Diffusion Length in Nanoporous Photoelectrodes of Dye-Sensitized

Nov 26, 2012 - In addition, we found a correlation between the carrier diffusion lengths ... The diffusion length was measured for various operating c...
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Diffusion Length in Nanoporous Photoelectrodes of Dye-Sensitized Solar Cells under Operating Conditions Measured by Photocurrent Microscopy Jae-Ku Park, Ji-Chul Kang, Sang Yong Kim, B. H. Son, Ji-Yong Park, Soonil Lee, and Y. H. Ahn* Department of Physics and Division of Energy Systems Research, Ajou University, Suwon 443-749, Korea S Supporting Information *

ABSTRACT: We determined the carrier diffusion lengths in nanoporous layers of dye-sensitized solar cells by using scanning photocurrent microscopy. The diffusion lengths were found to be 60−100 μm for the conventional cells. In addition, we found a correlation between the carrier diffusion lengths and the cell efficiency, which proved that improvement in the diffusion length is one of the crucial factors for optimizing device performance. The diffusion length was measured for various operating conditions by varying parameters such as solar light intensity and applied electrical voltage. In particular, we observed electric-field-driven, carrier transport phenomena (i.e., drift current) in modified cells. Fitting with the drift-diffusion model enabled us to extract the electric field strengths present in the TiO2 nanoporous layer. SECTION: Energy Conversion and Storage; Energy and Charge Transport

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illuminations from both the front- and back-sides of the cells. However, the question of which method predicts the diffusion length most accurately is still debated. In both of these approaches, the diffusion lengths are measured indirectly, which requires appropriate modeling and exact knowledge of other optical parameters. Only recently, scanning photocurrent microscopy (SPCM, also referred to as the “laser-beam induced current technique”) has been introduced to estimate the diffusion length directly by mapping the photovoltage induced by a localized laser source.21,22 However, diffusion length measurements have not been addressed in terms of the interplay between the microscopic transport parameters and the overall device performance. In addition, this has not been studied for different operating conditions, obtained by varying parameters such as solar intensity and electrical bias voltage. In this report, we measured the diffusion lengths in nanoporous layers of DSCs using an SPCM technique,23−29 which does not require knowledge of other optical and transport parameters. By imaging the localized photocurrent captured by a partially etched front-electrode, we obtained

ye-sensitized solar cells (DSCs) have attracted considerable attention for more than two decades owing to their low fabrication cost and high light-harvesting efficiency.1−12 Recently, the total cell efficiency has reached around 12% for optimized DSC devices;13 however, it is believed that there is plenty of room for improvement considering that the electron conversion efficiency of the light-absorbing dyes can approach 100%. Maximizing the total efficiency requires optimizing the efficiency of the charge collection from the nanoporous semiconducting electrode (generally, TiO2) to the external circuit. It is important to develop reliable characterization tools that can relate device performance to underlying processes. One of the key parameters is the diffusion length of the photogenerated carriers in the nanoporous electrode because charge transport in the TiO2 layers is dominated by the electron diffusion process.14−16 Two approaches have mainly been used to determine the electron diffusion length in DSCs.15−20 In the transient method, the electron diffusion coefficient and the electron lifetime are measured independently by recording the timedependent photocurrent and time-dependent photovoltage, respectively. By contrast, in the steady-state method, the diffusion length is determined by analyzing the incident photon-to-electron conversion efficiency (IPCE) spectra for © XXXX American Chemical Society

Received: October 30, 2012 Accepted: November 26, 2012

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Figure 2a shows a representative 2D image from the SPCM measured on a DSC with a partially etched FTO layer. The

diffusion lengths explicitly and found their correlation to overall device performance. In addition, diffusion lengths were investigated as a function of the solar intensity and applied electric fields. In particular, we designed laterally structured DSCs to interrogate the field-dependent transport phenomena in the nanoporous layers. Figure 1a shows our device configuration for diffusion length measurements. We fabricate DSCs using conventional

Figure 1. (a) Schematic of DSC device structure with partially etched FTO electrode for the diffusion length measurements. (b) Schematic of experimental setup equipped with 532 nm CW laser and two-axis galvo scanner. 150 W xenon lamp with an air mass 1.5G filter is used as a solar simulator.

