9732
J. Phys. Chem. B 2001, 105, 9732-9738
Potential Distribution and Photovoltage Origin in Nanostructured TiO2 Sensitization Solar Cells: An Interference Reflection Study M. Turrio´ n,†,‡,| B. Macht,†,⊥ H. Tributsch,†,# and P. Salvador*,‡,§ Department Solare Energetik, Hahn-Meitner Institut Berlin, Glienickerstr. 100, D-14109 Berlin, Germany, Department Matema´ ticas e Informa´ tica, UniVersity Islas Baleares, Cra. Valldemossa km 7,5 E-07071 Palma, Spain ReceiVed: NoVember 30, 2000
A well-defined modulation reflection spectrum due to a multiple interference process is originated in the TiO2 dye sensitizated solar cell (DSSC). Experimental evidence is shown that the interference process leading to the reflection spectrum takes place at the n-conducting F:SnO2(FTO) layer of the FTO/TiO2 back contact. Moreover, the interference reflectance spectrum is influenced by the applied potential and illumination bias and disappears when FTO is metallized with 10 Å of platinum. These results show that FTO/TiO2 cannot be considered as an ohmic but as a rectifying contact where the FTO behaves as a highly doped n-type semiconductor which absorbs an important part of the equilibrium contact potential in the dark. On the basis of our experimental results a new insight on the role of the dark equilibrium contact potential at the FTO/ TiO2 interface in the processes of electric charge separation and photovoltage generation is given. Evidence is shown that the theoretically maximum attainable photovoltage in a DSSC is in one direction limited by the equilibrium redox potential in the dark, and in the other direction by the (light intensity dependent) bottom of the TiO2 conduction band.
1. Introduction and Measurements Strategy Much speculation exists in relation to the electron transport and potential distribution at dye sensitizated solar cells (DSSC) [refs 1-7, and references therein]. Still today, it is not clear where and how the electric field is distributed, although it is generally accepted that it is largely expelled from the nanostructure into the FTO/TiO2 back contact due to the shielding capacity of the electrolyte within the pores. Basically, two models have been proposed to explain the operation of DSSC. One, the so-called kinetic model, assumes that the chemical potential gradient for photoinduced electrons in the sensitized TiO2 nanostructure is the driving force for charge transport.5 According to this model, the photovoltage should be determined by the photoinduced chemical potential gradient of TiO2 conduction band electrons.1 Moreover, some authors state that the maximum photovoltage is given by the difference in electron energies between the electrolyte redox level and the bottom of the electron’s conduction band, rather than by any difference in electrical potential in the cell in the dark.3 By contrast, the so-called junction model2 compares the DSSC with a p-n junction solar cell and posits that the redox couple determines the existence of electrochemical equilibrium in the dark at the TiO2/FTO interface, which is unbalanced by electron flow from TiO2 during illumination, as the real source of photopotential. All of the work up to now has shown that it is necessary to get more information about the processes that take place in the solar * Corresponding author. E-mail:
[email protected]. † Hahn-Meitner Institut Berlin. ‡ University Islas Baleares. § On leave from Instituto de Cata ´ lisis y Petroleoquımica, CSIC-Madrid, Spain. | E-mail:
[email protected]. ⊥ E-mail:
[email protected]. # E-mail:
[email protected].
