Investigation of the Li-Ion Insertion Mechanism for Amorphous and Anatase TiO₂ Thin-Films

300 mm TiN-coated Si wafers were used as substrate for the TiO₂ films. Titanium nitride (TiN) was deposited on the Si substrate by ALD in a Pulsar 3000 reactor (ASM). Before deposition, the Si wafer was cleaned by an ozonated water rinse, followed by an HF/HCl based etch. TiN was chosen as it functions as current collector and diffusion barrier for lithium into the underlying Si.¹⁹ Anatase was deposited directly on full 300 mm TiN-coated Si wafers in the clean room. For am-TiO₂, the TiN-coated Si wafers were manually cleaved in 2 × 2 cm² pieces. Amorphous and anatase TiO₂ films were deposited by ALD using two different processes. Am-TiO₂ films were deposited from a tetrakis dimethylamido titanium (Ti(N(CH₃)₂)₄ or TDMAT) and water precursor at 100°C in a custom built ALD reactor. TDMAT and H₂O were sequentially exposed to the TiN substrate for a total number of 700, 200 or 100 cycles, to deposit films with a nominal thickness of 35, 10 and 5 nm. The TDMAT process is chosen as it was known to form amorphous TiO₂ at a deposition temperature of 100°C.²⁰ Anatase films were deposited at 250°C using Ti(OCH₃)₄ and H₂O as precursors in a Pulsar 3000 reactor (ASM). A total number of 682 cycles (nominal thickness of 35 nm) were adopted, which leads to polycrystalline anatase films.²¹ A short comparison between H₂O and O₃ as the oxygen source was made for anatase films in terms of electrochemical properties (see Figure S1). No significant difference was found between the two precursors, and H₂O was chosen for the remainder of the work. The film thicknesses of the 35 nm anatase and am-TiO₂ films were confirmed using scanning electron microscopy (SEM). From ERDA experiments on TiO₂/TiN samples, it was found that oxygen and carbon impurities were below 1 at.% in the TiN layer (see Figure S2 for ERDA depth profile), and the compositions of the TiO₂ films are given in the results section. The bulk resistivity of our ALD TiN was measured to be around 5 × 10⁻⁶ Ω m.

The amorphous nature of the am-TiO₂ films and crystallinity of the anatase films were determined by grazing incidence X-ray diffraction (GI-XRD) and visualized with transmission electron microscopy (TEM). The film composition was determined with elastic recoil detection analysis (ERDA). GI-XRD was performed with an X-Pert PRO MRD (Panalytical), equipped with a Cu Kα X-ray source. On the incident beam side, a graded parabolic mirror and a 1/32° divergence slit were inserted, and on the diffracted side, a 0.04 rad Soller slit together with a parallel plate collimator. GI-XRD measurements were done at an incidence angle of 1°, and the signal was continuously recorded by scanning in the 2θ direction at a rate of 0.025° s⁻¹. TEM was performed with a Titan G2 (FEI) at an operating voltage of 120 kV. For the TEM sample preparation, a spin-on-carbon and Pt capping layer was applied on top of the TiO₂ layer, and a slice of this stack was removed by a focused ion beam for further analysis. For ERDA, a Cl⁴⁺ ion beam is accelerated to an energy of 8.0 MeV, and impinged onto the sample, using a scatter angle of 40.5°.^22,23 Either incident ions elastically scattered from atoms in the sample, or host atoms elastically recoiled from the sample are detected by a time-of-flight energy telescope. The kinetic energy as well as the speed (time-of-flight) of each atom reaching the detector allows for the identification of the corresponding element in the film. For the analysis, the signal from recoiled atoms were used for all elements except titanium, which is determined from scattered Cl⁴⁺. More information of our ERDA setup can be found in Ref. 14.