Figure 2. (a) Representative 2D SPCM image of a DSC sample with high-temperature sintering condition (525 °C). FTO edge is shown as a dashed line. (b) Photocurrent line profile (circles) as a function of the laser position (x0) from the FTO edge. Red line is a fit to the data (x0 > 0). (Inset) 2D plot of the calculated δn, in a cylindrical coordinate, whose spatial overlap with FTO area is to be integrated to give the photocurrent as a function of x0.

procedures, except that a part of the transparent conducting electrode, that is, the fluorine-doped tin oxide (FTO) layer, is removed. To fabricate the DSCs with partially etched frontelectrodes, we patterned the FTO electrodes using photolithography, followed by the wet etching process. The device showed efficiencies of 5.2 to 5.7% with fill-factors of 0.70 to 0.72 when we used the conventional electrolyte solution and nanoporous layers with a sintering temperatures of 525 °C. See the Supporting Information S1. In addition, we fabricated DSCs with different types of nanoporous films based on binder-free TiO2 paste (purchased from Nanopac and homemade,30 respectively). These pastes were compatible with the low-temperature process enabling us to use the indium tin oxide (ITO) as a transparent conducting electrode instead of FTO. The ITO film was also partially etched using photolithographic methods. The binder-free pastes were deposited on the patterned ITO electrodes and baked at 150 °C. The rest of the procedures were the same as in the case of conventional DSCs. The typical efficiency for these devices ranged from 2.0 to 2.5% as a result of the poor electrical connectivity of the nanoporous films. (See Supporting Information S1.) The diffusion lengths can be measured explicitly by using SPCM techniques on the DSCs with partially etched frontelectrodes. As schematically shown in Figure 1b, the focused laser spot illuminates the dyes in the nanoporous film, creating localized carriers that contribute to the current by the diffusion process in the film. Because the collected photocurrent decreases as we move the laser spot away from the FTO layers, we can determine the diffusion length by scanning the laser. A diode-pumped solid-state laser at 532 nm is focused using an objective lens and scanned using a two-axis galvo scanner. We also incorporated a solar simulator in the microscope to record the diffusion length while illuminating with solar light from 0 to 2 sun equivalent.

edge of the etched FTO layer in the front-electrode is indicated by a dashed line. The photocurrent signal was large when we illuminated the photoelectrode onto the remaining FTO areas, whereas it decreased as we moved the focused laser spot away from the etching interface as previously mentioned. We used a very slow scanning speed of 60 s/line throughout the experiments, considering that the total energy-conversion process in a solar cell occurs over a long period of time. (See the Supporting Informations S2.) Because the photocurrent is relatively uniform over the entire device, we primarily focus on the 1D profile that is perpendicular to the etching interface. The line profile of the photocurrent is plotted in Figure 2b as a function of the distance between the laser spot and the FTO edge (x0). By fitting the photocurrent curve, we can extract the photoinduced, carrier diffusion length as follows. To analyze the line profile, we used a 2D diffusion model as schematically shown in the inset of Figure 2b. The measured photocurrent as a function of x0 is described as the amount of excess carriers collected by the FTO electrodes, which can be obtained by integrating the excess carrier density δn over the semi-infinite FTO electrode area (Supporting Information S3). The collected photocurrent Icol analytically leads to the simple 1D exponential function for x0 > 0, which is as follows: eG exp( −x0/Ln) (1) 2 where e is the electron charge, G is the electron generation rate, and Ln = Dnτn1/2 is the diffusion length with electron diffusion coefficient Dn and electron lifetime τn. Therefore, the diffusion Icol =

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length can be extracted explicitly by fitting the photocurrent plot using a simple exponential function, without knowledge of the additional optical and transport parameters of the DSCs. We also note that this approach is advantageous compared with the photovoltage mapping techniques in which information on the background and the induced carrier density is needed to estimate the diffusion length.21,22 The fitting result is shown as a red line in Figure 2b with Ln = 60 μm. For most of the samples, the diffusion length ranges 60−100 μm in the case of nanoporous layers with conventional sintering conditions. The diffusion lengths measured from our experiments are evidently larger than the ∼10 μm length obtained from the steady-state measurements. Instead, it is close to those determined by dynamic methods, which estimate the diffusion lengths to be >50 μm. It has been asserted in recent studies15,16 that the diffusion length can be overestimated in the dynamic methods because the measurement of the diffusive coefficient can be overrated. However, in the steady-state methods, the accuracy of measuring the diffusion length is often limited by the thickness of the TiO2 film and requires the exact knowledge of other optical parameters such as the absorption coefficient. In addition, they are based on standard 1D models, which may result in misleading results, considering the highly disordered structures of TiO2. The diffusion length can be obtained unequivocally by using SPCM measurements. Figure 3 summarizes the diffusion length measurements for the four different groups of samples. In the first two panels, we

