Surface state electrons, equilibration

The concept of equilibration of surface states at an interface may be illustrated by the case in which the two contacting phases are solids. In such a case, the energy levels of the surface state electron can be used to explain the surface state equilibration that occurs on contact. When two dissimilar surfaces contact each other, the transfer of surface state electrons occurs to equilibrate the energy levels of surface state electrons at the newly created interface. When two surfaces are separated, each surface retains the equilibrium electron level, which has been just attained on the contact, leading to the creation of the static charge, if a material is, or both materials are, nonconducting. In such a case, the two surfaces stick together by the coulombic attraction and it is necessary to apply force to separate them. 

Completing a circuit and measuring the current that flows on contact or separation can quantify the transfer of electrons [2]. A typical result on contact electrification is shown in Figure 24.3. The time constants associated with the current peaks can be adjusted by inserting a series resistance in the measurement circuit. In real time, the equilibration of surface state electrons occurs instantaneously. In these experiments, the plasma polymer of tetrafluoroethylene (TFE) was deposited on two different substrate, nylon film and polished brass, and the contact and separation currents were measured with a (uncoated) brass probe... 

Figure 24.2 Schematic representation of the surface states equilibration illustrated by the transfer of surface state electrons.

The surface Fermi level, Cp, which depends on the surface state, is not the same as the interior Fermi level, ep, which is determined by the bulk impurity and its concentration. As electron transfer equilibrium is established, the two Fermi levels are equilibrated each other (ep = ep) and the band level bends downward or upward near the surface forming a space charge layer as shown in Fig. 2-31. 

Surface states can arise simply because the atomic bonding at a semiconductor surface is necessarily different from that in the bulk. For example, in a Si lattice, the bonds at the Si surface are not ftilly coordinatively saturated. To relieve this unsaturation, either a surface reconstruction can occur and/or bonds to the metallic material can be formed. This distinct type of surface bonding results in a localized electronic structure for the surface which is different from that in the bulk. The energies of these localized surface orbitals are not restricted to reside in the bands of the bulk material, and can often be located at energies that are inside the band gap of the semiconductor. Orbitals that reside in this forbidden gap region are particularly important, because they will require modifications of our ideal model of charge equilibration at semiconductor/metal interfaces. ... 

As discussed in Section 2, one key assumption of reaction field models is that the polarization field of the solvent is fully equilibrated with the solute. Such a situation is most likely to occur when the solute is a long-lived, stable molecular structure, e g., the electronic ground state for some local minimum on a Bom-Oppenheimer potential energy surface. As a result, continuum solvation models... 

Let us refer to Figure 5-7 and start with a homogeneous sample of a transition-metal oxide, the state of which is defined by T,P, and the oxygen partial pressure p0. At time t = 0, one (or more) of these intensive state variables is changed instantaneously. We assume that the subsequent equilibration process is controlled by the transport of point defects (cation vacancies and compensating electron holes) and not by chemical reactions at the surface. Thus, the new equilibrium state corresponding to the changed variables is immediately established at the surface, where it remains constant in time. We therefore have to solve a fixed boundary diffusion problem. 

According to the Franck-Condon principle, the photoexcitation triggers a vertical transition to the excited state, which is followed by a rapid nuclear equilibration. Without donor excitation, the electron transfer process would be highly endothermic. However, after exciting the donor, electron transfer occurs at the crossing of the equilibrated excited state surface and the product state. 

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