap was predicted for a compensated sample of InP on the insulating side of the metal-insulator transition in terms of the relation sigma = sigma 0exp(-(T 0/T)s).
Abstract: Analysis of conductivity data taken over the temperature range 4.2-0.3K for a compensated sample of InP on the insulating side of the metal-insulator transition in terms of the relation sigma = sigma 0exp(-(T0/T)s) indicates that s=1/2, in agreement with the Efros and Shklovskii (1975) Coulomb gap prediction.

26 citations


Journal ArticleDOI
TL;DR: In this paper, the temperature and concentration dependences of the conductivity and of the thermopower at high nickel concentrations (x  0·4) are discussed in terms of variable-range hopping and of nearest-neighbour hopping in an energy distribution of localized states.
Abstract: Electrical conductivity and thermoelectric power measurements have been made on single crystals of nickel ferrous ferrite, NixFe3-xO4 of compositions 0x0·9, in the temperature range 10 to 300 K. The temperature and concentration dependences of the conductivity and of the thermopower at high nickel concentrations (x  0·4) are discussed in terms of variable-range hopping and of nearest-neighbour hopping in an energy distribution of localized states, or the 'Anderson band'. It is argued that there is evidence for the formation of a Coulomb gap and for many-electron hopping in samples of low nickel content (x<0 4).

22 citations


Journal ArticleDOI
TL;DR: Conductance fluctuations due to variable-range hopping in 1D metal-oxide-semiconductor field-effect transistors are investigated in the presence of a magnetic field and the Zeeman effect shifts the fluctuations to lower or higher chemical potentials.
Abstract: Conductance fluctuations due to variable-range hopping in 1D metal-oxide-semiconductor field-effect transistors are investigated in the presence of a magnetic field. With an increase in magnetic field, the Zeeman effect shifts the fluctuations to lower or higher chemical potentials. These shifts reflect the relative populations and occurrence of hopping from singly and doubly occupied sites. Combined with density-of-states measurements, they can provide an estimate of the intrasite Coulomb repulsion in 1D metal-oxide-semiconductor field-effect transistors. The orbital effect on conductance fluctuations is also discussed.

18 citations


Journal ArticleDOI
TL;DR: In this paper, a wide frequency range of ac field and dc field have been adopted for the measurements and a magnetic field cooling treatment has been used for controlling the alignment of c -axis (magnetic easy axis below T v ).
Abstract: Dielectric and conducting properties of synthesized single crystals of magnetite have been studied below the Verwey point T v =122 K. A wide frequency range of ac field and dc field have been adopted for the measurements. A magnetic field cooling treatment has been used for controlling the alignment of c -axis (magnetic easy axis below T v ). The properties along the c -axis and perpendicular to it show a considerable contrast. Also, a conspicuous dielectric relaxation has been found below 70 K. The low temperature ac conductivity fits in with the relation σ ac ∝ω s ( s ∼0.7 at 6.8 K), consistent with the well known hopping conduction mechanism. The dc conductivity is well represented by σ c // ∝exp (-74.5 T -1/4 ), and σ c ⊥ ∝exp (-55.0 T -1/4 ), suggesting that the mechanism of variable range hopping of charge carriers predominates.

18 citations


Journal ArticleDOI
TL;DR: A review of hopping conduction in small MOSFET devices at low temperatures is given in this paper, where the theoretical predictions of Mott, extended to the quasi-one-dimensional limit, are compared with experiments and it is shown that in the limit where only a few states exist within a few k B T of the Fermi energy the conduction properties take on a radically different form.