cell during conversion of solar energy into electrical energy. The results presented here try to shed some light on the problem of the participation of the FTO-TiO2/electrolyte junction potential in the DSSC function. A well-known optical tool for investigating surface reactions in electrochemistry is the internal reflection spectroscopy (IRS) technique developed by Kuwana and co-workers8-10 for spectral observations of optically transparent electrodes (OTE), such as FTO thin films, at or near the electrode-solution interface. Spectral changes due to variations of the optical constants of OTE or the electrochemical generation of intermediates or products were mainly examined by these authors. Frova et al.,11 studied the electromodulation of the interference spectrum of a Ta2O2 thin film, which was attributed to optical path changes because of the electrooptic modulation of its refraction index. In like manner, S. Nonomura et al.12 evaluated the built-in field of an amorphous silicon (a-Si:H) solar cell by electromodulation of its reflection spectrum. The process taking place in all these electromodulation experiments can be described as follows: the internal electric field distribution in the thin film, E(x;VAC) is modified by under application of an alternative potential, VAC, which affects the spatial distribution of the thin film absorption coefficient, R2(λ,x;VAC). Essentially, the incident light beam undergoes multiple reflections in the thin film, giving rise to an interference phenomenon because of the difference of the refraction index of the thin film (FTO in our case) and the glass substrate.8-14 The ratio of the field-modulated reflectance to the total reflectance, dR/R, is then directly recorded as a function of wavelength. Here we show that the modulation reflection spectrum (dR/R vs λ) of the FTO layer at the back contact of a DSSC can be used in order to evaluate the potential distribution at the FTO/TiO2/electrolyte interface and its dependence on the voltage and illumination bias. Two main facts confirm that the electromodulation spectrum is due to multiple reflections in the
10.1021/jp004341a CCC: $20.00 © 2001 American Chemical Society Published on Web 09/14/2001
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J. Phys. Chem. B, Vol. 105, No. 40, 2001 9733
Figure 2. Interference phenomenon due to multiple reflections in a FTO thin film of plane, parallel plates supported on a thick glass substrate, in contact with an electrolyte. Figure 1. Schematic representation of the modulation reflection experimental setup.
FTO film. First, the good agreement of the FTO refractive index calculated from our modulation reflection measurements with literature values.8,15 Second, the coincidence of the maxima and minima of the FTO electromodulation spectrum with the of maxima and minima position of the corresponding reflection spectrum (R vs λ),10 as expected for a logarithmic derivative spectrum (dR/R vs λ). 2. Experimental Section All experiments were performed with a DSSC prepared following the method described by Nazeeruddin et al.16 A FTO coated glass obtained from Solems Z. I. Les Glaises, with a square resistance of 9 Ω and a thickness of about 3 mm (FTO thickness ≈ 0.8 µm), was used as a substrate. A thin film of nanostructured TiO2, which was sensitizated with a Ru-complex dye (cis-RuII(LH2)2(NCS)2, with LH2 ) 2,2′-bipyridyl-4,4′dicarboxylic acid from Solaronix Inc.), was deposited onto the glass-FTO substrate. A platinized F:SnO2 sheet (30 Å Pt) was used as counter electrode. The cell was filled with organic electrolyte (acetonitrile, 0.5 M LiI, 50 mM I2, 0, 2 M 4-tertbutylpyridine) and sealed with Surlyn 1702-Dupont. The experimental setup used for the interference reflectance measurements is schematically shown in Figure 1. The DSSC was illuminated with a 150 W Xe lamp followed by a monochromator (Oriel Corporation). The illumination was performed on the TiO2 film from the FTO side (backside illumination). When the DSSC was directly illuminated with monochromatic light, interference effects involving multiple reflections generated in the FTO film were observed. These interference effects could be easily detected by simultaneously measuring the reflected light signal from a photodetector under application to the DSSC of (1) a DC bias from a potentiostat (Wenking POS 73), and (2) a modulation voltage (VAC ) 0.3 V, f ) 230 Hz) from a waveform generator. The in-phase and in-quadrature components of the modulated reflected light (dR/ R, where dR represents the field-induced changes in the reflectance, R, under the periodic perturbation VAC) were detected with the help of a lock-in amplifier which received the signal coming from the photodetector. Interference reflection spectra (dR/R vs λ) were obtained by sweeping λ at a constant speed with the help of the monochromator. In some experiments simultaneous illumination of the TiO2 film from the electrolyte side (front side illumination) with a quartz lamp was necessary.
