11484
J. Phys. Chem. B 2000, 104, 11484-11488
Dependence of the Photocurrent Conversion Efficiency of Dye-Sensitized Solar Cells on the Incident Light Intensity T. Trupke and P. Wu1 rfel* Institut fu¨ r Angewandte Physik, UniVersita¨ t Karlsruhe, Kaiserstrasse 12, D-76128 Karlsruhe, Germany
I. Uhlendorf Institut fu¨ r Angewandte PhotoVoltaik, Munscheidstrasse 14, D-45886 Gelsenkirchen, Germany ReceiVed: April 13, 2000; In Final Form: August 20, 2000
The incident photon to current conversion efficiency (IPCE) of dye-sensitized solar cells is measured as a function of the incident photon current density. A characteristic dependence of the IPCE on the incident light intensity with a maximum value for absorbed photon current densities in the range of jγ,abs ) 1017 cm-2 s-1 is observed for all cells investigated in this study. The IPCE decreases significantly for large absorbed photon current densities (jγ,abs > 1018 cm-2 s-1) and for small absorbed photon current densities (jγ,abs < 1016 cm-2 s-1). The decrease of the IPCE at large incident light intensities is due to the diffusion limitation of the electrolyte within the nanocrystalline TiO2 electrode. The decrease of the IPCE at low incident light intensities can be explained by the loss of photogenerated electrons via surface-state-mediated electron transfer into the electrolyte. The strong dependence of the IPCE on the incident light intensity has consequences for the efficiency of a dye-sensitized solar cell at low illumination levels. It also suggests that spectral measurements of the IPCE of dye-sensitized solar cells and of nanocrystalline electrodes cannot be used to predict the solar or white light IPCE unless they were taken with bias light or with very high intensities of monochromatic light, especially at weakly absorbed wavelengths.
Introduction Since the first report on energy conversion efficiencies of dye-sensitized solar cells (DSCs) of up to 7.9% for AM1.5 illumination,1 this system has been the focus of many investigations. A DSC basically consists of a nanocrystalline TiO2 electrode covered with a monolayer of a charge-transfer dye. The pores in the nanocrystalline TiO2 electrode are filled by an electrolyte containing a redox couple. This system is sandwiched between two transparent conducting glass electrodes, one of which is covered with a thin Pt layer which serves as a catalyst for the redox reaction. A detailed description of the geometry and of the preparation of a DSC can be found, for example, in refs 2 and 3. In a DSC, efficient solar energy conversion is connected with sufficient light absorption by the adsorbed dye molecules, efficient electron injection from the excited dye into the TiO2 conduction band, the transport of electrons through the nanocrystalline TiO2 electrode without electron recombination, and the regeneration of the dye molecule in its ground state by electron injection from a reduced ion in the electrolyte into the HOMO (highest occupied molecular orbital) of the adsorbed dye. The overall efficiency of these processes can be checked experimentally by measuring the incident photon to current conversion efficiency (IPCE), which is defined as the number of electrons flowing through an external circuit under short* To whom correspondence may be addressed. Fax: 49-721/607 593.
