Exciton-like trap states limit electron mobility in TiO₂ nanotubes

Nanoparticle films have become a promising low-cost, highsurface-area electrodematerial for solar cells and solar fuel production1,2. Compared to sintered nanoparticle films, oriented polycrystalline titania nanotubes offer the advantageof directed electron transport, and are expected to have higher electron mobility3–7. However, macroscopic measurements have revealed their electron mobility to be as low as that of nanoparticle films8,9. Here, we show, through time-resolved terahertz spectroscopy10, that low mobility in polycrystalline TiO2 nanotubes is not due to scattering from grain boundaries or disorderinduced localization as in other nanomaterials11,12, but instead results from a single sharp resonance arising from exciton-like trap states. If the number of these states can be lowered, this could lead to improved electron transport in titania nanotubes and significantly better solar cell performance. Alternative energy sources such as those based on solar power must be developed in order to cut back on greenhouse gas emissions and move away from fossil fuels, and in the last two decades there has been an ever increasing effort to make use of nanomaterials in alternative solar cell designs. One such nanomaterial, discovered in 2001, is composed of ordered titania nanotubes13. It has been proposed that anodic titania nanotubes may have unique electron transport properties that make them an enabling technology for next-generation solar cells4,14,15, including dye-sensitized solar cells (DSSCs)4–6, and in photoelectrochemical cells for the production of solar hydrogen16,17. Both applications require that free carriers (electrons) be transported through an anodic TiO2 electrode, either along the length of nanotubes in the case of nanotube electrodes, or through a porous nanoparticle network by means of a random walk in standard DSSCs2,3,8. Several authors have suggested that nanotubes would be superior to nanoparticle networks regarding the vectorial electron transport required in applications such as DSSCs5,6,18. However, whole-cell evaluation of electron mobility through nanotubes has found that they are not much better than nanoparticle films8. In this study we use time-resolved terahertz spectroscopy (TRTS) to directly probe and reveal the microscopic electron transport properties of nanotube arrays. We have previously used TRTS to directly probe electron transport in TiO2 nanoparticle films 12. TRTS revealed that electrons are surprisingly mobile within nanoparticles, but that transport through the nanoparticle film is impeded by the strong backscattering and/or disorder-induced localization of electrons. In other words, electron localization involves the whole particle and thus suggests structural disorder as being the dominant impediment to transport in nanoparticle films. Ordered TiO2 nanotubes are fabricated by anodizing titanium foil in an electrolyte containing fluoride or chloride, as described in the Methods4–9,13,15–18. The halogen anions in the electrolyte disrupt passivation during the electrochemical oxidation of the titanium foil, resulting in the formation of nanotubes (Fig. 1) as the metal foil is transformed into the oxide15,18. The as-anodized nanotube films are amorphous and are subsequently transformed into polycrystalline anatase by low-temperature annealing4–9,13,15–18. Here, we probe electron injection, cooling and transport in TiO2 nanotubes on a sub-picosecond timescale using TRTS. We find that, unlike nanoparticles, there is no evidence of significant backscattering or disorder-induced localization. Instead, the conductivity spectrum of the nanotubes reveals a distinct resonance at 7.5 meV, which corresponds to an exciton-like entity. Hence, even though macroscopic measurements have shown similarly low electron mobilities in TiO2 nanoparticles when compared to nanotube films, the underlying reasons for this are very different. In previous work we obtained the frequency-dependent complex photoconductivity, ŝ(v) = s1(v) + is2(v), of rutile single crystals and nanoparticle films over terahertz frequencies12. As can be seen in Fig. 2 the single crystal demonstrates ideal Drude conductivity. On the other hand, anatase and rutile nanoparticle films of various sizes (7–200 nm)12,19,20, as well as ZnO nanoparticle and nanowire films11, do not all conform to classical Drude behavior, but instead demonstrate behaviour that can be consistently fit by the extended Drude–Smith model12,19,21,22. In all of these samples, the imaginary conductivity, s2(v), is negative at low frequencies, corresponding to a Drude–Smith parameter c close to –1, which suggests transport dominated by backscattering and/or disorderinduced localization. A representative ŝ(v) spectrum for TiO2 nanotubes is also shown in Fig. 2. In both the nanotube and nanoparticle samples, d.c. conductivity is suppressed, that is, s1,dc,nano≪ s1,dc,crystal , as v 0 (where s1 is the real part of the complex-valued conductivity), suggesting comparably low electron mobility. However, the nanotube spectrum is fundamentally different from that for single-crystal or nanoparticulate TiO2, and is dominated by a sharp resonance at 1.8 THz (7.5 meV). Even though the experimental bandwidth extends only up to 1.6 THz when probing the single crystal and nanoparticle samples, it is clear from the lack of downward curvature in s2 that no oscillator component is present. Furthermore, Tiwana and colleagues recently measured the TiO2 nanoparticle photoconductivity spectrum to 2.0 THz and did not observe a resonant feature20 (see Supplementary Information for a detailed discussion). As can be seen in Fig. 3 and the plots in the Supplementary Information, the resonance at 1.8 THz is present in all polycrystalline nanotube samples, whether annealed at 400 8C or 475 8C, whether stained with N3 (also known as red dye) and photoexcited at 400 nm, or N749 (also known as black dye) and photoexcited at 800 nm. The observed resonance can be fit in all spectra by a single classical Lorentz oscillator (see Supplementary Information for fitting equations and parameter values obtained). Our ŝ(v)