Illumination bias intensity was controlled by changing the distance between the Xe lamp and the DSSC. 3. Results Figure 2 shows how the light ray enters the conducting FTO film through the transparent glass substrate and undergoes multiple reflections, giving rise to an interference phenomenon because of the different refractive index of the glass substrate and the FTO film. As already explained in the Experimental Section, the wavelength-dependent intensity of the reflected light, R, under external modulation of the electric field at the FTO/electrolyte interface, dR, was at the base of our experiments. The electromodulation spectrum (dR/R vs λ) in fact corresponds to the derivative of the reflection spectrum (R vs λ).10 The measured signal is normalized to the intensity of the reflected beam. In this way the logarithmic derivative of the reflectivity with respect to the modulation agent is obtained, the intensity of the incident light being eliminated.13 This method offers the advantage that only the periodic intensity variation of the reflectivity, dR, has to be amplified, leading to a much higher sensitivity of the measurements. It can be seen in Figure 2 how the incident light beam suffers different reflections while crossing the system. Part of the light coming from the film-electrolyte interface is reflected and part is transmitted through the electrolyte. An interference process takes place because of the optical path difference between the light reflected from the glass-FTO film interface and that reflected from the FTO film-electrolyte interface (beams 1 and 2). The well-known maximum and minimum interference conditions for a thin film are17
2n2d M
(1)
4n2d 2m + 1
(2)
λMax ) λmin )
where λMax and λmin are, respectively, the wavelength of the interference reflection spectrum maxima and minima, with interference orders M,m ) 0,1,2..., d is the thickness of the FTO film and n2 the real part of its complex refraction index (nˆ 2 ) n2 + ik2). When an alternative voltage, VAC, is applied to the DSSC a modulation reflection signal, dR, appears. Figure 3 shows the modulation reflection spectra corresponding to the DSSC for three different values of the FTO thickness. A shift in the
9734 J. Phys. Chem. B, Vol. 105, No. 40, 2001
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Figure 3. Modulation reflection spectra corresponding to a DSSC under short-circuit conditions (VDC ) 0) for three different thickness of the FTO film: (a) d ) 0.74 µm, (b) d ) 0.71 µm, and (c) d ) 0.69 µm. In agreement with eq 1, a shift of the spectrum to lower energies as d increases, is observed. Figure 5. Modulation reflection spectra of the DSSC for three redox couples (I-/I2, Br-/Br2, hydroquinone H2Q/quinone Q) with different redox potentials (Eredox). Quoted Eredox refer to water as solvent (a shift of Eredox has to be expected in acetonitrile, although their relative positions must remain invariable). As Eredox become more positive the bandbending at the FTO/electrolyte interface increases and Ne decreases; consequently, according to eq 6, n2 decreases and dR/R increases.
Figure 4. Modulation reflection spectra under short circuit conditions (VDC ) 0) of: (a) whole DSSC, (b) DSSC with TiO2 without dye, (c) DSSC without TiO2, (d) DSSC in which a Pt thin film was deposited onto the FTO at the back contact. Observe that in cases (a), (b), and (c) the spectrum shape does not change appreciably although it shifts, probably due to variations of the FTO film thickness (see Figure 3). In case (d) the signal disappears because the applied VAC potential is enterely absorbed by the Helmholtz layer at the FTO/Pt interface (no modulation of the FTO depletion layer electric field is possible).
position of the maxima and minima toward higher energies can be observed when d increases, as expected from eqs 1 and 2. The interference reflection spectra of three cells with different structures are shown in Figure 4. Spectrum (a) corresponds to the whole DSSC, while spectra (b) and (c) correspond to DSSC where dye and TiO2 were removed. As can be seen, the DSSC structure does affect maxima and minima positions but not the spectrum shape. Finally, to make sure that the signal comes from the FTOfilm, a further experiment was performed. A special DSSC was made by depositing a 10 Å Pt layer onto the FTO substrate at the back contact. No modulation spectrum could be observed in this case (see Figure 4d).
