Electron Fermi levels

Since electrons are charged particles, the electrochemical potential of electrons (Fermi level, Ep) depends on the inner potential, of the electron ensemble as in... 

Figure 2. Electronic and ionic disorder in ionic solids and in water in physical" (top) and chemical language (bottom).20 The coupling of the ionic and electronic Fermi levels takes place via the chemical potential of the neutral components (here + + Jt = //Ag ) (see Fig. 3). A further relevant example could be the breaking-up of an ion...

Fig. 12. Energy diagram for the process of electron transfer from electrode into solution during electrochemical generation of solvated electrons. 1 thermoemission 2 dissolution of electrons ej delocalized electron e solvated electron Fermi level in metal. Dashed line shows the solvated electron potential well in solution...

Fig. 33 is a schematic illustration of a porous semiconductor electrode interpenetrated with a redox electrolyte. Two situations are shown the dark equilibrium situation and the situation under constant illumination from the electrolyte side (comparable illustrations for a bulk semiconductor/electrolyte interface are given in Figs. 4 and 5). In the dark at equilibrium, the electron Fermi-level in the porous network, Ep , is equal to the Fermi-level of the redox system Ep,redox = — Ueq) and independent of the spatial co-ordinate x normal to the substrate. If an electrolyte with a sufficiently positive redox potential is chosen, can be located in the middle of the gap, which means that the density of electrons in the nanostructured network is... 

Fig. 33. Schematic representation of photoinduced current flow in a nanostructured electrode interpenetrated with a solution with a redox system Ox/Red. The band edges Ec and Ey are shown, together with the electron Fermi-level Ef, (x). The upper diagram illustrates the equilibrium situation in the dark when f, does not depend on x and is equal to the Fermi-level of the redox system. The lower figure shows what happens when under constant illumination from the electrolyte side. Photogenerated holes are consumed in oxidation of Red, and a gradient in Ef x) induces electron transport to the substrate. The photocurrent density is equal to J x = d)/q.

Fig. 1 A scheme of the energetics at an n-type semiconductor electrode in contact with a redox system in an electrolyte solution, (a) The situation under conditions of electronic equilibrium. The electrochemical potential of the electrons is the same in both phases, i.e. the electron Fermi-level in the semiconductor Ep.n has the same value as the Fermi-level of the electrons in the redox system fRed/Ox- (t>) Case in which the energy bands in the semiconductor are flat this situation, corresponding to maximum photovoltage, is reached under strong illumination at open circuit. Wsc is the width of the depletion layer and e(j>sc is the band-bending.

In Fig. 17(a), the energetics of a typical interfacial region between an n-type semiconductor and an electrolyte solution is shown (see also Sect. 2.1.2.2). Electronic equilibrium exists between the semiconductor and a redox system present in the solution the electrochemical potential of electrons /Xg in the solid is equal to that in the liquid phase, and does not change with the spatial coordinate x, perpendicular to the solid/liquid interface. The electrochemical potential of the electrons is also equal to the electron Fermi level, denoted as and can be written as... 

A change in electrical potential energy by application of bias, V, will not be translated solely into a shift in electron Fermi level, but will be divided between a shift in Fermi level Afipn and a shift in electrostatic potential energy AEg. 

Fisher and coworkers combine this observation with the observed (exponential) dependence of photovoltage on light intensity to derive a relationship between Deff and electron Fermi level,... 

Now, we are in a position to define the thermodynamic criteria for light-driven water splitting under short-circuit conditions in a two-electrode photoelectrolysis cell. E needs to lie above the H /H2 redox Fermi level, and pEp needs to lie below the Oj/HjO redox Fermi level. As the electron Fermi level for n-type semiconductors is close to the conduction band, this means in practice that the conduction band energy should lie well above the H" /H2 redox potential. At the same time, the valence band needs to be sufficiently far below the O2/H2O Fermi level to ensure that water oxidation by holes is feasible. In addition to satisfying these thermodynamic criteria, the semiconductor needs to be stable under illumination. Many semiconductors are either oxidized or reduced under illumination as a consequence of the reaction of holes or electrons with the crystal lattice. For example, n-type ZnO is oxidized by photogenerated holes to form Zn " " and oxygen. 

The analysis given applies whether or not there is an insulating layer, and can be used to study the effect of it on the electrostatic regime. Consider first the n-type case. Photogeneration of carriers causes the electron Fermi level to rise in the semiconductor, and more acceptor-type surface states are able to capture electrons from the semiconductor. The semiconductor space charge density P (x), now no longer considered to be x-independent,... 

G is a local generation rate, and / is a recombination rate. At the extraction contact the carrier density is controlled by the voltage. The voltage is given by the rise of the electrons Fermi level, with respect to the redox level, as indicated in Fig. lb ... 

Fig. 8 Scheme showing electron accumulation in a nanoraystalline semiconductor electrode and the compensation by positive charge in the electrolyte to produce local electroneutrality. The electrolyte may contain several species of anions, catirms, and redox molecules, as well as molecules that have the role of modifying the surface to produce some beneficial effects. The energy diagram shows the change of electrons Fermi level that causes a photovoltage... 

Fig. 19 Recombination in a DSC according to the Marcus model of charge transfer in an exponential distribution of surface states. Horizontal axis is the voltage or equivalently the electron Fermi level. The position of the conduction band, Eq, is indicated. Plots at different values of reorganization energy as indicated, (a) Electron transfer probability, (b) Electron recombination resistance. Simulation parameters are T = 300 K, Tq = 1,200 K, a = 0.25, / = 0.75, e = 1 eV vs E edox, = 1 x 10 cm s Rqx = 10 cm ...

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