Semiconductor-solution interface potential difference

When a semiconducting electrode is brought into contact with an electrolyte solution, a potential difference is established at the interface. The conductivity even of doped semiconductors is usually well below that of an electrolyte solution so practically all of the potential drop occurs in the boundary layer of the electrode, and very little on the solution side of the interface (see Fig. 7.3). The situation is opposite to that on metal electrodes, but very similar to that at the interface between a semiconductor and a metal. 

At a semiconductor/solution interface, an n-type semiconductor (carrier density of 10 electrons cm A is in contact with a nonaqueous system using a redox system, i.e., no surface states. The capacity of this interface is 4 pF cm-2. Evaluate the potential differences within the semiconductor. (Bockris)... 

In the case of an electrode-solution interface, the thermodynamic equilibrium between the media in contact is attained by means of electron-ion exchange processes. Since the process of attaining the equilibrium is governed by charged particles, the equilibrium state is characterized by a certain potential difference between the phases. If they are in direct contact, we deal with the potential difference between two points in different media, for example, inside a semiconductor electrode and inside a solution. This potential difference is called the Galvani potential. 

Perhaps the simplest explanation for the pH independence of back-ET rates at metal oxide semiconductor-solution interfaces is that the formal potential of the dye moves in registry with the conduction-band edge. The energy difference, Ecb — Ef (dye), is then unchanged with respect to pH and the back-ET reaction experiences a pH-independent driving force. To amplify briefly, the idea is that... 

Now, for the semiconductor/solution interface, there are two reasons for the potential difference concentrating inside the semiconductor (Fig. 10.1) and being small at the conductivity interface with the solution. On the one hand, the electronic conduction of semiconductors is many orders of magnitude less than that of a... 

Fig. 10.15. p-Type semiconductor/solution interface in the presence of high-density surface states. The potential difference in the Helmholtz part of the double layer, (i.e., that in the solution) is greatly increased compared with a situation with a negligible number of surface states. Correspondingly, the potential difference within the semiconductor is greatly diminished compared with one containing negligible surface states. 

In the Schottky barrier approximation for photoelectrodes, virtually all the potential differences near the semiconductor solution interface lie inside the semiconductor. However, for photoelectrodes that evolve Hj and 02 (i.e., are photo water splitters), the H and O adsorbed on the surface of the semiconductor cause surface states for electrons there. In such a high surface state (Helmholtz) approximation case, the potential difference around the semiconductor/ solution surface moves out into the solution and the potential difference in the semiconductor is greatly reduced in extreme cases, becoming negligible. 

The driving force of the electron transfer process in the interface is the difference of energy between the levels of the semiconductor and the redox potential of the species close to the particle surface. The thermodynamically possible processes occurring in the interface are represented in Fig. 9 the photogenerated holes give rise to the D -> D + oxidative reaction while the electrons of the conduction band lead to the A -> A reductive process. The most common semiconductors present oxidative valence bands (redox potentials from +1 to + 3.5 V) and moderately reductive conduction bands (+ 0.5 to - 1.5 V) [115]. Thus, in the presence of redox species close or adsorbed to the semiconductor particle and under illumination, simultaneous oxidation and reduction reactions can take place in the semiconductor-solution interface. 

The size of barrier height,, at the semiconductor/solution interface for an ra-type semiconductor is defined by the difference between and p at all times. When p is perturbed away from the open-circuit potential of the system in the dark (i.e. -qU(A/A )) by an applied bias or photon flux, will not always necessarily equal q[Pg.540]

For the ideally polarized semicondutor electrode, a space-charge region in the semiconductor forms when a potential is apphed across the semiconductor-solution interface so that the electrode potential is displaced from fb- Surface states are energy levels arising from orbitals localized on atoms of the lattice near a surface. It is easy to see, for example, that silicon atoms in a surface plane cannot be surrounded with the tetrahedral symmetry found in the bulk solid. Thus, the electronic properties of these atoms differ. Often surface states have energies in the band gap and have a big effect on the electronic properties of any junction made with the surface. 

ABSTRACT The chemical and electrical implications of charge transfer are discussed. The basic differences between chemical and electrochemical reactions are highlighted. Electrochemical kinetics and its various aspects are treated in detail. Tunneling, electronic, and surface states are discussed in the context of interfaces. A current potential relation at semiconductor-solution interfaces receives attention, as do insulator-solution interfaces. 

The main difference appears in the exponential term. The expressions at the metal-solution interface contains the factor a in the exponential term, the value of which is less than one, but the similar expression at a semiconductor solution interface does not have an a term. This is because the change in the potential drop in the semiconductor-solution interface has been considered to occur inside the semiconductor (Figure 18). However, in the presence of a large number of surface states (lO cm ) the surface of the metal becomes metallized, and in such a situation the change in potential drop mainly occurs in the Helmholtz layer of the double layer. Hence, for such a metallized semiconductor-solution interface the exponential term of the current potential relation involves the transfer coefficient, a. 

