Equivalent Fermi level

Fig. 4-21. Electron energy levels of an ionic electrode of silver-silver chloride in ion transfer equilibrium cfia ) = Fermi level of electron in silver part of electrode snvAfCici-) = equivalent Fermi level to transfer equilibriiun of silver ions and chloride ions in silver-silver chloride electrode.

In order that the oxidative and the reductive dissolution reactions may proceed, the affinity for the reaction is required to be positive the reaction affinity is represented by the difference between the Fermi level, ef(sc), of the electrode and the equivalent Fermi level Er(dK) of the ion transfer reaction (Refer to Sec. 4.4.). 

Fig. 9-18. Band edge levels and equivalent Fermi levels of oxidative and reductive dissolution reactions of compound semiconductors in aqueous sohitions at pH 7 en ) - F(a

Figure 9-18 illustrates the band edge levels of compound semiconductor electrodes in aqueous solutions and the equivalent Fermi levels of the following oxidative and reductive dissolution reactions ... 

Charge transfer reactions on semiconductor electrodes proceed under the condition of anodic and cathodic polarization in which the Fermi level epfsc) is different either from the Fermi level Eputicox) of redox electron transfer reactions or from the equivalent Fermi level ep,ioN) of ion transfer reactions. For redox electron transfer reactions, thermodynamic requirement for the anodic and cathodic reactions to proceed is given by the following inequalities ... 

Fig. 3. (a) Depiction of central Brillouin zone and allowed graphene sheet states for a [4,3] nanolube conformation. Note Fermi level for graphene occurs at K points at vertices of hexagonal Brillouin zone, (b) Extended Brillouin zone pie-ture of [4,3] nanotube. Note that top left hexagon is equivalent to bottom right hexagon. 

By comparing Figure 11.9 and the characteristic Po2(Uwr) rate breaks of the inset of Fig. 11.9 one can assign to each support an equivalent potential Uwr value (Fig. 11.10). These values are plotted in Figure 11.11 vs the actual work function G>° measured via the Kelvin probe technique for the supports at po2-l atm and T=400°C. The measuring principle utilizing a Kelvin probe and the pinning of the Fermi levels of the support and of metal electrodes in contact with it has been discussed already in Chapter 7 in conjunction with the absolute potential scale of solid state electrochemistry.37... 

In solid-state physics, the electrochemical potential of the electron pe(a) is mostly replaced by the equivalent energy of the Fermi level eF. While the electrochemical potential is usually related to one mole of particles, the Fermi energy is related to a single electron, so that... 

In this chapter we introduce and discuss a number of concepts that are commonly used in the electrochemical literature and in the remainder of this book. In particular we will illuminate the relation of electrochemical concepts to those used in related disciplines. Electrochemistry has much in common with surface science, which is the study of solid surfaces in contact with a gas phase or, more commonly, with ultra-high vacuum (uhv). A number of surface science techniques has been applied to electrochemical interfaces with great success. Conversely, surface scientists have become attracted to electrochemistry because the electrode charge (or equivalently the potential) is a useful variable which cannot be well controlled for surfaces in uhv. This has led to a laudable attempt to use similar terminologies for these two related sciences, and to introduce the concepts of the absolute scale of electrochemical potentials and the Fermi level of a redox reaction into electrochemistry. Unfortunately, there is some confusion of these terms in the literature, even though they are quite simple. 

Fermi level to or hypothetical Fermi level of the metal ion transfer equilibrium i.e. the Fermi level of hypothetical electrons equivalent to the metal ion level in the ion transfer equilibrium. 

Further, the electron level of adsorbed particles differs from that of isolated adsorbate i>articles in vacuum as shown in Fig. 5-5, this electron level of the adsorbate particle shifts in the course of adsorption by a magnitude equivalent to the adsorption energy of the particles [Gomer-Swanson, 1963]. In the illustration of Fig. 5-5, the electron level of adsorbate particles is reduced in accordance with the potential energy curve of adsorption towards its lowest level at the plane of adsorption where the level width is broadened. In the case in which the allowed electron energy level of adsorbed particles, such as elumo and ehcmio, approaches the Fermi level, ep, of the adsorbent metal, an electron transfer occurs between... 

As the Fermi level of the electrode approaches the surface state level of high state density, the surface state is charged or discharged as a capacitor. For convenience sake, we express the sum of a. and in Eqn. 5-86 as the surface state charge Qu and the capacity due to the surface state charge as the surface state capacity C.. Then, the interfadal capadty C is represented by the capadly of an equivalent drcuit shown in Fig. 5-60. 

The surface state capacity, Ch, is apparently zero in the range of potential where the Fermi level is located away from the surface state level (the state of band edge level pinning). As the Fermi level is pinned at the surface state, the capacity Ch increases to its maximum which is equivalent to the capacity Ch of the compact layer, because the surface state charging is equivalent to the compact layer charging in the state of Fermi level pinning. 

