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2007, 111, 16100-16104 Published on Web 10/17/2007
A Reappraisal of the Electron Diffusion Length in Solid-State Dye-Sensitized Solar Cells J. R. Jennings and L. M. Peter* Department of Chemistry, UniVersity of Bath, Bath BA2 7AY, United Kingdom ReceiVed: August 11, 2007; In Final Form: September 25, 2007
The performance of dye-sensitized solar cells (DSCs) depends on the competition between transport and interfacial recombination of electrons. A key parameter in this context is the electron diffusion length, which is given by Ln ) (Dτ)1/2, where D and τ are, respectively, the diffusion coefficient and lifetime of mobile electrons. A new approach to the reliable estimation of Ln is described, which involves use of a titanium contact to measure the short-circuit value of the electron quasi-Fermi level on the side of the TiO2 film furthest from the anode contact. This information is used to define conditions under which the effects of electron trapping/detrapping can be eliminated from the calculation of Ln. The method is illustrated by measurements of a solid-state DSC based on the organic hole conductor 2,2′,7,7′-tetrakis(N,N-di-pmethoxyphenylamine)9,9′-spirobifluorene (spiro-OMeTAD), which show that Ln is significantly greater than had been thought previously.
Introduction Dye-sensitized solar cells (DSC)1,2 based on mesoporous nanocrystalline TiO2 layers sensitized with a ruthenium polypyridyl complex have achieved AM 1.5 solar efficiencies in excess of 11%.3 These high-efficiency cells utilize a liquid electrolyte containing the I3-/I- redox couple, and concerns over the long-term resistance to leakage has prompted efforts to identify solid-state hole-conducting media (HCM) to replace the liquid electrolyte. DSCs fabricated using p-type semiconductors such as CuSCN4 and CuI5 have achieved some success, although there are problems with pore filling. Organic HCM such as 2,2′,7,7′-tetrakis(N,N-di-p-methoxyphenylamine)9,9′spirobifluorene (spiro-OMeTAD) have also attracted interest since the material can be doped by chemical or electrochemical oxidation to achieve the desired conductivity.6-10 The present study investigated electron transport and back reaction in spiroOMeTAD cells using a range of techniques, including a recently developed approach in which an internal electrode on the electrolyte side of the TiO2 film is used to probe the local electron density under illumination.11,12 A key parameter that influences the performance of DSCs is the electron diffusion length Ln ) (Dτ)1/2, where D and τ are the diffusion coefficient and lifetime of electrons, respectively. Ln effectively determines the efficiency for the collection of electrons injected into the TiO2 under illumination, and it is desirable to ensure that Ln is considerably greater than the oxide film thickness, which for an electrolyte-based DSC is typically on the order of 10 µm. It appears that this requirement is easily met for DSCs utilizing the I3-/I- redox shuttle, but replacement of this redox system by HCM with significant hole densities is expected to reduce the electron lifetime as a consequence of more rapid back reaction of electrons. If Ln is reduced in solid* To whom correspondence
[email protected].
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state cells using HCM, thinner TiO2 films with higher dye loadings are required in order to prevent losses in electron collection efficiency. In an earlier publication, we used intensitymodulated photocurrent and photovoltage spectroscopy (IMPS and IMVS) to measure Dn, τn, and hence Ln for spiro-OMeTAD cells (IMPS measurements are made under short-circuit conditions to avoid complications due to RC attenuation, whereas IMVS measurements are made under open-circuit conditions to eliminate transport effects). However, it has become clear from recent work13 that experimental determination of Ln from transient or periodic photocurrent and photovoltage data is complicated by the effects of trapping and detrapping of electrons. Since the occupation of electron traps is lower under short-circuit conditions than that under open-circuit conditions at the same light intensity, measurement of D and τ under conditions of constant incident photon flux leads to significant underestimation of Ln14. In the present work, a condition of constant average trap occupancy was imposed in order to derive a reliable estimate of Ln that can be used for optimization of spiro-OMeTAD cells. The results show that our earlier estimate of Ln for spiro-OMeTAD (4.4 µm) was too low. This has important implications for the design of high-efficiency solidstate DSCs since, in principle, the TiO2 layer can be thicker than had been thought previously. Theory Apparent values of the diffusion coefficient and the lifetime of electrons, Dn and τn, are generally determined by non-steadystate methods, and the observed time (or frequency) dependences of the photocurrent and photovoltage are influenced by trapping and detrapping. The theoretical basis of the multiple trapping model and its consequences for measurements of Dn and τn have been reviewed recently in this journal.14 The model, developed by Bisquert and Vikhrenko,13 explains the observed intensity dependence of Dn and τn in terms of the progressive filling of © 2007 American Chemical Society
Letters
J. Phys. Chem. C, Vol. 111, No. 44, 2007 16101 (QFL) (and hence the trap occupancy) is the same (cf. eqs 1 and 2). In a previous study of spiro-OMeTAD cells,9 values of Dn and τn were derived as a function of illumination intensity, I0, and found to obey power laws of the form Dn ∝ I0n and τn ∝ I0-n, with n ) 0.62. This led us to postulate that the diffusion length was independent of intensity and given by (Dnτn)1/2. The diffusion length estimated in this way was 4.4 µm. However, a subsequent theoretical analysis of the QFL profiles has suggested that our earlier approach was flawed since the QFL at short circuit was substantially lower than that at open circuit.14 This, in turn, means that the product (Dnτn)1/2 determined under conditions of constant incident photon flux is substantially lower than the true value of the diffusion length (D0τ0)1/2. The steady-state profiles of conduction band electron density, nc(x) can be obtained by solving the continuity equation using appropriate boundary conditions
Figure 1. Calculated dependence of the apparent values of the electron lifetime (τn) and electron diffusion coefficient (Dn) on the electron quasiFermi level, nEF - EF,redox; Nc ) 1021 cm-3, Nt,0 ) 1020 cm-3, T0 ) 1000 K, D0 ) 0.4 cm2 s-1, τ0 ) 10-3 s.
