Solid Solutions of Rare Earth Cations in Mesoporous Anatase Beads and Their Performances in Dye-Sensitized Solar Cells

Solid solutions of the rare earth (RE) cations Pr3+, Nd3+, Sm3+, Gd3+, Er3+ and Yb3+ in anatase TiO2 have been synthesized as mesoporous beads in the concentration range 0.1–0.3% of metal atoms. The solid solutions were have been characterized by XRD, SEM, diffuse reflectance UV-Vis spectroscopy, BET and BJH surface analysis. All the solid solutions possess high specific surface areas, up to more than 100 m2/g. The amount of adsorbed dye in each photoanode has been determined spectrophotometrically. All the samples were tested as photoanodes in dye-sensitized solar cells (DSSCs) using N719 as dye and a nonvolatile, benzonitrile based electrolyte. All the cells were have been tested by conversion efficiency (J–V), quantum efficiency (IPCE), electrochemical impedance spectroscopy (EIS) and dark current measurements. While lighter RE cations (Pr3+, Nd3+) limit the performance of DSSCs compared to pure anatase mesoporous beads, cations from Sm3+ onwards enhance the performance of the devices. A maximum conversion efficiency of 8.7% for Er3+ at a concentration of 0.2% has been achieved. This is a remarkable efficiency value for a DSSC employing N719 dye without co-adsorbents and a nonvolatile electrolyte. For each RE cation the maximum performances are obtained for a concentration of 0.2% metal atoms.

. The number of papers dedicated to systematic studies of the effect of heteroatoms and their concentration in the anatase lattice on the performances of DSSCs are far less numerous. For instance, among the papers of Grätzel and coworkers on DSSCs, only two are dedicated to this topic (one to the effect of Ga 3+ and Y 3+ in mesoporous anatase and one to the effect of Nb 5+ in nanocrystalline anatase for DSSCs' photoanodes) 13,14 . Anatase predisposition to be doped with both cations and anions (probably because of its open crystal structure in comparison with TiO 2 more thermodynamically stable polymorph, rutile) may lead to substantial improvements in the performances of photoanodes for both DSSCs and PSSCs. Our research group has been involved in the study of new materials and electrolytes for DSSCs for several years, and interesting results have been achieved and published [15][16][17][18] . One of our papers 16 has shown the beneficial effect of Sc 3+ doping of mesoporous anatase beads on the performances of DSSCs. This result has encouraged a systematic study of the effect of RE cations on anatase beads for the same use. In addition, the development of a new, nonvolatile electrolyte has allowed us to achieve a remarkable efficiency value of 8.1% with a conventional, two-layered (transparent layer + scattering layer) photoanode made of commercial titania sensitized with N719 dye 17 . The aforementioned results have stimulated our research to fully exploit the potential of our new electrolytic composition in conjunction with a better performing photoanode, that is also simpler to be realized, being the functions of the transparent and the scattering layers joined in one layer when anatase beads are used 19 .
Because of their unique properties, rare earth ions lend themselves to a systematic study on anatase electronic properties modulation through the combined effects of both ionic size and dopant concentration with the key opportunity of keeping the same valence state. In fact, they have nearly identical chemical properties (with the notable exceptions of Ce and Eu), they all have the trivalent oxidation state as the most stable one (except for Ce), but their ionic radius (for trivalent cations) decreases monotonically along the series due to the lanthanide contraction effect. Hence, a systematic work of synthesis, characterization and test of DSSC photoanodes containing mesoporous anatase beads doped with RE cations was carried out in our labs. Solid solutions were prepared with all the RE possessing commercially available alkoxides, i.e. Pr, Nd, Sm, Gd, Er, and Yb with concentrations 0.1, 0.2 and 0.3% of total metal atoms.

