Electrolyte-semiconductor interface equilibrium

Figure 4, Semiconductor-electrolyte solution interface in the dark. An n-type semiconductor with a depletion layer at the surface is illustrated. E is electron energy, Ej and pEj . are the equal Fermi leveh for electrons and holes at equilibrium, other symbols as in Figure 3 (13).

The basic requirement of the redox oxidant in contact with n-type semiconductors is that it has an equilibrium potential more negative than the decomposition potential of the semiconductor and more positive than the lower edge of the semiconductor conduction band. The basic requirement of the reductant electrolyte is that its redox equilibrium potential be negative of the oxidant electrolyte and more positive than the lower edge of the semiconductor conduction band. More work will be necessary at characterizing solid electro-lyte/semiconductor interfaces with those solid electrolytes available before satisfactory solid-state devices capable of photocharge can be realized. 

An electrical double layer arises at the semiconductor elec-trode/electrolyte solution interface, as in the case of the metal/sol-ution interface. The double layer consists of the plates carrying charges of opposite sign, each plate being located in one of the phases in contact. In the near-surface region of the semiconductor the charge is formed as a result of redistribution of electrons and holes, while in the solution it is formed as a result of ion redistribution. Under equilibrium conditions, the absolute values of these charges are the same. 

Although Vredox(vac. scale) is determined as a measure for the Fermi level of a metal which is in equilibrium with a redox couple, it has a unique value for the redox couple, and, therefore, it can be considered as a measure of the electronic energy level of the redox couple on a vacuum scale. Thus, as at a metal/metal or a metal/semiconductor interface, Al p can be determined at the solid phase/electrolyte interface as a difference between M and eVredox(vac. scale), which can be considered as a reverse of the real potential or the effective work function of the redox couple. At equilibrium, the Fermi level of the solid phase and the electronic energy level of the redox couple is the same (/ij1 = /I ) and sometimes the energy level of the redox couple is called the Fermi level of the redox couple in analogy to that of the solid phase.5,23 26 32 54 55 As already mentioned, Fermi statistics is not applicable to the redox couple and, therefore, there is no Fermi level in an electrolyte, but one may accept this terminology with the understanding that the Fermi level of the redox couple actually means the Fermi level of the solid phase in equilibrium with the redox couple. 

Semiconductor Electrode, Fig. 2 Energy diagrams at an n-type semiconductor-electrolyte solution interface (a) at equilibrium, (b) under forward bias, and (c) under reverse bias. Ec (, or or is required). Energy of the... 

When the semiconductor is put into contact with a liquid electrolyte containing a redox couple, thermodynamic equiUbrium dictates that electrons will flow between the semiconductor and the electrolyte solution until the electrochemical potential (or Fermi level) on both sides of the interface is the same. This movement of charges results in the development of an electric field across the interface, which compensates the difference between the Fermi level position in the semiconductor before equilibrium and the electrochemical potential of the redox pair. If the semiconductor is n-type, the presence of ionised donor species leads to an excess of positive charges, which are spread out over a depletion region with... 

Figure Bl.28.9. Energetic sitiration for an n-type semiconductor (a) before and (b) after contact with an electrolyte solution. The electrochemical potentials of the two systems reach equilibrium by electron exchange at the interface. Transfer of electrons from the semiconductor to the electrolyte leads to a positive space charge layer, W. is the potential drop in the space-charge layer.

Figure 29.4 shows an example, the energy diagram of a cell where n-type cadmium sulfide CdS is used as a photoanode, a metal that is corrosion resistant and catalytically active is used as the (dark) cathode, and an alkaline solution with S and S2 ions between which the redox equilibrium S + 2e 2S exists is used as the electrolyte. In this system, equilibrium is practically established, not only at the metal-solution interface but also at the semiconductor-solution interface. Hence, in the dark, the electrochemical potentials of the electrons in all three phases are identical. 

Consider the interface between a semiconductor and an aqueous electrolyte containing a redox system. Let the flat-band potential of the electrode be fb = 0.2 V and the equilibrium potential of the redox system o = 0.5 V, both versus SHE. Sketch the band bending when the interface is at equilibrium. Estimate the Fermi level of the semiconductor on the vacuum scale, ignoring the effect of dipole potentials at the interface. 

Although a family of OgS - Jig8 values are allowed under Equation 7 the actual equilibrium state of the oxide/solution interface will be determined by the dissociation of the surface groups and the properties of the electrolyte or the diffuse double layer near the surface. For surfaces that develop surface charges by different mechanisms such as for semiconductor, there will be an equation of state or charge-potential relationship that is analogous to Equation 7 which characterizes the electrical response of the surface. 

Upon immersion of the CdSe semiconductor into the electrolyte, electron exchange at the interface occurs until equilibrium is attained. At equilibrium, the Fermi level of the semiconductor is adjusted by the presence of a space charge layer at the semiconductor surface. This layer is due to the difference between the Fermi level of the semiconductor and the Fermi level of the electrolyte which is measured at the redox couple (X) The potential drop at the space charge layer and the amount of band bending also depend on the degree of Fermi level mismatch at the semiconductor-... 

Equilibrium between the two phases at a semiconductor-electrolyte interface, solid and liquid, can only be achieved if their electrochemical potential is the same, that is ... 

Fig. 3.9 Energy diagram of the semiconductor-electrolyte interface under equilibrium, (a) The Fermi level Ep is equal to redox potential energy, Ep, redox (b) The Fermi level, Ep is equal to reference electrode energy, Ereference- (c) Potential disMbution. (d) Charge across the interface.

As shown in Fig. 3.13(b) and 3.13(c) when ratio n/nsfl is less than or greater than 1 the system is in non-equilibrium resulting in a net current, with the electron transfer kinetics at the semiconductor-electrolyte interface largely determined by changes in the electron surface concentration and the application of a bias potential. Under reverse bias voltage, Vei > 0 and ns,o > ns as illustrated in Fig. 3.13(b), anodic current will flow across the interface enabling oxidized species to convert to reduced species (reduction process). Similarly, under forward bias, Ve2 < 0 and ns > ns,o as illustrated in Fig. 3.13(c), a net cathodic current will flow. 

For an interface described by a constant Helmholtz potential electron exchange between the semiconductor and redox electrolyte solution. The result is that dV = d(psc, and for a non-equilibrium system one can obtain the current-voltage relation ... 

Salvador [100] introduced a non-equilibrium thermodynamic approach taking entropy into account, which is not present in the conventional Gerischer model, formulating a dependence between the charge transfer mechanism at a semiconductor-electrolyte interface under illumination and the physical properties thermodynamically defining the irreversible photoelectrochemical system properties. The force of the resulting photoelectrochemical reactions are described in terms of photocurrent intensity, photoelectochemical activity, and interfacial charge transfer... 

Fig. 4.12 Diagram illustrating space charge layer formation in microcrystalline and nanocrystalline particles in equilibrium in a semiconductor-electrolyte interface. The nanoparticles are almost completely depleted of charge carriers with negligibly small band bending.

Similar photovoltaic cells can be made of semiconductor/liquid junctions. For example, the system could consist of an n-type semiconductor and an inert metal counterelectrode, in contact with an electrolyte solution containing a suitable reversible redox couple. At equilibrium, the electrochemical potential of the redox system in solution is aligned with the Fermi level of the semiconductor. Upon light excitation, the generated holes move toward the Si surface and are consumed for the oxidation of the red species. The charge transfer at the Si/electrolyte interface should account for the width of occupied states in the semiconductor and the range of the energy states in the redox system as represented in Fig. 1. 

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