A custom-made three-electrode polytetrafluoroethylene (PTFE) cell was used which is clamped onto the substrate using a Kalrez O-ring (exposed surface area of 1.1 cm²) and filled with a liquid electrolyte (10–15 mL). The substrate is sandwiched between a copper foil and the electrochemical cell (see Figure S3). The cell contains two compartments, into which Li metal strips were placed, and which served as the counter and reference electrode. The compartment with the Li reference electrode was connected to the main compartment through a Luggin capillary close to the surface of the working electrode (at 4 mm). Electrical contact is made to the TiN current-collector by scratching the uncovered (Si) side of the sample and applying a Ga-In eutectic paste on the back and edges of the sample, which is then in contact with the copper foil. Note that an O-ring seal prevents the electrolyte solution from contacting the Si substrate and Cu/Ga-In/TiN current collectors (see Figure S3), thus preventing any insertion or alloying reactions to occur with these components. All experiments were performed at room temperature (21°C) using a LiClO₄ in propylene carbonate (PC) electrolyte solution. For ease of preparation, an ampoule containing LiClO₄ (100 g, battery grade, dry, 99.99%, Sigma Aldrich) was dissolved in propylene carbonate (100 mL, 99.7%, Sigma Aldrich), which results in a 0.94 M solution. The substrate edges were softly scratched and covered with a silver paste to contact the TiN current collector. Measurements were done in an Ar filled glove box with O₂ and H₂O levels below 1 ppm. The electrochemical cell was controlled through a PGSTAT101 Autolab (Metrohm) potentiostat/galvanostat, using the Nova 1.10 software. Cyclic voltammetry was performed between 1.0 V and 3.2 V or 0.1 and 3.2 V, with scan rates ranging from 1 mV s⁻¹ to 100 mV s⁻¹. Constant current lithiation and delithiation experiments were done with charging rates (C-rate) between 1 C and 500 C. A rate of 1 C is based on the theoretical capacity of anatase as determined from the Ti content from ERDA and by assuming the reduction of Ti(IV) to Ti(III). PITT was performed in the voltage range of 3.0–1.0 V, with potential step increments of ±10 mV. Each consecutive step was applied after a cutoff current of ±0.44 μA cm⁻² (∼0.1 C) was reached. All potentials are given vs Li⁺/Li.

The crystallinity of the TiO₂ films was examined by GI-XRD (Figure 1a). The 35 nm anatase film show the characteristic diffraction peaks for the (101), (103) and (200) crystal planes, at 2ϑ angles of 25.3°, 36.8° and 48.1°, respectively. On the other hand, the 35 nm am-TiO₂ film is devoid of clear features, besides a peak related to the TiN current collector at 42.5°, which confirms the amorphous nature of the TiO₂ film. TEM analysis of anatase and am-TiO₂ films was also performed. Figure 1b shows the as-deposited anatase thin-film. The polycrystalline anatase structure is clearly revealed. Crystalline grains are detected that span the full thickness of the TiO₂ layer and are 50 to 100 nm in length. Lattice distances obtained after Fast Fourier transform of crystalline regions were matched to the anatase structure. Cross-sectional TEM images of am-TiO₂ were made for as-deposited films (Figure 1c) and for samples after electrochemical testing (Figure 1d). Both for as-deposited and electrochemically cycled am-TiO₂, the structure is seen to be mainly amorphous. Only for a few images, some small crystalline regions were detected (<5 nm), and were indexed to a rutile TiO₂ structure. Overall the am-TiO₂ samples are amorphous and remained so even after electrochemical cycling.

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The compositions determined by ERDA of the 35 nm films are given in Table II. For the anatase film, the O:Ti ratio is 1.7, which shows that the films are oxygen deficient. Also, hydrogen, carbon and nitrogen contamination are below 0.4 at.%. For the am-TiO₂ film, an O:Ti atomic ratio of 1.7 is also measured. In this case, several at.% of hydrogen, carbon and nitrogen impurities are detected, which likely originate from incomplete removal or partial decomposition of the -N(CH₃)₂ ligand during the deposition.

The total Ti content for am-TiO₂ is considerably lower than that of the anatase film even though they have the same thickness, indicating a lower density of the amorphous film. Based on the Ti content, the density for the anatase film was calculated at 3.7 g cm⁻³, which is close to the theoretical density of 3.8 g cm⁻³,²⁴ and 2.3 g cm⁻³ for am-TiO₂. Assuming that 1 Li per Ti can be inserted (i.e. reduction from Ti(IV) to Ti(III)), this corresponds to a maximum capacity of 1230 and 770 mAh cm⁻³ (i.e. 336 mAh g⁻¹) for these anatase and am-TiO₂ films, respectively.