16 citations


Journal ArticleDOI
TL;DR: In this article, a quasi-two-dimensional impurity band formed in the inversion layer of a silicon-doped silicon metal-oxide--semiconductor field effect transistor was measured as a function of the impurity concentration, surface electric field, and carrier density.
Abstract: The temperature dependence (380 mKT80 K) and electric field dependence (50 mV/cmF150 V/cm) of hopping conduction have been measured as a function of the impurity concentration, surface electric field, and carrier density in a quasi-two-dimensional impurity band formed in the inversion layer of a sodium-doped silicon metal-oxide--semiconductor field-effect transistor. The conductivity is found to be an exponential function of the temperature and applied electric field. Our observations can be accommodated by noninteracting, single-particle hopping models based on percolation theory in which the Coulomb repulsion between electrons on different sites is ignored. For impurity concentrations in the range 2\ifmmode\times\else\texttimes\fi{}${10}^{11}$ to 1.14\ifmmode\times\else\texttimes\fi{}${10}^{12}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ and localization lengths from 3.4 to 7.5 nm, the noninteracting theories accurately describe eight-orders-of-magnitude change in the conductivity of a half-filled impurity band observed for a factor-of-80 change in temperature, and three-orders-of-magnitude change in the non-Ohmic current observed for a factor-of-15 change in electric field. The observed temperature dependence of the conductivity is not consistent with the temperature dependence predicted by Efros and Shklovskii for a Coulomb gap in the single-particle excitation spectrum, although their theory was expected to predict the conductivity under the conditions examined in this experiment.

16 citations


Journal ArticleDOI
TL;DR: In this paper, the observed temperature dependence of a wide variety of carbon resistance thermometers is compared with the simple models of variable-range hopping, and it is shown that for some resistors at very low temperatures, the 1/3-power law (for hopping in 2 D) provides a slightly more accurate fit than the 2/4 power law for hopping in 3 D.

12 citations


Journal ArticleDOI
TL;DR: The electrical resistivity and Seebeck coefficient of both stoichiometric and nonstoichiometric YFe 2 O 4 were measured in the temperature range 140 to 290 K as mentioned in this paper.
Abstract: The electrical resistivity and the Seebeck coefficient of both stoichiometric and nonstoichiometric YFe 2 O 4 were measured in the temperature range 140 to 290 K The activation type conduction was observed with the activation energy of 022 eV above T N for both oxides Below T N , the conduction in the nonstoichiometric oxide is probably due to the variable range hopping in the two dimensional lattice Resistivity of the stoichiometric oxide obeys the Hurd's model superficially However, it will not be the atomic vibration effect but would be the gap narrowing effect

Journal ArticleDOI
TL;DR: In this article, the authors studied the AC conductivity of n-type germanium irradiated by 1.5 MeV electrons at liquid helium temperatures and found that the formation of complex defects by annealing of the samples at 60 and 110K leads to a hopping conductance obeying Mott's law ( sigma infinity exp-b/T14/).
Abstract: AC conductivity is studied in crystalline germanium irradiated by 1.5 MeV electrons at liquid helium temperatures. A sufficient degree of damage occurs to allow the observation of nearest-neighbour hopping conductance. In n-type germanium the formation of complex defects by annealing of the samples at 60 and 110K leads to a hopping conductance obeying Mott's law ( sigma infinity exp-b/T14/). Two different values of b are observed in the temperature region 4-70K, the lower one being attributed to electron-electron interaction (variable-number hopping) and the higher one to variable-range hopping.

Journal ArticleDOI
TL;DR: In this article, the effect of quantum hopping on the one-particle density of states of a system of localized electrons interacting with each other via the long-range Coulomb force was studied.
Abstract: We study the effect of quantum hopping on the one-particle density of states of a system of localized electrons interacting with each other via the long-range Coulomb force. It is found that (1) contrary to the previous classical theories, there is no Coulomb gap in two dimensions, in agreement with recent experiments on doped Si inversion layers, and (2) in three dimensions the Coulomb gap is first reduced in width and then disappears when the hopping rate exceeds a critical value. This reduction of the Coulomb gap is discussed in connection with the reduction of the effective interaction between localized quasiparticles.