Results and Discussion
The X-ray diffraction patterns of all samples show only the presence of the reflections due to the anatase phase of TiO 2 . In Fig. 1, panel a, one pattern is given as an example (TiO 2 : Er 3+ 0.2%), while in panel b the positions and the relative intensities of the reference pattern 20 are reported. The results of the Rietveld refinement of the experimental patterns (unit cell parameters and mean crystallite size) are given in Table 1. The dopant nature and its concentration have no substantial effect on the unit cell parameters. This is not surprising, if the small concentration of RE cations in the lattice is considered. Obviously, from powder diffraction patterns no information concerning the positioning of RE cations in the anatase lattice, i.e. substitutional or interstitial, can be inferred. Our previous work on Sc 3+ -containing anatase solid solutions 16 , in which the position of Sc cation was determined by EXAFS spectroscopy, showed that Sc was in substitutional sites up to very high Sc concentrations (10% metal atoms). Hence, we expect to find the same situation in the case of RE cations because of the strong similarity they have with Sc cation. The substitutional hypothesis is also supported by other works for trivalent cations in general 13 . It is worth noting that plotting the crystallite mean size vs. the RE 3+ /Ti 4+ radius ratio 21 for the best performing compositions, i.e. 0.2% metal atoms for all the RE under consideration, a satisfactory linear fit with negative slope can be obtained (Fig. 2). A possible explanation of this trend could lie in the Fajans' rules 22 . Cations of equal charge form compounds with less ionic character as the ionic radius decreases, and their compounds with basic anions (hydroxides 23 , alkoxides, etc) become less basic with decreasing ionic radius. Thus lighter (and consequently bigger) RE cations give more basic alkoxides which may catalyse the hydrolysis reaction and producing more nuclei in the initial stages of the reaction, resulting in smaller particles.
SEM micrographs for the 0.2% metal atoms samples are given in Figs 3 and 4    In Table 2 a summary of the results of BET specific surface area values for 0.2% samples are reported, and also in this case, the results for the other compositions are analogous. All the samples possess quite high specific surface area values, ranging from about 60 to 100 m 2 /g. The mean pore size diameter calculated by the BJH method is around 15-16 nm for all the samples.
In Table 3 the photoanode thickness and the dye loading values are presented. No evident correlation is present between the amount of the adsorbed dye and the specific surface area, also taking into account the film thickness (assuming a constant film density). Besides, no correlation is present between the dye loading and the radius ratios (Figs 5 and 6, respectively). These lacks of correlation, together with the lack of correlation between the open circuit voltage under illumination (Voc) values and the radius ratios (see later), implies that the introduction of RE cations in the anatase lattice modifies the surface chemistry of the solid solutions in a quite unpredictable way. In fact, rare earth ions modify both the chemisorption equilibrium of the dye with the surface and the equilibrium of adsorption of electrolyte additives as TBP, guanidinium cation and Li + ; consequently the Voc values are sensibly affected by blocking effect and/or shifting the TiO 2 conduction band edge 24,25 .
The results obtained from band gap measurements and from the J-V curves under AM 1.5 G simulated sunlight, i.e. η, short circuit current density Jsc, Voc, fill factor FF, series resistance Rs, and in dark, i.e. saturation current J 0 , ideality factor m and calculated Voc are presented in Table 4. The data obtained from the J-V curves in dark were have been calculated by using the modified diode equations: where q is the elementary charge and k B the Boltzmann constant. The terms J 0 and m have been extracted from the high voltage part of the dark current curves where eqn. 1 can be approximated as: The linear fit of the ln J dark vs. V allows to extrapolate J 0 and m from the intercept and the slope, respectively, considering that: For comparison purposes, the data of a DSSC made with mesoporous beads of pure TiO 2 are presented. In Fig. 7 the J-V curves under illumination (panel a) and in dark (panel b) for 0.2% samples are shown.
Two facts immediately stand out: (i) all the RE with the exception of Pr and Nd improve the performances of the devices; (ii) for all the RE the maximum performances are obtained for a concentration of RE cations of 0.2% metal atoms.
A possible explanation of these phenomena may be found in the electron scattering caused by defects. The excessive distortion of the anatase lattice caused by the biggest cations may hinder electron transport and, in fact, the photoanodes made with Pr and Nd doped anatase present the lowest Jsc values. In Fig. 8, Jsc is plotted against the radius ratios for the 0.2% samples and its decreasing trend is quite apparent. The 0.2% optimal concentration is more difficult to explain, but may be a sort of "threshold" value, over which the defect scattering of electrons become so important that any possible beneficial effect would be overcome. A strong support to this hypothesis is the fact that also in the case of Sc 3+ solid solutions,   the best performances have been observed for the same concentration 16 . The plot of the η values vs. the radius ratios ( Fig. 9) shows an asymptotic behaviour which can be fitted by an equation of the type: The highest η value (8.7%) has been obtained for the Er 0.2% sample,. which is a valuable result for a DSSC using a nonvolatile electrolyte and N719 dye without co-adsorbents and/or surface passivating agents. The efficiency value for the Yb 0.2% sample is only slightly lower (8.4%).
