Fermi equilibration

Semiconductor - Electrolyte Interlace The electric field in the space charge region that may develop at the semiconductor electrolyte interface can help to separate photogenerated e /h 1 couples, effectively suppressing recombination. When a semiconductor is brought into contact with an electrolyte, the electrochemical potential of the semiconductor (corresponding to the Fermi level, Ey of the solid [50]) and of the redox couple (A/A ) in solution equilibrate. When an n-type semiconductor is considered, before contact the Ey of the solid is in the band gap, near the conduction band edge. After contact and equilibration the Ey will... 

Fermi level equilibration in quantum dot-metal nanojunctions, J. Phys. Chem. B 105 (2001) 8810-8815. 

V. Subraniam, E. Wolf, P.V. Kamat, Catalysis with Ti02/gold nanocomposites. Effect of metal particle size on the Fermi level equilibration, J. Am. Chem. Soc. 126 (2004) 4943-4950. 

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. 

At equilibrium the Fermi level is equilibrated between the electrode and the redox particles (erm) = erredox)) hence, Eqn. 8-18 gives Eqn. 8-19 ... 

Figure 8-11 shows as a function of electron energy e the electron state density Dgdit) in semiconductor electrodes, and the electron state density Z e) in metal electrodes. Both Dsd.t) and AKe) are in the state of electron transfer equilibrium with the state density Z>bei)ox(c) of hydrated redox particles the Fermi level is equilibrated between the redox particles and the electrode. For metal electrodes the electron state density Ai(e) is high at the Fermi level, and most of the electron transfer current occurs at the Fermi level enio. For semiconductor electrodes the Fermi level enao is located in the band gap where no electron level is available for the electron transfer (I>sc(ef(so) = 0) and, hence, no electron transfer current can occur at the Fermi level erso. Electron transfer is allowed to occur only within the conduction and valence bands where the state density of electrons is high (Dsc(e) > 0). 

When the cell circuit is closed in the dark, as shown in Fig. 10-25(b), the Fermi level is equilibrated between the metallic cathode and the n-lype semiconductor anode. As a result, a depletion layer of space charge (potential barrier, is formed in the semiconductor anode, thereby shifting the potential of the anode from the flat band potential to a more anodic (more positive) potential (= + ). In the dark, however, the anodic hole transfer... 

Figure 10-30(a) applies to an open circuit cell in the dark Fig. 10-30(b) applies to a short circuit cell in the dark. After the cell circuit is closed in the dark, the Fermi level is equilibrated between the two electrodes thereby forming a space charge layer both in the n-tyi>e anode and in the p-type cathode. The overall potential, AE, generated in the two space charge layers nearly equals the difference of the flat band potential between the n-type anode and the p-type cathode as eiqpressed in Eqn. 10-57 ... 

The electrochemical potential of the solution and semiconductor, see Fig. 3.6, are determined hy the standard redox potential of the electrolyte solution (or its equivalent the standard redox Fermi level, Ep,redo, and the semiconductor Fermi energy level. If these two levels do not lie at the same energy then movement of charge across the semiconductor - solution interface continues until the two phases equilibrate with a corresponding energy band bending, see Fig. 3.8. 

Hetero junctions, forming a Schottky barrier like a metal-semiconductor junction, normally change the energy levels of conduction and valence bands. When the Fermi level of the semiconductor equilibrates with the energy level of the redox couple in the solution, the electric energy level at the surface is pinned and a depletion layer is formed. This is postulated since the rectified current can be observed at semiconductor plate electrodes. The bending of the band in the semiconductor at the surface can be described as a solution of the one-dimensional Poisson-Boltzmann equation... 

The amorphous nucleation layer has the consequence that the Fermi level of the growing ZnO films reaches its equilibrium value already at very low thickness ( 2nm). This is particularly important for ZnO Al films, where the Fermi level changes by more than 1 eV upon the addition of oxygen to the sputter gas. The amorphous nucleation layer, therefore, substitutes the space charge layer, which is usually necessary for charge equilibration at the interface. This important effect is illustrated in Fig. 4.25. 

An insulator, on the other hand, has an ill-defined Fermi level which does not equilibrate with the spectrometer. Instead, the vacuum level of the insulator (E ) aligns with the local electrostatic potential surrounding its surface. An insulator more than a micron thick (which is the case for most catalyst samples analyzed by XPS) will not be within the local potential of the metal sample holder. The insulator will be separated from the spectrometer vacuum level (EJ) by some voltage (Vp) (30). This voltage will depend on the geometry of the sample holder and on the energy and flux of electrons from the x-ray source, the flood gun, the sample itself, and all other sources within the chamber. The potential Vp cannot be reliably measured. 

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