For the first electrochemical tests, cyclic voltammetry (CV) measurements were done in two different potential ranges: 3.2–1.0 V, and 3.2–0.1 V. Fresh anatase and am-TiO₂ films (35 nm thickness) were cycled three times in these potential ranges (Figure 2). During the first three cycles in Figure 2a, anatase films shows a typical reduction peak around 1.6 V, which corresponds to Li⁺-ion insertion (Eq. 1). A small shoulder is apparent after the peak at 1.6 V, which is also typically seen for anatase TiO₂.²⁵ For subsequent cycles in the same potential range, the current in the cathodic region slightly diminishes, which can be attributed to the reduction of surface bound water or decomposition of the electrolyte solution. On the anodic side, a peak around 2.2 and 2.4 V is measured, for the anatase samples scanned to 1.0 and 0.1 V, respectively, which is attributed to Li⁺-extraction. Scanning to 0.1 V results in lower peak current densities for lithiation and delithiation, and shifts the delithiation peaks to a higher potential. On the other hand, from the charge measured during the cathodic and anodic scans, it is found that approximately 30% more lithium can be inserted and extracted into anatase when scanning to 0.1 V. Interestingly, when more lithium is inserted, the delithiation potential is shifted to higher values with broadening of the anodic peak, which suggests a more sluggish delithiation kinetics.

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The CV scans for am-TiO₂ show a quite different behavior compared to anatase (Figure 2b) and the selected potential range now affected the shape of the voltammogram. Am-TiO₂ cycled down to 1.0 V showed no clear peak features in both the cathodic and anodic regions. Subequent scans did not alter the current response. However, when scanned down to 0.1 V the am-TiO₂ was activated with a large cathodic peak at 0.57 V in the first scan. In the reverse scan, a broad anodic peak at 1.6 V for delithiation of am-TiO₂ film is observed, which returns reproducibly in the following scans. Interestingly, from the second cycle on, a reproducible cathodic peak also appears at 1.5 V and is attributed to Li⁺-ion insertion upon reduction of Ti(IV) to Ti(III). The peak around 0.57 V is still present, albeit 200 mV shifted more negative and quickly reduces in intensity upon cycling. A much larger capacity of −1170 mAh cm⁻³ under the cathodic peak at 0.5 V in the first scan versus the +600 mAh cm⁻³ in the anodic scan, points to an irreversible component in the first activation scan. At this point, the exact reaction is unclear, however it must involve some transformation of the amorphous material as merely the formation of an SEI layer cannot explain the activation behavior. Activation of amorphous ALD deposited thin films has been observed also for other material systems.^26,27 For the remainder of the CV analysis, a voltage range of 3.2–0.1 V was adopted.

To further investigate the lithium insertion and extraction kinetics, additional CV experiments of 35 nm am-TiO₂ and anatase films were performed in the 3.0–0.1 V range at varying scan rates between 1 and 100 mV s⁻¹ (Figure 3). The 10, 20, 50 and 100 mV s⁻¹ scans are shown for am-TiO₂ (Figure 3a) and anatase (Figure 3b) films. Note that since am-TiO₂ resulted in higher current densities, the scale of the "current density" axis for am-TiO₂ (Figure 3a) is four times larger than for anatase (Figure 3b). First, the peak potential as a function of scan rate is examined for am-TiO₂ (Figure 3c), and anatase (Figure 3d). For am-TiO₂, at low scan rate, the lithiation and delithiation peak potentials are very close, (1.75 V for lithiation and 1.81 V for delithiation at 1 mV s⁻¹), with an average peak potential, U_av = (U_lith + U_delith)/2, of 1.78 V. The average potential of am-TiO₂ is very near the average potential measured with PITT (see next section), which is about 1.77 V. The average peak potential at low scan rates corresponds to the standard redox potential of the insertion/extraction reactions. Upon increasing the scan rate, mostly the lithiation peak potential shifts to more negative values, which also shifts the average potential. Shifting peak potentials are related to overpotentials induced by charge-transfer resistance and other ohmic resistances such as the ionic and electronic resistance of the electrode. A shift in the average peak potential indicates that the lithiation and delithiation reactions no longer follow Nernstian equilibrium conditions. For am-TiO₂, the cathodic peak potentials shift significantly more than the anodic peak potentials, which shows that lithiation is more kinetically hindered than delithiation. The peak potentials of anatase (Figure 3d) are shifted compared to am-TiO₂, with peak potential values at 1.69 V and 2.26 V (1 mV s⁻¹), for lithiation and delithiation, respectively. The crystalline anatase has potentials determined by a two-phase transformation equilibrium²⁸ whereas amorphous titania follows Nernstian behavior as for solid solutions. Indeed, there is a significant separation in the cathodic and anodic peak potential of about 0.57 V (at 1 mV s⁻¹) for anatase, whereas this is only few tens of millivolts (∼50 mV) for am-TiO₂. The average peak potential (standard redox potential) of anatase at this low scan rate (1.98 V) is about 0.2 V more positive than for am-TiO₂ (1.8 V) showing that they have different thermodynamic properties as well.

