Electron transport localized states

Solid mixed ionic-electronic conductors (MIECs) exhibit both ionic and electronic (electron-hole) conductivity. Naturally, in any material there are in principle nonzero electronic and ionic conductivities (a i, a,). It is customary to limit the use of the term MIEC to those materials in which a, and 0, 1 do not differ by more than two orders of magnitude. It is also customary to use the term MIEC if a, and Ogi are not too low (o, a i 10 S/cm). Obviously, there are no strict rules. There are processes where the minority carriers play an important role despite the fact that 0,70 1 exceeds those limits and a, aj,i< 10 S/cm. In MIECs, ion transport normally occurs via interstitial sites or by hopping into a vacant site or a more complex combination based on interstitial and vacant sites, and electronic (electron/hole) conductivity occurs via delocalized states in the conduction/valence band or via localized states by a thermally assisted hopping mechanism. With respect to their properties, MIECs have found wide applications in solid oxide fuel cells, batteries, smart windows, selective membranes, sensors, catalysis, and so on. 

The above mechanistic aspect of electron transport in electroactive polymer films has been an active and chemically rich research topic (13-18) in polymer coated electrodes. We have called (19) the process "redox conduction", since it is a non-ohmic form of electrical conductivity that is intrinsically different from that in metals or semiconductors. Some of the special characteristics of redox conductivity are non-linear current-voltage relations and a narrow band of conductivity centered around electrode potentials that yield the necessary mixture of oxidized and reduced states of the redox sites in the polymer (mixed valent form). Electron hopping in redox conductivity is obviously also peculiar to polymers whose sites comprise spatially localized electronic states. 

From the data of literature it is known that water-soluble derivatives of fullerenes are able to be localized in mitochondria and influence their state as well as enzyme system (Foley et al., 2002). Such intracellular localization of fullerenes C60 could explain biologic effects under irradiation, because generation of free oxygen radicals in the cells occurs during emission of electrons from electron-transport chain of mitochondria. 

D.c. electrical conductivity, thermal conductivity, Seebeck effect and Hall effect are some of the common electron-transport properties of solids that characterize the nature of charge carriers. On the basis of electrical properties, solid materials may be classified into metals, semiconductors, and insulators where the charge carriers move in band states (Fig. 6.1) there are other semiconductors and insulators where charge carriers are localized and their motion involves a diffusive process (Honig, 1981). We shall briefly present the important relations involved in interpreting the transport phenomena in solids. 

Electronic conduction in crystalline semiconductors (except for the case of extremely high doping levels or very low temperatures) invariably involves motion in extended states. However, because of the high densities of defect centers, the possibility exists for transport by direct tunneling between localized states. 

Considering the case of electronic transport at a specific energy, the carrier mobility is envisaged as decreasing rather sharply in the vicinity of the boundary between extended and localized states. Consequently, this dividing energy has been termed a mobility edge. ... 

For p-type conductivity one can expect that only neutral impurities, whose ionization potential is less than the potential of the molecules actively taking part in the charge transfer, will act as traps. Moreover the impurities with high ionization potential are not essential for charge transfer due to the added activation energy needed for holes to be transported to these localized states often. These proposals were confirmed for lexan films with IPC and TPA [291]. So the influence of the outside molecule on the charge transfer can be predicted knowing the relevant ionization potential and electron affinity. 

An X-ray photoelectron spectroscopic study of Ni(DPG)2I showed no evidence of trapped valence or any appreciable change in the charge on the metal upon oxidation.97 The site of partial oxidation and hence the electron transport mechanism is still unclear but one explanation of the relatively low conductivity is that the conduction pathway is metal centred and that the M—M distances are too long for effective orbital overlap. Electron transport could be via a phonon-assisted hopping mechanism or, in the Epstein—Conwell description, involve weakly localized electronic states, a band gap (2A) and an activated carrier concentration.101... 

As the prospective systems for spintronics, two-dimensional semiconducting electron structures where electrons are localized in the -direction and free in the lateral ones, are assumed. High mobilities of electrons (n > I (P cm2/(Vs)) achievable there make the electron transport easy. In order to discuss the possible effects of SO coupling we will consider three types of structures shown in Fig.l. In these structures, the electron states are extended along... 

The ratio Vo/B determines the transition from coherent diffusive propagation of wavefunctions (delocalized states) to the trapping of wavefunctions in random potential fluctuations (localized states). If I > Vo, then the electronic states are extended with large mean free path. By tuning the ratio Vq/B, it is possible to have a continuous transition from extended to localized states in 3D systems, with a critical value for Vq/B. Above this critical value, wave-functions fall off exponentially from site to site and the delocalized states cannot exist any more in the system. The states in band tails are the first to get localized, since these rapidly lose the ability for resonant tunnel transport as the randomness of the disorder potential increases. If Vq/B is just below the critical value, then delocalized states at the band center and localized states in the band tails could coexist. 

It was pointed out in Chapter I that the / electrons are always best described by a HL approach, but that the d electrons may be described by either a collective or a localized model, depending upon the situation. If a collective description is appropriate for some of the d orbitals and the corresponding d states are only partially occupied, the compound is metallic (or has a small activation energy for electron transport if R Rc and there is an integral number of d electrons per atom) unless the cations themselves form a two-... 

Figure 20 Energy level scheme of molecular ionic states and selected electronic transitions in unperturbed (a) and defect-controlled (b) local environments. Dominating intermolecular electron LUMO —> LUMO transition in case (a) meets a competing process of intermolecular electron LUMO — HOMO transition (cross-transition) due to an energy barrier (AE) for electron transport in case (b).

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