Localized electron levels

The addressing of nanoelectronic assemblies metal-molecule (nanocluster)-metal with device-like functions, such as rectifiers, switches, or transistors requires a source and a drain, and one or more localized electronic levels. The roles of source and drain (both as working electrodes WEI and WE2) may be represented by the tip of an STM, combined with an appropriate substrate or, alternatively, a pair of nanoelectrodes see Fig. 3. 

The donor electron level, cd, which may be derived in the same way that the orbital electron level in atoms is derived, is usually located close to the conduction band edge level, ec, in the band gap (ec - Ed = 0.041 eV for P in Si). Similarly, the acceptor level, Ea, is located close to the valence band edge level, ev, in the band gap (ea - Ev = 0.057 eV for B in Si). Figure 2-15 shows the energy diagram for donor and acceptor levels in semiconductors. The localized electron levels dose to the band edge may be called shallow levels, while the localized electron levels away from the band edges, assodated for instance with lattice defects, are called deep levels. Since the donor and acceptor levels are localized at impurity atoms and lattice defects, electrons and holes captured in these levels are not allowed to move in the crystal unless they are freed from these initial levels into the conduction and valence bands. 

As mentioned in Sec. 1.3, the electrochemical potential of electrons in condensed phases corresponds to the Fermi level of electrons in the phases. There are two possible cases of electron ensembles in condensed phases one to which the band model is applicable (in the state of degenera< where the wave functions of electrons overlap), and the other to which the band model cannot apply (in the state of nondegeneracy where no overlap of electron wave functions occurs). In the former case electrons or holes are allowed to move in the bands, while in the latter case electrons are assumed to be individual particles rather than waves and move in accord with a thermal hopping mechanism between the a4jacent sites of localized electron levels. 

Fig. 2-26. Localized electron levels of lattice defects and impurities in metal oxides Mi = interstitial metal ion Vm = metal ion vacancy V = oxide ion vacancy D = donor impurity A = acceptor impurity.

Fig. 2-27. Localized electron levels oflattice defects in zincoxide. [From Kroger, 1974.]...

As shown in Fig. 2- 3, localized electron levels arise (A and C in the figure) near the band edges at relatively high state densities tailing into the band gap these are called diffuse band tail states. Further, localized electron levels may occur due to dangling bonds and impurities (B in the figure) in the band gap, which are called gap states. 

In the case of aqueous solutions containing dissolved particles (solutes), a number of localized electron levels associated with solute particles Eirise in the mobility gap of aqueous solutions as shown in Fig. 2-34. These localized electron levels of solutes may be compared with the localized impiuity levels in semiconductors. In electrochemistry, the electron levels of the solutes of general interest are those located within the energy range from - 4 eV to - 6 eV (around the electron levels of the hydrogen and oxygen electrode reactions) in the mobility gap. 

Fig. 2-35. Localized electron levels of gaseous redox particles, Fe /Fe I = ionization energy of Fe A = electron affinity of Fe (STO) = standard gaseous electrons tsro = standard gaseous electron level (reference zero level).

The localized electron level of hydrated particles in aqueous solutions, different from that of particles in solids, does not remain constant but it fluctuates in the range of reorganization energy, X, because of the thermal (rotational and vibrational) motion of coordinated water molecules in the hydration structure. The electron levels cox,a and esmo are the most probable levels of oxidants and reductants, respectively. 

As the localized electron level of hydrated redox particles distributes itself in a rather wide range, we may assume the presence of energy bands in which the redox electron level fluctuates the reductant particles form a donor band, and the oxidant particles form an acceptor band. The donor and acceptor bands overlap in the tailing of their probability densities as shown in Fig. 2-39. 

The interface of semiconductor electrodes iiequently contains more or less localized electron levels called either surface states or interface states. In this textbook we use the term of surface states. 

Observations with microcrystals of semiconductor sihcon have shown that the transition from the model of localized electron levels quantum size) to the band model of delocalized electron levels (microscopic or macroscopic size) occurs at about 2 nm [Kanemitsu-Uto-Masumoto, 1993]. It appears, then, that the band model can apply to passive films thicker than 2 nm. Further, accoimting that the film interacts with the substrate metal, the band model may apply even to the range of thickness less than 2 nm. 

Most of the modern theories of the photoconductivity sensitization consider that local electron levels play the decisive role in filling up the energy deficit The photogeneration of the charge carriers from these local levels is an essential part of the energy transfer model. Regeneration of the ionized sensitizer molecule due to the use of the carriers on the local levels takes place in the electron transfer model. The existence of the local levels have now been proved for practically all sensitized photoconductors. The nature of these levels has to be established in any particular material. A photosensitivity of up to 1400 nm may be obtained for the known polymer semiconductors. There are a lot of sensitization models for different types of photoconductors and these will be examined in the corresponding sections. 

The main scheme is shown in Fig. 17. The photogenerated electron hole pairs transfer to the soliton-antisoliton pairs in 10 13s. Two kinks appeared in the polymer structure, which separates the degenerated regions. Due to the degeneration, two charged solitons may move without energy dissipation in the electric field and cause the photoconductivity. The size of the soliton was defined as 15 monomer links with the mass equal to the mass of the free electron. In the scheme in Fig. 17, the localized electron levels in the forbidden gap correspond to the free ( + ) and twice occupied ( — ) solitons. The theory shows the suppression of the interband transitions in the presence of the soliton. For cis-(CH)n the degeneration is absent, the soliton cannot be formed and photoconductivity practically does not exist. 

As discussed early in this chapter, quantum confinement has little effect on the localized electronic levels of lanthanide ions doped in insulating nanocrystals. But when the particle size becomes very small and approaches to a few nanometers, some exceptions may be observed. The change of lanthanide energy level structure in very small nanocrystals (1-10 nm) is due to a different local environment around the lanthanide ion that leads to a drastic change in bond length and coordination number. Lanthanide luminescence from the new sites generated in nanoparticles can be found experimentally. The most typical case is that observed in nanofilms ofEu Y203 with a thickness of 1 nm, which exhibits a completely different emission behavior from that of thick films (100-500 nm) (Bar et al., 2003). 

For a positive polaron (Figure 5-5b), two localized electronic levels, bonding and antibonding, are formed within the band gap. One electron is removed from the polaron bonding level. Thus, a positive polaron is expected to have the following three intragap transitions ... 

The electronic structure of a positive bipolaron is shown in Figure 4-5d. Since the geometric changes for a bipolaron are larger than those for a polaron, localized electronic levels appearing in the band gap for a bipolaron are farther away from the band edges than for a polaron. Two electrons are removed from the bipolaron... 

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