Fermi level in solution

Figure 5. n-Type semiconductor—electrolyte solution interface with a surface depletion layer, in the dark and with two intensities of illumination. Symbols as in Figure 3 and 4 with Ec and E the band edges of the conduction and valence bands, respectively, under illumination, and Ef(H2) Ef(Om) abbreviations for Ef(H20/h2) and Ep(02/H20)y respectively. The quasi-Fermi levels Ei> and pEp are at different positions in the surface region than in the bulk as a result of the limited penetration of light into the interior. Fermi levels in solution as in Figures 3 and 4(13). 

H. Gerischer, Z. Physikal. Chem. 26 223 (1960). Absolute potential Fermi level in solution. 

The mechanism of an electrochemical reaction at semiconductor electrodes depends upon the position of the redox Fermi level in solution with respect to the position of the bandedges of the semiconductor. In this study we investigated the reduction of copper ions on Si surfaces in HF solutions and we examined the effect of adding HCI to the HF solutions. 

Hence, the use of the determination of solution Fermi level from standard redox potential (cf. Figure 16) is not applicable in the absence of the value of (/> However, the question is whether the Fermi level in solution is... 

The existence of the oxidized and reduced forms of a redox couple thus determine a kind of Fermi level in solution, [see Pleskov and Gurevich for a statistical mechanical derivation]. The Nernst equation for the half-reaction, referenced to vacuum, is then given by ... 

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. 

Marcus theory assumes that these solvent shells vibrate harmonically and with identical frequency so that the potential energies of both components in a redox couple can be represented by identical but mutually shifted parabolae. Only electrons from the Fermi level in the electrode and from the ground state of the redox system in solution participate in the redox process. 

Figure 3. Schematic of a semiconductor-aqueous electrolyte solution interface, ignoring band bending, Ec and are the band edges of the conduction and valence bands, respectively, Ef(H20/h2> and Ef(02/h20) are the Fermi levels in the solution for the redox reactions indicated. The quasi-Fermi levels with illumination by light of energy hv are designated Ef and pEi respectively, for electrons and holes (13).

Before leaving this subject, it is a good idea to remark that the term Fermi energy of electrons in solution is not the most helpful one and has led to a degree of misunderstanding. Thus, as mentioned, the Fermi level in a metal deals with electrons that obey a certain distribution law. This law arises from Pauli s principle Only two... 

The electrons in the Fermi level in a metal—those that undergo the Fermi distribution law—are mobile and that is where the difference comes from electrons in solution which are, in fact, in the bound levels of ions. Such electrons are not mobile and the statement that they have a Fermi energy may therefore be misleading, for they do not obey the same distribution law as the electrons with which they are in equilibrium.4... 

Fig. 5.1 Schematic energy band bending for (A) large particle, (B) small particle, and (C) metal-deposited particle. R, radius of the particle Lsc, space charge layer E(red/ox), redox level in solution E , Fermi level in semiconductor

The Schottky barrier in polymers is very different from the barriers in Metal-Si. Earlier computer simulations showed that in n+/n- junction no depletion is formed, instead accumulation is formed. Also if d is small, in n+/p- junction, there are not enough carriers to bring the Fermi levels in one line. In numerous cases analytical solutions give erroneous results and create understanding. Extensive computer simulations are required. 

When a metal is immersed in a solution containing ions of that metal, die electrochemical potential of the ions in the metallic lattice and in die solution will usually be unequal The same will be true for the free electrons (near the Fermi level) in the metal and electrons in the energy levels of electron acceptors m the solution. 

In the liquid environment the situation is different from that described above. Highly doped electrodes are often avoided because they present an enhanced reactivity with the solution. The sample and tip biases are set independently with respect to levels in solution and the position of the band edges of the semiconductor is fixed with respect to the tip Fermi level iU is indeed generally fixed within a narrow potential window). It follows that the situation is often the one shown in Fig. 6, with the tip Fermi level located in the band gap. In this situation, maintaining the tip at a constant height above the surface requires that the n-type electrode be cathodically biased so as to provide a sufficiently large density of electrons (Fig. 6 c). The stability of this situation is governed by the sample bias and not by the tip bias since the position of the tip Fermi level is not critical here, unless it is outside the band gap. 

Figure 25b. Cathodic electron transfer between a metal and a simple redox system in solution for a moderate deviation from equilibrium, /i > /r(Ox/Red). The energy distribution of the occupied and empty electron levels in the metal and in the redox system are depicted. Elastic tunneling occurs between occupied and empty levels on both sides of the interface. The rate of exchange is maximal at around the Fermi-level in the metal (see length of arrows).

FIGURE 1.2. Representation of the formation of a semiconductor/electrolyte interface in the dark (a) before the contact (b) after the contact and eiectrostatic equilibration when the Fermi level in the semiconductor and the redox potential of the solution become equal. 

Equations 1 A.l 1 and 1A.12 correspond to paths a and b respectively between points P2 and Pi in Fig. lA.l. Thns [/ei/si(abs) is the energy of an electron at the local vacuum level of the solution (point Pi) compared with that of an electron at the Fermi level in the electrode (point P2). Both terms on the right-hand side of eq. 1 A. 12 are measurable, so in principle f/ei/si (abs) is also measurable. 

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