Hopping of electrons

Inter-atomic two-centre matrix elements (cp the hopping of electrons from one site to another. They can be described [7] as linear combmations of so-called Slater-Koster elements [9], The coefficients depend only on the orientation of the atoms / and m. in the crystal. For elementary metals described with s, p, and d basis fiinctions there are ten independent Slater-Koster elements. In the traditional fonnulation, the orientation is neglected and the two-centre elements depend only on the distance between the atoms [6]. (In several models [6,... 

From a theoretical point of view, charge propagation in films containing space-distributed redox centers can be achieved either by the physical displacement of the sites or by the transference (hopping) of electrons from neighboring reduced to oxidized sites or by the combination of both processes. In the case of free diffusing couples immobilized in oppositely charged polyelectrolytes, both processes occur and an apparent diffusion coefficient can be defined and measured [136, 142, 143] ... 

Figure 20. Electronic structure and transport in mixed conducting perovskites. (a) Band picture of electronic structure in the high-temperature metallic phase of Lai- r tCo03-(5. (Reprinted with permission from ref 109. Copyright 1995 Elsevier.) (b) Localized picture of electron/ hole transport in semimetallic Lai- 3r Fe03-(5, involving hopping of electrons and/or electron holes (depending on the oxidation state of iron).

Solid HjPMo o reduced by H2 at a lower temperature shows a very weak ESR signal intensity of Mo5 +, probably because most of the Mo5+ ions are not detectable due to the rapid hopping of electrons. Heat treatment, which eliminates oxide ions from the heteropoly anion, leads to development of the Mo5 + signal, indicating the localization of electrons (101, 102). Early reports of ESR spectra of reduced PMo C o are likely due to these species. Several different species are observed in highly reduced samples. 

It is known that for a set of ID and 2D quantum spin models the exact ground state of which can be represented in the RVB form [15, 6, 36, 13, 31]. It is natural to try to find electronic models with an exact ground state at half-filling formed by SB functions in the same manner as for above mentioned spin models. The electronic models of these types include the correlated hopping of electrons as well as the spin interactions and pair hopping terms. 

The compoimd CuMnCr04 showed low value of resistivity i.e. 10 ohm-cm. This may be due to the formation of some Mn " " ions at tetrahedral and some Cul+ ions at the octahedrcil sites. Here the mechanism of conduction is via hopping of electrons between Mn3+ and Mn +... 

In the quasi one-dimensional systems these fluctuations are suppressed to some extent by the interchain hopping of electrons (see e.g. and this makes the transitions possible. However... 

The inter-chain hopping of electrons observed by the NMR experiment could be the same mechanism for the transverse conductivity. Assuming the diffusive mechanism for the transverse conductivity, qj., Cj. is given by... 

A similar behaviour of the microwave conductivity and dielec trie constant was reported for many well- and moderately conducting TCNQ complexes /1/. It is often attributed to the hopping of electrons between localized states in the band gap, in a similar way as observed in amorphous semiconductors. 

Formerly, Bradley and Hammes [152] studied dc conductivity phenomma on a number of metal-free and some metal-containing plasma polymers. They foimd plots of Igdc resistivity versus 1/T to be generally linear and concluded that a single activation process is responsible, with activation energies of 1.36 eV for metal-free polymers and < 1 eV for metal-doped polymers. For evaporated Cu/poly-ethylene films [129] the Ig sheet resistance revealed a linear dependence on The conduction process was explained in terms of hopping of electrons between traps in localized states dose to the Fermi level. 

The first report on the electrical properties of composite hard carbon films was published by Jones and Stewart [154] who slightly doped their a-C H films with phosphorus, boron, or nitrogen and found increased conductivity with phosphorus and boron. For the conduction process they proposed a hopping of electrons in a region of high density of localized states for both doped and undoped samples. 

Under conditions where this point defect equilibrium accurately reflects the situation, electron n-type conductivity is possible due to the hopping of electrons from Fe " to Fe ". The electronic conductivity will depend upon the amount of Fe " present. This will depend upon the partial pressure of oxygen and can be derived from the equilibrium constant equation as... 

An extensively studied multi-phase problem is the redox chemistry of a film deposit (Fig. n. 1.24a). Well-known characteristic voltammetric responses may be observed for a thin film deposit with a thickness much less than the diffusion layer (see Fig. II.1.10) or for a thick film deposit with diffusion only within the film. The transport of charges in the film deposit may be possible via diffusion or hopping of electrons [116] but transport of ions is also required to achieve charge neutrality. 

FIGURE 46.41. Schematic illustration of ionic suppression of intergrain hopping. Compensation by cations of charge of acceptors removes the nearby localiz states on the polymer backbone that provide for holes easy hopping of electrons between grains. Reprinted from Ref. [235] > (2005) with permission from Elsevier. 

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