Fermi level, pinning

As a consequence of Fermi level pinning, the Schottky barrier height ) = 

Equivalent Circuit and Capacitance of Semiconductor/Electrolyte Interface 

The total potential change AV is divided between the space charge layer and the Helmholtz layer  

FIGURE 1.9. Surface charge in an n-type semiconductor space charge, at various doping levels at AFs of -0.3 and -l.OV and surface state charge, i2s as a function of surface state density, assuming half-occupancy. Potential drop across the Helmholtz layer is AVh = 0.085 (pC/cm ) assuming 8n = 4 and d = 3 A. (Reprinted with permission from Bard et al. 1980 American Chemical Society.) 

The overall capacity C is related to each of the capacities according to 

For many electrode materials, surface defects were found to play an important role for the surface recombination of charge carriers , leading to a loss in the conversion efficiency, but also for the charge transfer to the electrolyte These surface defects may be already present without electrolyte contact, caused, e.g., by crystal defects, or are introduced by adsorbed species from the electrolyte . Also charge transfer via surface defects was suggested for PcH2 .  

Illumination of electrodes of PeZn in contact with a variety of redox electrolytes under open circuit conditions showed positive photovoltages as expected for a p-type electrode, when the rest potential in the dark is negative of its flat band potential. Measurements in KCl solutions containing various electroactive species 

Under the assumption of a uniform energy distribution of the surface defects in the examined potential region, a semiquantitative model was introduced to interpret partial FLP according to the equation 

Assuming further that is constant over the whole range of the energy gap (1.65 eV for PeZn), the overall number of surface defects was estimated to about 0.7 X 10 cm based on a = —0.21. This value is of a similar size as the calculated number of 0.6 to 2 x 10 cm molecules of PeZn present at the surface, if all possible orientations of the molecules are considered equally. According to this estimation a considerable part of the surface molecules represents surface defects, which can be filled with electrons. 

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The degree of surface cleanliness or even ordering can be determined by REELS, especially from the intense VEELS signals. The relative intensity of the surface and bulk plasmon peaks is often more sensitive to surface contamination than AES, especially for elements like Al, which have intense plasmon peaks. Semiconductor surfaces often have surface states due to dangling bonds that are unique to each crystal orientation, which have been used in the case of Si and GaAs to follow in situ the formation of metal contacts and to resolve such issues as Fermi-level pinning and its role in Schottky barrier heights. 

Singh P, Singh R, Gale R, Rajeshwar K, DuBow J (1980) Surface charge and specific ion adsorption effects in photoelectrochemical devices. J Appl Phys 51 6286-6291 Bard AJ, Bocarsly AB, Pan ERF, Walton EG, Wrighton MS (1980) The concept of Fermi level pinning at semiconductor/liquid junctions. Consequences for energy conversion efficiency and selection of useful solution redox couples in solar devices. J Am Chem Soc 102 3671-3677... 

Bocarsly AB, Bookbinder DS, Dominey RN, Lewis NS, Wrighton MS (1980) Photoreduction at illuminated p-type semiconducting silicon photoelectrodes. Evidence for Fermi level pinning. J Am Chem Soc 102 3683-3688... 

Manipulating surface states of semiconductors for energy conversion applications is one problem area common to electronic devices as well. The problem of Fermi level pinning by surface states with GaAs, for example, raises difficulties in the development of field effect transistors that depend on the... 

The conclusions from these considerations are that semiconductor photoelectrodes can be used to effect either reductions (p-type semiconductors) or oxidations (n-type semiconductors) in an uphill fashion. The extent to which reaction can be driven uphill, Ey, is no greater than Eg, but may be lower than Eg owing to surface states between Eqb and Eye or to an Inappropriate value of Ere(jox. Both Eg and Epg are properties that depend on the semiconductor bulk and surface properties. Interestingly, Ey can be independent of Ere(jox meaning that the choice of Ere(jox and the associated redox reagents can be made on the basis of factors other than theoretical efficiency, for a given semiconductor. Thus, the important reduction processes represented by the half-reactions (3)-(5) could, in principle, be effected with the same efficiency at a Fermi level pinned (or... 

Dislocations are localized interruptions in a crystal s periodic network. These interruptions result in dangling bonds. Dislocations can be localized at a point, along a line or over an area. In the latter case, with the Fermi level pinned near midgap, an areal dislocation forms two Schottky barriers... 

In cases in which the surface state density is high Nc/i,Nm, Ny/i,Nm - 1), electron distribution in the siuface state conforms to the Fermi function (the state of degeneracy) and the Fermi level is pinned at the surface state level. This is what is called the Fermi level pinning at the surface state. 

Fig. 2-81. Surface degeneracy caused by Fermi level pinning at a surface state of high state density (a) in flat band state (Ep ep), G>) in electron equilibrium (cp = cp). cp = surface Fermi level = surface ccmduction band edge level.

Fig. 2-32. Surface caused by Fermi level pinning (a) in the conduction band and (b) in the valence band.

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. 

Band Edge Level Pinning and Fermi Level Pinning... 

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. 

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.

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. 

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. 

As the potential Ai )sc of an inversion layer increases and as the Fermi level at the electrode interface coincides with the band edge level, the electrode interface is in the state of degeneracy (Fermi level pinning) and both the capacity Csc and the potential A4>sc are maintained constant. Figure 5-48 shows schematically the capacity of a space charge layer as a function of electrode potential. As the electrode potential shifts in the anodic (positive) direction from a cathodic (negative) potential, an accumulation, a depletion, and an inversion layer are successively formed here, the capacity of the space charge layer first decreases to a minimum and then increases to a steady value. 

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. 

When the total overvoltage ti is distributed not only in the space charge layer t)8c but also in the compact layer tih, the Tafel constants of a and a each becomes greater than zero and the Tafel constants of a and each becomes less than one. In such cases, Kiv) and ip(T ) do not remain constant but increase with increasing overvoltage. Further, if Fermi level pinning is established at the interface of semiconductor electrodes, the Tafel constant becomes dose to 0.5 for... 

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.

Fig. 8-27. Polarization curves for transfer of redox electrons at n-type and p-type semiconductor electrodes solid curve near Egaxa = reaction with the Fermi level of redox electrons dose to the valence band edge dashed curve near F redok = reaction with the Fermi level of redox electrons dose to the conduction band edge dot-dash curve (FLP)= reaction in the state of Fermi level pinning.

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.). 

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