Spatial Extent of Lithium Intercalation in Anatase TiO2

extraction of lithium ions has taken place a small region at the surface of the electrode has a .... tion of anatase, also indicated in Figure 2, the ...
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J. Phys. Chem. B 1999, 103, 7151-7159

7151

Spatial Extent of Lithium Intercalation in Anatase TiO2 Roel van de Krol,*,† Albert Goossens,‡ and Joop Schoonman§ Laboratory for Inorganic Chemistry, Faculty of Applied Sciences, Delft UniVersity of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands ReceiVed: March 23, 1999; In Final Form: June 21, 1999

Thin smooth anatase TiO2 films are obtained by electron beam evaporation of reduced TiO2. These films show a preferential (004) orientation when deposited on electron beam evaporated amorphous titanium. Electrochemical lithium insertion into these films is studied with several optical and electrochemical techniques. A coloration efficiency of 13 cm2 C-1 is found, which is twice as high as that reported for TiO2 films grown by chemical vapor deposition (CVD). Potential-dependent capacitance measurements show that after the extraction of lithium ions has taken place a small region at the surface of the electrode has a much higher dielectric constant than that of the bulk of the electrode. This is explained by the presence of irreversibly trapped lithium ions in the region where a (reversible) phase transformation from anatase TiO2 to anatase Li0.5TiO2 has occurred. The extent of this region depends strongly on the intercalation potential; values of 7 and 17 nm are found after 2.5 h of intercalation at -1.0 and -1.2 V vs SCE, respectively. The dielectric constant of the modified surface region is found to range between 500 and 900. A scheme is proposed that describes the mechanism of lithium insertion in terms of a moving TiO2|Li0.5TiO2 phase front.

Introduction In recent years, much research effort has been directed toward the development of renewable energy conversion and storage devices. For economically and environmentally viable devices, the right choice of materials is of crucial importance. An important material in this respect is titanium dioxide, whose combination of semiconducting properties and chemical stability makes it a candidate for use in, for example, rechargeable lithium ion batteries1-5 and solar cells.6-8 TiO2 can be used as an electrode material in rechargeable lithium ion batteries, which is based on the ability of the anatase TiO2 lattice to accommodate charge in the form of small foreign ions, such as H+ and Li+. These ions can be inserted and extracted from anatase TiO2 electrodes using an electric field as a driving force, a process referred to as intercalation. The insertion of positively charged ions has to be balanced with an uptake of electrons to preserve overall charge neutrality. For insertion of lithium ions in TiO2, the reaction can be written as

TiO2 + xLi+ + xe- f LixTiO2

(1)

The charge-compensating electrons occupy the conduction band of the TiO2, which results in a dark coloring of the TiO2 (electrochromism) due to free electron absorption. However, the electrons are not completely delocalized but are weakly bound to Ti4+ ions9,10 caused by the ionic character of TiO2. The coloration of TiO2 has therefore also been interpreted as the absorption band corresponding to the Ti3+/Ti4+ transition. A definite assignment is still lacking despite the numerous studies of the electrochromic effect in titanium dioxide.11-22 Earlier studies have reported the composition of lithiumintercalated anatase TiO2 to be LixTiO2, with maximum insertion †

E-mail: [email protected]. E-mail: [email protected]. § E-mail: [email protected]. ‡

ratios ranging from x ) 0.5 to x ) 1.23-25 During intercalation, the originally tetragonal anatase phase (space group I41/amd) undergoes an orthorhombic distortion that results in the Li0.5TiO2 phase (space group Imma).25 The change in symmetry starts at insertion ratios larger than 0.0523 and involves a decrease of the unit cell dimensions along the c axis and an increase along the b axis. The overall distortion of the atom positions accompanying the phase transition is relatively small and results in more regular TiO6 octahedra in Li0.5TiO2 than in anatase TiO2.25 The lithium ions are randomly distributed over half of the available interstitial octahedral sites. The Li-Li interactions are reported to be attractive and strong enough to promote phase separation.23 The Li0.5TiO2 phase considered here is referred to as anatase Li0.5TiO2, as a reference to its parent phase. A different polymorph, known as ramsdellite Li0.5TiO2 (space group Pbnm) has also been reported26 but shall not be considered here. Higher insertion ratios than x ) 0.5 have been reported at elevated temperatures2,23 and for chemical intercalation reactions with n-butyllithium,3,27 which has a potential of 1 V vs Li. Beyond x ) 0.5 the Li-Li interactions become repulsive, which results in a maximum insertion ratio of x ) 0.7 at room temperature.25 Ohzuku et al.4,5,20 report the intercalation product to be Li1.0TiO2 for electrochemical cells at room temperature. However, comparison with later reported diffraction data by Cava et al.25 reveals that the presented X-ray diffraction (XRD) patterns4 indicate the presence of the orthorhombic anatase Li0.5TiO2 phase instead of the suggested cubic LiTiO2 phase. The maximum insertion ratio of x ) 0.5 seems to be the most reliable value for electrochemical intercalation at room temperature.23,28 For practical devices the extent, reversibility, and speed of intercalation are of prime importance. A common way to meet these demands is by using nanostructured electrodes. The large effective surface area provides a concomitant large number of adsorption sites for the intercalating ions, while the high surface-