circuit conditions per incident photon. For a dye-sensitized solar cell, the IPCE can be written as
IPCE(pω) ) A(pω) ηinjηcoll
(1)
where the absorptivity A(pω) is the fraction of the incident light which is absorbed by the adsorbed dye molecules, ηinj is the injection efficiency, that is, the probability that the excitation of an adsorbed dye molecule leads to electron injection into the TiO2 conduction band, and ηcoll is the collection efficiency, which is the probability that the injected electron contributes to the current through the external circuit. The injection of electrons from photoexcited dye molecules into the TiO2 conduction band has been measured to be ultrafast.4 The injection efficiency can therefore be assumed to be close to unity. A decrease of the IPCE of dye-sensitized nanocrystalline TiO2 electrodes in the red region (λ > 700 nm) has been mentioned in ref 3 for incident light intensities below 0.2 mW/cm2. A more systematic study of the dependence of the IPCE of dyesensitized solar cells on the incident light intensity has recently been published by Fisher et al. in this journal.5 In that study, a variation of the incident photon current density over 5 orders of magnitude down to very low values in the range of jγ,inc ≈ 1010 cm-2 s-1 resulted in a comparatively slight variation of the IPCE of about 35%. As we show in this paper, the IPCE of our cells decreases strongly at low and at very large absorbed photon current densities. This characteristic dependence of the IPCE on the
10.1021/jp001392z CCC: $19.00 © 2000 American Chemical Society Published on Web 11/10/2000
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photon current density was found for all cells investigated in this study. The possible origin of the decrease of the IPCE and the information about a loss channel in the DSC which can be obtained from it are discussed in this paper. The experimental evidence for a strong dependence of the IPCE on the incident light intensity is of general importance for measurements of the efficiency and of the IPCE of DSCs. Experimental Section The IPCE has been measured as a function of the incident photon current density for different wavelengths. A 100 mW/ 680 nm laser diode, a frequency-doubled 50 mW/532 nm Nd: YAG laser, or a 150 W halogen lamp in combination with a 1/4 m Jobin-Yvon monochromator was used as a monochromatic light source. A variable neutral filter with a transmission between T ) 0.8 and T ) 10-4 was used to control the incident light intensity. A glass sheet was used as a beam splitter to direct a small portion of the incident light beam toward a calibrated Si diode. The proportion of light at the location of the Si diode and at the location of the DSC was measured at each wavelength and was found to be independent of the light intensity, which allows the use of the short-circuit current of the Si diode as a measure for the incident photon current density. With this setup, the incident photon current density and the photocurrent of the solar cell can be measured simultaneously. The experimental IPCE values are thus independent of possible fluctuations of the monochromatic light source. The photocurrent of the Si diode and of the DSC were measured under short-circuit conditions with two identical current-voltage converters (HMS 530) with a transimpedance of 104 V/A and with Keithley (196 System DMM) voltmeters. An alternative experimental technique for measurements of the IPCE, which is particularly useful for measurements on dyesensitized solar cells, consists of illuminating the cell with constant bias light in addition to low-intensity monochromatic modulated light. The intensity of the constant bias light must be in the intensity range of jγ,abs ≈ 1017 cm-2 s-1 where, as will be shown below, the IPCE is almost constant (i.e., the photocurrent density is linear in the incident photon current density). In this case, the cells were illuminated with white bias light from a 50 W halogen lamp in addition to the monochromatic light which was modulated with a chopper. The output of the current voltage converters was connected to digital lock-in amplifiers (Stanford Research Systems, SR830). Because of the very slow photocurrent response of dyesensitized solar cells,6,7 the incident light was modulated at a frequency of 1 Hz. Materials. Dye-sensitized solar cells were prepared as described recently by Franco et al.8 in this journal. The electrolyte was composed of methyl-hexylimidazolium iodide (MHImI), iodine, tert-butylpyridine, and acetonitrile. The nanocrystalline TiO2 layers were prepared by screen printing on a conducting glass plate a suspension of TiO2 obtained by hydrolysis of titanium dioxide using a method which yields only the anatase phase of TiO2. The dye-sensitized films were obtained by dipping TiO2 films for 2 h in a 3 × 10-4 M solution of the ruthenium dye cis-di(thiocyanato)-N,N-bis(2,2′-dicarboxylate)ruthenium(II) in ethanol. Cells with different TiO2 film thicknesses (3.9-12 µm) were investigated. Results and Discussion The dependence of the IPCE of a 3.9 µm cell on the wavelength of the incident light, the so-called photocurrent
Figure 1. 1. Photocurrent action spectrum of the cell (9) measured with modulated monochromatic light and additional white bias light and literature data (ref 3) of an absorption spectrum in arbitrary units of a 3.5 × 10-5 M solution of the N3 dye in ethanol.
