Band edge level pinning

Band Edge Level Pinning and Fermi Level Pinning... 

Figure 5-41 illustrates the profile of electron level across the interfadal double layer of a semiconductor electrode (A) in the state of band edge level pinning and (B) in the state of Fermi level pinning. In Fig. 5-41 the cathodic polarization... 

Fig. S-41. Band edge levels and Fermi level of semiconductor electrode (A) band edge level pinning, (a) flat band electrode, (b) under cathodic polarization, (c) under anodic polarization (B) Fermi level pinning, (d) initial electrode, (e) under cathodic polarization, (f) imder anodic polarization, ep = Fermi level = conduction band edge level at an interface Ev = valence band edge level at an interface e = surface state level = potential across a compact layer.

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. 

In the state of band edge level pinning, the band edge levels, Sc and Cy, at the interface of electrodes remain unchanged and independent of the electrode potential. Figure 8-18 shows both the band edge level of several semiconductor... 

Next, we consider the anodic reaction current of redox electron transfer via the conduction band, of which the exchange reaction current has been shown in Fig. 8-16. Application of a slight anodic polarization to the electrode lowers the Fermi level of electrode fix>m the equilibrium level (Ep(sc)( n = 0) = eiiOTSDca)) to a polarized level (ep(8C)( n) = ep(REDox)- n)withoutchanging at the electrode interface the electron level relative to the redox electron level (the band edge level pinning) as shown in Fig. 8-20. As a result of anodic polarization, the concentration of interfacial electrons, n, in the conduction band decreases, and the concentration of interfadal holes, Pm, in the valence band increases. Thus, the cathodic transfer current of redox electrons, in, via the conduction band decreases (with the anodic electron im ection current, ii, being constant), and the anodic transfer current of redox holes, (p, via the valence band increases (with the cathodic hole injection... 

Under the condition of band edge level pinning, where the interfacial electron level of electrode relative to the redox electron level of redox particles is imchanged, the level differences of ej - ered and ej. - eqx remain constant irrespective of any change of the electrode potential. Consequently, the anodic transfer current of redox electrons, in(T ), in Eqn. 8—60 is independent of the overvoltage and remains equal to the exchange current ia.o as expressed in Eqn. 8-62 ... 

Tafel constant Band edge level pinning (t) = nsc) Fermi level pinning (r = tih)... 

Fig. 8-24. Redox reaction currents via the conduction and the valence bands of semiconductor electrode as functions of electrode potential of semiconductor anodic polarization corresponds to Figs. 8-20, 8-21 and 8-22. i (i )= anodic (cathodic) current in (ip) = reaction crnrent via the conduction (valence) band BLP = band edge level pinning FLP = Fermi level pinning.

The polarization curves shown in Fig. 8-27 correspond to Eqns. 8-62 to 8-65 while the electrode is in the state of band edge level pinning. As examples, Fig. 8-28 shows the cathodic polarization curves of several redox reactions at an... 

Equation 9-36 3delds the anodic ion transfer current, i, in the state of band edge level pinning (ti = isc, t h = 0) as shown in Eqn. 9-37 ... 

Generally, the band edge level pinning arises at low overvoltages at which the Fermi level at the interface is within the band gap whereas, the Fermi level pinning arises at high overvoltages at which the Fermi level at the interface is in the valence band (Refer to Sec. 5.7.). 

Equation 9-54 indicates that when tiie electrode interface is in the state of band edge level pinning is constant), the concentration of surface cations increases with increasing anodic polarization. 

In the state of band edge level pinning where all the change in electrode potential occurs in the space diarge layer, Mec, the anodic polarization curve of the oxidative dissolution follows Eqn. 9-53. As anodic polarization increases, the electrode interface enters a state of Fermi level pinning, in which all the change in electrode potential occurs in the compact layer, A ir, and the concentration of surface cations in Eqns. 9-54 then decreases with increasrng anodic polarization. 

Fig. 9-16. Polarization curves of anodic oxidative dissolution and cathodic reductive dissolution of semiconductor electrodes of an ionic compound MX iiixcp) (iMxh )== anodic oxidative (cathodic reductive) dissolution current solid curve = band edge level pinning at the electrode interface, dashed curve = Fermi level pinning.

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...

We consider dehydration-adsorption of hydrated protons (cathodic proton transfer) and desorption-hydration of adsorbed protons (anodic proton transfer) on the interface of semiconductor electrodes. Since these adsorption and desorption of protons are ion transfer processes across the compact layer at the interface of semiconductor electrodes, the adsorption-desorption equilibrium is expressed as a function of the potential of the compact layer in the same way as Eqns. 9-60 and 9-61. In contrast to metal electrodes where changes with the electrode potential, semiconductor electrodes in the state of band edge level pinning maintain the potential d(hi of the compact layer constant and independent of the electrode potential. The concentration of adsorbed protons, Ch , is then determined not by the electrode potential but by the concentration of h3 ated protons in aqueous solutions. 

It follows that the ratio of concentrations Ch /ch , in adsorption equilibrium on semiconductor electrodes, in the state of band edge level pinning, changes with changing electrode potential as shown in Fig. 9-20. This differs from the case of metal electrodes where the ratio of concentrations remains constant irrespective of the electrode potential (Refer to Sec. 9.3.). Combining Eqns. 9-60 and 9-67 to produce Eqn. 9-68 describes the concentration of adsorbed hydrogen atoms as an exponential function of the electrode potential ( 4>sc) for low adsorption coverages ... 

When the n-type anode and the p-type cathode are in the state of band edge level pinning, the overall potential due to the two space charge layers remains constant even in the state of photoexcitation. 

In the active state, the dissolution of metals proceeds through the anodic transfer of metal ions across the compact electric double layer at the interface between the bare metal and the aqueous solution. In the passive state, the formation of a thin passive oxide film causes the interfadal structure to change from a simple metal/solution interface to a three-phase structure composed of the metal/fUm interface, a thin film layer, and the film/solution interface [Sato, 1976, 1990]. The rate of metal dissolution in the passive state, then, is controlled by the transfer rate of metal ions across the film/solution interface (the dissolution rate of a passive semiconductor oxide film) this rate is a function of the potential across the film/solution interface. Since the potential across the film/solution interface is constant in the stationary state of the passive oxide film (in the state of band edge level pinning), the rate of the film dissolution is independent of the electrode potential in the range of potential of the passive state. In the transpassive state, however, the potential across the film/solution interface becomes dependent on the electrode potential (in the state of Fermi level pinning), and the dissolution of the thin transpassive film depends on the electrode potential as described in Sec. 11.4.2. 

In the range of potential of the passive state the passive oxide film is in the state of band edge level pinning at the film/solution interface hence, the potential A( )h across the film/solution interface remains constant irrespective of the electrode potential of the passive metal. With increasing anodic polarization and in the... 

Fig. 11-11. Potential at a film/solution interface and potential dfp in a passive film as a fimction of anodic potential of a passive metal electrode in the stationary state the interface is in the state of band edge level pinning to the extent that the Fermi level e, is within the band gap, but the interface changes to the state of Fermi level pinning as e, coincides with the valence band edge Cy.

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