Showing papers on "Variable-range hopping published in 1976"
TL;DR: In this paper, the authors generalize the Heikes formula to include several cases of interacting Fermi systems with spin and show that the high-temperature limit for the thermopower of a system of interacting localized carriers is governed entirely by the entropy change per added carrier.
Abstract: The high-temperature limit for the thermopower of a system of interacting localized carriers is governed entirely by the entropy change per added carrier. The calculation of this quantity reduces to a simple combinatorial problem dependent only on the density of carriers and the interactions stronger than the thermal energy. We have thus been able to generalize the Heikes formula to include several cases of interacting Fermi systems with spin.
515 citations
TL;DR: In this paper, a generalisation of Mott's model of an amorphous solid is used to investigate the characteristics of carrier transport by hopping in an extended temperature range, and it is shown that three types of behaviour can be expected, the Mott T−-1/4 variable-range hopping at low temperatures, nearest-neighbour hopping at high temperatures and low hop site densities, and a weakly temperature-dependent long-range hop at high densities and high temperatures.
Abstract: A generalisation of Mott's model of an amorphous solid is used to investigate the characteristics of carrier transport by hopping in an extended temperature range. It is shown that three types of behaviour can be expected, the Mott T−-1/4 variable-range hopping at low temperatures, nearest-neighbour hopping at high temperatures and low hop site densities, and a weakly temperature-dependent long-range hopping at high densities and high temperatures. Criteria for the observation of these three regions are established and the transitional behaviour of the conductivity is determined. A number of experimental observations of hopping transport are examined and analysed in terms of the densities of localised states.
104 citations
76 citations
TL;DR: In this paper, the effect of interaction between electrons on variable-range hopping was investigated, and it was shown that interaction can lead to deviations at higher T, and decreases the preexponential factor.
Abstract: The effect of interaction between electrons on variable-range hopping is investigated. It is shown that interaction between electrons on localized states produces a band gap for single-particle excitations, but not for those of the many-electron system. Variable-range hopping with σ proportional to exp (– B/T1/4) still occurs in the limit of low T, but interaction may lead to deviations at higher T, and decreases the pre-exponential factor.
75 citations
TL;DR: In this paper, a new experimental technique, time domain spectroscopy (TDS), which enables the dielectric properties of materials to be measured over a wide range of frequencies is described.
Abstract: A new experimental technique, time domain spectroscopy (TDS) which enables the dielectric properties of materials to be measured over a wide range of frequencies is described. Results are presented of such measurements on amorphous germanium, prepared by thin film evaporation. The d.c. conductivity is shown to obey Mott's variable range hopping formula, whilst the a.c. conductivity has a frequency dependence of the form σ(ω)∝ω8, where 0.7
27 citations
TL;DR: In this paper, the metal-nonmetal transition in amorphous Si 100- x -Au x system has been investigated as a function of Au concentration, and it was found that the variable range hopping is a dominant mechanism for electrical conduction at low temperatures in the Au concentration region below 5% and that the metal nonmetal transition occurs at x ≊ 5%.
24 citations
01 Jan 1976
TL;DR: In this article, a review on the hopping conductivity in disordered solids is given, where variable range hopping between localized electronic states near the Fermi level in amorphous tetrahedrally coordinated semiconductors is discussed.
Abstract: A review is given on the hopping conductivity in disordered solids. Variable range hopping between localized electronic states near the Fermi level in amorphous tetrahedrally coordinated semiconductors is discussed in particular. The percolation theory for this type of transport is presented and used to discuss the various transport experiments. These include the dependence of the dc conductivity on heat treatment, applied field, thickness of the samples, and on ion bombardment. It is shown that these effects can be explained satisfactorily by ad hoc models for the density of localized states, although a real understanding of the nature and distribution of these states is still lacking.
19 citations
TL;DR: In this paper, a theoretical derivation of the hopping conductivity of granular metals using the critical percolation conductance method is presented, based on the assumption that the hopping of electrons is predominantly between nearest neighbours.
Abstract: The hopping conductivity of granular metals is known to be of the form sigma varies as exp (-(T0/T)12/) in the temperature range 20K
17 citations
TL;DR: In this paper, an account of the different conduction mechanisms possible in thin amorphous semiconductor films is given, with special attention paid to the low temperature regime where variable range hopping between states near the Fermi level is supposed to be most important.
16 citations
TL;DR: In this article, it is suggested that the carriers at the Fermi energy, which give conduction at low temperature by variable-range hopping, are responsible for the effect.