The mathematical formulation of the current-potential relation at the insulator-solution interface is similar to that at the semiconductor-solution interface. The main difference is that the range of potential is much higher in the case of the insulator electrode compared to that at the semiconductor electrode. The applied potential usually ranges from 10 to 10 V at the insulator, but at the semiconductor electrode it ranges from +0 to 2V. 

This is the conventional picture of the semiconductor-solution interface but a different situation develops when surface states exist on the surface of the semiconductor (Fig. 13). Here, the potential difference which arises across the interface as the outside source supplies charges now goes largely on the Helmholtz layer, as with metals, and only to a small extent on the inside of the semiconductor. 

Fig. 4.12 Dependence of concentrations of negative charge carriers (ne) and positive charge carriers (np) on distance from the interface between the semiconductor (sc) and the electrolyte solution (1) in an w-type semiconductor. These concentration distributions markedly differ if the semiconductor/electrolyte potential difference A cp is (A) smaller than the flat-band potential AF

For semiconductor electrodes and also for the interface between two immiscible electrolyte solutions (ITIES), the greatest part of the potential difference between the two phases is represented by the potentials of the diffuse electric layers in the two phases (see Eq. 4.5.18). The rate of the charge transfer across the compact part of the double layer then depends very little on the overall potential difference. The potential dependence of the charge transfer rate is connected with the change in concentration of the transferred species at the boundary resulting from the potentials in the diffuse layers (Eq. 4.3.5), which, of course, depend on the overall potential difference between the two phases. In the case of simple ion transfer across ITIES, the process is very rapid being, in fact, a sort of diffusion accompanied with a resolvation in the recipient phase. 

Direct measurement of the change in interfacial potential difference at the oxide-electrolyte interface with change in pH of solution can be measured with semiconductor or semiconductor-oxide electrodes. These measurements have shown d V g/d log a + approaching 59 mV for TiC (36, 37). These values are inconsistent with the highly sub-Nernstian values predicted from the models with small values of K. (Similar studies 138.391 have been performed with other oxides of geochemical interest. Oxides of aluminum have yielded a value of d t)>q/A log aH+ greater than 50 mV, while some oxides of silicon have yielded lower values.)... 

Although a family of OgS - Jig8 values are allowed under Equation 7 the actual equilibrium state of the oxide/solution interface will be determined by the dissociation of the surface groups and the properties of the electrolyte or the diffuse double layer near the surface. For surfaces that develop surface charges by different mechanisms such as for semiconductor, there will be an equation of state or charge-potential relationship that is analogous to Equation 7 which characterizes the electrical response of the surface. 

A representative potential distribution across the interface is shown in Fig. 3.9(c), taking the potential of the bulk solution as zero. The potential difference across the space charge region (psd occurs over a larger distance than that of the Helmholtz layer (pn). For an n-type semiconductor, (psc results from the excess positive charge of ionized donors in the bulk of the space charge region within the... 

Fig. 7.24. The current-potential relation at a p-n semiconductor junction differs from that of an electrode/solution interface by being totally asymmetrical.

In the other scheme the photosensitive interface operates in the photo-galvanic pair regime (Goryachev et al, 1970 Goryachev and Paritsky, 1973). The method is based on the occurrence of a potential difference between illuminated and nonilluminated areas on the surface of a semiconductor electrode in a solution (cf. Section 1 lb). As a result of nonuniform illumination, local anodes and cathodes arise on the surface and this, in turn, leads to nonuniform deposition of metal onto the surface. 

In summary, at nanostructured tin-oxide semiconductor-aqueous solution interfaces, back ET to molecular dyes is well described by conventional Marcus-type electron-transfer theory. The mechanistic details of the reaction, however, are remarkably sensitive to the nature of the semiconductor-dye binding interactions. The mechanistic differences point, potentially, to differing design strategies for kinetic optimization of the corresponding liquid-junction solar cells. 

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. 

The second important difference is that the interface potential is present at the (outer) Helmholtz layer of the semiconductor/soiution interface. The interface potential is produced by surface dipoles of surface bonds as well as surface charges due to ionic adsorption equilibria between the semiconductor surface and the solution. If the interface potential can be regulated by a change in the chemical structure of the semiconductor surface, then the semiconductor band energies can be shifted to match the energy levels of the solution species (oxidant or reductant). This is another advantage of the semiconductor system because this enables improvement of the electron transfer rate at the semiconductor/soiution interface and the energy conversion efficiency. 

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... 

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