Information S4.) This confirms that diffusion length is one of the key factors that determines the improvement in cell efficiency. This is unexpected considering that the thickness of the nanoporous layer is only ∼12 μm, which is considerably smaller than the diffusion length of >70 μm, and that the cell efficiency does not improve as the thickness (d) increases for d > Ln.15,16,19 The typical optimized cell thickness of 10−18 μm has been determined empirically, and increasing the thickness further does not improve the cell efficiency. However, if we consider the highly disordered structures of the TiO2 layers, then many of the photogenerated carriers would travel considerably longer pathways until they finally reach the FTO photoelectrode. Therefore, we believe that the effective travel distance of a photogenerated carrier in a nanoporous layer would be even larger than or comparable to the diffusion lengths of the materials, even when the thickness is smaller than the diffusion length. Using our techniques, diffusion lengths can be measured under various operating conditions. Thus far, in this work, the diffusion length was obtained without using solar illumination or external electric fields. The dependence of the diffusion length on solar intensity has been addressed; however, the explanations are often controversial. For instance, it has been found that diffusion length increases with increasing light intensity,31−33 whereas in a multiple trapping model with the quasi-static approximation, it has been inferred that the diffusion length does not change significantly over a wide range of illumination intensities.18 First, in Figure 4a, we show a plot of diffusion lengths as a function of solar intensity for the three different DSCs sintered at high temperature (D1 and D2) and low temperature (D3).

Figure 3. Summary of measured diffusion lengths (boxes) and cell efficiencies (circles), respectively, for the four different groups of samples. For H1 and H2, nanoporous layers from the conventional TiO2 pastes were sintered at high-temperature (525 °C), and for L1 and L2, binder-free pasts that were sintered at low-temperatures (150 °C) were used.

show the results for the conventional DSCs sintered at a temperature of 525 °C with each panel corresponding to the TiO 2 pastes from Dyesol (H1) and Nanopac (H2), respectively. The average diffusion length ranges from 75 to 95 μm; however, as shown in the last two panels, the diffusion lengths were considerably shorter in the low-temperature (150 °C) processed DSCs (L1 and L2) at 30−40 μm. The cell efficiencies for the individual groups are shown together as open circles. The average efficiency for the high-temperature cells (H1 and H2) was 5.4%, whereas that for the lowtemperature case (L1 and L2) was 2.3%. A significant finding is that the measured diffusion length correlates well with the cell efficiency; in other words, Ln is longer for higher cell efficiency. (See also Supporting

Figure 4. (a) Plot of diffusion lengths as a function of solar intensity for the three different DSCs with nanoporous layers sintered at the high temperature (D1 and D2) and at the low temperature (D3), respectively. Light from the solar simulator illuminates the whole laserscanning area. (b) Plot of diffusion lengths as a function of electrical voltage for a DSC with partially etched front electrode. In this geometry, the electric field is applied perpendicular to the direction of carrier diffusion. 3634

