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2008, 112, 18730–18733 Published on Web 11/07/2008
Determination of Electron Diffusion Coefficient and Lifetime in Dye-Sensitized Solar Cells by Electrochemical Impedance Spectroscopy at High Fermi Level Conditions Chuan He,*,† Linan Zhao,‡ Zhi Zheng,‡ and Fang Lu† Surface Physics Laboratory, Laboratory of AdVanced Materials, Fudan UniVersity, Shanghai 200433, People’s Republic of China, and Research and Technology Laboratory, Honeywell Technology Solutions China, Shanghai 201203, People’s Republic of China ReceiVed: September 27, 2008; ReVised Manuscript ReceiVed: October 20, 2008
The electron diffusion coefficient Dn and lifetime τn of a dye-sensitized solar cell (DSC) are determined from the electrochemical impedance spectra at potentials beyond the open-circuit potential. At these potentials, the Warburg feature associated with electron diffusion is observable from the impedance spectra. The fitting result shows that Dn and τn remain nearly constant within this potential range, and possible reasons for this phenomenon are given. The constant Dn and τn are used approximately as their conduction band values in a steady-state model to yield a short-circuit electron Fermi level profile. It is shown that direct recombination through surface trap states must be considered to accurately interpret the short-circuit characteristics of DSCs. Introduction Dye-sensitized solar cells (DSCs) have achieved AM 1.5 solar efficiencies above 11% and are very promising candidates for next-generation solar cells.1,2 Under illumination, electrons are injected into the nanocrystalline TiO2 film from the dye molecule and then transported through the film toward the fluorine doped tin oxide (FTO) substrate contact where they are collected. During the transport, photoinjected electrons may recombine with the oxidized species in the electrolyte. These processes, characterized by the electron diffusion coefficient Dn and electron lifetime τn, are key efficiency-determining factors and have been studied extensively by many authors using kinetic techniques such as intensity modulated photocurrent/photovoltage spectroscopy (IMPS/IMVS),3-6 electrochemical impedance spectroscopy (EIS),2,7 and the open-circuit voltage decay (OCVD)8 technique. A general conclusion of the experiments employing the above-mentioned techniques is that both Dn and τn vary exponentially with the electron Fermi level EFn, controlled by applied bias or illumination.2-7 This exponential dependence has been explained by the multiple-trapping (MT) model proposed by Bisquert and Vikhrenko, who assumed that electron diffusion and recombination occur only via the conduction band of TiO2 but are delayed in kinetic measurements by trapping and detrapping events.9 According to the MT model, Dn and τn should exhibit saturation to the free electron diffusion coefficient Dc and lifetime τc under high Fermi level condition which, however, has not been observed in previous studies.2,10 It has been pointed out that high carrier density regime studies are required to further investigate the transport mechanism in DSCs.10 * To whom correspondence should be addressed. E-mail: 072019019@ fudan.edu.cn. † Fudan University. ‡ Honeywell Technology Solutions China.
10.1021/jp8085733 CCC: $40.75
In this paper, we report an EIS measurement for a DSC carried out at very high potentials, from 0.925 to 1.225 V. We select this range because Ec, the conduction band edge of TiO2 in DSCs, is believed to lie 0.9-1.0 V above the dark equilibrium Fermi level EF,redox.10 Thus, it is likely that the bias potentials applied in our experiments can place the electron Fermi level EFn close to Ec, where the behavior of free electrons can be probed. It is observed that the obtained Dn and τn both remain nearly constant within this potential range. However, it will be pointed out that this behavior does not necessarily result from a conduction band dominated transport mechanism unless the band unpinning effect4 can be excluded. Finally, we present a brief steady-state model based on the measured Dn and τn to obtain the short-circuit electron Fermi level profile for comparison with recent experiments.11,14 Experimental Section The DSC sample is prepared on a SnO2/F-coated glass substrate (FTO) with a sheet resistance of 15 Ω/0. A compact layer of tense TiO2 with a thickness of ∼100 nm was first deposited on the substrate by dip coating and pyrolysis as the blocking layer. A nanocrystalline TiO2 layer with an average particle diameter of 12 nm (Solaronix) and thickness of 3 µm was then deposited on the blocking layer by a doctor blading technique. The TiO2 film was sensitized with N719 dye (Solaronix). The counter electrode was platinized FTO, and the cell was filled with MPN100 I-/I3- electrolyte from Solaronix. All electrochemical measurements are carried out on a Zahner electrochemical workstation (IM6ex). The frequency range in EIS measurements was 0.05-105 Hz, and the magnitude of the alternative signal was 10 mV. The applied bias potential ranges from 0.925 to 1.225 V with a step of 0.025 V. All measurements are carried out in the dark. The Thales software packed with Zahner IM6ex is employed to fit the impedance spectra. 2008 American Chemical Society
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J. Phys. Chem. C, Vol. 112, No. 48, 2008 18731
Figure 1. Impedance spectra at three different applied potentials: 0.95 V (blue square), 1.0 V (green triangle), and 1.05 V (red circle). Lines represent corresponding fit results. Inset is the enlarged part of the high frequency region of the TiO2 arc. The dotted line in the inset is a guide to the eye showing the Warburg feature.
