Depletion layers kinetic

Otherwise, the effect of electrode potential and kinetic parameters as contained in the relevant expression for the PMC signal (21), which controls the lifetime of PMC transients (40), may lead to an erroneous interpretation of kinetic mechanisms. The fact that lifetime measurements of PMC transients largely match the pattern of PMC-potential curves, showing peaks in accumulation and depletion of the semiconductor electrode and a minimum at the flatband potential [Figs. 13, 16-18, 34, and 36(b)], demonstrates that kinetic constants are accessible via PMC transient measurements, as indicated by the simplified relation (40) derived for the depletion layer of an n-type electrode. 

Macroscopic n-type materials in contact with metals normally develop a Schottky barrier (depletion layer) at the junction of the two materials, which reduces the kinetics of electron injection from semiconductor conduction band to the metal. However, when nanoparticles are significantly smaller than the depletion layer, there is no significant barrier layer within the semiconductor nanoparticle to obstruct electron transfer [62]. An accumulation layer may in fact be created, with a consequent increase in the electron transfer from the nanoparticle to the metal island [63], It is not clear if and what type of electronic barrier exists between semiconductor nanoparticles and metal islands, as well as the role played by the properties of the metal. A direct correlation between the work function of the metal and the photocatalytic activity for the generation of NH3 from azide ions has been made for metallized Ti02 systems [64]. 

Type II. Equilibrium is established between the surface states and the majority carriers within the semiconductor. Under these circumstances, a fraction of the potential change will be dropped across the depletion layer and a fraction across the Helmholtz layer. If a redox couple is present in solution, and the kinetics of electron transfer between this and the surface states are also rapid, then a large dark current will be found. 

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... 

The expected Tafel slope of 60mV/decade is not always found. There are a number of reasons for this, aside from kinetic effects in the bulk of the semiconductor. The kinetic effects associated with faradaically active surface states is of considerable significance, as shown below, but another common problem is that part of the potential change may appear across the Helmholtz layer rather than across the depletion layer. A well-known case in point is germanium, for which the surface is slowly converted from "hydride to "hydroxylic forms as the potential is ramped anodically. This conversion gives rise to a change in the surface dipole and hence Aij/ AT. In fact, the anodic dissolution of p-germanium is found to follow a law [106]... 

Equation (423) represents the best that has been achieved hitherto using formal analytical procedures and the problem, as has already been emphasised, lies with the nature of the recombination formula, eqn. (352). As the band-bending increases, n must decrease to the point where a shift in the kinetic law is expected at some point in the depletion layer. 

The distribution of the interfacial potential drop over the semiconductor and the depletion layer is an important problem in the field of electrochemistry. It is often strongly related to the kinetics of interfacial electron transfer [15]. 

A second technique that has been used is the measurement of photovoltage. The basis of this technique is that, on illumination under open-circuit conditions, the potential distribution will be modified so as to eliminate the potential drop within the depletion layer. In fact, as has been demonstrated by Kautek and Gerischer [7], the theory of the photovoltage effect is far from straightforward, especially in the presence of surface states. The effect is a steady-state rather than equilbrium phenomenon the potential distribution will change until the flux of holes to the surface is equal to the flux of electrons and the potential at which this occurs will depend on the recombination kinetics at the surface. Only when these kinetics are slow, i.e. when the surface states are slow and the main surface state equilbrium is with the redox couple in solution, is the technique likely to give results that can be interpreted within a consistent framework. 

The timescales of the processes occurring after photo-generation of an electron hole pair can be shorter or longer than the RC time constant of the photo-electrochemical cell, Tceii- In many cases, the time scale for interfacial processes at a semiconductor/electrolyte junction is longer than Xceit, whereas electron-hole separation and electron transit through the depletion layer are much faster. The apparatus used to probe electron-hole separation is therefore different from that used to study the kinetics of photoinduced interfacial processes. 

This section presents results that show how the rates of photoelectrochemical processes can be derived from time resolved measurement of the photoinduced current or potential in the external circuit of a photoelectrochemical cell. The capacitance of the Helmholtz-double layer is of the order of lO Fcm , the depletion layer capacitance of an extrinsic semiconductor junction is typically 10 -10 Fcm , while the capacitance of an insulator is orders of magnitude lower. With a value of 100 Ohm for the resistance Rd + R of the cell, the time constant of photoelectrochemical cells is 10 s for metallic electrodes, 10 -10" s for semiconductor electrodes and much lower for insulator electrodes. The rates of photoelectrochemical processes also span a wide range. This makes photoelectrochemical kinetics a rich, albeit demanding, area for research. 

Several techniques can be used to determine the flatband potential of a semiconductor. The most straightforward method is to measure the photocurrent onset potential, ( onset- At potentials positive of (/>fb a depletion layer forms that enables the separation of photogenerated electrons and holes, so one would expect a photocurrent. However, the actual potential that needs to be applied before a photocurrent is observed is often several tenths of a volt more positive than ( fb- This can be due to recombination in the space charge layer [45], hole trapping at surface defects [46], or hole accumulation at the surface due to poor charge transfer kinetics [43]. A more reliable method for determining ( fb is electrolyte electroreflectance (EER), with which changes in the surface free electron concentration can be accurately detected [47]. The most often used method, however, is Mott- chottky analysis. Here, the 1/ Csc is plotted as a function of the applied potential and the value of the flatband... 

Dynamic behavior of an ensemble or array of nanomaterial is dependent on the time scale in chronoamperometry, frequency in electrochemical impedance spectroscopy (EIS) and scan rate for a voltammetric measurement. It depends on three parameters diffusion or depletion layer thickness ( ), size or radius of curvature of each nanocomponent ((), spaeing between nanocomponents in sparse distribution or width of nanodeposit or roughness For sparse nanostructures, response switch between kinetic or... 

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