Letter pubs.acs.org/NanoLett
Trap-Free Transport in Ordered and Disordered TiO2 Nanostructures Julio Villanueva-Cab,† Song-Rim Jang,‡ Adam F. Halverson,§ Kai Zhu, and Arthur J. Frank* National Renewable Energy Laboratory, Golden, Colorado 80401-3393, United States S Supporting Information *
ABSTRACT: Understanding the influence of different film structures on electron diffusion in nanoporous metal oxide films has been challenging. Because of the rate-limiting role that traps play in controlling the transport properties, the structural effects of different film architectures are largely obscured or reduced. We describe a general approach to probe the impact of structural order and disorder on the charge-carrier dynamics without the interference of transport-limiting traps. As an illustration of this approach, we explore the consequences of trap-free diffusion in vertically aligned nanotube structures and random nanoparticle networks in sensitized titanium dioxide solar cells. Values of the electron diffusion coefficients in the nanotubes approached those observed for the single crystal and were up to 2 orders of magnitude greater than those measured for nanoparticle films with various average crystallites sizes. Transport measurements together with modeling show that electron scattering at grain boundaries in particle networks limits trap-free diffusion. In presence of traps, transport was 103−105 times slower in nanoparticle films than in the single crystal. Understanding the link between structure and carrier dynamics is important for systematically altering and eventually controlling the electronic properties of nanoscaled materials. KEYWORDS: Trap-free transport, TiO2 nanotubes, grain boundaries, electron scattering, dye-sensitized solar cells
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only marginally faster in the arrays27−29 due to their larger trap density and proportion of deep traps compared with those in the nanoparticles.27 Because traps play a dominant role in limiting transport, the relationship between the film architecture and transport is largely obscured. The structural effects of order and disorder on the charge-carrier dynamics in which traps play no rate-limiting role is an interesting if little explored aspect of the enormous subject on nanostructured materials. Because transport is a major determinant of the performance of energy conversion and electrical energy storage devices that increasingly rely on nanostructures,31−34 understanding the connection between structure and carrier dynamics is important for systematically altering and eventually controlling the electronic properties of nanoscaled materials. In this paper, we explore the consequences of trap-free diffusion in DSSCs containing polycrystalline anatase TiO2 nanotube arrays and nanoparticle films. The carrier dynamics in these film architectures are compared with those in the anatase TiO2 single crystal. Temperature-dependent intensity-modulated photocurrent spectroscopy (IMPS) measurements of the transport properties reveal that the trap-free electron diffusion coefficients (D0) is considerably larger in the nanotube arrays than in the nanoparticle films and approaches values35 of the diffusion coefficient in the single crystal. A model based on the proposition that electron scattering at grain boundaries limits
uring the past decade, several new photovoltaic concepts for achieving efficient solar-to-electric energy conversion with inexpensive materials and manufacturing processes have challenged traditional solar cells. One of these technologies is the sensitized (nanostructured) solar cell.1 Sensitizers can range from molecular dyes2 to inorganic semiconductors3,4 to quantum-confinement structures.5,6 The prototypical sensitized cell is the liquid-electrolyte-based dye-sensitized TiO2 solar cell (DSSC or Grätzel cell). The film architecture is at the heart of DSSCs, coupling light absorption, charge injection, and chargecarrier transport to generate electrical power. Electron transport in the nanoporous films is markedly slow, ranging from milliseconds to seconds depending on the density of photoinjected electrons.7−9 From this dependence it has been inferred that trapping and detrapping events in an intrinsic exponential density of band gap states limit transport.10−15 Other types of trap states that strongly affect transport in metal oxide films include those produced by the intercalation of protons from moisture/water in a cell16−19 and Li+ ions from the electrolyte.8 Exciton-like trap states in dry titania nanotubes associated with impurities from the nanotubes fabrication process also slow transport.20 Structural disorder connected with the three-dimensional, random particle network (e.g., large number of interparticle connections)21,22 and interparticle contact area also impede transport.23,24 One strategy to reduce both the structural disorder and dimensionality of the network is to use vertically aligned, one-dimensional nanowire and nanotube arrays.25−30 However, studies of polycrystalline TiO2 nanotube arrays and nanoparticle films reveal that transport is © XXXX American Chemical Society
Received: December 12, 2013 Revised: March 28, 2014
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transport in the nanoparticle films describes the quantitative effects of crystallite size on D0. When traps are allowed to participate in transport, the crystallite size effects on the electron diffusion coefficient become less evident. Diffusion of electrons in an electrolyte-filled TiO2 is ambipolar, meaning that the electron motion in the TiO2 film is electrostatically coupled to the cation motion in solution.7,9,36 However, because the mobile cation density vastly exceeds the photoinjected electron density, the ambipolar diffusion coefficient and electron diffusion coefficient are essentially equal under the normal operating conditions of DSSCs.7 Assuming for simplicity that multiple trapping of electrons occurs within the framework of the multiple trapping model with an exponential density of band gap states, the electron diffusion coefficient (D) can be expressed in terms of the total photoelectron density (N) and the effective density of trap states (NC) at the transport (mobility) edge.7 D ≈ D0(N /NC)((1/ α) − 1)
Figure 1. Temperature dependence of the electron diffusion coefficient on the photoelectron density in a DSSC containing a TiO2 nanoparticle film. The average crystallite size is 15 nm, and the film porosity is 60 ± 2%. The best fit of the D(N,T) data (eq 1) yield D0 = 1.4 × 10−3 cm2 s−1, NC = 3 × 1018 cm−3, and T0 = 641 K. Experimental details are given in the Supporting Information.