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We measured the SPCM while illuminating the sample with the solar simulator. The measured diffusion length gradually increases from ∼70 to ∼105 μm for regular cells (depicted as circles (D1) and triangles (D2)) as we increase the light intensity from 0 to 2 sun. Similar behaviors were found in the low-temperature sintering case (D3), as depicted with squares in Figure 4a (from 40 to 55 μm). These results are consistent with the previous experimental findings based on the steadystate and the transient methods, as mentioned above. The variation in diffusion length as a function of solar intensity can be attributed to the interplay between the reduced carrier lifetime (due to the recombination losses) and the increased diffusion coefficient (by filling the charge traps that originate from solar light).31−33 Therefore, our results of the gradual increase in Ln with the light intensity can be explained by the increase in the diffusive coefficient, which is not fully compensated by the corresponding reduction of the carrier lifetime.16,31 Alternatively, it has been also suggested that the additional recombination process from deep surface states that saturate at the low intensity would suppress the recombination loss effects. In this case, multiple τn values corresponding to each recombination process should be introduced in the analysis at the low intensity, which requires future investigations. In Figure 4b, we show the dependence of the diffusion lengths on the voltage for a typical partially etched cell with the high-temperature sintering condition. It has been asserted that the transport phenomenon in DSCs is governed by the diffusion process, whereas the field-dependent drift motion has been ignored thus far because the high dielectric constant of TiO2 or the strong screening effects of the electrolyte solution do not allow for electric fields inside the nanoporous layers.17,34 This indicates that the diffusion lengths do not change noticeably with the applied voltage. We changed the voltage from −0.2 to 6.5 V and found that the diffusion lengths did not change remarkably with voltage variation as predicted. However, our observation of constant diffusion lengths can be misleading because, as we will explain below, the external electric field is perpendicular to the direction of the carrier diffusion in our experimental geometry. As a result, our observation does not reflect the transport phenomena occurring in an actual device. To study properly electron transport properties in conjunction with external fields, a substantial modification to the device geometry is needed whereby the electrical bias can be applied parallel to the direction of the carrier transport. We present the diffusion length measurements of nanoporous layers in specially designed DSCs. As shown in Figure 5a, the photoelectrode, nanoporous layer, and the counterelectrode are placed laterally on the same substrate. Such lateral structures are beneficial in that they can be fabricated by onestep printing methods or by inkjet printing techniques for future DSC fabrication.8 In addition, this structure allows us to measure the diffusion length with an electrical field applied parallel to the carrier diffusion direction. A titanium electrode (200 nm thick) was defined on a portion of a TiO2 strip (∼12 μm thick) to form a photoelectrode, whereas platinum (25 nm thick) was used as a counter-electrode. The work function of Ti is similar to that of FTO, and hence Ti forms a good electrical contact to the TiO2 films. In addition, the electrolyte solution is noncorrosive against Ti. The platinum electrode is placed 1 mm from the Ti electrode; therefore, it was not in contact with the photoelectrode or the TiO2 layer, whose length (lNP)

Figure 5. (a) Schematic of laterally structured DSCs where the photoelectrode (Ti), nanoporous film (TiO2), and the counterelectrode (Pt) are placed laterally on the same substrate. lNP denotes length of the nanoporous layer. (b) A representative 2D image of SPCM measured on a laterally structured DSC with lNP = 700 μm (sintered at 525 °C). (c) The line profile of photocurrent as a function of the focused laser position. The diffusion length was measured to be 52 μm at zero bias voltage by fitting the data as shown as a red line.

ranged from 200 to 700 μm. The measured cell efficiency was about 0.3 to 0.5% when normalized by the active nanoporous area. (See Supporting Information S5.) Figure 5b shows a representative image of SPCM measured on a laterally structured DSC with lNP = 700 μm. Again, the photocurrent was strongest when the focused laser spot illuminated the TiO2 layer near the current-collecting electrode (Ti), and it decreased exponentially as the spot moved away from the electrode. The diffusion length was measured to be 52 μm (40 to 70 μm, in general) at zero bias voltage for a hightemperature sintering condition (525 °C), as shown in the plot of the line profile in Figure 5c. Surprisingly, the diffusion length (hereafter referred to as decay lengths because they can be a contribution from the drift motion) varied dramatically with voltage, as shown in Figure 6a, for another cell with lNP = 400 μm. As we increased the voltage, the decay length increased from 40 μm up to the maximum values of ∼63.4 μm for V = 0.6 V. The decay length decreased as we further increased the voltage. We also found the similar tendency in the low-temperature sintered cells. (See the Supporting Information S5.) We note here that this effect was not observed when the electric field was perpendicular to the carrier transport, as shown in Figure 4b, which excludes the possibility of electrochemical effects such as a change in the iodine concentration in the electrolyte solution. The increase in decay length under the influence of an electric field has been observed in semiconductor carrier transport phenomena and well-explained by the drift-diffusion model as schematically shown in Figure 6b.25,26,35,36 Therefore, we suggest that electron transport through a nanoporous layer of DSCs is influenced by field-dependent drift motion. This is important considering that the solar cells are operated near V = Vmax, where Vmax is the voltage for maximum power efficiency. As 3635

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⎛ μn ⎞2 ⎛ 1 ⎞2 E⎟ + ⎜ ⎟ ⎜ ⎝ 2Dn ⎠ ⎝ Ln ⎠

