Localized electronic states

In electron transfer reactions one studies the conversion of an electron state localized on A to one localized on B. One can also consider the relaxation of a charge localized state to the adiabatic delocalized state [366],... 

Finally, interface states, that is, electronic states localized at the interface, are always present in the case of semiconductors and may be very important in fixing the Fermi level at the interface (Fermi level pinning) and modify the barrier height. In the case of organic solids in general, and of CPs, the existence of a surface does not imply that of dangling (i.e.,... 

Sic-Oi bonding, however, has almost the same bond order as that in cluster (c), suggesting that the central region Sic-Oi bonding has less influence from embedding than the peripheral structure. This means that electronic states near the cluster center are little affected by both the cluster size and the embedding units. In other words, electronic states localized near the center are stable in silicate clusters, and thus suitable for e raction of glass properties. 

The temperature behavior of conductivity follows the variable length hopping conductivity via electron states localized near the Fermi level and is described by the expression... 

In the tight binding model we start from electronic states localized on individual atoms and explore the consequence of coupling between these atomic centers. Here our starting point is the free electron, and the periodic lattice potential enters as a small perturbation. Thus, writing... 

Fig. 17. Local density of surface states (solid line) for the Kahn et al. [166] model of the 110 surface of GaAs. Electronic states localized on the first two layers of Ga and As atoms are shown. The broken line is the bulk density of states, shown for comparison. Only strongly localized surface states are shown. The densities of states have been Gaussian broadened (after Chadi [194]).

Surface state Electronic state localized at the surface. 

At the (111) surface of Pt, this narrows the if-band by approximately 13.5 % compared to the bandwidth on the bulk Pt atom. The computed density of states shown in Fig. 21.1a, b agrees weU with this prediction. Consequent shift in the d-band center closer to the Fermi level is observed. However, narrowing of the d-band due to a lower coordination on the surface of particles is not the only factor that should be cmisidered. In addition to the bulk-like smooth t/-band profile, the new electronic states localized at the vicinity of the surface exist due to the spatial electron confinement perpendicular to the surface [75]. In large crystals, an overall contribution of these states is proportiOTial to the number of surface atoms, and it becomes negUgible for macroscopic aystals. When spatial dimension is further reduced, as in... 

Typical absorption spectra of the conjugated polymers are shown in Fig. 10 for PPV, CNMBC polymer PDSiPV [90J, film and polythiophene derivative PURET [79,105] film. The ab.sorption maximum at 420 nm of the fully converted PPV film is red shifted from that of precursor polymer [106]. The other peaks are located at 250 and below 200 nm. In comparison with the theoretical energy dispersion based on the 7r-band structure [107], the rr—tt transition corresponding to the band gap is assigned at 420 nm. For the other peaks, it was suggested that the peak at 200 nm corresponds to the tt—tt transition for ir-electron states localized within a... 

To base considerations on states with localized extra electrons or holes, the Wannier-type transformation is introduced, yielding localized states within each unit cell. The number of these states equals the number of bands included in the Wannier transformation. In the case of elemental semiconductors such as diamond or siUcon these are one-electron states localized at the middle of the nearest atoms bonds so that n=l,2,3,4 (see Chap. 3 for the discussion of the connection between Bloch and Wannier states). A local description arises through the decomposition of the bkn into a sum of local operators marked with a cell index R (translation vector of the direct lattice) ... 

Fig. 7. Charge pair generation model. Si and S are electronic states localized within a single conjugated polymer segment. CP is the charge pair state and CPp is that modified by the applied electric field.

When we deal with the real polymer systems, disorder effects have to be taken into consideration. This is because in the (quasi) one-dimensional system the disorder tends to make the electronic states localized in cooperation with the electron-lattice coupling [12]. If the disorder is severe, the charges will be transported via hopping among the localized states accompanied by disorder potential as in the case of classical amorphous or non-crystalline media. This will be discussed in sections 2.3.2 and 2.3.3 in relation to the charge transport and recombination in the materials. 

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