to yield values of the trap-free electron diffusion coefficient D0 (1.4 × 10−3 cm2 s−1), total density of trap states at the transport edge NC (3 × 1018 cm−3), and characteristic temperature T0 (641 K). The D0 value for the nanoparticle anatase TiO2 film is about 2 orders of magnitude smaller than the DCrystal value for 0 2 −1 35 = 0.1−0.4 cm s ). The single crystal anatase TiO2 (DCrystal 0 difference between the D0 value for the particle film and DCrystal 0 value for the single crystal is due to the number of grain boundaries (number of interparticle contacts) in the nanostructured film. At photoelectron densities greater than NC, the electron quasi-Fermi level at or above the transport edge losses its physical significance as does D values greater than D0.7,38 One would expect that when the electron quasi-Fermi level approaches the transport edge (N ≈ NC) the diffusion coefficient D should reach a constant value (D = D0). It is informative to compare the transport edge energy of the nanoparticle anatase TiO2 film with the estimated conduction band edge energy of the anatase single crystal relative to a redox energy level (Eredox). With the aid of the NC value of 3 × 1018 cm−3 from Figure 1 and the graphical relationship between the open-circuit photoelectron density and open-circuit voltage (VOC = nEF − Eredox, where nEF is the quasi-Fermi level) displayed in Figure S3 (Supporting Information), one finds that the transport edge of the TiO2 nanoparticle film is located at 0.85 eV, which is 100 meV below the estimated conduction band edge (ECB = 0.95 eV)39 of the single crystal. Others have also reported that the transport edge lies below the conduction band.37,40 However, the 100 meV energy difference observed in the present system may not be significant considering the uncertainties associated with the estimations39 used in calculating the conduction band edge energy and the likelihood that the actual conduction band edge position is shifted with respect to the value of the conduction band edge energy reported in the literature.39 Such shifts can result from, for example, potential-determining species (e.g., ions) adsorbed to the TiO2 surface.8,37,40,41 Moreover, the connection between the various film structures and carrier dynamics in the absence and presence of traps and the effects of the redox electrolytes on D0 discussed below supports the depiction of freely mobile electrons occurring at or above the transport edge. Figure 2 shows the trap-free electron diffusion coefficient as a function of the average crystallite size (particle diameter) in nanoparticle films deposited on TCO substrates. All of the particle films had the same porosity (60 ± 2%) and, therefore, had the same average interparticle coordination number.21
(1)
where the parameter α = T/T0 is a measure of the degree of disorder, T is the temperature, and T0 is the characteristic temperature, which is related to the steepness of the trap distribution or the average trap depth of the trap distribution. A small α value indicates a long exponential distribution of band tail states corresponding to a highly energetically disordered system. D0 is the diffusion coefficient of freely mobile electrons at or above the transport edge of the TiO2 nanoporous films.7,9 The transport edge (transport energy level) serves the same function in the multiple-trapping model as the conduction band edge does in homogeneous crystalline materials.7,9 In such crystalline materials, the transport edge may be identified with the edge of the conduction band. It follows that D0 is unaffected by energetic disorder associated with the exponential distribution of band gap states and with surface traps associated with the adsorption of electrolyte species, dye molecules, or impurities. The value of D0 should be, however, affected by structural disorder associated with, for instance, the crystallite (grain) size, the number of interparticle connections, and interparticle contact area. Thus, studies of the D0 dependences can provide valuable information about the influence of nanostructured morphology on transport, especially in relationship to different film architectures (e.g., nanoparticle vs nanotube films) and the single crystal. Equation 1 offers a general approach for evaluating D0. The essential idea is to create a family of power-law plots of D versus N at different temperatures and then to extrapolate them to large values of the photoelectron density and diffusion coefficient. The plots converge at a single point to yield NC and D0. A similar approach has been used for evaluating the D0 value in TiO2 nanoparticle films.37 Graphical extrapolation circumvents direct experimental measurements that would involve increasing the photoelectron density (or light intensity) until all the trap states are filled and electrically inert (N = NC) or raising the temperature of the DSSC until all photoinjected electrons are thermally excited to the transport edge (T = T0). Either of these direct approaches would lead to rapid degradation of the DSSCs. Figure 1 shows the temperature dependence of the electron diffusion coefficient on the photoelectron density in a DSSC containing a nanoparticle film with an average crystallite size of 15 nm. It can be seen that at sufficiently high photoelectron densities the various plots converge at a single point (NC, D0) B
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The experimental results in Figure 2 together with the model represented in Figure 3 support the conclusion that electron scattering at grain boundaries limits the trap-free diffusion of electrons in nanoparticle films. Figure 4 compares the effects of traps and morphology on the electron diffusion coefficient in nanoparticle films. Plots of
Figure 2. Effect of the average crystallite size on the trap-free electron diffusion coefficient D0 in nanoparticle films used in various DSSCs. The average crystallite size ranges from 15 to 28 nm, and the porosity of the films is 60 ± 2%. The solid line represents the fit of the experimental data to D0 ∝ (average crystallite size)2. The single crystal values (DCrystal = 0.1−0.4 cm2 s−1) were obtained from anatase DCrystal 0 0 Hall mobility measurements35 in the temperature range of 273−333 K.
