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Fig. 5.63 Scheme of a photoelectrochemical cell with sensitized semiconductor anode interface to form the oxidized, S + (reduced, S ) ground-state form via the majority charge carrier injection into the conduction (valence) band of the n- (p-) type semiconductor electrode. 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. The charge injection from the sensitizer, S*, dissolved in the electrolyte solution, might formally be considered as a photogalvanic process. The S* molecules must be able to diffuse to the semiconductor surface during their lifetime, r 0 . Assuming the usual lifetime, T O ^ 1 0 ~ 6 to 10" 4 s and the diffusion coefficient, D of 10~ 5 cm 2 /s, the effective diffusion distance of S*, (5D (see Eq. 2.5.9) is very small: <5D = (jtDr)V2 56 nm (5.10.26)
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Let us assume that the electrolyte is illuminated through the semiconductor electrode as shown in Fig. 5.58 (this is, in principle, possible since the semiconductor is transparent for wavelengths X>hcleg at which the sensitizer absorbs the radiation). The relative intensity of radiation transmitted to the distance <5D is given by the Lambert-Beer law: log (/// 0 ) = -8cdD (5.10.27)
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where e is the extinction coefficient of S and c its concentration. The light-harvesting efficiency 0 L is defined as: <pL = (1 -1/I o ) = 1 10~ C 6 D
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(5.10.28)
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For a typical extinction coefficient e 107cm2/mol (cf. Table 5.6) and c = 1 M, the calculated, (pL values (Eqs (5.9.42) and (5.9.44)) are only ca. 12 per cent. The number of active S* molecules is further reduced by the quantum yield of the formation of the triplet state cpT (cf. Table 5.6) and the quantum yield of the injection of the majority charge carriers from S* into
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the semiconductor electrode (<p,). Thus, the overall quantum yield of photocurrent (IPCE = incident photon to current efficiency) is a product of all the three quantities: IPCE = <pL cpT <p, (5.10.29)
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It actually denotes the number of electrons flowing through the interface per one photon impinging on it, IPCE is usually considered for monochromatic light (radiant power, P, in W/cm2) whose wavelength (A) matches the wavelength of the absorption maximum of the sensitizer, Amax. A more practical equation for IPCE can easily be derived by combining the photocurrent density, ; p h with the radiant power and wavelength: IPCE =jphhc/XPe (5.10.30)
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where c is the velocity of light. The light-harvesting efficiency of an electrode covered with an adsorbed sensitizer can be expressed in the form similar to Eq. (5.10.28): <p L =l-10- a d s r > (5.10.31)
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where ads is the extinction coefficient of adsorbed sensitizer, T is the surface concentration of the adsorbate (in mol/cm2 of the physical surface area) and r is the roughness factor of the electrode. The latter is defined as the ratio of physical to geometrical surface areas (polycrystalline materials, such as semiconducting oxides may achieve the r values of about 102-103). The extinction coefficient, eads, can be approximated by the usual extinction coefficient of the solution, e (in cm2/mol). For a typical monomolecular coverage, T 10"1() mol/cm2, an electrode roughness factor r = 1000 and an extinction coefficient e a d s = 107cm2/mol, the light-harvesting efficiency is, in comparison to the preceding case, very high, cpL = 90 per cent. Moreover, the adsorbed sensitizer is in intimate contact with the semiconductor surface, hence the conditions for charge injection from S* into the semiconductor are almost ideal (c^ >100 per cent). The most successful sensitizers so far tested are complexes of Ru(II) with various derivatives of 2,2' bipyridine, e.g. 2,2'-bipyridine 4,4'-dicarboxylic acid (L). The Ru(II)L3 complex is adsorbed from an aqueous solution of suitable pH value to oxidic semiconductors via electrostatic bonds between COO~ groups of the ligands and the positively charged (protonized) semiconductor surface. The sensitization of n-TiO2 by RuL3 was studied in detail by M. Gratzel et al. The photoelectrochemical reaction is initiated by an electron injection into the conduction band of TiO2: *Ru(II)L3-> Ru(III)L3 + ec-b(TiO2) (5.10.32)
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The standard redox potential of Ru(III)L 3 /Ru(II)L 3 equals 1.56 V( protonated form). Even energetically highly demanding processes, such as
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406 oxidation of water to oxygen (E{)= 1.229V) and bromide to Br2 (Eo = 1.0873 V) are thermodynamically possible. Two reactions deserve special attention, since they enable the construction of highly efficient regenerative cells 2Ru(III)U- + 21" -> 2Ru(II)U- 4-I2, 2Ru(III)U- + 2Br"-* 2Ru(II)L^" 4- Br2, IPCE (450 nm) - 70% IPCE (450 nm) - 55%
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The best parameters of the I~/I2 cell were achieved by using a non-aqueous electrolyte and the anatase electrode of nanometer-sized particles, sensitized with Rul^ju - (NC)Ru(CN)(bpy)2)2. In 1991, B. O'Regan and M. Gratzel described a cell attaining parameters competitive to commercial, solid-state photovoltaic devices. 5.10.6 Photoelectrochemical solar energy conversion The solar spectrum corresponds roughly to the radiation of a black body at the temperature 5750 K. If we denote the photon flux in the wavelength interval from A to (A + dA) (in photons/m2 s) as /(A), the total solar power flux (in W/m2) is given as: Ps = hc\ /(A)dA (5.10.33)
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The power flux corrected for atmospheric absorptions equals about 1 kW/m2 if the Sun stands at zenith and the sky is clear. This situation is customarily labelled AM 1 (one standard air mass). The total world consumption of energy (ca. 3.1020 J/year) can be met by converting the solar energy impinging on about 0.01 per cent of the Earth's surface, which is about 0.3 per cent of the desert areas. The research on solar energy conversion is further encouraged by the existence of natural photosynthesis, which provides all the fossile energy resources of the Earth. The natural photosynthesis transforms about 0.1 per cent of the solar energy impinging on the Earth, but the energy conversion in green plants is not as efficient as that attained by currently available photovoltaic cells and other artificial devices. The solar energy conversion efficiency is defined as: CE = Pout/Ps (5.10.34) where Fout is the maximum power output of the cell per unit illuminated area. For a regenerative photoelectrochemical cell, the maximum value of Pout has to be derived from the photocurrent/potential characteristic of the cell (Fig. 5.64). The quality of the cell is also described by the so-called fill factor,/:
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