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The scan rate dependence of the lithiation peak currents (i_p,lith) for amorphous and anatase films are investigated in Figure 4a. In general, the peak current density for am-TiO₂ is higher than anatase. Importantly, the peak currents for am-TiO₂ are linearly dependent with scan rate (i.e. a slope of 1.0 in the log-log plot), while anatase shows a near-square root dependency (i.e. a slope of 0.58). Hence, insertion is not limited by solid-state diffusion for am-TiO₂, (i_p,lith ∝ ν), while it is for anatase (i_p,lith ∝ ).^29,30 This suggests that the average Li⁺-ion diffusion coefficient is higher for am-TiO₂ than for anatase, since the maximum diffusion distance for Li⁺-ions is the same in both films. The behavior of the diffusion coefficient as a function of electrode potential will be analyzed in more detail by PITT in the next section. The peak currents were also plotted as a function of overpotential (η) in Figure 4b. The lithiation and delithiation overpotentials were determined by subtracting the average or formal potential determined at the lowest scan rate from the measured peak potentials. The plot reveals that for both the lithiation and the delithiation reactions, am-TiO₂ requires a smaller overpotential to achieve a certain peak current, suggesting overall more facile kinetics compared to anatase.

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The rate-performance of the 35 nm anatase and am-TiO₂ films were probed by constant current lithiation and delithiation experiments (Figure 5). Typical potential-capacity profiles for delithiation at 1 C rate are shown in Figure 5a. The lithiation and delithiation steps were performed at the same current density or C-rate. The cutoff potential was 0.1 V and 3.0 V for lithiation and delithiation, respectively. For the analysis, only the delithiation curves were considered to assess the reversible charge stored. The potential-capacity profiles of Figure 5a show quite some differences, and a significantly higher capacity for am-TiO₂ compared to anatase.

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For easier comparison of the potential profile shapes, we normalized the capacities to their maximum value upon reaching the cutoff potential (Figure 5b). The potential profile of anatase shows a clear plateau at 2.0 V typical for a two-phase transformation reaction, whereas am-TiO₂ shows a sloped profile across the full potential range, resembling a a solid solution type insertion. Also, about 20% of the total Li⁺ is inserted/extracted below 1.0 V for am-TiO₂, while only a small fraction is inserted below 1.0 V for anatase TiO₂. The C-rate performance of 35 nm thick anatase and am-TiO₂ films is shown in Figure 5c. At 1 C, anatase reaches 285 mAh cm⁻³ (i.e. 77 mAh g⁻¹ or Li_0.24TiO₂), while am-TiO₂ achieves 851 mAh cm⁻³ (370 mAh g⁻¹ or Li_1.1TiO₂). The stoichiometry of Li_1.1TiO₂ for am-TiO₂ could mean that more than 1 Li/Ti is inserted, or that ERDA slightly underestimated the Ti content (by 10%). It is likely that the latter is the case, as it is known that the ERDA signal for Ti is less accurate than for the heavier elements (at least 4% error is expected). At a rate of 115 C, the accessible capacity for anatase decreases to 11% of the maximum capacity, whereas this is still 67% for am-TiO₂; i.e. about 18 times higher. The enhanced rate performance of am-TiO₂ corroborates well the CV results.

