Carrier surface concentration

Figure 12. Energy diagram of a semiconductor/electrolyte interface showing photogeneration and loss mechanisms (via surface recombination and interfacial charge transfer for minority charge carriers). The surface concentration of minority...

There is an additional simple relation between the surface concentration Aps of photogenerated minority carriers and the charge recombination and charge transfer rates sr and kr to be considered ... 

The combination of photocurrent measurements with photoinduced microwave conductivity measurements yields, as we have seen [Eqs. (11), (12), and (13)], the interfacial rate constants for minority carrier reactions (kn sr) as well as the surface concentration of photoinduced minority carriers (Aps) (and a series of solid-state parameters of the electrode material). Since light intensity modulation spectroscopy measurements give information on kinetic constants of electrode processes, a combination of this technique with light intensity-modulated microwave measurements should lead to information on kinetic mechanisms, especially very fast ones, which would not be accessible with conventional electrochemical techniques owing to RC restraints. Also, more specific kinetic information may become accessible for example, a distinction between different recombination processes. Potential-modulation MC techniques may, in parallel with potential-modulation electrochemical impedance measurements, provide more detailed information relevant for the interpretation and measurement of interfacial capacitance (see later discus-... 

The surface concentration of minority carriers can be calculated on the basis of the same formalism ... 

The surface concentration of minority carriers (20) is obviously contained in the expression for the photoinduced microwave conductivity (18) so that we can write... 

Let us now investigate the case of a semiconductor with a relatively slow interfacial charge transfer. In this case the surface concentration of minority carriers is high and we can neglect the second term (which does not contain Ps). For higher values of electrode potential, the term L Qxp(-AUqfkT) can also be neglected. 

In our approximation we start with relation (20) for the surface concentration of minority charge carriers and derive /pi, via formula (11). 

As outlined at the beginning of this chapter, combined photocurrent and microwave conductivity measurements supply the information needed to determine three relevant potential-dependent quantities the surface concentration of excess minority carriers (Aps), the interfacial recombination rate (sr), and the interfacial charge-transfer rate ( r). By inserting the... 

The theoretically derived formula (21) relating PMC measurements to the surface concentration of minority carriers and interfacial rate constants contains a proportionality constant, S, the sensitivity factor. This factor depends on both the conductivity distribution in the semiconductor elec-... 

Successful and reproducible preparation of highly dispersed catalysts crucially depends on the state of the carrier surface and on the concentration and pH of the impregnating solution. It is an art and a science for which several goodbooks and reviews exist.1 5... 

A particular important property of silicon electrodes (semiconductors in general) is the sensitivity of the rate of electrochemical reactions to the radius of curvature of the surface. Since an electric field is present in the space charge layer near the surface of a semiconductor, the vector of the field varies with the radius of surface curvature. The surface concentration of charge carriers and the rate of carrier supply, which are determined by the field vector, are thus affected by surface curvature. The situation is different on a metal surface. There exists no such a field inside the metal near the surface and all sites on a metal surface, whether it is curved not, is identical in this aspect. 

Electrochemical properties of silicon single crystals, usually cuts of semiconductor wafers, have to be considered under two distinct respects (1) As an electrode, silicon is a source of charge carriers, electrons or positive holes, involved in electrochemical reactions, and whose surface concentration is a determining parameter for the rate of charge transfer. (2) As a chemical element, silicon material is also involved in redox transformations such as electroless deposition, oxide generation, and anodic etching, or corrosion processes. 

The work of Misono et al. (55) illustrates how acid strength distributions for silica-alumina catalyst can be deduced from catalytic titration measurements by use of an appropriate series of reactants. Surface concentration of amine, pyridine in this case, was adjusted by proper choice of amine partial pressure and desorption temperature while carrier gas flowed over the catalyst sample. At each level of chemisorbed pyridine, pulses of the reactants were passed over silica-alumina at 200°C and the products analyzed. The reactants were t-butylbenzene, diisobutylene, butenes, and f-butanol. It was concluded that skeletal transformations require the presence of very strong acid sites, that double-bond isomerization occurs over moderately strong acid sites, and that alcohol dehydration can occur on weak acid sites. 

These two conditions (Eqs. (4.97) and (4.98)) are usually sufficient for assuming the medium as quiescent in dilute systems in which both cua.s and cda,oo are small. However, in nondilute or concentrated systems the mass transfer process can give rise to a convection normal to the surface, which is known as the Stefan flow [Taylor and Krishna, 1993]. Consider a chemical species A which is transferred from the solid surface to the bulk with a mass concentration cua.oo- When the surface concentration coa,s is high, and the carrier gas B does not penetrate the surface, then there must be a diffusion-induced Stefan convective outflux, which counterbalances the Fickian influx of species B. In such situations the additional condition for neglecting convection in mass transport systems is [Rosner, 1986]... 

In the presence of surface recombination, the minority carrier density at the surface is determined by the rate of their arrival from the collection region W + LP and the rate of their removal by the routes illustrated in Fig. 8.5. The concentration of holes accumulating at the surface can be expressed in terms of the equivalent surface concentration, ps (cm-2) = (Px=o since this allows a convenient formulation of the kinetic equations. Further simplification is achieved by considering the concentrations of redox species and majority carriers to be time invariant. This simplified scheme is illustrated for the case of an n-type semiconductor in Fig. 8.5. 

Consideration of the rates of arrival, charge transfer, trapping and recombination of minority carriers leads to expressions for the time dependent surface concentrations (cm-2) of free ps,(Tee and trapped pJ>trap holes ... 

The parameter / is the characteristic length for a unit cell, E0 is the surface concentration of a carrier protein molecule, and a2, a3, a4, a5 are the reaction rate parameters analogous to that half saturation constants. Table 11.3 displays the experimental effective diffusion coefficients and the volume fraction of intracellular phase A. In the first four sets... 

The use of insoluble, highly cross-linked anisotropic networks created by the polymerisation of photoreactive monomers, eliminates the problem of crystallisation, at least for organic materials, since polymer networks are macromole-cular structures incapable of crystallising, see Chapter 6. Furthermore, the fabrication of multilayer devices would be facilitated by the use of a cross-linked stable HTL next to the anode on the solid substrate surface, onto which subsequent layers can be deposited by vapour deposition. Multilayer OLEDs are intrinsically more stable than monolayer devices due to a better balance of charge-carriers and concentration of the charged species away from the electrodes. The synthesis and cross-linking of a suitable aromatic triarylamine derivative with a polymerisable oxetane group at each end of the molecule for use as a HTL has been reported recently, ... 

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