From simulations of nanoparticle films at different porosities,22 we estimate that the average coordination number of a particle in a film with 60% porosity is about 4. When the average particle size in the films is varied from 15 to 28 nm, the D0 values increased with the square of the average crystallite size. As noted in the discussion of Figure 1, the difference between the D0 value for the nanoparticle film and the DCrystal value for 0 the single crystal TiO2 is ascribed to the number of grain boundaries. Increasing the average crystallite size substantially reduces the number of grain boundaries for a given film thickness and augments the interparticle contact area, leading to faster transport. In the large particle size limit in which the average particle size in a film approaches that of the macroscopic single crystal and the number of grain boundaries becomes negligible, the value of D0 approaches that of DCrystal . 0 The relationship between the trap-free electron diffusion D0 and the square of the average crystallite size (d2) can be understood in terms of the model depicted schematically in Figure 3. The model assumes that the time that an electron
Figure 4. Effects of trap states and morphology on the electron diffusion coefficient in nanoparticle films. The diffusion coefficient values35 for single crystal anatase TiO2 are given for comparison.
the temperature-dependent diffusion coefficient D in the presence of surface traps are displayed in Figure 1. From analyses of the plots in Figure 1 and Figure S4 (Supporting Information), the total trap density of exponential band gap states in the nanoparticle film is about 3 × 1018 cm−3. Relative to the diffusion coefficient for single crystal anatase DCrystal , the 0 trapping/detrapping of electrons in these localized states in the energy gap slow transport by 2−5 orders of magnitude, depending on the photoinjected electron density. Also, relative to the DCrystal values of the anatase single crystal, we estimate 0 that in the absence of transport-limiting traps, the scattering of electrons at grain boundaries in a film slows transport by up to 2 orders of magnitude. Thus, decreasing both energetic and structural disorder is required to approach values of the electron diffusion coefficient for the single crystal. Figure 5 displays the temperature dependence of the electron diffusion coefficient D on the photoelectron density in a
Figure 3. Schematic depicting the model used to explain the dependence of D0 with the particle size d.
spends crossing the particle−particle boundary is rate limiting and that the electron diffusion time within the bulk of a particle is negligible. For these conditions, electron transport in a trapfree three-dimensional network can be described by the relation: D0 = (d2/6Δt), where d is the average distance between electron scattering events and Δt is the average time that electrons spend crossing particle−particle boundaries. From this relation, it follows that
D0 ∝ d 2
Figure 5. Temperature dependence of the electron diffusion coefficient D on the photoelectron density in a DSSC containing a TiO2 nanotube film. The best fit of the D(N,T) data (eq 1) yield D0 = 1.4 × 10−1 cm2 s−1, NC = 2.2 × 1019 cm−3, and T0 = 1426 K. Experimental details are given in Supporting Information.
(2) C
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nanotube film. From the analyses of scanning electron microscopy data in Figure S1 and other measurements (Supporting Information), we determined that the film porosity was 56% and that the average NT had a length of 12 μm, an inner pore diameter of 46.5 nm, a wall thickness of 32.6 nm, and a center-to-center intertube distance of 145 nm. As in the case of the nanoparticle films, the plots converge at a single point (NC, D0) to yield values of the trap-free electron diffusion coefficient D0 (1.4 × 10−1 cm2 s−1), total trap density at the transport edge NC (2.2 × 1019 cm−3), and characteristic temperature T0 (1426 K). A comparison of the D0 values from the plots in Figures 1 and 5 shows that the trap-free electron diffusion coefficient is 2 orders of magnitude larger in the nanotube arrays (1.4 × 10−1 cm2 s−1) than in the nanoparticle films (1.4 × 10−3 cm2 s−1) with an average crystallite size of 15 nm. Moreover, a comparison of NC and T0 values indicates that the total trap density is 7-times larger in the nanotube film (NC of 2.2 × 1019 cm−3) than in the nanoparticle films (NC = 3 × 1018 cm−3). Similarly, the characteristic temperature, which is a measure of the average trap depth of the exponential distribution of band gap states, is more than 2 times greater in the nanotube film (T0 = 1426 K) than in the nanoparticle films (T0 = 641 K). These results indicate that the nanotube film has a larger trap density and a larger proportion of deep traps than the nanoparticle films. These observations are consistent with the results of other studies,27,28,30 which report that transport is only marginally faster in the nanotube arrays than in the nanoparticle films, even though the orientationally ordered nanotube film morphology should favor much faster transport. Figure 6 illustrates schematically the structural effects of nanotube and nanoparticle film architectures on D0. The trap-