The dependence of film thickness on the rate-performance was investigated for am-TiO₂ films only. Charge/discharge experiments were performed with 35, 10, and 5 nm thin am-TiO₂ films for C-rates between 1−500 C in the voltage range of 3.0–1.0 V to limit the background current which was most prominent for the thinnest film (Figure 6). For comparison, the 35 nm am-TiO₂ films show a volumetric capacity of about 450 mAh cm⁻³ (196 mAh g⁻¹ or Li_0.58TiO₂) at 1 C in this voltage range. Interestingly, the 35 nm films show a rapid drop in capacity for C-rates larger than 10 C with only 10% of the maximum capacity remaining at 500 C. The thinnest films of 10 and 5 nm am-TiO₂, on the other hand, show a smooth and gradual decrease in capacity with C-rate with 50% of the capacity remaining at 500 C. Hence, at these high C-rates, the 5 and 10 nm have about 5 times the volumetric capacity of a 35 nm film.

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The C-rate performance improves as the thickness of the films decreases. This follows from the shorter Li diffusion path for the thinner films. Whereas the CV results showed that the 35 nm films were not limited by bulk diffusion (determined by the peak current), the charge/discharge results show that the delithiation rate is still limited for currents >40 µA cm⁻². This indicates that diffusion may be still limiting at higher charges (Li loadings) than those at the peak current in the cyclic voltammograms. This can be illustrated when plotting the current against lithium loading obtained with the CV experiments (see Figure S4). Since the Li-ion transport properties depend on the Li content (see next section), it is possible that a CV can show no indication of diffusion limitation (i.e. at the peak current), whereas this is still observed in a charge/discharge experiment which probes a much wider capacity range.

The rate-performance of the 10 and 5 nm films is similar and the continuous change in Figure 6 indicates that the kinetics remains fast for all Li loadings. The mechanism for Li insertion and extraction will be discussed further on.

The kinetics of the 35 nm am-TiO₂ and anatase films was studied in more detail using potentiostatic intermittent titration technique (PITT). The electrode potential is stepped in small potential increments of 0.01 V, and subsequent current transients are recorded until the new equilibrium Li-content at the new potential is reached. Since only a small perturbation is applied, the system can be considered in near-equilibrium state. PITT measurements were performed in the voltage range of 3.0–0.1 V for am-TiO₂ and 3.0–1.0 V for anatase as insertion/extraction is negligible for the latter below 1 V (see Figure 5a).

A series of current transients is shown for a selected potential range for am-TiO₂ (Figure 7a) and anatase (Figure 7b). Overall, the current transients for am-TiO₂ and anatase show a quite different response. For am-TiO₂ an exponential-like current decay is measured for each consecutive step over the whole potential range. For anatase, most of the current flows during a certain series of potential steps in a specific potential region. Furthermore, the current spikes are lower, and the time of subsequent steps varies considerably; i.e. from a few seconds to a few thousands seconds. During these long current transients, the current shows a phase nucleation-like behavior, which is marked by first a quick fall, then rise, and finally it falls again as it evolves over time. The incremental charge passed after each potential step is plotted against the electrode potential (Figures 7c–7d). For am-TiO₂ (Figure 7c), lithium ions are inserted and extracted broadly across the whole potential range, with broad peaks centered at 1.77 V for both the incremental insertion and extraction capacity. The peak positions and shapes are very similar to those seen in the cyclic voltammograms and confirms a solid-solution type insertion-extraction. Below 0.5 V an irreversible charge is seen, which points to the contribution of electrolyte solution decomposition at these low potentials. For anatase (Figure 7d), most of the lithium ions are inserted at 1.78 V and extracted at 1.90 V. This is a result of the sudden onset of phase transition between the lithium rich and lithium poor phase.

