Surface states, charging and

The causes for this anomalous behavior are still not fully understood. It appears likely that many factors are involved surface film formation, varying potential drop across the Helmholtz region caused, for example, by surface state charging, and so on. Even crystallographic orientations appear to be important [59). These aspects have been discussed by other authors [14, 55, 60). 

The potential i sc of the space charge layer can also be derived as a fixnction of the surface state charge Ou (the surface state density multiplied by the Fermi function). The relationship between of a. and M>sc thus derived can be compared with the relationship between and R (Eqn. 5-67) to obtain, to a first approximation, Eqn. 5-68 for the distribution of the electrode potential in the space charge layer and in the compact layer [Myamlin-Pleskov, 1967 Sato, 1993] ... 

As the Fermi level of the electrode approaches the surface state level of high state density, the surface state is charged or discharged as a capacitor. For convenience sake, we express the sum of a. and in Eqn. 5-86 as the surface state charge Qu and the capacity due to the surface state charge as the surface state capacity C.. Then, the interfadal capadty C is represented by the capadly of an equivalent drcuit shown in Fig. 5-60. 

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))... 

FIGURE 1.9. Surface charge in an n-type semiconductor space charge, at various doping levels at AFs of -0.3 and -l.OV and surface state charge, i2s as a function of surface state density, assuming half-occupancy. Potential drop across the Helmholtz layer is AVh = 0.085 (pC/cm ) assuming 8n = 4 and d = 3 A. (Reprinted with permission from Bard et al. 1980 American Chemical Society.)... 

Light absorption (hvf) by (regular and irregular) surface states Lj and Dj leads to generation of surface free charge carriers and surface excitons (step 9). 

Fig. 6.1 Band diagrams of a n-type semiconductor (a) prior to contact with the electrolyte solution (assuming no defects or surface state charges), (b) in contact with the solution in absence of illumination, (c) in contact with the solution in the presence of moderate illumination, and (d) in contact with the solution in the presence of intense illumination and at the Ef. Illustrated are the conduction band (Ec), Fermi level ( p), and valence band ( v) of the semiconductor. Also shown are the Gaussian distribution of the redox states in the solution, shown as the density of states of oxidized (Doxidized) and reduced (Dreduced) species along with the corresponding Fermi level (fipsoiution), as described in more detail elsewhere [1]...

A detailed physicochemical model of the micelle-monomer equilibria was proposed [136], which is based on a full system of equations that express (1) chemical equilibria between micelles and monomers, (2) mass balances with respect to each component, and (3) the mechanical balance equation by Mitchell and Ninham [137], which states that the electrostatic repulsion between the headgroups of the ionic surfactant is counterbalanced by attractive forces between the surfactant molecules in the micelle. Because of this balance between repulsion and attraction, the equilibrium micelles are in tension free state (relative to the surface of charges), like the phospholipid bilayers [136,138]. The model is applicable to ionic and nonionic surfactants and to their mixtures and agrees very well with the experiment. It predicts various properties of single-component and mixed micellar solutions, such as the compositions of the monomers and the micelles, concentration of counterions, micelle aggregation number, surface electric charge and potential, effect of added salt on the CMC of ionic surfactant solutions, electrolytic conductivity of micellar solutions, etc. [136,139]. 

Figure 9. The effect of surface-state density and insulator charge on conversion efficiency (Ref 23)...

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