free electron diffusion coefficient is 2 orders of magnitude larger in the TiO2 nanotube array than in the nanoparticle films with an average crystallite size of 15 nm (Figures 1 and 5). As the average crystallite size increases (Figure 2), the D0 values for the nanoparticle films approach that for the nanotube films. Also, electron transport in the individual nanotubes of an array occurs along nominally one-dimensional pathways, whereas the transport in the random nanoparticle network proceeds along three-dimensional pathways. Transport along a one-dimensional pathway is much shorter than transport pathways in a three-dimensional network.29 In addition, the structural disorder associated with the number of grain boundaries and the randomness of the crystallite (grain) orientation is much less in the nanotube arrays than in the nanoparticle films. Indeed, a comparison of the trap-free electron diffusion coefficient for the nanotube array (D0 = 1.4 × 10−1 cm2 s−1) and single crystal (DCrystal = 0.1−0.4 cm2s−1)35 shows that the 0 D0 value for the nanotube array comes close to that of the single crystal, indicating that structural disorder in the nanotube array is significantly reduced. Ambipolar effects associated with the electrolyte are assumed to have little, if any, impact on transport data in this study. An examination of Table 1 shows that changing from one electrolyte to another had no influence on D0 for the nanoparticle films. This result is not surprising inasmuch as changing the electrolyte composition would affect mainly the energy distribution and density of surface traps neither of which would alter D0, which is independent of energetic disorder. Table 1 also shows that the electron-collecting substrates TCO and the Ti foil used for the nanoparticle films also had no effect on the D0 value. This is also understandable inasmuch as the total surface area of the nanoparticle film is several orders of magnitude larger than the contact area between the nanoparticles and the electron-collecting substrate. Thus, the contributions of the electrolyte and charge-collecting substrate to D0 in this study are negligible. In conclusion, both energetic disorder (e.g., localized states in the band gap) and structural disorder (e.g., film architecture) govern transport in TiO2. At normal DSSC operating conditions, energetic disorder is the primary mechanism limiting transport. In the presence of traps, the effects of structural disorder associated with the individual particles (e.g., crystallite size) and different film architectures (e.g., nanoparticle films vs nanotube arrays) are obscured or reduced. Under the condition in which all trap states are fully occupied and, therefore, are electrically inert, electron scattering at particle−particle boundaries in nanoparticle networks is shown to limit diffusion. Increasing the interparticle contact area and reducing orientational disorder in the nanostructured films by changing from a three-dimensional randomly packed nano-
Figure 6. Comparison of the trap-free electron diffusion coefficient D0 in nanoparticle films and in oriented polycrystalline nanotube arrays in values for the single crystal.35 DSSCs with the DCrystal 0
Table 1. Effect of Film Architecture, Electrolyte Composition, and Electron-Conducting Substrate on D0 parameter
Nanoparticles on TCOa
Nanoparticles on Ti foilb
Nanotubes on Ti foilb
d (nm) D0 (cm2 s−1)c T0 (K)c NC (cm−3)c
20 (5.2 ± 0.5) × 10−3 804 ± 34 (3 ± 0.2) × 1018
20 (5.5 ± 0.5) × 10−3 658 ± 21 (6.1 ± 1) × 1018
-(1.4 ± 0.4) × 10−1 1426 ± 78 (2.2 ± 0.2) × 1019
a The electrolyte consisted of 0.6 M 1-butyl-3-methylimidazolium iodide, 0.1 M LiI, 0.05 M I2, 0.5 M 4-tert-butylpyridine, and 0.1 M guanidinium thiocyanate in acetonitle/valeronitrile (85:15, v/v). bThe electrolyte consisted of 0.8 M 1-hexyl-2, 3-dimethylimidazolium iodide and 50 mM iodine in methoxypropionitrile. cFitting parameters (D0, T0, and NC,) were determined from the respective plots in Figure S4 (Supporting Information) for the nanoparticle films and Figure 5 for the nanotube film.
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(14) 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, 10281−10289. (15) Solbrand, A.; Lindström, H.; Rensmo, H.; Hagfeldt, A.; Lindquist, S. E.; Södergren, S. J. Phys. Chem. B 1997, 101, 2514−2518. (16) Chen, W. P.; Wang, Y.; Chan, H. L. W. Appl. Phys. Lett. 2008, 92, 112907. (17) Wang, Q.; Zhang, Z.; Zakeeruddin, S. M.; Grätzel, M. J. Phys. Chem. B 2008, 112, 7084−7092. (18) Koudriachova, M. V.; de Leeuw, S. W.; Harrison, N. M. Phys. Rev. B 2004, 70, 165421. (19) Halverson, A. F.; Zhu, K.; Erslev, P. T.; Kim, J. Y.; Neale, N. R.; Frank, A. J. Nano Lett. 2012, 12, 2112−2116. (20) Richter, C.; Schmuttenmaer, C. A. Nat. Nanotechnol. 2010, 5, 769−772. (21) van de Lagemaat, J.; Benkstein, K. D.; Frank, A. J. J. Phys. Chem. B 2001, 105, 12433−12436. (22) Benkstein, K. D.; Kopidakis, N.; van de Lagemaat, J.; Frank, A. J. J. Phys. Chem. B 2003, 107, 7759−7767. (23) Cass, M. J.; Walker, A. B.; Martinez, D.; Peter, L. M. J. Phys. Chem. B 2005, 109, 5100−5107. (24) Cass, M. J.; Qiu, F. L.; Walker, A. B.; Fisher, A. C.; Peter, L. M. J. Phys. Chem. B 2003, 107, 113−119. (25) Mor, G. K.; Shankar, K.; Paulose, M.; Varghese, O. K.; Grimes, C. A. Nano Lett. 2006, 6, 215−218. (26) Enache-Pommer, E.; Liu, B.; Aydil, E. S. Phys. Chem. Chem. Phys. 2009, 11, 9648−9652. (27) Zhu, K.; Neale, N. R.; Miedaner, A.; Frank, A. J. Nano Lett. 2007, 7, 69−74. (28) Jennings, J. R.; Ghicov, A.; Peter, L. M.; Schmuki, P.; Walker, A. B. J. Am. Chem. Soc. 2008, 130, 13364−13372. (29) Zhu, K.; Vinzant, T. B.; Neale, N. R.; Frank, A. J. Nano Lett. 2007, 7, 3739−3746. (30) Mohammadpour, R.; Zad, A. I.; Hagfeldt, A.; Boschloo, G. ChemPhysChem 2010, 11, 2140−2145. (31) Warren, S. C.; et al. Nat. Mater. 2013, 12, 842−849. (32) Law, M.; Greene, L. E.; Johnson, J. C.; Saykally, R.; Yang, P. Nat. Mater. 2005, 4, 455−459. (33) Arico, A. S.; Bruce, P.; Scrosati, B.; Tarascon, J.-M.; van Schalkwijk, W. Nat. Mater. 2005, 4, 366−377. (34) Frank, A. J.; Kopidakis, N.; van de Lagemaat, J. Coord. Chem. Rev. 2004, 248, 1165−1179. (35) Forro, L.; Chauvet, O.; Emin, D.; Zuppiroli, L.; Berger, H.; Lévy, F. J. Appl. Phys. 1994, 75, 633−635. (36) van de Lagemaat, J.; Frank, A. J. J. Phys. Chem. B 2001, 105, 11194−11205. (37) Wang, Q.; et al. J. Phys. Chem. B 2006, 110, 25210−25221. (38) Bisquert, J. J. Phys. Chem. B 2004, 108, 2323−2332. (39) Lobato, K.; Peter, L. M.; Wurfel, U. J. Phys. Chem. B 2006, 110, 16201−16204. (40) Liu, Y.; Jennings, J. R.; Zakeeruddin, S. M.; Gratzel, M.; Wang, Q. J. Am. Chem. Soc. 2013, 135, 3939−3952. (41) Schlichthörl, G.; Huang, S. Y.; Sprague, J.; Frank, A. J. J. Phys. Chem. B 1997, 101, 8141−8155.