Figure 6. Influence of the potential bias (VDC) on the modulation reflection spectrum amplitude. As in Figure 5, dR/R reaches its maximum amplitude for VDC ) 0 (short circuit conditions, i.e., as EF ) Eredox), where the FTO bandbending is maximum, and decreases as VDC increases (i.e., as EF is pushed upward and the bandbending diminishes).
To determine the influence of the electrolyte redox potential on the modulation spectrum, three redox-couples were alternatively dissolved in the electrolyte (I-/I2, Br-/Br2, hydroquinone H2Q/quinone Q). An amplitude increase can be observed in Figure 5 as the redox potential becomes more positive. Figure 6 shows the influence of the external potential bias (VDC) on the DSSC modulation reflection spectrum, while Figure 7 evidences the effect of front side illumination bias. Clear changes of dR/R amplitude are observed in both cases but not spectrum shifts. 4. Discussion The light interference process in thin films is described by eqs 1 and 2, according to which interference maxima and minima shift toward smaller energies as the film thickness increases. The ratio of the wavelengths corresponding to two
Nanostructured TiO2 Sensitization Solar Cells
J. Phys. Chem. B, Vol. 105, No. 40, 2001 9735 there exists an harmonic perturbation of frequency ω due to the electromagnetic field, Eem, associated with incident photons. The electric currents associated with both electric perturbations, are19
Figure 7. Influence of front side illumination bias (see Figure 1) on the amplitude of the modulation reflection spectrum for VDC ) 0 (short circuit conditions). In this case the rate of electron injection from TiO2 nanoparticles to the FTO conduction band increases with illumination intensity, so that Ne increases and dR/R decreases.
consecutive maxima (λM and λM+1) is obtained from eq 1 to be
λM/λM+1 )
M+1 M
(3)
Equation 3 allows M to be estimated without knowing the exact value of n2 and d. So, we can say that the crossover points localized around 1.55 and 1.80 eV in the modulation spectra of Figure 3 correspond to minima for m ) 3 and maxima for M ) 4, respectively, in the corresponding reflection spectrum reported by Kuwana et al.8,9 Values of n2 for SnO2 between 1.80 and 2.05 can be found in the literature.8,9,18 In our case, taking a d ) 0.73 µm and replacing in eq 1 the appropriate values of M and λM, a reasonable value of n2 ) 1.95 is obtained. 4.1. Influence of the Cell Structure on the Electromodulation Spectrum. The reflection spectrum (R vs λ) of a SnO2 film-coated glass (d ) 0.69 µm) in contact with water reported by Winograd and Kuwana10 shows an array of maxima and minima localized at 508, 564, 635, and 729 nm, which reasonably coincides with the position of the crossover points of our derivative reflection spectra (dR/R vs λ) at about 516, 565, 651, and 730 nm (2.4, 2.2, 1.9, and 1.7 eV) (see Figure 4). Since the modifications of the DSSC structure (removal of both the nanostructured TiO2 layer and dye) do not substantially alter their reflection spectrum (compare (a) with (b) and (c)), it can be concluded that the signal (dR/R) must be attributed to the interference phenomenon of multiple reflections taking place at the FTO thin film used as electric back contact of the DSSC. The fact that the reflection spectrum disappears when the FTO is layered with a Pt thin film (see Figure 4d) can be explained as follows: Pt deposition introduces a huge amount of surface states, so that when the FTO/Pt junction is externally polarized the applied potential is fully absorbed in the Helmholtz layer (unpinning of the FTO band edges). Since the electric field at the FTO depletion layer cannot be modulated under application of the VAC potential no modulation reflection signal can be detected. 4.2. Influence of the Carrier Concentration on the Electromodulation Spectrum. Under modulation of the electric field at the FTO/electrolyte interface by an alternate potential bias (VAC w EAC ) E0e-iwt), the electron cloud of each atom is distorted, displacing it relative to the nucleus. Due to the harmonic electric field the electric charges undergo a time depending force proportional to VAC. The atoms behave like classic oscillators driven by the alternate field EAC. Moreover,