Figure 2. 2. Dependence of the IPCE of a DSC (3.9 µm thickness) on the incident photon current density for two different wavelengths, λ ) 532 nm (b, left/bottom axes) and λ ) 680 nm (0, right/top axes).
action spectrum, is shown in Figure 1 in comparison to an absorption spectrum (taken from the literature3) of the N3 dye in solution. These measurements of the IPCE were carried out with white bias light and modulated monochromatic light. As expected, the spectral dependence of the IPCE basically reflects the absorption properties of the adsorbed dye. We find that at a sufficiently low modulation frequency of 1 Hz the amplitude of the modulated monochromatic light has no significant influence on the measured IPCE values, which shows that under intense bias illumination the photocurrent is linear in the incident photon current density. The intensity of the dc illumination was on the order of jγ,abs ) 1017 cm-2 s-1. When measured with monochromatic dc illumination of low intensity, however, the IPCE is found to depend strongly on the incident light intensity. The IPCE of the cell is plotted as a function of the incident photon current density jγ,inc for λ ) 532 nm (left/bottom axes, measured with the Nd:YAG laser) and for λ ) 680 nm (right/top axes, measured with the 680 nm laser diode) in Figure 2. For both wavelengths, the curves have a similar shape. The IPCE converges toward a constant saturation value with increasing jγ,inc, whereas at low incident photon current densities the IPCE decreases strongly. Comparing the IPCE values in Figures 1 and 2, which were obtained from the same cell, we find that the saturation values of the IPCE in Figure 2, which were measured with monochro-
11486 J. Phys. Chem. B, Vol. 104, No. 48, 2000
Trupke et al.
Figure 3. 3. Collection probability as a function of the absorbed photon current (logarithmic scale) for λ ) 532 nm (0), λ ) 680 nm (b), and λ ) 720 nm (3). At 720 nm, the light intensity of the halogen lamp was too low to attain absorbed photon current densities larger than 1014 cm-2 s-1.
matic dc illumination at large incident photon current densities, coincide with the values in Figure 1. This shows that measurements with intense white bias light and additional monochromatic modulated light yield the saturation value of the IPCE at each wavelength. This observation was confirmed by additional measurements at several other wavelengths not shown in Figure 2. Because of the strong spectral dependence of the absorption of the dye, the curves for λ ) 532 and λ ) 680 nm in Figure 2 have largely different scales. For a better comparison of measurements at different wavelengths, the influence of the absorptivity A(pω) is eliminated by plotting the collection efficiency ηcoll as a function of the absorbed photon current density jγ,abs. According to eq 1, the collection efficiency is given by
ηcoll )
IPCE(pω) A(pω)
(2)
under the assumption of a unity injection efficiency, and the absorbed photon current density is simply given by the incident photon current density multiplied by the absorptivity. The numerical value of A(pω) must be known at each wavelength if the collection efficiency as a function of the absorbed photon current is calculated. Reliable values of the absorptivity of the adsorbed dye molecules in particular at weakly absorbed wavelengths are difficult to measure in transmission in a DSC. Therefore, we use the saturation value of the IPCE at each wavelength as a measure for the absorptivity, which implies that the collection efficiency is set to ηcoll ) 1 at large light intensities. At long wavelengths, where the monochromatic intensity from the halogen lamp is not large enough to attain the saturation value of the IPCE, the values from Figure 1, which were measured with white bias light, were used for the absorptivity. The collection efficiency as a function of jγ,abs is expected to be independent of the wavelength of the incident light if the influence of the inhomogeneous excitation over the thickness of the cell at strongly absorbed wavelengths can be neglected. A homogeneous generation rate of excited dye molecules can be assumed for wavelengths of λ > 600 nm, where the absorptivity of the dye molecules is below 15% (Figure 1). The collection efficiency ηcoll is shown as a function of the absorbed photon current density jγ,abs ) jγ,inc A(λ) in Figure 3
Figure 4. 4. IPCE of a 12-µm-thick cell as a function of the incident photon current density measured with focused illumination. The decrease of the IPCE at jγ,inc > 1018 cm-2 s-1 is due to the diffusion limitation of the electrolyte.