particle network to a one-dimensional array of vertically aligned nanotubes lead to values of the trap-free electron diffusion coefficient approaching those of the single crystal material. This study demonstrate a straightforward approach to probe the impact of structural order and disorder on the transport dynamics in the absence of the interfering contributions of energetic disorder associated with the exponential distribution of band gap states and with surface traps connected with the adsorption of electrolyte species, dye molecules, or impurities. The mechanistic insight gained from this study on the structural effects of different film architectures and grain boundaries on the carrier dynamics should find important usage in controlling the electronic properties of nanoscaled oxide materials for use in optoelectronics, photocatalysis, solar fuel cells, and electrical energy storage devices.
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ASSOCIATED CONTENT
S Supporting Information *
Experimental details and additional data. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Present Addresses
́ Departamento de Fisica Aplicada, CINVESTAV-IPN, Mérida, Yucatán 97310, México. ‡ Corporate R&D, LG Chem Research Park, LG Chem, Ltd., 104−1 Munji-dong, Yuseong-gu, Daejeon, 305−380, Korea. § GE Global Research, 1 Research Circle, Niskayuna, New York 12309. †
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, U.S. Department of Energy, under Contract No. DE-AC3608GO28308.
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REFERENCES
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Trap-Free Transport in Ordered and Disordered TiO2 Nanostructures Julio Villanueva-Cab,† Song-Rim Jang,‡ Adam F. Halverson,§ Kai Zhu, and Arthur J. Frank* National Renewable Energy Laboratory, Golden, Colorado 80401-3393, United States S Supporting Information *
ABSTRACT: Understanding the influence of different film structures on electron diffusion in nanoporous metal oxide films has been challenging. Because of the rate-limiting role that traps play in controlling the transport properties, the structural effects of different film architectures are largely obscured or reduced. We describe a general approach to probe the impact of structural order and disorder on the charge-carrier dynamics without the interference of transport-limiting traps. As an illustration of this approach, we explore the consequences of trap-free diffusion in vertically aligned nanotube structures and random nanoparticle networks in sensitized titanium dioxide solar cells. Values of the electron diffusion coefficients in the nanotubes approached those observed for the single crystal and were up to 2 orders of magnitude greater than those measured for nanoparticle films with various average crystallites sizes. Transport measurements together with modeling show that electron scattering at grain boundaries in particle networks limits trap-free diffusion. In presence of traps, transport was 103−105 times slower in nanoparticle films than in the single crystal. Understanding the link between structure and carrier dynamics is important for systematically altering and eventually controlling the electronic properties of nanoscaled materials. KEYWORDS: Trap-free transport, TiO2 nanotubes, grain boundaries, electron scattering, dye-sensitized solar cells
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only marginally faster in the arrays27−29 due to their larger trap density and proportion of deep traps compared with those in the nanoparticles.27 Because traps play a dominant role in limiting transport, the relationship between the film architecture and transport is largely obscured. The structural effects of order and disorder on the charge-carrier dynamics in which traps play no rate-limiting role is an interesting if little explored aspect of the enormous subject on nanostructured materials. Because transport is a major determinant of the performance of energy conversion and electrical energy storage devices that increasingly rely on nanostructures,31−34 understanding the connection between structure and carrier dynamics is important for systematically altering and eventually controlling the electronic properties of nanoscaled materials. In this paper, we explore the consequences of trap-free diffusion in DSSCs containing polycrystalline anatase TiO2 nanotube arrays and nanoparticle films. The carrier dynamics in these film architectures are compared with those in the anatase TiO2 single crystal. Temperature-dependent intensity-modulated photocurrent spectroscopy (IMPS) measurements of the transport properties reveal that the trap-free electron diffusion coefficients (D0) is considerably larger in the nanotube arrays than in the nanoparticle films and approaches values35 of the diffusion coefficient in the single crystal. A model based on the proposition that electron scattering at grain boundaries limits
uring the past decade, several new photovoltaic concepts for achieving efficient solar-to-electric energy conversion with inexpensive materials and manufacturing processes have challenged traditional solar cells. One of these technologies is the sensitized (nanostructured) solar cell.1 Sensitizers can range from molecular dyes2 to inorganic semiconductors3,4 to quantum-confinement structures.5,6 The prototypical sensitized cell is the liquid-electrolyte-based dye-sensitized TiO2 solar cell (DSSC or Grätzel cell). The film architecture is at the heart of DSSCs, coupling light absorption, charge injection, and chargecarrier transport to generate electrical power. Electron transport in the nanoporous films is markedly slow, ranging from milliseconds to seconds depending on the density of photoinjected electrons.7−9 From this dependence it has been inferred that trapping and detrapping events in an intrinsic exponential density of band gap states limit transport.10−15 Other types of trap states that strongly affect transport in metal oxide films include those produced by the intercalation of protons from moisture/water in a cell16−19 and Li+ ions from the electrolyte.8 Exciton-like trap states in dry titania nanotubes associated with impurities from the nanotubes fabrication process also slow transport.20 Structural disorder connected with the three-dimensional, random particle network (e.g., large number of interparticle connections)21,22 and interparticle contact area also impede transport.23,24 One strategy to reduce both the structural disorder and dimensionality of the network is to use vertically aligned, one-dimensional nanowire and nanotube arrays.25−30 However, studies of polycrystalline TiO2 nanotube arrays and nanoparticle films reveal that transport is © XXXX American Chemical Society
Received: December 12, 2013 Revised: March 28, 2014