JAC ) σEAC
(4)
Jem ) σ′Eem
(5)
where σ and σ′ are the conductivity response to both perturbations. Since the EAC frequency is about 30 orders of magnitude smaller than ω (λ ) 480 - 880 nm), the electric perturbation associated with VAC can be considered as a second-order perturbation in relation with the perturbation associated with incident photons (this electric field perturbation is used as a reference, so that reflectivity changes up to 10-6 can be measured). Therefore, the conductivity σ depends only on ω. However, the frequency dependence of the complex dielectric constant, ˆ , and therefore, of the complex refractive index, nˆ ) n + ik, arises not only from the dependence of σ on ω (free electrons contribution), but also from the frequency dependence of the real part of the dielectric constant (bound electrons contribution),17
ˆ ≡ nˆ 2 ) 0(ω) +
Nee2 1 m* ω(ω + iγ)
(6)
where 0 ) 3.8 is the optical, dielectric constant of the material in the absence of free charge carriers,18 Ne the concentration of FTO conduction band electrons, m* and e the effective mass and the charge of electrons, respectively, and γ the damping constant referred to unit mass. The real and imaginary parts of ˆ in eq 6 are
Re(ˆ ) t n2 - k2 ) 0 +
Im(ˆ ) ≡ 2kn )
Nee2 -1 m* ω2 + γ2
Nee2 γ 2 m* ω(ω + γ2)
(7)
(8)
Since Ne can be modulated under application of the AC potential bias, according to eq 6 a change in Ne will produce a change in nˆ .14 Therefore, the VAC induced changes in the spatial distribution of the electric field within the FTO layer, and therefore in Ne, will also produce changes in the absorption coefficient, R(λ,x;VAC) ) (4π/λ)k and so in Im(ˆ ). Is the change of the imaginary part of the refraction index which leads to a modification of the modulation reflection spectrum (dR/R vs λ),12 so that the following dependence of R on the FTO complex refraction index, nˆ (λ) exists20
R(nˆ (λ)) )
|
|
r 1 + r3 γ 1 + r1r3γ
2
(9)
where r1 and r3 refer to the reflection index of the glass/FTO and FTO/electrolyte interface, respectively, and γ ) exp((n + ik)2πd/λ). On the assumption of a quadratic dependence of R(λ,x;VAC) on the electric field (R ∝ E2),12,21 it can be seen how the theory predicts a linear dependence of dR on (V DC)1/2.22 Such a predicted linear dependence is in fact observed experimentally in Figure 8 for VDC e 900 mV. The loss of linearity for VDC g 900 mV can be attributed to the existence of partial Fermi level pinning in this potential range (unpinning of the FTO conduction and valence band edges as the Fermi level is
9736 J. Phys. Chem. B, Vol. 105, No. 40, 2001
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Figure 9. (A) dR/R amplitude dependence on the illumination bias power (Φ0) for dR/R spectra maxima at 1.83 eV of Figure 7. (B) Plot of (dR/R)2 vs lnΦ0 from (A). A linear dependence is observed for Φ0 g 2 mW/cm2. The lack of linearity for Φ0 e 2 mW/cm2 is attributed to partial Fermi level pinning as EF goes up and the FTO bandbending decreases. A similar behavior was observed in Figure 8. Figure 8. Plot of (dR/R)2 vs VDC for spectra maxima at 1.88 eV in Figure 6. The loss of linearity for VDC g 900 mV can be attributed to the existence of partial Fermi level pinning as the FTO bandbending decreases and flatband conditions are approached.
