Surface states density, potential drop

The relative changes in VH and Vsc as a function of surface state density are shown in Fig. 10.20. At low surface state density (<1012), the potential drop across the Helmholtz layer is small and remains almost constant with a change in electrode potential. However, at high surface state densities (>1013), the potential drop in the Helmholtz region increases and exceeds the potential drop in the space charge region for surface state densities greater than 5 x 1013 cm 2. 

Fig. 10.20. Relative potential drop in the space charge region and in the Helmholtz region as a function of surface state density. (Reprinted from K. Chandresakaran, R. C. Kainthla, and J. O M. Bockris, Elec-trochim. Acta 33 334, Fig. 12, copyright 1988, with permission from Elsevier Science.)...

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.)... 

So far only the effect of the surface states is considered, but if the carrier density is high, even when the surface state density is low, the potential drop in the Helmholtz layer may be more significant than that in the semiconductor. 

One must note that the situation shown in Fig. 2 is of an ideal case where the surface state density is low and the carrier density is not too high. If either the surface state density [20] or the carrier density [21] is very high, an appreciable portion of the potential drop occurs within the Helmholtz layer, i.e., the electrolyte side of the interface. In an extreme case, all of the potential drop occurs within the Helmholtz layer. This situation is often called Fermi level pinning [20]. 

The photocurrent density (/ph) is proportional to the light intensity, but almost independent of the electrode potential, provided that the band bending is sufficiently large to prevent recombination. At potentials close to the flatband potential, the photocurrent density again drops to zero. A typical current density-voltage characteristics of an n-semiconductor electrode in the dark and upon illumination is shown in Fig. 5.61. If the electrode reactions are slow, and/or if the e /h+ recombination via impurities or surface states takes place, more complicated curves for /light result. 

Typical values of transfer coefficients a and ji thus obtained are listed in Table 4 for single crystal and polycrystalline thin-film electrodes [69] and for a HTHP diamond single crystal [77], We see for Ce3+/ 41 system (as well as for Fe(CN)63 /4 and quinone/hydroquinone systems [104]), that, on the whole, the transfer coefficients are small and their sum is less than 1. We recall that an ideal semiconductor electrode must demonstrate a rectification effect in particular, a reaction proceeding via the valence band has transfer coefficients a = 0, / =l a + / = 1 [6], Actually, the ideal behavior is rarely the case even with single crystal semiconductor materials fabricated by advanced technologies. Departure from the ideal semiconductor behavior is likely because the interfacial potential drop is located in part in the Helmholtz layer (due e.g. to a high density of surface states), or because the surface states participate in the reaction. As a result, the transfer coefficients a and ji take values intermediate between those characteristic of a semiconductor (0 or 1) and a metal ( 0.5). 

At higher densities of surface states, it may be expected that the emptying and filling of surface states will cause a significant change in the potential within the depletion layer. Provided the dominant kinetics are those between surface state and semiconductor interior, we may then analyse the situation as a case II Fermi-level pinning problem. The total potential dropped in the interfacial region... 

Figure 29. Calculated current-potential characteristics for direct (dashed lines, 0/cm ) and surface state mediated electron transfer between an -type semiconductor electrode and a simple redox system. The plots show the transition from ideal diode behavior to metallic behavior with increasing density of surface states at around the Fermi-level of the solid (indicated in the figures). This is also clear from the plots below, which show the change of the interfacial potential drop over the Helmholtz-layer (here denoted as A(Pfj) with respect tot the total change of the interfacial potential drop (here denoted as A(p). Results from D. Vanmaekelbergh, Electrochim. Acta 42, 1121 (1997).

---