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The potential-capacity profile is obtained from the integrated charge (vs applied potential) during the PITT experiment. The lithium-ion content (x in Li_xTiO₂) is shown as a function of potential for am-TiO₂ in Figure 7e. The profile is similar to the one obtained during the charge/discharge experiment (see Figure 5a). A stoichiometry up to Li_0.98TiO₂ is obtained during lithiation. A discrepancy between the lithiation and delithiation charge is observed: only 0.87 Li/Ti is extracted during the delithiation step. This is likely attributed to the irreversible component introduced by the electrolyte decomposition at low potentials. There is also slightly less lithium inserted/extracted during PITT compared to the charge/discharge experiment. This could be attributed to some experimental error introduced by the low current (nA) measurements, or an internal self-discharge phenomenon related to the solvent/electrolyte decomposition at low voltage. Alternative, it is possible that lithiation/delithiation of am-TiO₂ at such a slow rate leads to some degradation of the material. The potential-capacity profile reproduced from the cumulated charge of the PITT experiment for anatase (Figure 7f) also matches our previous charge/discharge results (see Figure 5a). Lithium-ions are reversibly inserted/extracted up to Li_0.44TiO₂ (1.89 μAh cm⁻²). In this case, a higher capacity was obtained for the PITT experiment. Since the charge/discharge experiments for anatase were likely diffusion limited at 1 C, it follows that the slower PITT enabled more Li⁺-ions to be inserted/extracted. It is known that the amount of solid-solution insertion into anatase (before phase transition occurs) depends on its particle size.³¹ In our case, the Li-insertion proceeds up to a stoichiometry of Li_0.034TiO₂ before phase transition occurs at 1.78 V. This is similar to what Wagemaker et al. have shown for bulk anatase particles (i.e. 120 nm in size).³¹ From previous reports, the phase transition results in an orthorhombic Li_0.5TiO₂ phase. In our case, after the nucleation-like current transient (i.e. below 1.78 V), an average stoichiometry of Li_0.12TiO₂ is obtained for anatase, suggesting that not all crystallites transformed to the Li_0.5TiO₂ phase. At the end of lithiation (at 1 V), the stoichiometry reaches Li_0.44TiO₂.

By analyzing the current transients, information on the near-equilibrium transport properties can be obtained.³² Analytical solutions to the current transient are available for simple cases, for example based on assumptions of only semi-infinite diffusion (i.e. Cottrell equation),^33,34 or finite-length diffusion with or without inclusion finite reaction kinetics.^35,36 Often, graphical methods are used to determine diffusion time constants by finding maxima in It^1/2 vs t plots (the "Cottrellian region").³² The graphical method can be expanded to include effects of slow reaction kinetics by plotting (It^1/2)⁻¹ vs t^−1/2 for example, and fitting a linear function to the short time domain.³⁷ A problem that arises with such graphical methods, is the often arbitrary selection of the timespan used for fitting and oversimplification of underlying transport phenomena. A slightly more complicated, but vastly more powerful method, is the use of numerical inversion of Laplace transforms (NILT), as shown for example by Montella et al.^38–40 With this method, equivalent circuit models typically used for electrochemical impedance fitting can be transformed from the frequency domain to the time domain, and subsequently fitted by standard non-linear regression of I vs t data (see Figure 8). For example, NILT of the Warburg diffusion impedance is equivalent to the Cottrell equation. The advantage is that any arbitrary model expressed in terms of Laplace functionals can be used, and that the complete time domain can be represented (as opposed to the graphical methods). As the algorithm for NILT, the Gaver-Stehfest method³⁸ is used and implemented in the Mathematica software package,⁴¹ together with a non-linear regression procedure.

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All models suggested in Ref. 42 were tested with our data, such as the model representing finite reaction kinetics together with finite-length Warburg diffusion (FLW) or anomalous diffusion (trapping and release of ions). The model that best fitted our current transients (0.005< χ2< 0.1 for I vs t in μA), is shown in the inset in Figure 8. This relatively simple model consists of a "internal" resistor (R_Ω), Warburg diffusion element (W) and intercalation capacitance (C_int) in series. R_Ω is the sum of charge-transfer resistance (R_ct), series resistance (R_s) and electronic resistance of TiO₂ itself (R_e). From separate experiments, the series resistance is found to be below 100 Ω cm². The Warburg diffusion element has the Warburg coefficient, σ_W, which, together with the intercalation capacitance (C_int) is used to determine the diffusion coefficient. The intercalation capacitance is defined as:³²

where Δq is the incremental charge density integrated under the current transient and ΔU the applied potential step. C_int can either be determined as a fitting parameter, or directly by measuring the charge from the I vs t plot and dividing by the potential step. As a self-consistency check, the fitted value of C_int should be about the same as the measured one. In our case, the fitted C_int was about 1 to 4 times higher than the experimental one (see Figure S5), which is a relatively good match. The diffusion coefficient is given by:³⁵

with l the thickness of the electrode film. This model was successfully applied to the current transients of lithium insertion and extraction in our am-TiO₂ films in the voltage range of 3.0–1.0 V. For anatase TiO₂, the same model was used, but with omission of C_int, as reliable values could not be obtained. In this case, the following analytical solution is available:⁴³

with fitting parameters R_Ω and σ_W as given above. Using the fitting procedures introduced above, R_Ω, σ_W and C_int were determined (see Figure S5—6) and the chemical diffusion coefficient as a function of electrode potential was determined using Eq. 3 for am-TiO₂ (Figure 9a) and anatase (Figure 9b). Note that for anatase, the previously discussed phase nucleation-like transients are not described by the models introduced above, and are therefore omitted from the analysis (i.e. at 1.78 for lithiation and 1.90 for delithiation).