Results and Discussion Figure 1 shows the measured impedance spectra and corresponding fit at three different potentials. Three arcs can be observed for each potential. The left (high frequency) arc corresponds to the charge transfer process at the Pt counter electrode; the central arc arises from charge transport and recombination mechanism in TiO2; and the right (low frequency) arc is attributed to ion diffusion in the I-/I3- electrolyte. In the high frequency region of the central arc shown in the inset of Figure 1, the Warburg feature associated with electron diffusion in TiO2 is observable. When applied bias potential increases, the width of the left and central arc decreases, suggesting a reduced charge transfer resistance at the Pt/electrolyte and TiO2/ electrolyte interface. To the contrary, the arc belonging to I-/ I3- diffusion augments in size at higher potential because the current flowing through the cell increases. Meanwhile, the Warburg feature exhibits parallel displacement as can be seen in the inset of Figure 1. These observations and assignments are consistent with previous studies.7,12 All our EIS results are fitted into the transmission line model which has been discussed in detail in the literature.2,7 In the transmission line model, the electron transport and recombination mechanism in TiO2 is characterized by the chemical capacitance Cµ, the electron transport resistance Rt, and the charge transfer resistance Rr, which is related to recombination of electrons at the TiO2/ electrolyte interface. These three parameters are related to the electron diffusion coefficient and electron lifetime by Dn ) L2/ RtCµ and τn ) RrCµ, where L is the thickness of the nanocrystalline TiO2 film.7 Figure 2 presents the fitting results of Cµ, Rt, and Rr. It can be seen in Figure 2a that Cµ increases rather slowly with potential. This slow increase is inconsistent with the previous expressions for Cµ in which the position of Ec is assumed to be fixed.9 One possible reason for this is the band unpinning effect.4 Because of this effect, Ec starts to move up when EFn is approaching it. Another possible reason is the potential drop at other elements except TiO2 in the transmission line, i.e., the FTO, the electrolyte, and the Pt electrode. At such high potentials, the resistances of these elements become comparable with Rt and Rr. Therefore, the real potential that is applied on TiO2 may be smaller than measured by an external circuit. However, this Rs correction12 would not influence the absolute values of Cµ, Rt, and Rr. Figure 2b shows that Rt and Rr both display a slow decrease, and the reason for this is similar with that for Cµ. Computing Dn and τn using the above-mentioned expressions, we observe that both Dn and τn stay nearly constant at most
Figure 2. (a) Chemical capacitance Cµ and (b) electron transport resistance Rt (circle) and recombination resistance Rr (square) at different potentials obtained from impedance spectra.
Figure 3. (a) Electron diffusion coefficient Dn (square) and lifetime τn (circle) obtained from Cµ, Rt, and Rr; (b) Dn (square) and τn (circle) versus the corrected potential.
