Fermi level semiconductor electrodes

Fig. 8-16. Electron state density for a redox electron transfer reaction of h3rdrated redox particles at semiconductor electrodes (a) in the state of band edge level pinning and (b) in the state of Fermi level pinning dashed curve = band edge levels in reaction equilibrium solid curve = band edge levels in anodic polarization e p,sq = Fermi level of electrode in anodic polarization e v and c c = band edge levels in anodic polarization.

The effects of complexation of redox particles on the redox reaction kinetics are frequently more evident with semiconductor electrodes than with metal electrodes, since the transfer of electrons takes place at the band edge levels rather than at the Fermi level of electrodes. For example, the anodic transfer of... 

It is to be noted that the positive direction of the potential axis in the semiconductor is in conformity with the direction chosen as positive in the physical scale of energy (see Section 2.2). Indeed, in formula (17), the terms characterizing the position of the Fermi level and electrode potential have opposite signs. 

Figure 13-4. Encigy level diagnim of a single-layer OLED, where the organic malerial is depicted as a fully depleted semiconductor. The valence band Ey corresponds to the HOMO and the conduction band Ec corresponds to the LUMO. Tile Fermi levels of the two metal electrodes are marked as Et-. Upon contact a built-in potential is established and needs to be compensated for, before the device will begin to operating.

It follows from the Franck-Condon principle that in electrochemical redox reactions at metal electrodes, practically only the electrons residing at the highest occupied level of the metal s valence band are involved (i.e., the electrons at the Fermi level). At semiconductor electrodes, the electrons from the bottom of the condnc-tion band or holes from the top of the valence band are involved in the reactions. Under equilibrium conditions, the electrochemical potential of these carriers is eqnal to the electrochemical potential of the electrons in the solution. Hence, mntnal exchange of electrons (an exchange cnrrent) is realized between levels having the same energies. 

Because of the excess holes with an energy lower than the Fermi level that are present at the n-type semiconductor surface in contact with the solution, electron ttansitions from the solution to the semiconductor electrode are facilitated ( egress of holes from the electrode to the reacting species ), and anodic photocurrents arise. Such currents do not arise merely from an acceleration of reactions which, at the particular potential, will also occur in the dark. According to Eq. (29.6), the electrochemical potential, corresponds to a more positive value of electrode potential (E ) than that which actually exists (E). Hence, anodic reactions can occur at the electrode even with redox systems having an equilibrium potential more positive than E (between E and E ) (i.e., reactions that are prohibited in the dark). 

The electrons produced in the conduction band as a result of illumination can participate in cathodic reactions. However, since in n-type semiconductors the quasi-Fermi level is just slightly above the Fermi level, the excited electrons participating in a cathodic reaction will almost not increase the energy effect of the reaction. Their concentration close to the actual surface is low hence, it will be advantageous to link the n-type semiconductor electrode to another electrode which is metallic, and not illuminated, and to allow the cathodic reaction to occur at this electrode. It is necessary, then, that the auxiliary metal electrode have good catalytic activity toward the cathodic reaction. 

The band edges are flattened when the anode is illuminated, the Fermi level rises, and the electrode potential shifts in the negative direction. As a result, a potential difference which amounts to about 0.6 to 0.8 V develops between the semiconductor and metal electrode. When the external circuit is closed over some load R, the electrons produced by illumination in the conduction band of the semiconductor electrode will flow through the external circuit to the metal electrode, where they are consumed in the cathodic reaction. Holes from the valence band of the semiconductor electrode at the same time are directly absorbed by the anodic reaction. Therefore, a steady electrical current arises in the system, and the energy of this current can be utilized in the external circuit. In such devices, the solar-to-electrical energy conversion efficiency is as high as 5 to 10%. Unfortunately, their operating life is restricted by the low corrosion resistance of semiconductor electrodes. 

The photoelectrolysis of H2O can be performed in cells being very similar to those applied for the production of electricity. They differ only insofar as no additional redox couple is used in a photoelectrolysis cell. The energy scheme of corresponding systems, semiconductor/liquid/Pt, is illustrated in Fig. 9, the upper scheme for an n-type, the lower for a p-type electrode. In the case of an n-type electrode the hole created by light excitation must react with H2O resulting in 02-formation whereas at the counter electrode H2 is produced. The electrolyte can be described by two redox potentials, E°(H20/H2) and E (H20/02) which differ by 1.23 eV. At equilibrium (left side of Fig. 9) the electrochemical potential (Fermi level) is constant in the whole system and it occurs in the electrolyte somewhere between the two standard energies E°(H20/H2) and E°(H20/02). The exact position depends on the relative concentrations of H2 and O2. Illuminating the n-type electrode the electrons are driven toward the bulk of the semiconductor and reach the counter electrode via the external circuit at which they are consumed for Hj-evolution whereas the holes are dir tly... 