Figure 5. 5. Time dependence of the photocurrent after the illumination is switched on at t ) 0 for different illuminated areas at constant incident photon current. Decreasing the illuminated area (i.e., increasing the intensity) from curve 1 to curve 5 results in a faster initial increase of the photocurrent and in a decrease of the steady-state value of the photocurrent. The shape of curve 5 is characteristic for a diffusionlimited current.
for three different wavelengths (532, 680, and 720 nm). The three curves almost coincide except for slightly larger values at 532 nm for low intensities, which is due to the small penetration depth of 532 nm light. Most electrons are then generated close to the collecting electrode, resulting in a larger collection efficiency. Measurements of η at various other wavelengths not shown in Figure 3 have been made. For λ > 600 nm, all ηcoll(jγ,abs) curves are identical to the 680 nm curve in Figure 3. IPCE at Large Incident Light Intensities. Focusing the laser beam allowed measurements up to jγ,inc ) 5 × 1019 cm-2 s-1. We find a strong decrease of the IPCE at absorbed photon current densities jγ,abs > 1018 cm-2 s-1, which are at least 1 order of magnitude larger than typical values under solar illumination. Figure 4 shows a measurement carried out on a 12-µm-thick cell. This decrease of the IPCE at large light intensities is due to the diffusion limitation of the electrolyte inside the nanocrystalline electrode. The large photocurrent density leads to a significant depletion of the reducing ions at the location of the adsorbed dye molecules. This qualitative argument is confirmed by the time dependence of the photocurrent at large light intensities. In Figure 5, the photocurrent is shown as a function of time after the
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J. Phys. Chem. B, Vol. 104, No. 48, 2000 11487
illumination is switched on at t ) 0. In these experiments, the incident photon current was constant while the illuminated area was decreased from curve 1 to curve 5. The shape of these curves is similar to that of time-resolved electroluminescence measurements, which have been published recently.9 The initial increase of the photocurrent gets faster with a decrease of the illuminated area (i.e., larger light intensity) while the steady-state value of the photocurrent decreases. Similar to the explanations given in ref 9 for the time dependence of the electroluminescence, the initial slow increase of the photocurrent, which gets faster with increasing incident light intensity, is due to trap filling in the TiO2. The decrease of the signal as a function of time at large incident light intensities (curves 4 and 5) is characteristic for a diffusion-limited current. IPCE at Low Incident Light Intensities. The decrease of the IPCE at low absorbed photon current densities, however, indicates that there is a loss channel for photogenerated TiO2 conduction band electrons, which is nonlinear in the absorbed photon current density and independent of wavelength. One possible mechanism for this recombination channel is the surface-state-mediated electron transfer from the TiO2 conduction band into the electrolyte. Such reactions have been shown to play an important role for the charge transfer at semiconductor/electrolyte interfaces.10 The influence of trap states on the transport of photogenerated electrons in nanocrystalline TiO2 electrodes has also been investigated by de Jongh and Vanmaekelbergh.11 They could explain the dependence of the transit time of photogenerated electrons moving through the nanocrystalline TiO2 electrode on the incident light intensity by the filling of trap states in the TiO2 band gap. These trap states are due to surface states, which as a result of the large internal surface are present at high concentrations in nanocrystalline materials. In an investigation by Schwarzburg and Willig,6 the filling of trap states has also been found to be responsible for the very slow photocurrent response of nanocrystalline electrodes after an illumination is switched on. A Simple Numerical Model. In a simple theoretical approach, we assume the cell as being divided into two parts, one containing only the electrolyte with the redox couple and the other one made up by an effective medium, which consists of a homogeneous mixture of the dye-covered TiO2 and the electrolyte. Photon absorption and all kinds of electron reactions which are considered in our model take part only in the effective medium. Influences of spatial inhomogeneities within the effective medium, which are expected especially under shortcircuit conditions, are neglected in this simple approach. In the second part of the cell, which contains only the redox couple, the ions move via diffusion and may be distributed inhomogeneously. A homogeneous electron generation rate g, which is given by the absorbed photon current density divided by the thickness in the experiment, is switched on in the effective medium at t ) 0, and the time evolution of the system is calculated numerically. Electron exchange between the TiO2 conduction band and one single trap level takes place via trapping and detrapping. Electrons which are trapped can also be transferred into the electrolyte, and these electrons, contrary to electrons which undergo trapping and detrapping, are lost for the photocurrent. The rate rloss of this loss current is assumed to be proportional to the density nt of electrons in trap states.