pushed upward). A similar result was obtained from Mott-Sottky plots.25 This observation is in agreement with the idea that a Bardeen-type junction, instead of a Schottky-type junction, is formed at the TiO2/FTO interface.24 The potential obtained by extrapolation of the linear part for (dR/R)2 ) 0 (VDC = 1.1 V) should correspond to the bias under which flatband is reached in the absence of Fermi level pinning. The expected behavior of a nominally degenerated semiconductor like FTO (ND = 5 × 1020cm-3) should be near that of a metal (an important part of the applied potential must drop at the Helmholtz layer), as inferred from Figure 8. According to Figure 6, the electric field at the FTO/electrolyte interface must reach a maximum value for VDC ) 0.0 V (short-circuit conditions), where the Fermi level is pinned at the electrolyte redox potential, and should decrease as VDC increases and flatband conditions are approached. In other words, the increase of VDC must produce a decrease of the bandbending (∆φs) together with an increase of Ne(Ne ) ND exp(-φs/kT)), leading, according to eq 6 to a decrease of the dR, as in fact observed in Figure 6. A similar behavior should be noticed under shortcircuit conditions (VDC ) 0) by making more negative the electrolyte redox potential, Eredox. In fact, in this case, EF should be pinned by the Eredox level, and goes down as Eredox becomes more positive, so that both the bandbending and dR should increase, as in fact observed in Figure 5. The decrease of dR/R observed in Figure 7 when illumination bias intensity increases can also be explained in terms of an increase of Ne similar to that induced by applying a VDC > 0. Such an accumulation of electrons at the FTO conduction band means that the electron extraction from the FTO substrate to the external circuit is not fast enough, which has a great influence on the concentration electron contribution through the TiO2 phase and, therefore, on the photocurrent.6 Moreover, this increase of Ne is associated with a diminution of dR/R, in such way that the illumination bias depending behavior of dR/R can be used not only as a probe of the photoinduced compensation of the equilibrium potential existing at the FTO/TiO2/electrolyte interface in the dark, φeq, but also to determine the amount of φeq dropping at the FTO side of the FTO/TiO2 interface, which is compensated under illumination (see Figure 11). Figure 9A shows the dependence of dR/R on the illumination power (Φ0) from experimental data of Figure 7. On one hand we know that for VDC e 0.9 V (dR/R)2 depends linearly on VDC (see Figure 8); on the other hand, the open circuit potential, Voc, depends exponentially on Φ0. Since Voc must be propor-
Figure 10. Relationship between lnΦ0 and VDC obtained by combining experimental data from Figures 8 and 9B. Voc values are included for comparison. Observe that Voc = 2VDC, which indicates the existence of resistance losses at the external circuit.
tional to the band bending decrease (-∆φs) at the FTO layer, a logarithmic dependence of (dR/R)2 on Φ0 is to be expected. In fact, from experimental data of Figure 9A a linear dependence of (dR/R)2 on lnΦ0, can be observed in Figure 9B for Φ0 e 2 mW/cm2. The loss of linearity for Φ0 g 2 mW/cm2 takes place for (dR/R) 2 = 0.5 × 10-7, at about the same value at which (dR/R)2 vs VDC plot of Figure 8 loses linearity. This behavior confirms the appearance of Fermi level pinning when the FTO band bending (φs) decreases below a critical value, no matter whether this is reached under either potential or illumination bias. Finally, as expected, a linear relationship between VDC (-∆φs) and Φ0 is shown in the absence of Fermi level pinning (i.e., for VDC e 0.9 V) in Figure 10, where Voc values are included for comparison. In principle, it should be VDC ) Voc for any value of Φ0, as both VDC and Voc take into account the upward shift of EF from its position at equilibrium in the dark (i.e., for EF ) Eredox) to the position reached either under potential or illumination bias (see Figure 11). However, as can be seen in Figure 10, VDC is about twice Voc, which just indicates that only about 50% of the potential (VDC) is applied to the DSSC probably because of an in series resistance loss at the external circuit. 