Journal ArticleDOI
TL;DR: It is shown that labeled-particle motion is mean-field-like (single hopping rate given by average over distribution) but that vacancy motion takes place on two time scales: rapid motion for pairs of vacancies and much slower diffusion of vacancies which are isolated initially.
Abstract: Classical hopping of interacting particles on a regular lattice is considered in a model where strong repulsions at the saddle point make hopping to a vacant site unfavorable unless there is another vacant site nearby. This picture may be appropriate to metal hydrides at large hydrogen concentration. Physical arguments, analytic theory, and results of simulations are presented. They show that labeled-particle motion is mean-field-like (single hopping rate given by average over distribution) but that vacancy motion takes place on two time scales: rapid motion for pairs of vacancies and much slower diffusion of vacancies which are isolated initially. This picture is in agreement with the different hopping rates in PdH/sub x/ inferred from ultrasonic attenuation and NMR, and can explain the large prefactor anomalies seen in proton NMR. Implications for other experiments such as the Gorsky effect, quasielastic neutron scattering, and NMR of the metal nucleus are discussed.

Journal ArticleDOI
TL;DR: In this article, the authors show that extending the range of hopping in the well known Aubry model to include next-nearest-neighbour hopping gives rise to localised states in regions where the original model with only nearest-NEIGHBOR hopping gives all states extended.
Abstract: The effect of hopping beyond nearest neighbours on the electronic properties of incommensurate systems is discussed very little in the literature even though for example structural phase transitions from commensurate to incommensurate systems are impossible without interactions beyond nearest neighbours. The authors show here that extending the range of hopping in the well known Aubry model to include next-nearest-neighbour hopping gives rise to localised states in regions where the original model with only nearest-neighbour hopping gives all states extended. A short discussion of the relation of this result to the Aubry duality and the Soukoulis-Economou model is given.

Journal ArticleDOI
TL;DR: In this paper, the electrical conductivity of evaporated a-Si has been studied as a function of free-spin density in the temperature range where hopping conduction is dominant, and it has been found that the experimental results can be interpreted by a nearest-neighbour hopping mechanism.
Abstract: The electrical conductivity of evaporated a-Si has been studied as a function of free-spin density in the temperature range where hopping conduction is dominant. It has been found that the experimental results can be interpreted by a nearest-neighbour hopping mechanism. From the explicit dependence of the pre-exponential factor on the spin density, the phonon frequency, vph, and the decay constant of the localized wavefunction, α, in a-Si are evaluated.

Journal ArticleDOI
TL;DR: In this article, amorphous silicon-tellurium alloy thin films were fabricated by coevaporation over the composition range of 0-82 at. % Te. The electronic and optical properties of these films were systematically investigated over this same range of composition.
Abstract: Amorphous silicon–tellurium alloy thin films were fabricated by coevaporation over the composition range of 0–82 at. % Te. The electronic and optical properties of these films were systematically investigated over this same range of composition. The optical gap of these films was found to decrease monotonically with increasing Te content. Conduction near room temperature was due to extended state conduction, while variable range hopping dominated below 250 K. The incorporation of Te in concentrations of less than 1 at. % was found to produce an increase in the density of localized states at the Fermi level and a decrease in the activation energy. This was attributed to the Te being incorporated as a substitutional, fourfold coordinated, double donor in a‐Si. At approximately 60 at. % Te, a decrease in the density of localized states at the Fermi level, and an increase in the activation energy and photoresponse was indicated. This was attributed to the possible formation of a less defective a‐Si:Te compound.

Journal ArticleDOI
TL;DR: In this paper, the shape of the density of states and the process of conduction are due to the distribution of the sizes of the metallic grains, and it is shown that many processes for the hopping conduction can be simultaneously observed.
Abstract: A detailed analysis of the hopping conduction in granular metals is presented. The shape of the density of states and the process of conduction are resulting from the distribution of the sizes of the metallic grains. It is shown that many processes for the hopping conduction can be simultaneously observed. Under some conditions related to the range of temperature and to the width of the grain size distribution only one of these processes will be dominant. A brief application to real systems gives results which are in good agreement with the experimental data.