μ 1 =− n E+ 2Dn Ldec −1

≈ −(19.53 V )E +

⎛ 1 ⎞2 (19.53 V ) E + ⎜ ⎟ ⎝ Ln ⎠ −1 2 2

(3)

where we used the Einstein relation of Dn/μn = kT/e = 0.0256 (V) at room temperature. (See the Supporting Information S6.) The numerical calculations considering the finite size of cells (∼10 × 10 mm2) instead of using the semi-infinite FTO electrodes validate our approach (also described in Supporting Information S6). From eq 3, it is evident that the decay length increases as we increase the electric fields. Here the effective electric field in the nanoporous layer E can be expressed by E = αEext, where α is the fractional coefficient and Eext is the external electric field corresponding to the voltage V divided by the length of the TiO2 layers, which is in our case 400 μm. We plot in Figure 6c the measured decay length as a function of the applied voltage from −0.5 to 0.8 V. Our results in Figure 6c are fitted with eq 3 for the two different regions, yielding α = 0.10 for V < 0.1 V and 0.52 for V ranging from 0.1 to 0.6 V, respectively. In this manner, we could determine the effective electric fields induced in the nanoporous layers, which contribute to the transport motion of the photogenerated carriers. For instance, at V = 0.5 V, the effective electric fields in the nanoporous layer are found to be 0.65 mV/μm. The reason that the electric field increases abruptly at V ≈ 0.1 V is not clear and necessitates a future investigation. It is likely that the rectifying behavior originating at the Ti/TiO2 interfaces is responsible for this phenomenon. The decreasing tendency of the decay length with increasing voltage after V > 0.6 V can also be understood within the scope of the driftdiffusion model. The inset of Figure 6c shows a maximum photocurrent plotted as a function of the applied bias voltage from −0.5 to 0.8 V, which shows a clear polarity change at V = VOC ≈ 0.7 V. Because the direction of the net electron flow is away from the Ti electrode for V > VOC, the carriers with the opposite charge (i.e., hole carriers) are instead captured by the Ti electrode. In that case, the direction of the diffusion and the drift current is the same, causing a decrease in the decay length with an increase in the electric field, which can be achieved by reversing the sign of second term in eq 2.35,43 To conclude, by using SPCM, we measured the diffusion length of nanoporous layers in conventional DSCs to be 60− 100 μm. The diffusion length correlates well with cell efficiency, which confirms that improvement in the diffusion length of the present nanoporous layers will be an important step toward fabricating devices with optimum cell efficiency. Diffusion lengths have been measured for various operating conditions by varying parameters such as solar intensity and applied voltage. We found gradual increase in the diffusion length with an increase in solar intensity, whereas the field-driven transport phenomenon is also observed with applied voltage, which allows us to extract the effective electric fields inside the nanoporous layers. The results will trigger future study on the diffusion lengths for nanoporous films with various morphologies, electrolyte solutions, and dyes. Our proposed approach can be applied to various contemporary and future photovoltaic devices to obtain important guidelines for optimizing such devices.

Figure 6. (a) Photocurrent line profiles for the four different voltages from −0.5 V to 0.8 for a laterally structured DSC with lNP = 400 μm. Shown together as solid lines are fits to the data. (b) Schematic of electron energy band and the excess carrier distributions δn with and without the electric fields. ΦDiff and ΦDrift denote the fluxes of diffusion and drift motion of electron carriers, respectively. (c) Plot of the decay lengths extracted from panel a as a function of voltage. The solid lines are fits to the data from the drift-diffusion model. (Inset) Plot of the photocurrent peak extracted from SPCM as a function of voltage.

previously mentioned, it has been suggested that the charge transport in TiO2 layers is dominated by the electron diffusion process.15,37−42 However, it is more likely that with the applied voltage the induced electric field should be present inside the nanoporous layer because at one end it is in contact with the Ti electrode whose potential is different from that of the electrolyte solutions surrounding the rest of the nanoporous layer. Our results are consistent with the analysis based on the 2D drift-diffusion models. The steady-state, differential equation for electron carriers n in an the electric fields E⃗ = Ex̂ leads to Dn∇2 n + μn E

∂n n − =0 ∂x τn

(2)

where μn is the electron mobility and Dn is an electron diffusion coefficient. In our experimental configuration, the photocurrent can be simply described as Icol(x0) ∝ e−x0/Ldec, with the fielddependent decay length Ldec expressed as follows: 3636

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EXPERIMENTAL METHODS Measurement. For SPCM measurements, a diode-pumped solidstate laser at 532 nm is focused using an objective lens (NA = 0.10, 4×) in the microscope and scanned using a two-axis galvo scanner (Cambridge Technology). The photocurrent signals were collected by a current preamplifier (Femto Messtechnik) as a function of the laser positions. The full width at halfmaximum of the focused spot was