As the electrode potential is polarized fh>m the equilibritun potential of the redox reaction, the Fermi level efcid of electrons in the metal electrode is shifted from the Fermi level erredox) of redox electrons in the redox reaction by an energy equivalent to the overvoltage t) as expressed in Eqn. 8-24 ... 

Polarization shifts the Fermi level of the electrode epoo from the Fermi level of the redox electron ekredox) by an energy equivalent to an overvoltage tj as described in Eqn. 8-55 ... 

Fig. 9-17. Thermodynamic stability of electrodes of compound semiconductors relative to oxidative and reductive dissolution in the state of band edge level pinning (a) oxidative dissolution is thermodynamically impossible (eFXp.< Cb) oxidative dissolution may occur (er(p.dK)> Ev)> (c) reductive dissolution is thermodynamically impossible (cnn.M> E ), (d) reductive dissolution may occur < Cc) pip. sk) (cpbi. d i) = equivalent Fermi...

The quasi-Fermi level of interfacial holes nearly equals the Fermi level pe , ( pEp,.) in photoexcited p-type electrodes, but the quasi-Fermi level pej. of interfacial holes is lower than the Fermi level aSp,. (> p p,) in photoexcited n-type electrodes as shown in Fig. 10-21. It then follows that the range of electrode potential, where the anodic reaction occurs on the photoexcited n-type electrode, shifts itself, from the range of potential where the same anodic reaction occurs on the dark p-type electrode, toward the caliiodic (more negative) direction by an energy equivalent to (nEp - p p,). 

Figure 10-23 shows the electron levels and the polarization curves for the transfer of anodic redox holes both at a photoexcited n-fype electrode and at a dark p-type electrode of the same semiconductor. The range of potential where the anodic hole current occurs at the photoexcited n-type electrode is more cathodic (more negative) than the range of potential for the anodic hole current at the dark p-type electrode. The difference between the polarizatitm potential aE(i) (point N in the figure) of the photoexcited n-type electrode and the polarization potential pE(i) (point P in the figme) of the dark p-type electrode at a constant anodic current i is equivalent to the difference between the quasi-Fermi level pej of interfacial holes and the Fermi level bEf of interior holes (electrons) in the photoexcited n-type electrode this difference of polarization potential, in turn, equals the inverse overvoltage rip.sc(i) defined in Eqn. 10-46 ... 

Fig. 10-23. Energy levels and polarization curves for a redox reaction of anodic redox holes at a photoexdted n-type electrode and at a dark p-type electrode of the same semiconductor curve (1) = polarization curve of anodic transfer of photoexdted holes at an n-type electrode curve (2)= polarization curve of anodic transfer of holes at a p-type electrode in the dark (equivalent to a curve representing anodic current as a function of quasi-Fermi level of interfadal holes in a photoexdted n-type electrode) i = anodic transfer current of holes Eredox = equilibriiun potential of redox hole transfer N = anodic polarization at potential n (t) of a photoexdted n-type electrode P = anodic polarization at potential pE(i) of a dark p-type electrode.

When the n-type semiconductor anode is photoexcited, as shown in Fig. 10-25(c), the Fermi level of the anode is raised (the potential of the anode is lowered) by an energy equivalent to the photopotential at the same time, the Fermi... 

Since the highest possible Fermi level of the photoexcited n-type anode corresponds to the flat band potential of the semiconductor anode, the Fermi level of the metallic cathode short-circuited with the photoexcited n-lype anode can also be raised up to the level equivalent to the flat band potential of the semiconductor anode. In order for the cathodic electron transfer of hydrogen redox reaction to proceed at the metallic cathode, the Fermi level 1 of the cathode needs to be higher than the Fermi level of hydrogen redox reaction. Consequently, in... 

Fig. 10-32. Polarization curves of cell reaction for photoelectrolytic decomposition of water at a photoexdted n-type anode and at a photoezdted p-type cathode solid curve n-SC s anodic polarization curve of oxygen evolution at photoexdted n Qpe anode (Fermi level versus current curve) dashed curve n-SC = anodic polarization curve of oxygen evolution at dark p>type anode of the same semiconductor as photoexdted n-type anode (equivalent to the curve of current versus quasi-Fermi level of interfadal holes in photoezdted n-type anode) solid curve p-SC = cathodic polarization curve of hydrogen evolution at photoexdted p-type cathode (Fermi level versus current curve) dashed curve n-8Cr = cathodic polarization curve of hydrogen evolution at dark n-type electrode of the same semiconductor as photoezdted p-type cathode (equivalent to the curve of current versus quasi-Fermi level of interfadal electrons in photoexdted p-type cathode) > > = flat band potential of n-type (p-type) electrode nn.sc (v p sc) = inverse overvoltage for generation of photoexdted electrons (holes) in a p-type (n-type) electrode.

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. 

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