traps as the intensity is increased. If electron transport and back reaction with the HCM only involve free electrons in the conduction band of the oxide, it can be shown that the measured apparent values Dn and τn are related to the true (conduction band) values D0 and τ0 by
( (
) )
Dn ) 1 +
∂nc D ∂nt 0
(1)
τn ) 1 +
∂nt τ ∂nc 0
(2)
An important point to note here is that whereas Dn and τn are intensity-dependent quantities, D0 and τ0 are properties of free electrons; therefore, they may reasonably be assumed to be independent of intensity. The derivatives ∂nc/∂nt and ∂nt/∂nc are related to the rate at which the densities of conduction band electrons (nc) and trapped electrons (nt) change when the quasiFermi level (QFL: nEF) is altered, for example, by changing the illumination intensity
∂nc ∂nEF ∂nc ) ∂nt ∂nEF ∂nt
(3)
The density of trapped electrons in the nanocrystalline oxides and hence the second term on the right-hand side of eq 3s depends on the position of the QFL and the density of states function, g(E), for electron traps in nanocrystalline TiO2, which commonly takes the general form
g(ET) )
Nt,0 -(Ec-ET/kBT0) e kBT0
(4)
where ET is the trap energy, Nt,0 is the total trap density, and T0 is a characteristic temperature. Figure 1 illustrates the calculated dependence of Dn and τn on the position of the quasi-Fermi level with respect to the equilibrium (dark) Fermi level, which is determined by the iodide/tri-iodide redox couple. The diffusion length for conduction band electrons is (D0τ0)1/2. This is only identical with (Dnτn)1/2 if the values of Dn and τn are determined under conditions where the quasi-Fermi level
∂2nc nc ∂n ) ηinjR(λ)e-R(λ)x + D0 2 - ) 0 ∂t τ0 ∂x
(5)
Here, η is the electron injection efficiency, R(λ) is the wavelengthdependent absorption coefficient of the dye-loaded layer, and D0 and τ0 are the diffusion coefficient and lifetime of free electrons, that is, those in the conduction band of the oxide. Typical calculated profiles for a 2 µm thick TiO2 layer are shown in Figure 2a for the open-circuit and short-circuit situations. The corresponding QFL profiles are obtained by noting that
(
nc ) NCexp -
)
E c - nE F kBT
(6)
where NC is the conduction band density of states. Figure 2b contrasts the open-circuit and short-circuit QFL profiles calculated from eq 5. It can be seen from Figure 2b that the QFL profile for the open-circuit case is flat, and the measured photovoltage, Uphoto, is equivalent to the difference between the QFL and the redox Fermi level, that is, qUphoto ) (nEF - EF,redox). By contrast, the QFL for the short-circuit condition decreases steeply close to the anode contact where electrons are withdrawn from the oxide. However, over the majority of the film, the QFL is relatively constant. In this calculated example, the separation between the open-circuit and short-circuit QFL profiles is on the order of 300 meV. We have demonstrated that the QFL on the electrolyte side of the oxide film can be measured in the case of an electrolyte-based DSC by using a passivated titanium contact.11,12 This suggests a way of approaching the problem of measuring Dn and τn under conditions where the QFL level is the same. This is to measure the QFL on the side of the TiO2 furthest from the anode and to use its value as an approximate measure of the average QFL under short-circuit conditions (in fact, the average value of nEF is lower than the value measured on the far side of the film so that the present approach will tend to underestimate Ln). The diffusion coefficient can then be obtained as a function of the QFL under short-circuit conditions by fitting the small amplitude photocurrent response. The electron lifetime is also obtained as a function of the QFL (i.e., of the open-circuit voltage). It follows that the electron diffusion length (D0τ0)1/2 can be obtained as a function of QFL and ultimately, therefore, as a function of illumination intensity. This methodology was adopted in the present study in order to obtain a reliable estimate of the electron diffusion length in spiro-OMeTAD cells.
