Potential drop surface states

Because of the charged nature of many Langmuir films, fairly marked effects of changing the pH of the substrate phase are often observed. An obvious case is that of the fatty-acid monolayers these will be ionized on alkaline substrates, and as a result of the repulsion between the charged polar groups, the film reverts to a gaseous or liquid expanded state at a much lower temperature than does the acid form [121]. Also, the surface potential drops since, as illustrated in Fig. XV-13, the presence of nearby counterions introduces a dipole opposite in orientation to that previously present. A similar situation is found with long-chain amines on acid substrates [122]. 

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. 

In many cases mass transfer is not the sole cause of unsteady-state limiting currents, observed when a fast current ramp is imposed on an elongated electrode. In copper deposition, in particular, as a result of the appreciable surface overpotential (see Section III,C) and the ohmic potential drop between electrodes, the current distribution below the limiting current is very different from that at the true steady-state limiting current. 

Figure 21. The energy band diagram (only the conduction band is shown) calculated for the silicon/electrolyte interface with a potential drop of 5 V and different radii of curvature. Ec is the conduction bandedge in the bulk and Ecs is the conduction bandedge at the surface. AE AEj, AE1/2, and AE1/5 are the possible tunneling energy ranges for different radii of curvature. The distribution of occupied states at the interface, Dred, is also schematically indicated. After Zhang.24...

Fig. 7.27. Changes in the potential energy of the electron in the p semiconductor and the potential drop at the semicon-ductor/soiution interface when there are surface states at the semiconductor electrode surface.

While many of the standard electroanalytical techniques utilized with metal electrodes can be employed to characterize the semiconductor-electrolyte interface, one must be careful not to interpret the semiconductor response in terms of the standard diagnostics employed with metal electrodes. Fundamental to our understanding of the metal-electrolyte interface is the assumption that all potential applied to the back side of a metal electrode will appear at the metal electrode surface. That is, in the case of a metal electrode, a potential drop only appears on the solution side of the interface (i.e., via the electrode double layer and the bulk electrolyte resistance). This is not the case when a semiconductor is employed. If the semiconductor responds in an ideal manner, the potential applied to the back side of the electrode will be dropped across the internal electrode-electrolyte interface. This has two implications (1) the potential applied to a semiconducting electrode does not control the electrochemistry, and (2) in most cases there exists a built-in barrier to charge transfer at the semiconductor-electrolyte interface, so that, electrochemical reversible behavior can never exist. In order to understand the radically different response of a semiconductor to an applied external potential, one must explore the solid-state band structure of the semiconductor. This topic is treated at an introductory level in References 1 and 2. A more complete discussion can be found in References 3, 4, 5, and 6, along with a detailed review of the photoelectrochemical response of a wide variety of inorganic semiconducting materials. 

One must recall, here also that the potential-distance relation for a semiconductor (at least, one without a significant concentration of surface states) is qualitatively different from the potential-distance relation at a metal/solution interface. The essential difference is shown in Figs. 10.1 (a) and 10.1(b). In the semiconductor, mostofthe potential difference at the interface is inside the solid, and only a few millivolts are in the solution. Of course, with the metal, it is mostly in the sudden drop in the double... 

Fig. 10.8. A schematic diagram of a p-type semicon-ductor/solution interface at two applied potentials, I/, and V2, in the absence of surface states. The diagram shows the potential drop in the solution s Helmholtz layer and exhibits no variation in Helmholtz layer potential difference with applied potentials. The Fermi level is not pinned.

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.)...

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). 

A drastic decrease of photovoltage in UHV is obtained by introduction of surface states at the semiconductor surface. Particle bombardement of cleaved (0001) faces leads to preferential sputtering of the chalcogenide. The metal is reduced and new electronic bandgap states are formed at the surface. As a consequence a Fermi level pinning effect occurs which results in a smaller shift of EB due to halogen adsorption and decreased photovoltages and consequently an increased double layer potential drop (Fig. 4). 

We can ask how effects of the double layer on electrode kinetics can be minimized and if the necessity of correcting values of a and of rate constants can be avoided In order for this to be possible, we have to arrange for s, that is all the potential drop between electrode surface and bulk solution is confined to within the compact layer, for any value of applied potential. This can be achieved by addition of a large quantity of inert electrolyte (—1.0 m), the concentration of electroactive species being much lower (<5mM). As stated elsewhere, other advantages of inert electrolyte addition are reduction of solution resistance and minimization of migration effects given that the inert electrolyte conducts almost all the current. In the case of microelectrodes (Section 5.6) the addition of inert electrolyte is not necessary for many types of experiment as the currents are so small. 

The surface concentration of electrons depends on the potential drop (band bending) in the semiconductor, and in the absence of complications due to surface state charging (Fermi level pinning), it is given by (cf. equation (8.5))... 

Oskam et al. [66] have used IMPS to investigate the role of surface states at the n-Si(lll)/NH4F interface. In this case, the redox reaction is simpler, and appears not to involve holes trapped at surface states. This is probably due to the presence of a surface oxide layer. Electron transfer is evidently exceptionally slow in this case, since these authors observed a modulated photocurrent even at potentials far from the flatband potential where recombination is expected to be negligible. Accumulation of holes modifies the potential drop across the Helmholtz (and presumably also surface oxide region), leading to a capacitive charging current. This effect has also been treated in more detail by Peter et al. [71]. 

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