measured potentials, as illustrated in Figure 3a. Below 1.0 V, there still exists a very slight increase in Dn and decrease in τn. From Figure 3a, we averaged the data points above 1.0 V to obtain Dn ) 6.05 × 10-5 cm2 s-1 and τn ) 2.00 × 10-3 s. However, these two values do not necessarily reflect the corresponding conduction band values Dc and τc. It should be
18732 J. Phys. Chem. C, Vol. 112, No. 48, 2008
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pointed out first that, as mentioned before, the potential in Figure 3a is not the real potential of the TiO2 electrode because of the contribution from other elements in the cell. If the potential of the TiO2 electrode is pinned due to this effect, Dn and τn also do not change with externally applied potential. To check this possibility, we subtract the contribution from the FTO, the electrolyte, and the Pt electrode and redraw Dn and τn in Figure 3b according to the corrected potential. It can be seen that the 0.3 V increase on the applied potential causes a 0.06 V increase on TiO2. And, although there is still an increase in the potential of TiO2, we cannot exclude the possibility that this increase actually corresponds to the band edge shift.4 If this is the case, the distance between EFn and Ec of TiO2 becomes fixed, and this can also explain the present results for Dn and τn. Therefore, the MT model cannot be fully confirmed unless it can be proved that the distance between EFn and Ec continues to decrease while both Dn and τn stay constant. Nonetheless, it appears that Dn ) 6.05 × 10-5 cm2 s-1 and τn ) 2.00 × 10-3 s are the closest possible values to Dc and τc that could be obtained for the present DSC sample and can be used as their corresponding lower and upper limit, respectively. It is now at a stage to discuss why Rt has been difficult to determine by an EIS technique at high Fermi level conditions2 and how it is determined in the present work. Under moderately high Fermi level conditions (about 0.7-0.8 V), if Rt is significantly smaller than Rr, as is required by eligible DSC samples,2 the Warburg feature associated with electron transport would become very small and completely immersed in the Pt/ electrolyte electron transfer arc in the EIS signal. This renders the electron transport mechanism unmeasurable, and this is the reason why Rt at a potential near the open-circuit potential (Voc, about 0.8 V for eligible DSCs) has rarely been determined. However, if the potential is increased beyond Voc, Rr would continue to decrease until it is comparable with Rt as shown in Figure 2b. Therefore, in this region beyond Voc, Rt and Rr have comparable contribution to the central arc in Figure 1, and the Warburg feature is observable again. The low value of the electron diffusion coefficient is a striking characteristic of the mesoporous nanocrystalline TiO2 films. Because the diffusion of electrons is rather slow, there would be a large amount of electrons stored in the film even under short-circuit conditions. Therefore, the short-circuit electron Fermi level inside the majority of the film away from FTO may remain at a high value. This has been confirmed by recent charge extraction experiments13 and direct measurement of short-circuit EFn at the electrolyte side of the TiO2 film.11,14 In the vicinity of this level, there are a large number of occupied surface trap states that are in good energy match with the acceptor states in the electrolyte.8 It can thus be inferred that suppressing direct recombination through surface trap states is especially important for enhancing the short-circuit performance of DSCs. If we approximately assume Dc ) 6.05 × 10-5 cm2 s-1 and τc ) 2.00 × 10-3 s according to the results discussed above, we are able to provide a steady-state description of DSCs. In the steady-state, the electron transport and recombination are described by the following continuity equation with the generally applied diffusion-controlled boundary condition11,14
∂nc(x, t) nc(x, t) - neq ∂2nc(x, t) c 0) + G(x) - Rst ) Dc 2 ∂t τ ∂x c
( )
nc(0) ) neq c exp
eV kBT
(1a) (1b)
Figure 4. Short-circuit electron Fermi level profile calculated from eq 1 and eq 2. Black solid line: Rst is considered; red dashed line: Rst is neglected; blue dotted line: Rst is neglected and Dc ) 6.05 × 10-4 cm2 s-1. Parameters: Dc ) 6.05 × 10-5 cm2 s-1, τc ) 0.002 s, Ec EF,redox ) 0.9 eV, Nc ) 6.8 × 1020 cm-3, Nst ) 1 × 1018 cm-3, T0 ) 1000 K, kt(st) ) 1 × 10-15 cm3 s-1, cox ) 3 × 1019 cm-3, λ ) 0.5 eV, incident photon flux I0 ) 1 × 1017 cm-2 s-1, absorption coefficient R ) 1000 cm-1, and temperature T ) 300 K.
