Space-charge potential

When the cell circuit is closed in the dark, as shown in Fig. 10-25(b), the Fermi level is equilibrated between the metallic cathode and the n-lype semiconductor anode. As a result, a depletion layer of space charge (potential barrier, is formed in the semiconductor anode, thereby shifting the potential of the anode from the flat band potential to a more anodic (more positive) potential (= + ). In the dark, however, the anodic hole transfer... 

Fig. 6.3 Schematic picture of the electrochemical potential ( > as a function of distance x in an oxide semiconductor electrolyte system a) bulk semiconductor potential b) solid/solution interface potential c) space charge potential d) flat band potential e) potential in the double layer (White, 1990, with permission.

It should additionally be emphasized that the behavior in chemical reactions of a solid oxidic or silicic catalyst may depend almost as much on the nature of the adsorbate as on the catalyst itself. Also, the nature of the surrounding fluid will also have a strong impact on the properties of highly dispersed mineral systems, via alteration of the space charge potential, as previously mentioned. 

While Fgb and Ubuik are deduced from the measurements, we still need the bulk concentration of vacancies to calculate the space charge potential according to Eq. (52). Using the room-temperature mobility of vacancies obtained from literature data [102], and sc as the bulk permittivity of AgCl, a bulk vacany concentration of 5.8 1015 cm 1 can be evaluated from the measured bulk conductivity. This value is used to determine an effective space charge potential of about 300 mV and a grain... 

Unlike the Debye length the effective width X depends on the space charge potential ... 

Figure 25. Grain boundary capacitance of a Fe-doped StTiOj polycrystal (rriFe = 6.5 x 10,9cm"3), normalized to the electrode surface and measured at various oxygen partial pressures as a function of reciprocal temperature.100 Typical space charge potentials vary between 300 and 800 mV. (Reprinted from I. Denk, J. Claus and J. Maier, Electrochemical Investigations of SrTiOj Boundaries. J. Electrochem. Soc. 144, 3526-3536. (Copyright 1997 with permission from The Electrochemical Society, Inc.)...

Depletion layers with respect to ionic conductors are no less interesting. In acceptor doped SrTi03,131-134 CeC>2135 136 and presumably also in Zr02,137-141 space charge layers have been found to exhibit a positive space charge potential. As a consequence the oxygen vacancies, the relevant ionic carriers, are depleted as well as holes, while e should be enriched. 

The last consequence to be discussed is the fact that a positive space charge potential does not only lead to a hole depletion but also to an accumulation of excess electrons. Their influence may be observed in SrTi03 only at very high space charge potentials,144 but has been clearly seen in nanocrystalline Ce02136,159 (space charge potential - 300 mV) and will be considered again in Section V.4. 

Consider the interfacial region shown in detail in Fig. 4. The total interfacial drop, ,-, is composed of three contributions 8C, the space-charge potential dropped inside the semiconductor, potential across the (uncharged) Helmholtz layer, and el, the potential dropped in the electrolyte. To solve for the potential distribution in the interfacial region, we make use of... 

Fig. 10. Theoretical values of the space charge capacities as a function of the space charge potential V ...

The magnitude of the space-charge potential is closely dependent on the local stmctme of the smface, as will be discussed in relation to work function measmements. In the... 

Fig. 7.20 Faraday current and charge transfer resistance vs. the potential across the space charge potential data taken from Fig. 7.19. (After ref. [33])...

In semiconductor electrodes, we have a space charge layer in addition to an electrical compact double layer (Helmholz layer) at the electrode interface. The electrode potential, then, is the sum of the space charge potential, Ac[>sc, and the interfacial potential, AH ... 

The electrode potential where the space charge potential becomes zero is called the flat band potential, E. The space charge is positive at electrode potentials more positive (i.e., more anodic) than Efo, and it is negative at electrode potentials less positive (i.e., more cathodic) than E. In fact, the space charge potential, ASC, is defined by the difference between the band edge level in the semiconductor interior and that at the semiconductor surface. Since the Fermi level is not allowed to move out of the band gap, the space charge potential always amounts to less than the band gap of the semiconductor. 

FIGURE 22.5 Electrode potential consisting of interfacial potential A(f>H and space charge potential Ac()sc for an intrinsic semiconductor = flat band potential, v = valence band edge potential, and... 

Since cGe4+ is one fourth the surface hole concentration, Chs, due to the electrical charge balance (cGe4+ = 4chs), the surface ion concentration, cGl,4, is described as a function of both the space charge potential, Acj>sc, and the hole concentration, cj[, in the bulk of the semiconductor ... 

Furthermore, as we saw in a foregoing section, photoexcitation produces in a semiconductor electrode electron-hole pairs and introduces a photo-potential, which reduces the space charge potential in the semiconductor. With an n-type semiconductor in contact with a corroding metal, photoexcitation raises the Fermi level up to the flat band level of the semiconductor, thus shifting the corrosion potential in the less positive direction toward the flat band potential of the n-type oxide as shown in Figure 22.35c. Photoexcitation therefore will shift the corrosion potential in the less positive (more cathodic) direction and the corrosion will then be suppressed. With some n-type oxides such as titanium oxide, photoexcitation brings the interfacial quasi-Fermi level, peF, down to a level lower than the Fermi level, F(redox> of the oxygen electrode reaction ... 

Perhaps the two most frequently measured electrical properties in surface science are the surface space charge potential Pdipoie the related work function . 

A more realistic model will take full account of the atomic nature of the surface and yield charge densities and electronic potentials similar to those obtained by the jellium model. In this circumstance, however, the charge density on the solid side of the surface exhibits fluctuations that are often called Friedel oscillations and which are due to the screening by the free electrons (Figure 5.1). The amplitude of this oscillation is a sensitive function of the electron density, as are the height and extent of the surface space-charge potential. 

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