rloss ) klnt
(3)
Figure 6. 6. Loss current density as a function of the absorbed photon current density. Squares correspond to the values calculated from the experiment. The fit (dotted line) is obtained from the simple model described in the text with kes ) 12 s-1, kt ) 2 × 10-19 s-1 cm-3, kd ) 0.1 s-1, Nt ) 7 × 1019 cm-3, and kl ) 0.026 s-1. The generation rate g and the loss rate rloss from the model have been multiplied by the thickness of the cell (3.9 µm) in order to transform them into current densities per unit area.
where kl is the rate constant for electron transfer from the trap state into the electrolyte. The time evolution of the density of filled traps is described by
dnt ) kt(Nt - nt)ne - kdnt - klnt dt
(4)
where Nt is the density of traps, ne is the density of TiO2 conduction band electrons, and kt and kd are the rate constants for trapping and detrapping. For the electron density, one obtains
dne ) g - kt(Nt - nt)ne + kdnt - kesne dt
(5)
where kes is the constant for electron escape from the TiO2 to the electrode, which describes the photocurrent. Equations 4 and 5 are equivalent to those used by Schwarzburg and Willig6 except for the rate rloss, which was not included in their equations. From these equations, the steady-state value of the density of occupied trap states is
nt )
[( ) ]
X 2 Nt g X 2 2 kl
1/2
(6)
with
X)
kes(kd + kl) g + Nt + kl ktkl
(7)
Using eqs 3 and 6 with the parameters given in the capture of Figure 6, the loss current density is calculated as a function of the generation rate. From our experimental data, the loss current density is calculated as the difference between the absorbed photon current density jγ,abs and the measured shortcircuit current density of the DSC. We find good agreement between the calculation and the experimental results (Figure 6). For the comparison with the experimental data in Figure 6, the generation rate g in the numerical calculations, which is a rate per unit volume, was multiplied by the thickness of the effective medium to transform it into a generation rate per unit area.
11488 J. Phys. Chem. B, Vol. 104, No. 48, 2000 As expected, the increase of the generation rate leads to a saturation of the density of filled trap states nt and thus (eq 3) to a saturation of the recombination rate via surface-statemediated electron transfer into the electrolyte. With further increasing absorbed light intensity, the influence of the almost constant recombination rate gets less significant. The collection efficiency becomes ηcoll ≈ 1, and the IPCE approaches its saturation value. As a test for the set of parameters which is used for the calculation of the loss current as a function of the generation rate, we also calculated the time evolution of nt(t) and of ne(t). As the photocurrent is assumed to be proportional to ne(t), the latter is a measure for the time evolution of the photocurrent after the generation rate is switched on. The results of these calculations are consistent with the experimental time dependence of the photocurrent after the illumination is switched on (Figure 5). The simple model presented here is not intended to describe the experimental results in every detail. Rather, it is used to show that the observed dependence of the IPCE on jγ,abs can be reproduced qualitatively. In this respect, the agreement between the experimental results and the numerical calculations (Figure 6) is quite satisfactory. In a more realistic model, a distribution of trap levels over the energetic range of the TiO2 band gap with an energydependent loss rate constant kl would have to be considered. But the influence of such an extension of the model must not be overestimated. Because of the limited energy range in which electron acceptor states in the electrolyte are available, electron recombination via surface states occurs only within a limited energy range in the band gap of the TiO2. We are aware of the possibility that the observed nonlinear dependence of the photocurrent on the incident photon current density could also be explained by completely different mechanisms (e.g., aggregation of adsorbed dye molecules or different kinetics for electron transfer to different oxidized species in the electrolyte). Additional experiments will be necessary to confirm our explanation. Conclusions It has been shown