Bulk electronic levels

In a simple electron transfer reaction, the reactant is situated in front of the electrode, and the electron is transferred when there is a favorable solvent fluctuation. In contrast, during ion transfer, the reactant itself moves from the bulk of the solution to the double layer, and then becomes adsorbed on, or incorporated into, the electrode. Despite these differences, ion transfer can be described by essentially the same formalism [Schmickler, 1995], but the interactions both with the solvent and with the metal depend on the position of the ion. In addition, the electronic level on the reactant depends on the local electric potential in the double layer, which also varies with the distance. These complications make it difficult to perform quantitative calculations. 

The physical properties necessary for the control of the electrical conductivity by surface traps may be indicated by a brief calculation. If we assume that the surface levels are deeper than the bulk donor levels, a large fraction of the electrons from the donors may be trapped on the surface, and the conductivity will be strongly dependent on the properties of the surface traps. 

The absence of an enormous enhancement in radiative decay rates in the nanocrystals can also be verified by electronic absorption spectroscopy. The original claim stated that the Mn2+ 47) —> 6A1 radiative decay lifetime dropped from xrad = 1.8 ms in bulk Mn2+ ZnS to xrad = 3.7 ns in 0.3% Mn2+ ZnS QDs ( 3.0 nm diameter) (33). This enhancement was attributed to relaxation of Mn2+ spin selection rules due to large sp-d exchange interactions between the dopant ion and the quantum-confined semiconductor electronic levels (33, 124— 127). Since the Mn2+ 47 > 6Ai radiative transition probability is determined... 

Fig. 5. (a) Bulk electronic concentration at the metal—oxide interface and electron-hole concentration at the oxide—oxygen interface associated with equilibrium interfacial reactions, (b) Electronic energy-level diagram illustrating the dielectric (or semiconducting) nature of the oxide, with the possibility of electron transport (e.g. by tunneling or thermal emission) from the metal to fill O levels at the oxide—oxygen interface to create a potential difference, VM, across the oxide. 

The bulk electronic properties of extrinsic semiconductors are largely determined by the level of doping that is used to make the materials n-type or p-type. For non-degenerate semiconductors, the electron concentration in the conduction band and the hole concentration in the valence band are related to the Fermi energy EF and to the effective densities of states in the conduction and valence bands (Nc and Ny respectively) by... 

Figure 2 Simplified explanation of transition from a small molecule (a) via a nanoparticle (b) to the bulk (c) with respect to the electronic situation. Between states a and c there is a situation to be expected with broadened electronic levels (b)...

The use of Eqs. (30) and (31) was criticized by Hupp and Weaver [131], because these equations imply that the activation occurs only by the transfer of translational energy. However, in the condensed phase the activation may occur through solvent polaron fluctuations and the transfer of oscillation energy of solvent molecules in the bulk to solvent molecules in the immediate vicinity of the reactant or even to electronic levels of the reactant [105, 132]. 

Since most "surface-sensitive" techniques sample at least a few atomic planes into the sample, it is difficult to experimentally separate the electronic structure of the outermost plane of atoms from that of the planes below. Theoretical calculations are able to clearly separate surface from bulk electronic structure, of course it is common to calculate a separate electronic density-of-states for each plane in the crystal structure ("layer density-of-states"). Significant changes from the bulk electronic structure are sometimes found for the surface planes in calculations. However, it is difficult to confirm those results experimentally [1]. In some oxides, the bandgap at the surface has been observed to narrow compared to that of the bulk. The measured core-level binding energies of partially coordinated surface atoms are often shifted, by as much as an eV, from their bulk values [32] these are referred to as "surface core-level shifts". However, the experimental separation of surface from bulk electronic structure is at present far from satisfactory. 

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