N-type semiconductor electrodes

The electrons produced in the conduction band as a result of illumination can participate in cathodic reactions. However, since in n-type semiconductors the quasi-Fermi level is just slightly above the Fermi level, the excited electrons participating in a cathodic reaction will almost not increase the energy effect of the reaction. Their concentration close to the actual surface is low hence, it will be advantageous to link the n-type semiconductor electrode to another electrode which is metallic, and not illuminated, and to allow the cathodic reaction to occur at this electrode. It is necessary, then, that the auxiliary metal electrode have good catalytic activity toward the cathodic reaction. 

Practically more important is the sensitization of the n-type semiconductor electrode (Fig. 5.63). The depicted scheme is virtually equivalent to that in Fig. 5.62 the only exception is that the hole is not created in the valence band but formally in the sensitizer molecule. 

While for a solar water splitting cell, light is directly absorbed by the semiconductor electrode (anode or cathode). The separation of electron-hole pairs is achieved in the built-in electric field near the semiconductor surface. The electric field is formed due to the charge transfer between the semiconductor electrode and the electrolyte as schematically shown in Fig. 17.5(b) [28]. Take an n-type semiconductor electrode for example... 

Fig. 5-44. Space charge layers of n-type semiconductor electrodes (c) an inversion layer, (d) a deep depletion layer.

Figure 5-46 shows the capacity observed for an n-type semiconductor electrode of zinc oxide in which an accumulation layer is formed at potentials more cathodic... 

Fig. 6-46. Differential capacity observed and computed for an n-type semiconductor electrode of zinc oxide (conductivity 0. 59 S cm in an aqueous solution of 1 M KCl at pH 8.5 as a function of electrode potential solid curve s calculated capacity on Fermi distribution fimction dashed curve = calculated capacity on Boltzmann distribution function. [From Dewald, I960.]...

Figure 5-49 illustrates the Mott-SchottlQ plot observed for two n-type semiconductor electrodes of zinc oxide in a potential range in which the depletion and... 

Fig. 6-48. Differential capacity of a space charge layer of an n-type semiconductor electrode as a function of electrode potential solid cunre = electronic equilibrium established in the semiconductor electrode dashed curve = electronic equilibrium prevented to be established in the semiconductor electrode AL = accumulation layer DL = depletion layer IL = inversion layer, DDL - deep depletion layer.

Fig. 5-56. Capacity Csc of a space charge layer and capacity Ch of a compact layer calculated for an n-type semiconductor electrode as a function of electrode potential Ct = total capacity of an interfadal double layer (1/Ct = 1/ Csc+ 1/Ch). [From Gerisdier, 1990.]...

Fig. 5-61. Mott-Schottky plot of an n-type semiconductor electrode in presence of a surface state ib = flat band potential with the surface state fully vacant of positive charge Eft, - flat band potential with the surface state fully occupied by positive charge Q = maximum charge of the surface state e, = surface state level, s capacity of the surface state ( Ch ).

Fig. 5-63. Flat band potential of two n-type semiconductor electrodes of zinc oxide in 1 M KCl (pH 8.5) as a function of donor concentration A= surface finished in 85 % H3PO4 B = surface finished in 2 M KOH = donor concentration. [From Dewald, I960.]...

Fig. 8-2S. Aoodic transfer reaction of redox holes with transport of mincnity charge carriers (holes) in an n-type semiconductor electrode il.r - anodic hole transfer current at an interface = limiting hole transport current i i = limiting diSiision current of redox partides.

Fig. 8-26. Cathodic iiyectian of minority charge carriers (holes) followed by recomlmation of minority charge carriers (holes) with majority charge carriers in an n-type semiconductor electrode ipr - cathodic current of hole transfer at an interface - current of electron-...

For n-type semiconductor electrodes in which a redox reaction of cathodic hole iiyection reaches its quasi-equilibrium state at the electrode interface, the recombination current of iiqected holes (minority charge carriers) with electrons (minority charge carriers), w, is given by Eqn. 8-70 [Reineke-Memming, 1992] ... 