5. Summary and Implications for DSSC From a systematic study of the interference modulation reflection spectra produced at the FTO/electrolyte interface in the DSSC, we have been able to detect the potential distribution changes at the FTO/TiO2/electrolyte contact induced either by illumination or potencial bias. In fact, we have observed that this interference phenomenon is critically influenced by the
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J. Phys. Chem. B, Vol. 105, No. 40, 2001 9737
Figure 11. Scheme of energy levels at the FTO/TiO2/electrolyte interface (A) in the dark before contact; (B) in equilibrium in the dark after contact; (C) under open-circuit condition and low illumination conditions (Φ0 = 0.1 mW/cm2); (D) under open-circuit and high illumination conditions (Φ0 = 5 mW/cm2). (FTO and TiO2 electronic affinity values in (A) are taken from ref 3). Under contact in the dark (B), an equilibrium potential φeq = 1.0 V is established, a part of which (φs ∼ 0.3 V) drops at the FTO depletion layer and the rest at the nanostructured TiO2 film (φeq - φs ∼ 0.7 V) within a distance, d, from the FTO/TiO2 contact of the same order of magnitude than the effective size of the aggregates of TiO2 nanoparticles.4 Under low illumination conditions (C), a photopotential, Voc, is developed; φeq is compensated by the same amount (Voc ) - ∆φeq). Observe the upward shift of the FTO conduction band edge due to its highly doped n-type character.25 Finally, under high illumination conditions (D), the part of the equilibrium potential dropping at the FTO depletion layer is almost fully compensated, and a Voc = 0.7 V is reached. However, φeq is not compensated by the same amount (Voc > - ∆φeq) because of the upward shift of the TiO2 conduction band edge (E/c ) Ec + ∆Ec) due to the filling of surface states (ss) below Ec as E/F reaches them. A new maximum theoretical open-circuit voltage (Voc)max ) φeq + ∆Ec is then obtained (compare (B) with (D)).
concentration of conduction band electrons in the FTO contact layer, which behaves as a highly doped n-type semiconductor. The amplitude of the modulation reflection spectrum (dR/R) has been shown to be determined by the magnitude of the electric field existing at the FTO depletion layer. So, changes in dR/R induced by illumination of the DSSC can be related with the compensation of the part of the equilibrium potential in the dark dropping at the FTO layer (φeq). This is further explained in detail Figure 11, which describes the electrostatic potential distribution across the nanoporous TiO2/FTO/electrolyte interface both in the dark (equilibrium condition) and under illumination (non equilibrium conditions). Some authors have assumed that φeq is controlled by the difference between the work function of the FTO and the electrolyte redox potential (E° (I-/I2))2. Other researchers reported that the photovoltage obtained with a DSSC is practically independent of the work function of the substrate used in the back contact (ITO, SnO2, Au, Pt).1,24 This unusual behavior has been attributed by Nakato el al. as due to the intrinsic nature of the nanostructured TiO2 film (huge density of surface states), so that the electrical junction at the contact TiO2/substrate interface behaves rather as a Bardeen than as a Schottky type junction.24 Our results indicate that the redox electrolyte determines the value of φeq, from which the photovoltage is being built up by electrons donated by photoinjected TiO2. Against the frequently accepted idea that FTO behavior is that of degenerated semiconductor (metal behavior),3 we have shown that it rather behaves like a highly doped n-type semiconductor where a considerable part of the potential bias (VDC) drops at the depletion layer.23,25 This means that, under equilibrium conditions in the dark, a part of φeq drops in the FTO depletion layer, the other part dropping in the nano-TiO2 layer, within a distance d from the FTO/TiO2 contact (d has the same order of magnitude as the effective size of the aggregates of TiO2 nanoparticles4) (see Figure 11). Following to Shockley,26 the current or flux of electrons, φ(x), at any coordinate x of the TiO2 phase can be described as a