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From Figure 9a, the diffusion coefficient of am-TiO₂ is shown to vary between 10⁻¹¹ and 10⁻¹⁵ cm² s⁻¹ depending on the electrode potential. Specifically, maxima in diffusion coefficient near 1.5 V of 1 × 10⁻¹² cm² s⁻¹ and 6 × 10⁻¹² cm² s⁻¹ are found for lithiation and delithiation, respectively, for which the electrode has the composition of Li_0.34TiO₂ (lithiation) and Li_0.49TiO₂ (delithiation) The potential where the maxima occur are close to the peak potentials from CV and the maxima in incremental charge from PITT (Figure 7c). For anatase (Figure 9b) the diffusion coefficient varies between 10⁻¹¹ and 10⁻¹⁵ cm² s⁻¹ depending on the electrode potential, with sharp minima near the insertion (i.e. 2.6 × 10⁻¹⁴ cm² s⁻¹) and extraction (8.8 × 10⁻¹⁴ cm² s⁻¹) peaks. Although values for the diffusion coefficients of am-TiO₂ and anatase span the same order of magnitude, near the peaks of insertion and extraction, the diffusion coefficient of am-TiO₂ is several orders of magnitude higher. Besides a higher diffusion coefficient, am-TiO₂ also shows an internal resistance that is about ten times lower compared to anatase (see Figure S5—6). As can be seen, the PITT analysis allowed the determination of both the diffusion coefficient as well as the internal resistance, while the CV analysis gave only an indication of the limiting process (diffusion or charge-transfer). Note that although the same PITT model was used to fit the current transients for both films, a striking difference in the D versus U relationship is revealed (i.e. a maximum for am-TiO₂ and minimum for anatase in D vs U). The higher diffusion coefficient for am-TiO₂ at the peak of Li⁺-ion insertion/extraction, together with the low charge-transfer resistance, explains the superior performance as seen from CV and rate-performance experiments.

Based on the previous results, we expect that Li⁺-ion insertion and extraction mechanism is different for am-TiO₂ than for anatase. First anatase is considered, as it follows a behavior more typical for Li⁺-ion insertion materials. From the CV results, Li⁺-ion insertion kinetics of anatase was found to be dominated by diffusion. A schematic of this process is given in Figure 10a, which shows the Li concentration profile in the electrode during lithiation. Note that the concentration drawn in the schematic considers the insertion of both Li⁺ and the accompanying electron, i.e. the reduced Ti(III) indicated by Li_xTi^4−xO₂, and we will refer this combined state as the Li concentration.

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In the case of anatase, three different stages can be identified as x (in Li_xTiO₂) increases:

When TiO₂ is (nearly) empty (t₀), Li⁺-ions are inserted via relatively fast solid-solution, leading to a nearly homogenous Li concentration profile throughout the film. As measured with PITT, the diffusion coefficient is near its maximum for low values of x (>10⁻¹² cm² s⁻¹). In this case, the characteristic diffusion time (τ_D = l²/D) is in the order of tens of seconds.

As x → 0.034, the diffusion coefficient drops dramatically (< 10⁻¹⁴ cm² s⁻¹) and Li builds up within TiO₂ near the electrode/electrolyte interface. A characteristic diffusion time in the order of 1000's of seconds is obtained. As x = 0.034 (t₂), phase-transition initiates segregation of Li-ions at the top of the electrodes to form a Li-rich orthorhombic Li_0.5TiO₂ domain. Any additional Li moves the Li-rich phase further into the empty TiO₂ phase (t₃).

If the Li flux into TiO₂ is higher than the moving Li_0.5TiO₂ phase can accommodate, Li will further accumulate at the top of the electrode near the electrode/electrolyte interface (t₃). It is known for anatase that an increase in the Li concentration (above Li_0.5TiO₂) can lead to a second phase transition (i.e. LiTiO₂), resulting in an additional orders of magnitude reduction in Li-ion diffusion coefficient.^44–46 The formation of a blocking LiTiO₂ domain is considered the main reason for the limited insertion capacity of anatase.