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transport in the nanoparticle films describes the quantitative effects of crystallite size on D0. When traps are allowed to participate in transport, the crystallite size effects on the electron diffusion coefficient become less evident. Diffusion of electrons in an electrolyte-filled TiO2 is ambipolar, meaning that the electron motion in the TiO2 film is electrostatically coupled to the cation motion in solution.7,9,36 However, because the mobile cation density vastly exceeds the photoinjected electron density, the ambipolar diffusion coefficient and electron diffusion coefficient are essentially equal under the normal operating conditions of DSSCs.7 Assuming for simplicity that multiple trapping of electrons occurs within the framework of the multiple trapping model with an exponential density of band gap states, the electron diffusion coefficient (D) can be expressed in terms of the total photoelectron density (N) and the effective density of trap states (NC) at the transport (mobility) edge.7 D ≈ D0(N /NC)((1/ α) − 1)
Figure 1. Temperature dependence of the electron diffusion coefficient on the photoelectron density in a DSSC containing a TiO2 nanoparticle film. The average crystallite size is 15 nm, and the film porosity is 60 ± 2%. The best fit of the D(N,T) data (eq 1) yield D0 = 1.4 × 10−3 cm2 s−1, NC = 3 × 1018 cm−3, and T0 = 641 K. Experimental details are given in the Supporting Information.
to yield values of the trap-free electron diffusion coefficient D0 (1.4 × 10−3 cm2 s−1), total density of trap states at the transport edge NC (3 × 1018 cm−3), and characteristic temperature T0 (641 K). The D0 value for the nanoparticle anatase TiO2 film is about 2 orders of magnitude smaller than the DCrystal value for 0 2 −1 35 = 0.1−0.4 cm s ). The single crystal anatase TiO2 (DCrystal 0 difference between the D0 value for the particle film and DCrystal 0 value for the single crystal is due to the number of grain boundaries (number of interparticle contacts) in the nanostructured film. At photoelectron densities greater than NC, the electron quasi-Fermi level at or above the transport edge losses its physical significance as does D values greater than D0.7,38 One would expect that when the electron quasi-Fermi level approaches the transport edge (N ≈ NC) the diffusion coefficient D should reach a constant value (D = D0). It is informative to compare the transport edge energy of the nanoparticle anatase TiO2 film with the estimated conduction band edge energy of the anatase single crystal relative to a redox energy level (Eredox). With the aid of the NC value of 3 × 1018 cm−3 from Figure 1 and the graphical relationship between the open-circuit photoelectron density and open-circuit voltage (VOC = nEF − Eredox, where nEF is the quasi-Fermi level) displayed in Figure S3 (Supporting Information), one finds that the transport edge of the TiO2 nanoparticle film is located at 0.85 eV, which is 100 meV below the estimated conduction band edge (ECB = 0.95 eV)39 of the single crystal. Others have also reported that the transport edge lies below the conduction band.37,40 However, the 100 meV energy difference observed in the present system may not be significant considering the uncertainties associated with the estimations39 used in calculating the conduction band edge energy and the likelihood that the actual conduction band edge position is shifted with respect to the value of the conduction band edge energy reported in the literature.39 Such shifts can result from, for example, potential-determining species (e.g., ions) adsorbed to the TiO2 surface.8,37,40,41 Moreover, the connection between the various film structures and carrier dynamics in the absence and presence of traps and the effects of the redox electrolytes on D0 discussed below supports the depiction of freely mobile electrons occurring at or above the transport edge. Figure 2 shows the trap-free electron diffusion coefficient as a function of the average crystallite size (particle diameter) in nanoparticle films deposited on TCO substrates. All of the particle films had the same porosity (60 ± 2%) and, therefore, had the same average interparticle coordination number.21
(1)
where the parameter α = T/T0 is a measure of the degree of disorder, T is the temperature, and T0 is the characteristic temperature, which is related to the steepness of the trap distribution or the average trap depth of the trap distribution. A small α value indicates a long exponential distribution of band tail states corresponding to a highly energetically disordered system. D0 is the diffusion coefficient of freely mobile electrons at or above the transport edge of the TiO2 nanoporous films.7,9 The transport edge (transport energy level) serves the same function in the multiple-trapping model as the conduction band edge does in homogeneous crystalline materials.7,9 In such crystalline materials, the transport edge may be identified with the edge of the conduction band. It follows that D0 is unaffected by energetic disorder associated with the exponential distribution of band gap states and with surface traps associated with the adsorption of electrolyte species, dye molecules, or impurities. The value of D0 should be, however, affected by structural disorder associated with, for instance, the crystallite (grain) size, the number of interparticle connections, and interparticle contact area. Thus, studies of the D0 dependences can provide valuable information about the influence of nanostructured morphology on transport, especially in relationship to different film architectures (e.g., nanoparticle vs nanotube films) and the single crystal. Equation 1 offers a general approach for evaluating D0. The essential idea is to create a family of power-law plots of D versus N at different temperatures and then to extrapolate them to large values of the photoelectron density and diffusion coefficient. The plots converge at a single point to yield NC and D0. A similar approach has been used for evaluating the D0 value in TiO2 nanoparticle films.37 Graphical extrapolation circumvents direct experimental measurements that would involve increasing the photoelectron density (or light intensity) until all the trap states are filled and electrically inert (N = NC) or raising the temperature of the DSSC until all photoinjected electrons are thermally excited to the transport edge (T = T0). Either of these direct approaches would lead to rapid degradation of the DSSCs. Figure 1 shows the temperature dependence of the electron diffusion coefficient on the photoelectron density in a DSSC containing a nanoparticle film with an average crystallite size of 15 nm. It can be seen that at sufficiently high photoelectron densities the various plots converge at a single point (NC, D0) B
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Nano Letters
Letter
The experimental results in Figure 2 together with the model represented in Figure 3 support the conclusion that electron scattering at grain boundaries limits the trap-free diffusion of electrons in nanoparticle films. Figure 4 compares the effects of traps and morphology on the electron diffusion coefficient in nanoparticle films. Plots of
Figure 2. Effect of the average crystallite size on the trap-free electron diffusion coefficient D0 in nanoparticle films used in various DSSCs. The average crystallite size ranges from 15 to 28 nm, and the porosity of the films is 60 ± 2%. The solid line represents the fit of the experimental data to D0 ∝ (average crystallite size)2. The single crystal values (DCrystal = 0.1−0.4 cm2 s−1) were obtained from anatase DCrystal 0 0 Hall mobility measurements35 in the temperature range of 273−333 K.