No correlation was found between the experimental values of Voc and those calculated by using eqn. 2 (Table 4). Probably the diode model is too simplistic to describe the behaviour of the DSSCs and an indirect proof of this is given by the very high values of the ideality factors. In fact, using a single parameter to describe all the deviations from the ideal diode model may result insufficient, especially when an electrolyte with a relatively low conductivity and high I 3 − anion diffusion coefficient is employed 17 .   The band gap values do not display any correlation with the dopant type and/or its concentration, probably because the concentration values are too low to have a significant effect, as in the case of unit cell parameters in XRD analysis. Electron diffusion lengths and charge collection efficiencies calculated from the fit of EIS spectra are reported in Table 5. Figures 10 and 11 show the trends of the electron diffusion length vs. the radius ratios and of the η values vs. electron diffusion length are shown, respectively for 0.2% samples. The electron diffusion length decreases with an approximately linear trend as the radius ratios increases, while the efficiency increases with an asymptotic law as the electron diffusion length increases. In this last case, the best fit of the values has been obtained with the equation type: x Both these results are in agreement with those obtained from the analyses of J-V curves under light and in dark.
In the case of the Er 0.2% and Yb 0.2% samples electron diffusion length and charge collection efficiency values apparently contradict the photovoltaic efficiency. In fact, the Er 0.2% sample shows higher photovoltaic performances compared to the Yb 0.2% despite possessing lower electron diffusion length and charge collection efficiency. These seemingly unexpected results can be justified by the higher series resistance value for the Yb 0.2% sample and by the following observations: -the efficiency values are very similar, being their difference only slightly higher than the uncertainty on the values, and the same applies to the electron collection efficiency values; -the ratio of electron diffusion length to film thickness is more significant than the diffusion length itself in determining the performances of the cells. Those ratios are practically identically for 0.2% Er and 0.2% Yb, if the uncertainties are taken into account.
From what observed and discussed until now, a fundamental question does not find answer, i.e. why do RE cations (heavier than Sm 3+ and including it) improve the performances of anatase in the photoanodes of DSSC with respect to pure anatase? A possible explanation is that trivalent RE cations, at low concentration levels, suppress the natural oxygen defectivity of anatase 26 which is responsible for electron trapping. In fact, Chandiran et al. 13 experimentally observed a surprising substantial decrease of resistivity in Y 3+ -doped anatase at low dopant concentration (~0.1%) in comparison to pure TiO 2 , since they expected creation of more oxygen vacancies that would theoretically create a trapping effect with an opposite effect on resistivity. In Fig. 12 the Nyquist plots (panel a) and the Bode plots (panel b) for the 0.2% samples and pure TiO 2 are reported. The suppression of the oxygen defectivity by RE cations is supported by the fact that the maximum frequency peak in the mid-frequency range of the phase Bode plot shifts to lower values for the samples containing rare earths ions with respect to pure TiO 2 . The shift is maximum for the best performing samples, i.e. Er 0.2% and Yb 0.2%. Similar features can be observed in the Nyquist plots: the recombination frequency (the maximum in the complex impedance graph) for the doped samples is lower than the one for pure TiO 2 . Consequently, all the RE doped cells have higher recombination lifetimes with respect to pure anatase. This explanation, coupled with the electron scattering by defects, would justify all the trends shown in Figs 8-11.
In Fig. 13 a comparison of normalized IPCE spectra are given for 0.2% samples. While samples containing Pr, Sm, Er and Yb all present very similar behaviours, those containing Nd and Gd are the ones that deviate most. The 0.2% Nd sample shows an enhanced response at lower wavelengths (< 500 nm) and a depressed one at higher wavelengths. The 0.2% Gd sample shows a substantially enhanced response in comparison with the other samples at wavelengths > 500 nm, and this may justify the fact that the cell has a high efficiency (7.9%) though it shows the second shortest electron diffusion length among the 0.2% samples after the Pr containing sample.

