Photopotential

This change of potential by illumination, AV, is defined as photopotential, Vph. 

The current measured at Vught is the sum of electron and hole currents i = ip + h-At the open-circuit potential condition the net current is zero, that is, ip = -in and the photopotential is called the open-circuit photopotential, Voc- When there is very little surface recombination and the electrode reaction is sufficiently fast so that the concentration of the reagents at the surface remains equal to their equilibrium values, the relation between open-circuit photopotential and light intensity for an n-type material can be expressed for a by 

When the photoeffect is limited mainly by the bulk recombination process, i.e., the diffusion of the minority carriers, the photopotential can be quantitatively related to the minority diffusion coefficient, Dp, and the diffusion length, Lp, at a photocurrent of 2ph  

The theoretical maximum value is, however, not praetieally aehievable due to many kinetie proeesses at the semieonduetor/eleetrolyte interfaee sueh as surfaee recombination and majority current. As a result, for a given silieon/eleetrolyte interface, constant photovoltage over a wide range of redox potentials ean oeeur, that is, band bending is independent of the redox potential value. Thus, photovoltages in praetieal systems are often not indicative of the barrier height. 

When a semiconductor electrode is at the flat band potential, photoexdted electrons and holes are soon annihilated by their recombination. In the presence of a space charge layer, however, the photoexdted electrons and holes are separated, vrith each moving in the opposite direction under an electric field in the space charge layer as shown in Fig. 10-4. 

Such a migration of photoexdted electrons and holes induces in the electrode an inverse potential which reduces the potential across the space charge layer and retards the migration of electrons and holes in the opposite direction as shown in Fig. 10-5. This inverse potential, induced by photoexdtation, is called the photopotential. Since the photopotential, AE. = - he,/c, arises in a direction to reduce the potential across the space charge layer, the Fermi level of the semiconductor interior rises by an energy of de j, (the electrode potential lowers 

It follows that the greatest possible photopotential, of semiconductor 

For semiconductor electrodes in which the concentration of impurities is relatively high (.No, Ni, lO cm ), the photopotential has been derived as a function of the concentration of electrons and holes to obtain Eqns. 10-10 and 10-11 [Myamlin-Pleskov, 1967]  

These are approxiinate equations that are applicable to the case in which no reactions proceed at the electrode interface. 

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The first estimations of for photoinduced processes were reported by Dvorak et al. for the photoreaction in Eq. (40) [157,158]. In this work, the authors proposed that the impedance under illumination could be estimated from the ratio between the AC photopotential under chopped illumination and the AC photocurrent responses. Subsequently, the faradaic impedance was calculated following a treatment similar to that described in Eqs. (22) to (26), i.e., subtracting the impedance under illumination and in the dark. From this analysis, a pseudo-first-order photoinduced ET rate constant of the order of 10 to 10 ms was estimated, corresponding to a rather unrealistic ket > 10 M cms . Considering the nonactivated limit for adiabatic outer sphere heterogeneous ET at liquid-liquid interfaces given by Eq. (17) [5], the maximum bimolecular rate constant is approximately 1000 smaller than the values reported by these authors. 

Despite the potential impact of novel photosynthetic routes based on these developments, the most ambitious application remains in the conversion of solar energy into electricity. Dvorak et al. showed that photocurrent as well as photopotential response can be developed across liquid-liquid junctions during photoinduced ET reactions [157,158]. The first analysis of the output power of a porphyrin-sensitized water-DCE interface has been recently reported [87]. Characteristic photocurrent-photovoltage curves for this junction connected in series to an external load are displayed in Fig. 22. It should be mentioned that negligible photoresponses are observed when only the platinum counterelectrodes are illuminated. Considering irradiation AM 1, solar energy conversions from 0.01 to 0.1% have been estimated, with fill factors around 0.4. The low conversion... 

The photopotential can also be expressed in terms of the relative change in the minority carrier density, Anmin, introduced by photoexcitation. By using... 

The magnitude of the photopotential is also related to light intensity and to the value of EDARK. The value of Elight cannot obviously exceed the flatband potential. At Dark = Efb, the photopotential drops to zero which can be used for a simple measurement of the flatband potential. 

The potential which controls the photoelectrochemical reaction is generally not the photopotential defined by Eqs (5.10.20) and (5.10.21) (except for the very special case where the values of v, REdox and the initial Fermi energy of the counterelectrode are equal). The energy which drives the photoelectrochemical reaction, eR can be expressed, for example, for an n-semiconductor electrode as... 

As predicted, the C2,C2 -isopropoxy and propoxy groups are more potent than the corresponding methoxy (0.8 and 1.5 pM vs. 6.4 pM). In addition, C3,C3 -substitution has an effect on both the potency and photopotentiation factor. Although the absorption at 670 nm was improved with C3 substitution, the potency against PKC decreased for analogs 90, 92, and 97. 

The flat band potential cem be estimated from the Mott-Schottl r plot of electrode capacity in the range of electrode potential where a depletion layer is formed as shown in Fig. 5-47 and in Fig. 5-49. The flat band potential can also be estimated by measuring the photopotential of semiconductor electrodes as shown in Fig. 5-62 the photopotential is zero at the flat band potential. 

Fig. 10-S. Photopotential and band bending in a space chaige layer of semiconductor electrodes (a) in the dark and (b) in a photoexcited state - Ae e - pbotopotential.

Fig. 10-6. Generation of the greatest possible photopotential in n-type and p-type semiconductor electrodes (a) in the dark, (b) in a highly photoezcited state. = -he /e = greatest possible photo-potential.

The fact that the photopotential is smaller with an accumulation layer than with a depletion layer is due to the maximum possible potential barrier which is smaller in the accumulation layer than in the depletion layer, as expected from the energy difference between the Fermi level and the band edge levels this energy difference is small in the accumulation layer but great in the depletion layer. 

Fig. 10-7. Photopotential as a function of electrode potential of n-type and p-type semiconductor silicon electrodes in an aqueous sulfate solution U = cell voltage before photoezcitation =...

Photopotential as a fimction of wave length of photons for zinc oxide and cadmium selenide electrodes in aqueous solutions X. = photon wave length. [From Williams, I960.]... 

It is shown in Pig. i0-7 that the photopotential changes its sign at a certain potential which corresponds to the flat band potential of electrodes (See Fig. 10-6.). This provides a way of estunating the flat band potential by measuring the potential at which the photopotential changes its sign. 

In the photoelectrol3dac reaction, the two electrodes are short-circuited and the cell voltage is slight so that no significant electric energy may be produced. The photopotential generated in the ceU provides the overvoltages for both anodic and cathodic reactions. 

Here, no net chemical change occurs. In the photovoltaic cell, almost all the photopotential generated exists between the two electrodes and can be used to produce electric energy. 

When the n-type semiconductor anode is photoexcited, as shown in Fig. 10-25(c), the Fermi level of the anode is raised (the potential of the anode is lowered) by an energy equivalent to the photopotential at the same time, the Fermi... 

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