that ηcoll, the probability that a photoinjected TiO2 conduction band electron contributes to the current through the external circuit, decreases strongly at low absorbed photon current densities, jγ,abs < 1016 cm-2 s-1, as well as at large absorbed photon current densities, jγ,abs > 1018 cm-2 s-1. This observation is found to be independent of the wavelength of the incident light for wavelengths λ > 600 nm. Although no systematic study of the influence of the thickness of the TiO2 layer on the intensity dependence of the IPCE has been made, it is observed that cells with quite different thicknesses ranging from 3.9 to 12 µm all showed qualitatiVely the same behavior, which shows that the thickness of the cell has no critical influence on our results. The decrease of the IPCE (i.e., of ηcoll) at large light intensities is due to the diffusion limitation of the electrolyte, which is confirmed by time-resolved measurements of the photocurrent at large incident light intensities. The decrease of the IPCE at low incident light intensities can be explained by the recombination of TiO2 conduction band
Trupke et al. electrons via surface-state-mediated electron transfer into the electrolyte. This qualitative explanation is supported by a simple numerical model. We investigated a large number of dye-sensitized solar cells including six cells which were kindly provided by the FMF in Freiburg, Germany. The same characteristic dependence of the IPCE on the incident light intensity (Figures 3 and 4) was observed for all cells investigated in this study. Repeated measurements on individual cells yielded reproducible results. However, the decrease of the IPCE with decreasing incident light intensity was found to vary for measurements on different cells. Apparently, this effect is dependent on certain details of the preparation of the cells. Therefore, the discrepancy between our observations and the measurements which are presented by Fisher et al. in ref 5 is probably due to different preparation conditions of the cells. The determination of the specific parameters which determine the dependence of the IPCE on the incident light intensity is the subject of current investigations. The strong dependence of the IPCE on the incident light intensity is of general importance for measurements of the IPCE of dye-sensitized solar cells and of nanocrystalline electrodes. If experimental IPCE values are representative for solar illumination conditions, one can use low-intensity modulated monochromatic light in addition to white bias light, the intensity and the spectrum of which should be close to the AM1.5 spectrum. The other possibility is to measure the IPCE with monochromatic dc illumination only. In this case, the incident photon current density must be large enough to result in an absorbed photon current density jγ,abs ≈ 1017 cm-2 s-1. Especially at weakly absorbed wavelengths, such large absorbed photon current densities cannot be achieved with a white lamp in combination with a monochromator and therefore such measurements would result in an underestimation of the IPCE. Acknowledgment. We thank S. Baumga¨rtner of the FMF in Freiburg, Germany, for providing dye-sensitized solar cells. References and Notes (1) O’Regan, B.; Gra¨tzel, M. Nature 1991, 353, 737. (2) Hagfeld, A.; Gra¨tzel, M. Chem. ReV. 1995, 95, 49. (3) Nazeeruddin, M. K.; Kay, A.; Rodicio, I.; Humphry-Baker, R.; Mu¨ller, E.; Liska, P.; Vlachopoulos, N.; Gra¨tzel, M. J. Am. Chem. Soc. 1993, 115, 6328. (4) Hannappel, T.; Burfeindt, B.; Storck, W.; Willig, F. J. Phys. Chem. B 1997, 101, 6799. (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) Schwarzburg, K.; Willig, F. Appl. Phys. Lett. 1991. (7) Sommeling, P. M.; Rieffe, H. C.; Kroon, J. M.; van Roosmalen, J. A. M.; Scho¨necker, A.; Sinke, W. C. 12th International Conference on Photochemical Conversion and Storage of Solar Energy, Berlin, 1998. (8) Franco, G.; Gehring, J.; Peter, L. M.; Ponomarev, E. A.; Uhlendorf, I. J. Phys. Chem. B 1999, 103, 692. (9) Trupke, T.; Baumga¨rtner, S.; Wu¨rfel, P. J. Phys. Chem. B 2000, 104, 308. (10) Vanmaekelbergh, D. Electrochim. Acta 1997, 42, 1121. (11) de Jongh, P. E.; Vanmaekelbergh, D. J. Phys. Chem. B 1997, 101, 2716. (12) Hagfeldt, A.; Bjo¨rkste´n, U.; Lindquist, S. E. Sol. Energy Mater. Sol. Cells 1992, 27, 293.