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Letters bipyridine, L′) 4,4′-dinonyl-2,2′-bipyridine) by soaking in a 0.5 mM solution in acetonitrile/tert-butanol (1:1 v/v) for 12 h. A layer of spiro-OMeTAD was deposited on top of the porous TiO2 layer by spin coating from a 0.1 M solution in chlorobenzene/acetonitrile (95:5 v/v), which also contained t-butyl pyridine (0.12 M) and lithium trifluromethanesulfonimide (13 mM). A gold contact layer was deposited onto the HCM layer by thermal evaporation. The open-circuit voltage of the cells as well as the voltage between the titanium and gold electrodes was measured at a range of different light intensities using a high-impedance buffer amplifier and digital voltmeter. The light intensity was varied using neutral density filters and a calibrated silicon photodiode. IMPS and IMVS measurements were carried out using a Solartron 1250 frequency response analyzer (FRA), which was used to drive a LED (λ ) 530 nm) that provided both the DC and AC components of the illumination. For IMVS measurements, a low-noise voltage amplifier was used between the cell and the FRA, and for IMPS measurements, a current amplifier was used. Results and Discussion
Figure 2. (a) Profiles of electron density (nc) calculated for shortcircuit and open-circuit conditions; Nc ) 1021 cm-3, D0 ) 0.4 cm2 s-1, τ0 ) 10-3 s, I0 ) 1017 cm-2 s-1, R ) 103 cm-1. The film thickness is 2 µm. (b) Profiles of the electron quasi-Fermi level corresponding to the electron density profiles in (a).
Experimental Section Fabrication of cells incorporating a titanium electrode has been described elsewhere.11,12 Dye-sensitized cells were prepared on SnO2/F-coated glass substrates (Hartford Glass, TEC 15). To prevent short circuiting between the SnO2/F and the titanium or gold electrodes, two strips of SnO2/F were removed from adjacent edges of the substrates by etching with concentrated HCl and Zn granules. A thin compact layer of TiO2 was deposited on the remaining SnO2/F by spray pyrolysis of a 0.2 M titanium(IV)bisacetylacetonate solution in isopropanol.15-18 A layer of a TiO2 colloid (Solaronix HT) was spread on top of the compact layer of TiO2 by a doctor blading technique. Electrodes were then heated to 450 °C in air, resulting in a ∼2 µm thick layer of porous nanocrystalline TiO2. A titanium electrode was deposited onto the porous TiO2 film by thermal evaporation, as described elsewhere.12 The electrodes were then heated to 450 °C for a further 30 min in order to passivate the titanium electrode by growth of an oxide layer. The electrodes were sensitized with cis-RuLL′(SCN)2 (ruthenium 520-DN, also known as Z907, Solaronix: L ) 4,4′-dicarboxylicacid-2,2′-
The voltage difference between the titanium electrode and the anode (VTi) was measured during recording of the IV characteristic of the cell. The shape of the VTi response is similar to that observed for a similar three-electrode DSC with liquid electrolyte, where we have shown that the variation of voltage corresponds to the predictions of the steady-state solution of the continuity equation for electrons.11 For the present study, only the value of VTi at short circuit was required. Figure 3a illustrates how the apparent values of the electron lifetime and electron diffusion coefficient (measured by IMVS and IMPS, respectively) depend on light intensity. It is worth noting that the measurements extend to high intensities that are relevant for solar cell operation under solar illumination. Figure 3b compares the intensity dependences of the open-circuit voltage and the voltage at the titanium electrode under shortcircuit conditions. It can be seen that the quasi-Fermi level on the cathode side of the film is 250 meV lower under shortcircuit conditions than that at open circuit, where the titanium electrode measures the open-circuit voltage. The results shown in Figure 3 allow estimation of the true diffusion length of electrons in the cell as a function of incident photon flux. The condition for calculation of Ln is that the values of τn and Dn must be for the same QFL. For this reason, the values of τn and Dn in Figure 3 have been replotted in Figure 4a as a function of QFL instead of light intensity. The best fit lines were then used to obtain the dependences of log τn and log Dn on the QFL. The dependence of Ln on the QFL can be obtained by noting that log Ln ) 0.5(log τn + log Dn). The final step in the analysis is to derive the intensity dependence of Ln using the experimental dependence of Voc on photon flux (cf. Figure 3b). As one would expect, the values of Ln obtained in this way are considerably higher than those estimated (incorrectly) from the product (τnDn)1/2 at constant incident light intensity. The results of these two approaches are compared in Figure 4b (see Figure 3b for the corresponding variation of nEF). It can be seen that the diffusion length estimated using the approach taken earlier is around five times smaller than the value calculated using the new self-consistent approach. This means that the restrictions on film thickness should be less stringent than thought previously. In practice, however, the performance of spiro-OMeTAD cells thicker than
Letters
Figure 3. (a) Intensity dependences of Dn and τn determined by IMPS and IMVS, respectively, as a function of illumination intensity. (b) Intensity dependence of the open-circuit voltage (Voc) and of the voltage (VTi) measured at the titanium electrode under short-circuit conditions.
