Valence band, semiconductor electrodes

The question of n- and p-type (excess charge carriers in conductivity and valence band, respectively) mechanisms of semiconductors is shown in Figs. 7.28 and 7.29. For this reason, p-type electrodes will be suitable as anodes,23 i.e., a deelectronation reaction, in which electrons are accepted from ions in the solution layer next to the electrode into the waiting holes in the valence band. Semiconductor doped n will be cathodes. 

In a light-emitting MSM structure the two metal electrodes selected such that the work functions of the electrodes are near the edge of the valence band (VB) and the conducting band (CB) of the semiconductor, respectively, so that oppositely charge carriers are injected from the opposite electrodes. An ohmic and a rectifying contact is therefore formed in the MSM structure (see Fig. 9-22). 

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.

Depending on the nature of the electrode and reaction, the carriers involved in an electrochemical reaction at a semiconductor electrode can be electrons from the conduction band (in the following to be called simply electrons), electrons from the valence band (holes), or both. The concentration of the minority carriers in semiconductors (electrons in p-type, and holes in n-type semiconductors) is always much... 

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. 

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. 

Practically more important is the sensitization of the n-type semiconductor electrode (Fig. 5.63). The depicted scheme is virtually equivalent to that in Fig. 5.62 the only exception is that the hole is not created in the valence band but formally in the sensitizer molecule. 

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). 

The charge carriers may reduce or oxidize the semiconductor itself leading to decomposition. This poses a serious problem for practical photoelectrochemical devices. Absolute thermodynamic stability can be achieved if the redox potential of oxidative decomposition reaction lies below the valence band and the redox potential of the reductive decomposition reaction lies above the conduction band. In most cases, usually one or both redox potentials lie within the bandgap. Then the stability depends on the competition between thermodynamically possible reactions. When the redox potentials of electrode decomposition reactions are thermodynamically more favored than electrolyte redox reactions, the result is electrode instability, for example, ZnO, Cu20, and CdS in an aqueous electrolyte. 

The electronic properties of silicon are essential in the understanding of silicon as an electrode material in an electrochemical cell. As in the case of electrolytes, where we have to consider different charged particles with different mobilities, two kinds of charge carriers - electrons and holes - are present in a semiconductor. The energy gap between the conduction band (CB) and the valence band (VB) in silicon is 1.11 eV at RT, which limits the upper operation temperature for silicon devices to about 200 °C. The band gap is indirect this means the transfer of an electron from the top of the VB to the bottom of the CB changes its energy and its momentum. 

In this type of DSSCs, once the dye is photoexcited, charge separation drives electrons from the valence band (vb) of the semiconductor to the photoexcited dye. Common to both types of DSSCs is the regeneration of the oxidized or reduced dye by a redox mediating electrolyte. The latter is mainly in the form of a liquid and/or a solid. Platinum films deposited onto ITO or FTO are the most utilized counter-electrodes and are required to close the electronic circuit. 

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. 

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.

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 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). 

The distribution of the exchange transfer current of redox electrons o(e), which corresponds to the state density curves shown in Fig. 8-11, is illustrated for both metal and semiconductor electrodes in Fig. 8-12 (See also Fig. 8-4.). Since the state density of semiconductor electrons available for electron transfer exists only in the conduction and valence bands fairly away from the Fermi level nsc), and since the state density of redox electrons available for transfer decreases remarkably with increasing deviation of the electron level (with increasing polarization) from the Fermi level CFciiEDax) of the redox electrons, the exchange transfer current of redox electrons is fairly small at semiconductor electrodes compared with that at metal electrodes as shown in Fig. 8-12. 

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