Journal ArticleDOI
TL;DR: P type copper gallium telluride (CuGaTe 2 ) synthesized from the elements was used as a source for the preparation of films by flash evaporation in this article.


Journal ArticleDOI
TL;DR: Amorphous phosphorus prepared by radio-frequency sputtering has been subjected to ion bombardment, and its dc resistivity then measured as a function of temperature, electric field and annealing temperature as discussed by the authors.
Abstract: Amorphous phosphorus prepared by radio-frequency sputtering has been subjected to ion bombardment, and its dc resistivity then measured as a function of temperature, electric field and annealing temperature. Variable range hopping is the dominant conduction mechanism after bombardment, even following thermal annealing at room temperature. After bombardment at 10 K and annealing at 100 K, the density of states deduced from a single-phonon model of this form of transport is 1.5−5×10 17 states eV −1 cm −3 , and the localisation length is ~10 A.

Journal ArticleDOI
TL;DR: Amorphous films of germanium were grown using a vacuum evaporation technique, on glass substrates kept at room temperature as mentioned in this paper, and they were irradiated with Q-Switched Nd-YAG laser pulses (λ=1.06 μm, 20nsec, 10 to 50Jcm−2).
Abstract: Amorphous films of germanium were grown using a vacuum evaporation technique, on glass substrates kept at room temperature. As-grown films were irradiated with Q-Switched Nd-YAG laser pulses (λ=1.06 μm, 20nsec, 10 to 50Jcm−2). The d.c. conductivity measurements were made in the temperature range 77 to 300 K. It was observed that the effect of laser irradiation was similar to the effect caused by the thermal annealing of the films. The d.c. conductivity data were analysed in the light of Mott's theory of a variable range hopping conduction process.

Journal ArticleDOI
S.A. Jackson1
TL;DR: In this article, a simple model of the localizing potential of electron-ripplon effects on thin films of liquid helium was proposed, and it was shown that a type of variable range hopping in this system can lead to a tunneling probability ∼ exp[−(d0d)2] which may explain recent experimental results on the mobility of electrons on thin helium films.

Journal ArticleDOI
Tadao Ishii1
TL;DR: In this paper, a conductivity formula for hopping of particles with vibrational degrees of freedom is given in the linear field approximation for a finite system having two eigenvalues for the transition rate.

Journal ArticleDOI
TL;DR: In this article, the authors studied the DC and AC conductivities in NaTCNQ-polymer composites of high NaTC NQ content composed of sodium 7,7,8, 8,8-tetracyanoquinodimethanide (NaTCNq) grains dispersed in polyvinyl chloride(PVC) and polyurethane(PU) blend polymer.
Abstract: DC and AC conductions in NaTCNQ–polymer composites of high NaTCNQ content composed of sodium 7,7,8,8-tetracyanoquinodimethanide (NaTCNQ) grains dispersed in poly(vinyl chloride)(PVC)–polyurethane(PU) blend polymer have been studied In the composites, NaTCNQ is mainly dispersed granularly and a slight proportion of NaTCNQ is molecularly The DC conduction has nonohmic characteristics and shows straight lines in logσdc−E1/2 plots On the other hand, its temperature dependence shows a linear relation in logσdc−1/T1/4 plots The DC conduction is interpreted in terms of the variable range hopping (VRH) conduction with the Poole–Frenkel-like field dependence It is deduced that the Poole–Frenkel (PF) mechanism mainly contributes to the generation of carriers and the carriers are transported due to the VRH mechanism; that is, the VRH carriers will generate under PF field dependence The frequency dependence of AC conductivity shows that the VRH is a multiple process and the multiplicity increases with temperature and NaTCNQ content