Conclusions
Mesoporous beads of solid solution of anatase containing the rare earth cations Pr 3+ , Nd 3+ , Sm 3+ , Gd 3+ , Er 3+ and Yb 3+ with cation concentrations 0.1, 0.2 and 0.3% of metal atoms have been prepared and characterized structurally, morphologically and optically. The nature of the rare earth cation does not substantially affect the morphology of the beads, which presents similar average dimensions, surface area and porosity. Structurally, the rare earth concentration in the lattice seems too low to affect unit cell parameters, while an evident correlation in 0.2% samples between the rare earth cation size and crystallite average size, probably as a result of the Fajans' rules, has been found. The band gap values of the solid solutions do not show significant deviations from that of pure anatase (3.2 eV).
The solid solutions have been used for the preparation of DSSCs' photoanodes using N719 dye and a nonvolatile electrolyte. The type of cation and its concentration have a profound influence on the behavior of the device. While Pr and Nd suppress the performances of the DSSCs, all the others improve them, and the best performances are obtained for a RE concentration of 0.2% metal atoms.
The cells were characterized by J-V curves under light and in dark, EIS spectroscopy and IPCE measurements. The maximum efficiency has been obtained for the sample containing 0.2% Er metal atoms (8.7%).
The structural analysis of the samples has been performed by X-ray powder diffraction using a Panalytical X'Pert Pro MPD diffractometer (Cu Kα radiation, λ = 1.54184 Å) equipped with a X'Celerator ultrafast RTMS detector. An angular range 10-90° in 2θ has been explored. The angular resolution (in 2θ ) was 0.001°. A 0.04 rad soller slit, a 1° divergence slit and a 20 mm mask have been used on the incident beam path, while a 6.6 mm anti-scatter slit and a 0.04 rad collimator have been used on the diffracted beam path. The Rietveld analysis of the diffraction patterns has been performed using the MAUD software package 32 , obtaining the values of the unit cell axes, volume and the mean crystallite size.
The geometrical area of the photoanodes has been measured according to literature procedure 28 . Morphological analysis of the samples has been performed by a FEI Magellan XHR scanning electron microscope.
An A.P.E. Research (Italy) MAP3D-25 stylus profilometer has been used to measure the thickness of photoanodes.
A Shimadzu (Japan) UV2600 UV-Vis spectrophotometer has been used for the quantification of the dye loading on each photoanode (by desorbing the dye after the sensitization with aqueous NaOH 0.02 M solution) and for the determination of the band gap value of the solid solutions. In this latter case, a ISR-2600 Plus integrating sphere has been connected to the spectrophotometer for the purpose, working in reflectance condition. As reflectance reference, BaSO 4 powder has been used. The band gap was calculated fitting the data with the Tauc's plot 33 assuming an allowed indirect interband transition 34 .
Specific surface area and pore size distribution measurements have been carried out using a Quantachrome Autosorb iQ gas sorption analyzer.
The 1286 Electrochemical Interface coupled with a 1260 Frequency Response Analyzer from Solartron Analytical, U.K., using the Full Combo ZPLOT/CorrWare software by Scribner Associates Inc., USA, has been used to collect the J-V curves under illumination and in dark and the electrochemical impedance spectra (EIS). The J-V curves under illumination has been acquired in potential stair-step mode with a step size of 10 mV and a step time of 1 s. Data acquisition has been repeated until a reproducible behaviour was observed. An Asahi Spectra (Japan) HAL-320, AM 1.5 G class A solar simulator has been used for determining the conversion efficiency. A calibrated Asahi Spectra Sun Checker has been used to check the intensity of the radiation to be within ± 1% of 1 sun.
Dark current curves have been collected with the same settings of those ones collected under illumination.
The EIS spectra were obtained under 1 sun illumination provided by a white light led with a DC bias of ~0.5 V. The spectra have been fitted using the ZView software adopting the transmission line model 35 .
The incident photon to current conversion efficiency (IPCE) has been measured in DC mode with a white light bias by a custom-made apparatus 16,36 . The white light bias was given by a white light led coupled with an optical fiber guide. All the measurements has been performed in the wavelength range 400− 800 nm with a scan interval of 5 nm.