proportion function of the quasi-Fermi level gradient, ∇E/F, (driving force)
φ(x) ) -µn*(x)∇E/F(x)
(10)
where µ and n*(x) represent the mobility and nonequilibrium concentration of electrons, respectively. In general the flux of electrons has a diffusion component and a migration component, which are driven by the corresponding forces ∇n* and electrostatic potential gradient ∇ψ, so that it can be written
∇E/F )
kT ∇n* - ∇ψ q n*
(11)
No electric field has been experimentally detected in the bulk of the nanocrystalline TiO2 film27,28 under nonequilibrium conditions (i.e., ∇ψ ) 0), which has been attributed not only to the small size of the TiO2 particles but also to the screening effect of electrolyte cations.1 In fact, under illumination, electrons photoinjected into the TiO2 particles from dye molecules become screened by the electrolyte cations, so that electron transport through the 3-dimensional network of TiO2 nanoparticles toward the FTO/TiO2 contact is not an electric field driven motion, as ∇ψ ) 0, but a diffusion motion. Therefore, eq 11 becomes ∇E/F ) (kT/q)(1/n*)∇n*, φ(x) ) -(kT/q)µ∇n* being the flux. When the electrons are finally transferred to the nanoparticles, at a distance d in close proximity with the FTO/TiO2 contact, this scheme ceases to be valid. Electrons become separated from their screening electrolyte countercharges because of the electric field existing at the FTO/ TiO2contact. Then, the driving force for efficient electron transport is ∇ψ (electrochemical potential gradient) rather than ∇n* (chemical potential gradient), becoming φ(x) ) µn*∇Ψ. Under open circuit conditions the steady state is reached when the rate of electron injection from the dye into the TiO2 (Vinj) equals the recombination rate (Vrec) of FTO and TiO2 conduction
9738 J. Phys. Chem. B, Vol. 105, No. 40, 2001 band electrons with I3- electrolyte species (delocalized holes). The photopotential is then given by the difference between the non equilibrium quasi-Fermi level, E/F, under illumination and the Fermi level under equilibrium conditions in the dark (Voc ) E/F - EF). Theoretically, the maximum achievable photopotential is (Voc)max ) E/c (TiO2) - E° (I-/I2), a situation which is reached when E/F = E/c (TiO2) and ∇E/F ) 0. Obviously, this situation is not reached in practice, since Vinj ) Vrec before E/F reaches E/c (TiO2). Observe that the energy of the TiO2 conduction band edge under illumination (E/c ) is shifted toward positive values with respect to its position in the dark (E/c > Ec) because of the existence of a high density of surface states producing partial Fermi level pinning.24 Although φeq is fully compensated under illumination, (Voc)max is not determined by the difference between the work function of the FTO substrate and E0redox. As shown in Figure 11, (Voc)max ) E/c - E0redox and, since E/c > Ec, it is obvious that (Voc)max > φeq. Acknowledgment. This work has been partially supported by La Caixa and the Deutsche Akademischer Austauschdienst under a European Interchange Program’s grant and by the CICYT, Spain, under contract Project: MAT 95-1631E. The authors thank Dr. Ellmer for the preparation of various thin layers and Prof. L. M. Peter and Dr. J. Bisquert as well as Prof. F. Willig and Dr. M. Schwarzburg for stimulating discussions. References and Notes (1) Pichot, F.; Gregg, B. J. Phys. Chem. B 2000, 104, 6. (2) Schwarzburg, M.; Willig, F. J. Phys. Chem. B 1999, 103, 5743. (3) Cahen, D.; Hodes, G.; Graetzel, M.; Guillemoles, J. F.; Riess, I. J. J. Phys. Chem. B 2000, 104, 2053. (4) Bisquert, J.; Garc×c1a Belmonte, G.; Fabregat Santiago, F. J. Solid State Electrochem. 1999, 3, 337.
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