From simulations of nanoparticle films at different porosities,22 we estimate that the average coordination number of a particle in a film with 60% porosity is about 4. When the average particle size in the films is varied from 15 to 28 nm, the D0 values increased with the square of the average crystallite size. As noted in the discussion of Figure 1, the difference between the D0 value for the nanoparticle film and the DCrystal value for 0 the single crystal TiO2 is ascribed to the number of grain boundaries. Increasing the average crystallite size substantially reduces the number of grain boundaries for a given film thickness and augments the interparticle contact area, leading to faster transport. In the large particle size limit in which the average particle size in a film approaches that of the macroscopic single crystal and the number of grain boundaries becomes negligible, the value of D0 approaches that of DCrystal . 0 The relationship between the trap-free electron diffusion D0 and the square of the average crystallite size (d2) can be understood in terms of the model depicted schematically in Figure 3. The model assumes that the time that an electron
Figure 4. Effects of trap states and morphology on the electron diffusion coefficient in nanoparticle films. The diffusion coefficient values35 for single crystal anatase TiO2 are given for comparison.
the temperature-dependent diffusion coefficient D in the presence of surface traps are displayed in Figure 1. From analyses of the plots in Figure 1 and Figure S4 (Supporting Information), the total trap density of exponential band gap states in the nanoparticle film is about 3 × 1018 cm−3. Relative to the diffusion coefficient for single crystal anatase DCrystal , the 0 trapping/detrapping of electrons in these localized states in the energy gap slow transport by 2−5 orders of magnitude, depending on the photoinjected electron density. Also, relative to the DCrystal values of the anatase single crystal, we estimate 0 that in the absence of transport-limiting traps, the scattering of electrons at grain boundaries in a film slows transport by up to 2 orders of magnitude. Thus, decreasing both energetic and structural disorder is required to approach values of the electron diffusion coefficient for the single crystal. Figure 5 displays the temperature dependence of the electron diffusion coefficient D on the photoelectron density in a
Figure 3. Schematic depicting the model used to explain the dependence of D0 with the particle size d.
spends crossing the particle−particle boundary is rate limiting and that the electron diffusion time within the bulk of a particle is negligible. For these conditions, electron transport in a trapfree three-dimensional network can be described by the relation: D0 = (d2/6Δt), where d is the average distance between electron scattering events and Δt is the average time that electrons spend crossing particle−particle boundaries. From this relation, it follows that
D0 ∝ d 2
Figure 5. Temperature dependence of the electron diffusion coefficient D on the photoelectron density in a DSSC containing a TiO2 nanotube film. The best fit of the D(N,T) data (eq 1) yield D0 = 1.4 × 10−1 cm2 s−1, NC = 2.2 × 1019 cm−3, and T0 = 1426 K. Experimental details are given in Supporting Information.
