Charge and Potential Distribution at the Interface

The formation of a double layer has considerable consequences for the chaise and potential distribution across the interface. In the case of a metal electrode the counter charges are located just below the surface. Since, however, the carrier density in a semiconductor is usually much smaller than in a metal electrode, the counter charges can be distributed over a considerable distance below the interface, that is, a space charge layer is formed, similar to that in pure solid devices (compare with Chapter 2). The potential and charge distribution across the Helmholtz layer, Gouy layer, and space charge region will be treated separately in 

---

The actual position of the energy bands at the semiconductor surface can be experimentally determined by investigating the charge and potential distribution across the interface. The latter is composed essentially of the potential drop 0h across the Helmholtz layer and 4>sd across the space-charge layer below the semiconductor surface. Thus, the total potential difference across the interface is given by... 

Two procedures may be applied to investigate the charge and potential distribution at the solid/liquid interface, which is important in assessing electrostatic stabilisa-... 

Underpotential deposition produces a change in the potential distribution at the interface, affects the organization of the solvent molecules at the interface, and shifts the potential of zero charge in the opposite direction to the effect observed with specific anion adsorption. 

Figure 1. Combined energy diagram for a regenerative photoelectrochemical cell with n-CdSe as the anode, metallic cathode and polysulfide as the electrolyte. The diagram indicates some of the charge accumulation modes that might contribute to the potential distribution at the interface. ((Qn) ionized donors (Qdt) deep traps ...

The foregoing discussion deals with interfaces between neat liquids, whereas the structure of interfaces between electrolyte solutions has been a topic of much debate over the past three decades [3, 5, 13]. The presence of electrolytes allows a variable potential to be imposed on the interface, via either the common-ion or external potentiostatic approach (see Section I). An important parameter arises for the electrolyte case, namely, what is the potential distribution at the interface between the two electrolyte phases The excess charge present on either side of the interface can be probed directly via macroscopic measurements of interfacial tension or capacitance and can thereby be used to infer structural information, albeit lacking in molecular detail. The developments along these lines up to the late 1980s/early 1990s have been reviewed [3, 5, 13, 49] hence only a brief outline of the bulk approaches to this problem will be presented here. 

Eventually the system relaxes to the distribution and (f>2 value obtained by the GCS approach (Section 13.3). A similar simulation approach was taken to calculate the charge and potential distributions in the space-charge region that forms inside the electrode at a semiconductor electrode/electrolyte interface (20) (See Section 18.2). Migrational effects in voltammetry can be taken into account in a similar way by using the full Nernst-Planck equation to treat mass transfer (21). 

In these cases, the standard free energy of adsorption can be obtained from the equilibrium condition and is a simple exponential function of the potential which does not depend significantly on the charge distribution at the interface for an uncharged adsorbate. The chemisorption thus corresponds to a vertical shift in the free energy curves as depicted in Fig. 12 and affects the energy of activation [76]. 

Photoelectrochemistry — In principle, any process in which photon absorption is followed by some electrochemical process is termed photo electro chemical, but the term has come to have a rather restricted usage, partly to avoid confusion with photoemission (q.v.). The critical requirements for normal photo electro chemical activity is that the electrode itself should be a semiconductor that the electrolyte should have a concentration substantially exceeding the density of -> charge carriers in the semiconductor and that the semiconductor should be reverse biased with respect to the solution. To follow this in detail, the differences in potential distribution at the metal-electrolyte and semiconductor-electrolyte interfaces need to be understood, and these are shown in Fig. 1, which illustrates the situation for an n-type semiconductor under positive bias. 

Fig. 8. Potential distribution at the semiconductor-electrolyte interface for (a) a negative charge density at the surface and (b) a positive charge density at the surface.

The most convenient method to obtain information about the distribution of charges at a charged interface is the measurement of the electrode capacity and its dependence upon the potential drop at the interface and the frequency of the a-c used. 

---