Fig. 8-28. Cathodic polarization curves for several redox reactions of hydrated redox particles at an n-type semiconductor electrode of zinc oxide in aqueous solutions (1) = 1x10- MCe at pH 1.5 (2) = 1x10 M Ag(NH3) atpH12 (3) = 1x10- M Fe(CN)6 at pH 3.8 (4)= 1x10- M Mn04- at pH 4.5 IE = thermal emission of electrons as a function of the potential barrier E-Et, of the space charge layer. [From Memming, 1987.]...

Fig. 8-82. Energy diagram for a redox electron transfer via the conduction band and via the surface state at an n-type semiconductor electrode X = reorganization energy of redox particles .,= surface state level.

Figure 9-16 illustrates the polarization curves for the anodic oxidative and the cathodic reductive dissolution of ionic compound semiconductors. The anodic oxidative dissolution proceeds readily at p-type semiconductor electrodes in which the mqjority charge carriers are holes whereas, the cathodic reductive dissolution proceeds readily at n-type semiconductor electrodes in which the majority charge carriers are electrons. 

Figure 10-3 juxtaposes the Fermi levels of the following redox reactions in aqueous solutions and the quasi-Fermi levels of interfacial electrons and holes in an n-type semiconductor electrode erhjo/Hj) of the hydrogen redox reaction F(0a/H20) of the oxj en redox reaction ersc) of the n- q)e semiconductor and... 

Fig. 10-3. Energy diagrams for an n-type semiconductor electrode (a) in the daik and (b) in a photoexdted state S = aqueous solution = conduction band edge level at an interface cy = valence band edge level at an interface = Fermi level of oxygen...

Fig. 10-9. Photoexcited reaction current (photocurrent) at semicon ductor electrodes (a) photoexcited reaction of cathodic electron transfer (OX + e - RED) at p-type semiconductor electrode, (b) photoexcited reaction of anodic hole transfer (RED - OX + e) at n-type semiconductor electrode, iph = photocurrent.

Fig. 10-11. Anodic photoexcited dissolution current of an n-type semiconductor electrode of gallium arsenide as a function of electrode potential in a 0.6 M sulfuric add solution lo - photon intensity = diotocurrent. [From Memming-Kelly, 1981.]...

Fig. 10-13. Anodic transfer of pho-toexdted boles (minority charge carrier) at an n>type semiconductor electrode E( -e 9o/e) = electrode potential E% (= — c /e) = potential of the valence band edge B02 (= - = equilibrium...

With n-type semiconductor electrodes, the anodic oiQ en reaction (Euiodic hole transfer) will not occur in the dark because the concentration of interfacial holes in the valence band is extremely small whereas, the same reaction will occur in the photon irradiation simply because the concentration of interfadal holes in the valence band is increased by photoexcitation and the quasi-Fermi level pEp of interfadal holes becomes lower than the Fermi level the o en redox... 

For illustrations, we compare the transfer of anodic holes at metal electrodes and the transfer of anodic photoexdted holes at n-type semiconductor electrodes for the oxygen redox reaction shown in Eqn. 10-16 ... 

For metal electrodes, the anodic 03Q n reaction proceeds at electrode potentials more anodic than the equilibrium potential Bo of the reaction as shown in Fig. 10-14. For n-type semiconductor electrodes, the anodic photoexdted oxygen reaction proceeds at electrode potentials where the potential E of the valence band edge (predsely, the potential pEp of the quasi-Fermi level of interfadal holes, pCp = — CpEp) is more anodic than the equilibrium oxygen potential Eq, even i/the observed electrode potential E is less anodic than the equilibrium oxygen potential E03. The anodic hole transfer of the o Qgen reaction, hence, occurs at photoexdted n-type semiconductor electrodes even in the range of potential less anodic than the equilibriiun potential Eq of the reaction as shown in Fig. 10-14. 

Fig. 10-14. Energy levels and polarization curves (current vs. potential) for anodic transfer ofphotoexdted holes in oxygen reaction (2 HgO. -t- 4h O24 4 H. ) on a metal electrode and on an n-type semiconductor electrode j = anodic reaction current ep(02 20)- Fermi level of oxygen electrode reaction dCpi, = gain of photoenergy q = potential for the onset of anodic photoexdted ox en reacti . 4 pi, (=-Ae.. le) = shift of potential for the onset of anodic oxygen reaction from equilibrium oxygen potential in the negative direction due to gain of photoenergy in an n-type electrode Eib = flat band potential of an n-type electrode.