(2) C
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nanotube film. From the analyses of scanning electron microscopy data in Figure S1 and other measurements (Supporting Information), we determined that the film porosity was 56% and that the average NT had a length of 12 μm, an inner pore diameter of 46.5 nm, a wall thickness of 32.6 nm, and a center-to-center intertube distance of 145 nm. As in the case of the nanoparticle films, the plots converge at a single point (NC, D0) to yield values of the trap-free electron diffusion coefficient D0 (1.4 × 10−1 cm2 s−1), total trap density at the transport edge NC (2.2 × 1019 cm−3), and characteristic temperature T0 (1426 K). A comparison of the D0 values from the plots in Figures 1 and 5 shows that the trap-free electron diffusion coefficient is 2 orders of magnitude larger in the nanotube arrays (1.4 × 10−1 cm2 s−1) than in the nanoparticle films (1.4 × 10−3 cm2 s−1) with an average crystallite size of 15 nm. Moreover, a comparison of NC and T0 values indicates that the total trap density is 7-times larger in the nanotube film (NC of 2.2 × 1019 cm−3) than in the nanoparticle films (NC = 3 × 1018 cm−3). Similarly, the characteristic temperature, which is a measure of the average trap depth of the exponential distribution of band gap states, is more than 2 times greater in the nanotube film (T0 = 1426 K) than in the nanoparticle films (T0 = 641 K). These results indicate that the nanotube film has a larger trap density and a larger proportion of deep traps than the nanoparticle films. These observations are consistent with the results of other studies,27,28,30 which report that transport is only marginally faster in the nanotube arrays than in the nanoparticle films, even though the orientationally ordered nanotube film morphology should favor much faster transport. Figure 6 illustrates schematically the structural effects of nanotube and nanoparticle film architectures on D0. The trap-
free electron diffusion coefficient is 2 orders of magnitude larger in the TiO2 nanotube array than in the nanoparticle films with an average crystallite size of 15 nm (Figures 1 and 5). As the average crystallite size increases (Figure 2), the D0 values for the nanoparticle films approach that for the nanotube films. Also, electron transport in the individual nanotubes of an array occurs along nominally one-dimensional pathways, whereas the transport in the random nanoparticle network proceeds along three-dimensional pathways. Transport along a one-dimensional pathway is much shorter than transport pathways in a three-dimensional network.29 In addition, the structural disorder associated with the number of grain boundaries and the randomness of the crystallite (grain) orientation is much less in the nanotube arrays than in the nanoparticle films. Indeed, a comparison of the trap-free electron diffusion coefficient for the nanotube array (D0 = 1.4 × 10−1 cm2 s−1) and single crystal (DCrystal = 0.1−0.4 cm2s−1)35 shows that the 0 D0 value for the nanotube array comes close to that of the single crystal, indicating that structural disorder in the nanotube array is significantly reduced. Ambipolar effects associated with the electrolyte are assumed to have little, if any, impact on transport data in this study. An examination of Table 1 shows that changing from one electrolyte to another had no influence on D0 for the nanoparticle films. This result is not surprising inasmuch as changing the electrolyte composition would affect mainly the energy distribution and density of surface traps neither of which would alter D0, which is independent of energetic disorder. Table 1 also shows that the electron-collecting substrates TCO and the Ti foil used for the nanoparticle films also had no effect on the D0 value. This is also understandable inasmuch as the total surface area of the nanoparticle film is several orders of magnitude larger than the contact area between the nanoparticles and the electron-collecting substrate. Thus, the contributions of the electrolyte and charge-collecting substrate to D0 in this study are negligible. In conclusion, both energetic disorder (e.g., localized states in the band gap) and structural disorder (e.g., film architecture) govern transport in TiO2. At normal DSSC operating conditions, energetic disorder is the primary mechanism limiting transport. In the presence of traps, the effects of structural disorder associated with the individual particles (e.g., crystallite size) and different film architectures (e.g., nanoparticle films vs nanotube arrays) are obscured or reduced. Under the condition in which all trap states are fully occupied and, therefore, are electrically inert, electron scattering at particle−particle boundaries in nanoparticle networks is shown to limit diffusion. Increasing the interparticle contact area and reducing orientational disorder in the nanostructured films by changing from a three-dimensional randomly packed nano-
Figure 6. Comparison of the trap-free electron diffusion coefficient D0 in nanoparticle films and in oriented polycrystalline nanotube arrays in values for the single crystal.35 DSSCs with the DCrystal 0
Table 1. Effect of Film Architecture, Electrolyte Composition, and Electron-Conducting Substrate on D0 parameter
Nanoparticles on TCOa
Nanoparticles on Ti foilb
Nanotubes on Ti foilb
d (nm) D0 (cm2 s−1)c T0 (K)c NC (cm−3)c
20 (5.2 ± 0.5) × 10−3 804 ± 34 (3 ± 0.2) × 1018
20 (5.5 ± 0.5) × 10−3 658 ± 21 (6.1 ± 1) × 1018
-(1.4 ± 0.4) × 10−1 1426 ± 78 (2.2 ± 0.2) × 1019
a The electrolyte consisted of 0.6 M 1-butyl-3-methylimidazolium iodide, 0.1 M LiI, 0.05 M I2, 0.5 M 4-tert-butylpyridine, and 0.1 M guanidinium thiocyanate in acetonitle/valeronitrile (85:15, v/v). bThe electrolyte consisted of 0.8 M 1-hexyl-2, 3-dimethylimidazolium iodide and 50 mM iodine in methoxypropionitrile. cFitting parameters (D0, T0, and NC,) were determined from the respective plots in Figure S4 (Supporting Information) for the nanoparticle films and Figure 5 for the nanotube film.
D
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particle network to a one-dimensional array of vertically aligned nanotubes lead to values of the trap-free electron diffusion coefficient approaching those of the single crystal material. This study demonstrate a straightforward approach to probe the impact of structural order and disorder on the transport dynamics in the absence of the interfering contributions of energetic disorder associated with the exponential distribution of band gap states and with surface traps connected with the adsorption of electrolyte species, dye molecules, or impurities. The mechanistic insight gained from this study on the structural effects of different film architectures and grain boundaries on the carrier dynamics should find important usage in controlling the electronic properties of nanoscaled oxide materials for use in optoelectronics, photocatalysis, solar fuel cells, and electrical energy storage devices.
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ASSOCIATED CONTENT
S Supporting Information *
Experimental details and additional data. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Present Addresses
́ Departamento de Fisica Aplicada, CINVESTAV-IPN, Mérida, Yucatán 97310, México. ‡ Corporate R&D, LG Chem Research Park, LG Chem, Ltd., 104−1 Munji-dong, Yuseong-gu, Daejeon, 305−380, Korea. § GE Global Research, 1 Research Circle, Niskayuna, New York 12309. †
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, U.S. Department of Energy, under Contract No. DE-AC3608GO28308.
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REFERENCES
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