Fermi pinning

Fermi pinning at semiconductor/metal contacts.In other words, for a 1-2 V change in the work function of the metal, this density of surface states is sufficient that the values of W and Vbi will not change. 

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. 

In the absence of either surface states, which may pin the Fermi level at the interface between the dielectric and the electrode, the energy barriers, which in turn... 

Figure 5.46 shows clearly how the application of potential changes the brightness and thus the workfunction O, of the grounded Pt catalyst-electrode (windows 2 and 3) and of the YSZ surface, (window 1), in accordance to the above discussed alignment (pinning) of the two Fermi levels. 

Equation (7.32) underlines the pinning of the Fermi levels of metal electrodes with the solid electrolyte and reminds the fact that the absolute electrode potential is a property of the solid electrolyte and of the gaseous composition but not of the electrode material.21... 

Consequently the absolute potential is a material property which can be used to characterize solid electrolyte materials, several of which, as discussed in Chapter 11, are used increasingly in recent years as high surface area catalyst supports. This in turn implies that the Fermi level of dispersed metal catalysts supported on such carriers will be pinned to the Fermi level (or absolute potential) of the carrier (support). As discussed in Chapter 11 this is intimately related to the effect of metal-support interactions, which is of central importance in heterogeneous catalysis. 

By comparing Figure 11.9 and the characteristic Po2(Uwr) rate breaks of the inset of Fig. 11.9 one can assign to each support an equivalent potential Uwr value (Fig. 11.10). These values are plotted in Figure 11.11 vs the actual work function G>° measured via the Kelvin probe technique for the supports at po2-l atm and T=400°C. The measuring principle utilizing a Kelvin probe and the pinning of the Fermi levels of the support and of metal electrodes in contact with it has been discussed already in Chapter 7 in conjunction with the absolute potential scale of solid state electrochemistry.37... 

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... 

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 fundamental quantity of interest, BE, is calculated from the KE (correcting for the work function 4>s). The sample is grounded to the spectrometer to pin the Fermi levels to a fixed value of the spectrometer (Fig. 1) so that the applicable work function is that of the spectrometer, sp [2], This instrumental parameter is a constant that can be measured. The BEs are then easily obtained from Eq. 2 ... 

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... 

The Schottky-Mott theory predicts a current / = (4 7t e m kB2/h3) T2 exp (—e A/kB 7) exp (e n V/kB T)— 1], where e is the electronic charge, m is the effective mass of the carrier, kB is Boltzmann s constant, T is the absolute temperature, n is a filling factor, A is the Schottky barrier height (see Fig. 1), and V is the applied voltage [31]. In Schottky-Mott theory, A should be the difference between the Fermi level of the metal and the conduction band minimum (for an n-type semiconductor-to-metal interface) or the valence band maximum (for a p-type semiconductor-metal interface) [32, 33]. Certain experimentally observed variations of A were for decades ascribed to pinning of states, but can now be attributed to local inhomogeneities of the interface, so the Schottky-Mott theory is secure. The opposite of a Schottky barrier is an ohmic contact, where there is only an added electrical resistance at the junction, typically between two metals. 

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.

The semiconductor surface where the Fermi level is pinned at a surface state of high density (Fig. 2-31) is in the state of degeneracy of electron levels, because of the high electron state density at the surface Fermi level. Similarly, the surface degeneracy is also established when the band bending becomes so great that the Fermi level is pinned either in the conduction band or in the valence band as shown in Fig. 2-32. 

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.

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