The potential, E, for the onset of the photoexdted reaction relative to the equilibrium electrode potential E of the same reaction can also be derived in a kinetics-based approach [Memming, 1987]. Here, we consider the transfer of anodic holes (minority charge carriers) at an n-type semiconductor electrode at which the hole transfer is in quasi-equilibrium then, the anodic reaction rate is controlled by the photogeneration and transport of holes in the n-type semiconductor electrode. The current of hole transport, has been given by Eqn. 8-71 as a function of polarization ( - ,) as shown in Eqn. 10-20 ... 

Fig. 10-16. Polarization curves for anodic oxygen and cathodic hydrogen redox reactions on an n-type semiconductor electrode of titanium oxide in the dark and in a photoex-cited state i = anodic current in the dark (zero) = anodic current...

Figure 10-16 shows polarization curves observed for the anodic ox en reaction (anodic hole transfer) and for the cathodic hydrogen reaction (cathodic electron transfer) on an n-type semiconductor electrode of titanium oxide. The data in Fig. 10-16 show that the anodic current due to the transfer of holes (minority... 

Pig. 10-18. (a) PolarizatioD curves of anodic dissolution and (b) Mott-Schottky plots of an n-type semiconductor electrode of molybdenum selenide in the dark and in a photo-excited state in an acidic solution C = electrode capacity (iph) = anodic dissolution current immediately after photoexdtation (dashed curve) ipb = anodic dissolution current in a photostationary state (solid curve) luph) = flat band potential in a photostationary state. [From McEv( -Etman-Memming, 1985.]... 

Pig. 10-19. (a) Capture of photogenerated holes in surface states to form siuface ions and (b) anodic dissolution of surface ions to form hydrated ions on an n-type semiconductor electrode Oj = rate of hole capture in surface states oqx = rate of anodic dissolution of surface ions Cn = surface state level S, = surface atom of semiconductor electrode h(vs) = hole in the valence band h(n> = hole captured in smface states h(soH-) = hole in dissolved ions. 

Similarly, the flat band potential also shifts itself at photoexdted n-type semiconductor electrodes on which a transfer reaction involving anodic redox holes occurs via the surface state level e , if the rate of hole capture at the surface state is greater than the rate of hole transfer across the compact layer, as shown in Fig. 10-20(a). 

Fig. 10-20. Capture of photogenerated holes and cathodically iiyected holes in surface states on n-type semiconductor electrodes (a) surface states capture photogenerated holes at the rate followed by anodic hole transfer to redox particles, (b) surface states capture cathodically injected holes.

This conclusion is valid regardless whether the electrode is n-fype or p-fype. Consequently, if the quasi-Fermi level of interfacial holes in a photoexcited n-type semiconductor electrode equals the quasi-Fermi level of interfacial holes pEp, (eq ial to the Fermi level pEp., of the interface) in a p-type electrode of the same semiconductor in the dark, the current due to anodic holes will be the same on the two electrodes and, hence, the curves of the anodic reaction current as a function of the quasi-Fermi level of interfacial holes will be the same for the two electrodes as suggested in Fig. 10-21. The curves of the anodic reaction current represented as a function of the electrode potential (the Fermi level of the electrode), instead of the quasi-Fermi level of interfacial holes, are not the same for the two electrodes, however. 

The energy equivalent to the inverse overvoltage corresponds to the gain of energy due to the absorption of photons in n-type semiconductor electrodes. 

In photoexcited n-type semiconductor electrodes, photoexcited electron-hole pairs recombine in the electrodes in addition to the transfer of holes or electrons across the electrode interface. The recombination of photoexcited holes with electrons in the space charge layer requires a cathodic electron flow from the electrode interior towards the electrode interface. The current associated with the recombination of cathodic holes, im, in n-type electrodes, at which the interfadal reaction is in equilibrium, has already been given by Eqn. 8-70. Assuming that Eqn. 8-70 applies not only to equilibrium but also to non-equilibrium transfer reactions involving interfadal holes, we obtain Eqn. 10-43 ... 

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