a few microns tends to be poor. The most probable reason for this is the difficulty of ensuring complete pore filling by the organic HCM. The present work suggests that if these problems could be overcome, thicker cells with more efficient light harvesting should be feasible. The relatively small variation of Ln over nearly six decades of light intensity suggests that analysis based on the quasistatic model with back reaction predominantly via the conduction band is basically correct. It would be interesting to compare the values of Ln derived by the present approach with those obtained under open-circuit conditions using the photovoltage rise time method suggested by O’Regan et al.19 Work on this is currently in progress, but the measurements become difficult to perform at high light intensities, where the photovoltage rise time becomes very short. Conclusions The approach discussed in this paper offers a new way of obtaining reliable estimates of the electron diffusion length for new cells that employ alternative oxides, sensitizers, and holeconducting media. This information should be a valuable input into the formulation of quantitative strategies for DSC optimization.
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Figure 4. (a) Variation of Dn and τn with the position of the electron quasi-Fermi level (QFL). In the short-circuit case, the QFL is approximated by the value measured at the titanium electrode. (b) Comparison of the Ln values estimated using the constant QFL condition with the values calculated (incorrectly) from the Dn and τn values measured at constant light intensity rather than at constant QFL.
Acknowledgment. This work is supported by EPSRC and is part of the research being carried out by the EPSRC-funded SUPERGEN Excitonic Solar Cells Consortium. The authors wish to thank Wendy Howie and Killian Lobato for advice on spiro-OMeTAD cells and fabrication of titanium electrodes, respectively. References and Notes (1) O’Regan, B.; Gra¨tzel, M. Nature 1991, 353, 737. (2) Peter, L. M. Phys. Chem. Chem. Phys. 2007, 9, 2630. (3) Chiba, Y.; Islam, A.; Watanabe, Y.; Komiya, R.; Koide, N.; Han, L. Y. Jpn. J. Appl. Phys., Part 2 2006, 45, L638. (4) O’Regan, B.; Lenzmann, F.; Muis, R.; Wienke, J. Chem. Mater. 2002, 14, 5023. (5) Konno, A.; Kitagawa, T.; Kida, H.; Kumara, G. R. A.; Tennakone, K. Curr. Appl. Phys. 2005, 5, 149. (6) Bach, U.; Lupo, D.; Comte, P.; Moser, J. E.; Weissortel, F.; Salbeck, J.; Spreitzer, H.; Gra¨tzel, M. Nature 1998, 395, 583. (7) Kruger, J.; Bach, U.; Gra¨tzel, M. AdV. Mater. (Weinheim, Ger.) 2000, 12, 447. (8) Kruger, J.; Plass, R.; Gra¨tzel, M.; Matthieu, H. J. Appl. Phys. Lett. 2002, 81, 367.
16104 J. Phys. Chem. C, Vol. 111, No. 44, 2007 (9) Kruger, J.; Plass, R.; Gra¨tzel, M.; Cameron, P. J.; Peter, L. M. J. Phys. Chem. B 2003, 107, 7536. (10) Howie, W. H.; Harris, J. E.; Jennings, J. R.; Peter, L. M. Sol. Energy Mater. Sol. Cells 2007, 91, 424. (11) Lobato, K.; Peter, L. M.; Wu¨rfel, U. J. Phys. Chem. B 2006, 110, 16201. (12) Lobato, K.; Peter, L. M. J. Phys. Chem. B 2006, 110, 21920. (13) Bisquert, J.; Vikhrenko, V. S. J. Phys. Chem. B 2004, 108, 2313.
Letters (14) Peter, L. M. J. Phys. Chem. C 2007, 111, 6601. (15) Kavan, L.; Gra¨tzel, M. Electrochim. Acta 1995, 40, 643. (16) Cameron, P. J.; Peter, L. M. J. Phys. Chem. B 2003, 107, 14394. (17) Cameron, P. J.; Peter, L. M.; Hore, S. J. Phys. Chem. B 2005, 109, 930. (18) Cameron, P. J.; Peter, L. M. J. Phys. Chem. B 2005, 109, 7392. (19) O’Regan, B. C.; Bakker, K.; Kroeze, J.; Smit, H.; Sommeling, P.; Durrant, J. R. J. Phys. Chem. B 2006, 110, 17155.