In general, an insertion mechanism where a small increase in Li concentration leads to a sharp decrease in diffusion coefficient, likely forms a blocking interface near the surface (i.e. at the electrode/electrolyte side). In other words, such a mechanism can be considered a "top-down" filling mechanism. As any additional lithium will further decrease its diffusion, such a mechanism can be considered self-limiting and prevents full capacity utilization of the electrode. Such a top-down insertion mechanism has also been formulated before for "thick" anatase TiO₂ films (135 nm) based on optical and electrochemical results.²⁸

Next, it is useful to consider the ideal case of insertion under (near-)equilibrium conditions (Figure 10b). If Li is inserted slowly and without phase-transition, homogenous distribution of Li-ions throughout the electrode can be obtained. At each time (t₁₋₃), the concentration of Li is (nearly) equal across the electrode. This requirement is likely fulfilled for am-TiO₂ during CV scans performed at low scan rate (i.e. 1 mV s⁻¹), since the analysis neither showed diffusion limitations (Figure 4a) nor any influence of overpotentials (Figure 4b).

However, as seen from the CV analysis of am-TiO₂ for higher scan rates, although there was no indication of diffusion limitation, an increasing overpotential was measured. In a system purely controlled by charge transfer kinetics, the overpotential in CV should have a logarithmic dependence on the peak current. In our case, a linear relationship between the peak current and overpotential was measured. From this relationship, an "ohmic" resistance was calculated of about 1.2k Ω cm⁻². This value corresponds quite well with the internal resistance determined using PITT (see Figure S5b) for am-TiO₂. This suggests that the largest contribution to the internal resistance is the electrode resistance (R_e), as this would also follow an ohmic behavior.

For our thin-film electrodes, during Li-ion insertion, the corresponding electrons are introduced via the current-collector. If the electronic conductivity is higher than the ionic conductivity, association of Li⁺ with an electron (e⁻) occurs near electrode/electrolyte interface, as in the case of anatase TiO₂. The neutral Li⁺/e⁻ pair is then primarily transported through the film via diffusion. However, it is known that am-TiO₂ has typically a lower electrical conductivity compared to anatase.⁴⁷ Combined with the fact that am-TiO₂ has a higher diffusion coefficient than anatase, a different insertion mechanism is possible. In this case, association of Li⁺ with e⁻ occurs near the current-collector/electrode interface. Li⁺ is then transported through the film via migration and associates with e⁻ near the current-collector.

This situation for am-TiO₂ can be considered a "bottom-up" fill mechanism, as the Li concentration (i.e. Li⁺/e⁻ pair) grows from the current-collector/electrode to the electrode/electrolyte interface. The benefit of such an insertion mechanism is that Li⁺ are continuously transported through an "empty" TiO₂ phase. As the diffusion coefficient drops several orders of magnitude as x → 1, increasing the Li concentration from the bottom up is the most efficient way to fill the electrode. A schematic showing the bottom-up fill is given in Figure 10c. At t₁, Li-ions are transported toward the current collector, and associate with the electron to form the Li_xTiO₂ phase. In this case, LiTiO₂ forms at the bottom, and as more Li-ions are inserted (t₂), the LiTiO₂ phase grows upwards, until it starts to reach the electrolyte (t₃).

A similar phenomena has been observed for delithiation of LiFePO₄ in a solid-state microbattery using scanning transmission X-ray microscopy.⁴⁸ By following the Fe²⁺/Fe³⁺ states within the electrode using X-ray Absorption Near Edge Structure (XANES), the delithiation/lithiation could be followed microscopically. It was shown that during delithiation of LiFePO₄, the FePO₄ phase grew from the current-collector toward to solid-electrolyte; opposite of what would be expected based on a purely diffusion controlled process. This was explained by the faster Li-ion conductivity within LiFePO₄ compared to the electron conductivity. Similar to our case, the enhanced Li-ion conductivity relative to its electron conductivity will lead to a filling mechanism which occurs opposite of where Li⁺ is inserted. To further support this hypothesis, it would be interesting to perform in situ XANES with am-TiO₂ films and follow the Ti³⁺/Ti⁴⁺ states during lithiation/delithiation.