dnc )0 dx |x)L
(1c)
where the origin (x ) 0) is taken as the FTO/TiO2 contact. The electron concentration nc(x) is related to the electron Fermi level EFn(x) as
[
nc(x) ) Nc exp
EFn(x) - Ec kBT
]
(2)
eq and nc ) neq c when EFn(x) ) EF,redox, where nc is the dark equilibrium electron concentration in the conduction band with Nc being the density of states. Rst represents the electron loss rate caused by surface trap states and is expressed as the integral of the product of surface state distribution function gst(E) and (st) (E)8 transition probability eox
Rst )
∫EE
F
F,redox
gst(E) ) (st) e(st) ox (E) ) 2kBTkt
gst(E)e(st) ox (E)dE
( )
Nst E - Ec exp kBT0 kBT0
[
(E - Eox)2 exp 4λkBT √4πλkBT cox
(3a) (3b)
]
(3c)
where kB is the Boltzmann constant; Nst is total density of surface is the rate trap states; T0 is the characteristic temperature; k(st) t constant for isoenergetic TiO2/electrolyte electron transfer; cox and Eox are the concentration and the most probable energy level for the oxidized species of the electrolyte, respectively; and λ is the reorganization energy. Note that zero temperature approximation is used in eq 3a. Here we will only focus on providing a description of the short-circuit electron Fermi level EFnSC profile using eq 1 because this will provide a way to interpret the experimental data on EFnSC.11,14 The result is shown in Figure 4. It can be seen that because Dc has a rather small value Rst has a significant influence on the profile of EFnSC. Increasing Dc has a similar effect to move EFnSC downward. In Figure 4, if Rst is considered, at x ) L EFnSC has a value of 0.57 eV and is similar with typically measured values in the literature.11,14 This EFnSC value can be fitted either by neglecting Rst and using a high Dc or by considering Rst and using a low Dc. Meanwhile, detailed OCVD experiments have shown that in the region where EFn is around 0.5 eV above EF,redox recombination is typically dominated by trap states.8 Therefore,
Letters the interpretation of short-circuit characteristics of DSCs should be carefully reexamined and needs further discussion. Conclusion The electron diffusion coefficient Dn and lifetime τn are obtained from EIS measurements at very high bias potentials. Although a saturation behavior is observed, the reason is complicated. The use of EIS technique to probe the free electron behavior may be very difficult because of potential correction and band edge shift. In a steady-state model using the obtained Dn and τn, it is shown that direct recombination through surface trap states is a key factor that determines the short-circuit characteristics of DSCs. Acknowledgment. This work is supported by Honeywell Technology Solutions China. References and Notes (1) Gra¨tzel, M. Inorg. Chem. 2005, 44, 6841.
J. Phys. Chem. C, Vol. 112, No. 48, 2008 18733 (2) Wang, Q.; Ito, S.; Gra¨tzel, M.; Fabregat-Santiago, F.; Mora-Sero´, I.; Bisquert, J.; Bessho, T.; Imai, H. J. Phys. Chem. B 2006, 110, 25210. (3) Dloczik, L.; Ileperuma, O.; Lauermann, I.; Peter, L. M.; Ponomarev, E. A.; Redmond, G.; Shaw, N. J.; Uhlendorf, I. J. Phys. Chem. B 1997, 101, 10281. (4) Schlichtho¨rl, G.; Huang, S. Y.; Sprague, J.; Frank, A. J. J. Phys. Chem. B 1997, 101, 8141. (5) Fisher, A. C.; Peter, L. M.; Ponomarev, E. A.; Walker, A. B.; Wijayantha, K. G. U. J. Phys. Chem. B 2000, 104, 949. (6) Oekermann, T.; Zhang, D. S.; Yoshida, T.; Minoura, H. J. Phys. Chem. B 2004, 108, 2227. (7) Fabregat-Santiago, F.; Bisquert, J.; Garcia-Belmonte, G.; Boschloo, G.; Hagfeldt, A. Sol. Energy Mater. Sol. Cells 2005, 87, 117. (8) Bisquert, J.; Zaban, A.; Greenshtein, M.; Mora-Sero´, I. J. Am. Chem. Soc. 2004, 126, 13550. (9) Bisquert, J.; Vikhrenko, V. S. J. Phys. Chem. B 2004, 108, 2313. (10) Bisquert, J. J. Phys. Chem. C 2007, 111, 17163. (11) Lobato, K.; Peter, L. M.; Wu¨rfel, U. J. Phys. Chem. B 2006, 110, 16201. (12) Fabregat-Santiago, F.; Bisquert, J.; Palomares, E.; Otero, L.; Kuang, D.; Zakeeruddin, S. M.; Gra¨tzel, M. J. Phys. Chem. C 2007, 111, 6550. (13) Wu¨rfel, U.; Wagner, J.; Hinsch, A. J. Phys. Chem. B 2005, 109, 20444. (14) Wu¨rfel, U.; Peters, M.; Hinsch, A. J. Phys. Chem. C 2008, 112, 1711.
JP8085733
