Hopping conduction, effect

In materials that have high ionic conductivity, effects such as the above are undoubtedly very important. They show up particularly in materials that have a high concentration of mobile ions and in experimental values of the ac conductivity measured as a function of frequency. In materials with a high carrier concentration, mobile ions are inevitably quite close together, separated by at most a few angstroms. Consequently, ions cannot hop in isolation but are influenced by the distribution of mobile ions in their vicinity. This contrasts with the behaviour of dilute defect systems with low carrier concentrations. In these, the mobile ions are well separated from each other and their conduction can largely be treated in terms of isolated hops. 

The Hall effect for hopping conduction is discussed in Chapter 5. 

A more recent review of the properties of this material has been given by von Molnar and Penney (1985 see also von Molnar et al 1983, 1985). Results discussed in this article, involving the effects of disorder and electron-electron interaction, are described in Chapters 5 and 9. Briefly, the semiconductor-to-metal transition in an increasing magnetic field leads to a conductivity, at 300 mK, that increases linearly with H (von Molnar et al 1983). This is shown in Fig. 3.7. Hopping conduction is observed with an index indicating the influence of a Coulomb gap (Washburn et al 1984), and near the transition a temperature dependence of a as a+mT, with m positive (von Molnar et al 1985). 

Other experimental evidence that the index for is unity is scanty. If we are right in thinking that hopping conduction near the transition is not affected by a Coulomb gap (Chapter 1, Section 15), evidence can be obtained from this phenomenon Castner s group (Shafarman et ai 1986) give evidence for v = 1 in Si P. For early work in a two-dimensional system see Pollitt (1976) and Mott and Davis (1979, p. 138), which give evidence that v = 1. In two-dimensional systems there is evidence (Timp et ai 1986) that the Coulomb gap has little effect on hopping conduction. 

As in the case of other polymers containing saturated cyclic side chains the a relaxation is obscured by low-frequency conductive effects. Moreover in the case of PCBuMM, dielectric activity is also observed. Therefore both polymers show important conductivity contributions at high temperatures and low frequency. The conductivity analysis in this case is also performed using the hopping model... 

The agreement between the experimental data and the equation achieved using the assumption of cation-hopping conduction [114] testify that this hypothesis is in concordance with the experimental data. It is interesting to recognize the difference between the measured apparent activation energies for sodium and calcium zeolites (see Table 4.10 [114]). As was hitherto observed for the polarization phenomena, Na+ cations are more mobile than Ca2+ cations this effect also explains the observed differences in the measured apparent activation energies for cationic conduction for Na+ and Ca2+. 

Evidence that double-stranded DNA molecules are adsorbed in such a way that the helical axis becomes parallel to the electrode surface, the base-pairs being vertically oriented against the electrode surface [45] leads to the conclusion that the thickness of a monolayer of adsorbed DNA at the electrode surface is less than 2 nm. This fact has been applied to use DNA adsorbed at a glassy carbon electrode as an effective electron promoter enabling electron transfer via hopping conduction through electrode-/base-pair/cytochrome c [91]. 

DNA adsorbed on a glassy carbon electrode was also used as an effective electron promoter enabling electron transfer via hopping conduction through electrode/base pair/cytochrome c by Ikeda et al. [128]. Gold electrodes modified with short oligonucleotides inunohilized via thiol chemisorption were described hy Lisdat et al. [129] to study the promotion of electron transfer to cytochrome c. 

In DLTS, as we shall see, the time scales of measurement are typically much shorter (10- 300 msec) and fixed over the entire spectrum. Thus weak effects due to hopping conduction and leakage may be discriminated against more readily. Indeed, it will probably be possible to study these alternative kinds of equilibrating mechanisms by comparing TSCAP with DLTS methods. 

Shortly after Holstein published his work on polarons in molecular crystals. Miller and Abrahams introduced a very useful description of hopping conduction in terms of a phonon-assisted electron tunneling process [38]. Miller-Abrahams theory does not include the polaronic effect. Nevertheless it... 

The non-ohmic conductivity at high electric fields was discussed in crystalline and amorphous semiconductors and dielectrics in terms of such theoretical models as Pool-Frenkel effect [78], ShHovsldi nonlinear hopping conduction in disordered sohds [79,80], and tunneling in granular structures [81]. 

Islam MN, Pradhan A, Kumar S (2005) Effects of crystallite size distribution on the Raman-scattering profiles of silicon nanostructures. J Appl Phys 98 024309 Islam MN, Ram SK, Kumar S (2007) Band edge discontinuities and carrier transport in c-Si/porous silicon heterojunctions. J Phys D Appl Phys 40 5840 Islam MN, Ram SK, Kumar S (2009) Mott and Efros-Shklovskii hopping conductions in porous silicon nanostructures. Physica E 41 1025... 

Zhang L, Coffer JL, Gnade BE, DaXue X, Pinizzotto RF (1995) Effects of local ambient atmosphere on the stability of electroluminescent porous silicon diodes. J Appl Phys 77 5936 Zimin SP (2000) Classification of electrical properties of porous silicon. Semiconductors 34 353 Zimin SP (2006) Hopping conductivity in low-porosity mesoporous silicon formed on p -Si -B. Semiconductors 40(11) 1350... 

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