Degeneracy can be introduced not only by heavy doping, but also by high density of surface states in a semiconductor electrode (pinning of the Fermi level by surface states) or by polarizing a semiconductor electrode to extreme potentials, when the bands are bent into the Fermi level region. 

The electrochemical potential of an electron in a solid defines the Fermi energy (cf. Eq. 3.1.9). The Fermi energy of a semiconductor electrode (e ) and the electrolyte energy level (credox) are generally different before contact of both phases (Fig. 5.60a). After immersing the semiconductor electrode into the electrolyte, an equilibrium is attained ... 

In addition to the stoichiometry of the anodic oxide the knowledge about electronic and band structure properties is of importance for the understanding of electrochemical reactions and in situ optical data. As has been described above, valence band spectroscopy, preferably performed using UPS, provides information about the distribution of the density of electronic states close to the Fermi level and about the position of the valence band with respect to the Fermi level in the case of semiconductors. The UPS data for an anodic oxide film on a gold electrode in Fig. 17 clearly proves the semiconducting properties of the oxide with a band gap of roughly 1.6 eV (assuming n-type behaviour). 

There is a fundamental difference between electron-transfer reactions on metals and on semiconductors. On metals the variation of the electrode potential causes a corresponding change in the molar Gibbs energy of the reaction. Due to the comparatively low conductivity of semiconductors, the positions of the band edges at the semiconductor surface do not change with respect to the solution as the potential is varied. However, the relative position of the Fermi level in the semiconductor is changed, and so are the densities of electrons and holes on the metal surface. 

Consider the interface between a semiconductor and an aqueous electrolyte containing a redox system. Let the flat-band potential of the electrode be fb = 0.2 V and the equilibrium potential of the redox system o = 0.5 V, both versus SHE. Sketch the band bending when the interface is at equilibrium. Estimate the Fermi level of the semiconductor on the vacuum scale, ignoring the effect of dipole potentials at the interface. 

The maximum voltage of the DSSC is given by the energy gap between the Fermi level of the semiconductor electrode and the redox potential of the mediator. 

Since the electron state density near the Fermi level at the degenerated surface (Fermi level pinning) is so high as to be comparable with that of metals, the Fermi level pinning at the surface state, at the conduction band, or at the valence band, is often called the quasi-metallization of semiconductor surfaces. As is described in Chap. 8, the quasi-metallized surface occasionally plays an important role in semiconductor electrode reactions. 

Simple calculation gives a comparable distribution of the electrode potential in the two layers, (64< >h/64( sc) = 1 at the surface state density of about 10cm" that is about one percent of the smface atoms of semiconductors. Figure 5—40 shows the distribution of the electrode potential in the two layers as a function of the surface state density. At a surface state density greater than one percent of the surface atom density, almost all the change of electrode potential occurs in the compact layer, (6A /5d )>l, in the same way as occurs with metal electrodes. Such a state of the semiconductor electrode is called the quasi-metallic state or quasi-metallization of the interface of semiconductor electrodes, which is described in Sec. 5.9 as Fermi level pinning at the surface state of semiconductor electrodes. 

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.

In the state of Fermi level pinning, the Fermi level at the interface is at the surface state level both where the level density is high and where the electron level is in the state of degeneracy similar to an allowed band level for electrons in metals. The Fermi level pinning is thus regarded as quasi-metallization of the interface of semiconductor electrodes, making semiconductor electrodes behave like metal electrodes at which all the change of electrode potential occurs in the compact layer. 

Such an interfacial degeneracy of electron energy levels (quasi-metallization) at semiconductor electrodes also takes place when the Fermi level at the interface is polarized into either the conduction band or the valence band as shown in Fig. 5-42 (Refer to Sec. 2.7.3.) namely, quasi-metallization of the electrode interface results when semiconductor electrodes are polarized to a great extent in either the anodic or the cathodic direction. This quasi-metallization of electrode interfaces is important in dealing with semiconductor electrode kinetics, as is discussed in Chap. 8. It is worth noting that the interfacial quasi-metallization requires the electron transfer to be in the state of equilibrimn between the interface and the interior of semiconductors this may not be realized with wide band gap semiconductors. 

Figure 5-45 shows the differential capacity for an intrinsic semiconductor electrode of germanium estimated by calculation as a function of electrode potential. Here, the capacity is minimum at the flat band potential, Ea, where is zero. As the electrode potential shifts so far away from that the Fermi level at the interface may be dose to the band edge levels, Fermi level pinning is reaUzed both with A sc remaining constant and with Csc being constant and independent of the electrode potential. 

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