Abstract: The esr-induced decrease in the resistance of doped silicon and germanium for concentrations in the intermediate region is discussed. The model put forward by Morigaki and co-workers, that the effect is due to hot electrons at a mobility edge, is shown to conflict with current ideas about carriers at mobility edges in non-crystalline systems, because the mobility there should decrease with increasing temperature. It is suggested that the carriers at the Fermi energy, which give conduction at low temperature by variable-range hopping, are responsible for the effect. A mechanism for the transfer of the esr energy due to the combined action of the exchange and the spin-orbit interaction is proposed.
13 citations
TL;DR: In this paper, the conductivity results of the phonon-assisted hopping process in n-type GaAs at low temperatures were analyzed in terms of the percolation theory results.
TL;DR: Using a perturbation expansion, a moment method of calculating the hopping conductivity in the tight-binding representation is described in this paper, where a moment-based method is used to calculate hopping conductivities.
Abstract: Using a perturbation expansion, a moment method of calculating the hopping conductivity in the tight-binding representation is described.
01 Jan 1976
TL;DR: The relationship between hopping conductivity and random walks in random systems is described in this article, where the randomness of the system is shown to play a major role in determining the frequency dependence of the ac conductivity.
Abstract: The semiclassical theory of hopping conductivity in disordered semiconductors is reviewed The relationship between hopping conductivity and random walks in random systems is described The randomness of the system is shown to play a major role in determining the frequency dependence of the ac conductivity The dc conductivity is controlled by the electron diffusivity which involves the product of the mean hopping frequency and the mean square distance moved per hop The mean hopping frequency is calculated for simple models and shown to contain no exponential factors The mean square distance moved per hop is exponentially smaller than the mean square nearest neighbour intersite spacing It is calculated for simple models by using an approach derived from percolation theory
TL;DR: In this article, the 1: 1 volume ratio of co-evaporated semiconducting Nb/Al2O3 films is determined by the high density of localized levels in the energy gap of the alumina.
Abstract: Electrical conduction in co-evaporated semiconducting Nb/Al2O3 films (1: 1 volume ratio) is determined by the high density of localized levels in the energy gap of the alumina. The tunnelling between the metal particles occurs via a hopping mechanism on these states. The transitions have an activation energy of the order of kT, due to the continuous distribution in energy of the localized levels. The conductivity dependence on temperature in the ohmic range leads to a density of states times mobility product increasing exponentially above the Fermi level. The current-field dependence in the high-field regime gives information about the density of states, which is inferred to increase linearly with energy above the Fermi level.
TL;DR: In this article, it was shown that the basic exponential dependence of the polaron hopping mobility in a d-dimensional disordered structure can essentially differ from the Mott law in a certain range of "intermediate" temperatures.
Abstract: It is shown that the basic exponential dependence of the polaron hopping mobility in a d-dimensional (d=2,3) disordered structure can essentially differ from the Mott law in a certain range of 'intermediate' temperatures due to the polaron effect. The conditions for the realisation of such dependences are analysed.
TL;DR: In this article, a computational model of electrical conductivity processes via variable range hopping of electrons between localized states (sites) in quasi-one-dimensional disordered systems is presented.
TL;DR: In this paper, a balance equation describing the kinetics of electron hopping between localized states in disordered semiconductors was derived for systems with a small nonadiabaticity.
Abstract: Equations of motion for the nonequilibrium single-frequency density matrix are used to obtain a balance equation describing the kinetics of electron hopping between localized states in disordered semiconductors. Conclusions are drawn about the applicability of the theory of multiphonon processes to systems with a small nonadiabaticity. The decoupling used is a generalization of one used earlier to the multiphonon case. The balance equation found in the Markov approximation for the average number of sites occupied in an electric field contains the field dependence of the multiphonon-transition probability, tending to the well-known weak-field limit.
TL;DR: In this article, the conditions under which a linear (and not exponential) temperature dependence of hopping conductivity can be observed were investigated using the bond percolation method, which is used to investigate the conditions for a linear and not exponential temperature dependence.
Abstract: The bond percolation method is used to investigate the conditions under which a linear (and not exponential) temperature dependence of hopping conductivity can be observed.
TL;DR: The percolation approach is used to study the vanishing of the linear section in the temperature dependence of the hopping conductivity of disordered semiconductors in a strong magnetic field.
Abstract: The percolation approach is used to study the vanishing of the linear section in the temperature dependence of the hopping conductivity of disordered semiconductors in a strong magnetic field.