10.1021/jp9909964 CCC: $18.00 © 1999 American Chemical Society Published on Web 08/10/1999

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to-volume ratio ensures minimal diffusion path lengths. Compared to thin solid films, a three-dimensional network of nanoparticles has a much larger tolerance for mechanical stresses that occur during intercalation, which is beneficial to both the reversibility and cyclability of the device. Although the nanostructured morphology of the electrodes is advantageous from a device point of view, the complex topology also introduces numerous problems for the research on these systems. Reliable values for the effective surface area require laborious adsorption isotherm measurements.28 Advanced techniques, such as electrolyte electroreflectance (EER)29 and intensity-modulated photocurrent spectroscopy (IMPS),30-33 are necessary to gain some qualitative insight into the potential distributions within the nanoparticles34 and the porous film. Here, the mechanism of lithium intercalation in anatase TiO2 is investigated using thin smooth films obtained with electron beam evaporation. Various aspects of the intercalation process can now be studied with detailed knowledge of the electrode surface area, potential distribution, and crystallographic orientation of the sample. Normally, transparent conducting oxides (TCO’s), such as tin-doped indium oxide (ITO) or fluoride-doped tin oxide, are used as a back-contact for current collection. The optical absorption of these (highly doped) semiconducting back-contacts can sometimes lead to unwanted photocurrent contributions. Furthermore, the high concentration gradients of indium, tin, or fluoride at the TCO|TiO2 interface can lead to contamination of the TiO2 film by diffusion of these ions. To avoid these effects, a thin titanium metal film, also made with electron beam evaporation, is used as a back-contact. This approach is similar to that of Lindquist et al.,35 who studied the properties of rutile TiO2 thin films made by partial thermal oxidation of an evaporated titanium metal film.

electrode (SCE). All potentials are vs SCE, unless stated otherwise. The electrolyte used was 1.0 M LiClO4 (Alfa, anhydrous, 99.5%) in propylene carbonate (PC, Alfa, 99%). All chemicals were used as received. The sample was mounted with epoxy resin on a PVC disk with a circular hole through which the sample was exposed to the electrolyte. The exposed surface area of the sample was 7.0 mm2. A potentiostat (EG&G PAR model 283) was used to provide potential control over the sample, in combination with a frequency response analyzer (Solartron model 1255) for capacitance measurements. The constant current discharge curves were recorded with a potentiostat/galvanostat (EG&G PAR model 273). For the optical measurements a 250 W tungsten halogen lamp was used with an Acton Research Corp. S275 grating monochromator. The detection system consisted of a Hamamatsu R636 photomultiplier tube connected to a Keithley 2001 multimeter.

Experimental Aspects Titanium films were deposited on quartz substrates (ESCO, S1-UV grade), cut to 12 × 12 × 1 mm3, by electron beam evaporation of titanium metal (Alfa, 99.99%) contained in a graphite crucible. After the chamber was flushed with argon a few times, the chamber was evacuated to a final background pressure of less than 2 × 10-6 mbar. During deposition of titanium metal, the total pressure decreased to less than 5 × 10-7 mbar, caused by ion-gettering of the titanium. The substrate temperature was kept at 200 °C. The film growth could be monitored with a quartz-crystal microbalance and was approximately 10 nm/min. Directly after the titanium deposition the target turret position was changed for the deposition of titanium dioxide without influencing the vacuum. The target material for the TiO2 deposition was rutile TiO2 powder (Acros Chimica, 99.95+%), reduced at 1000 °C for 6 h in a hydrogen atmosphere to increase its conductivity. By use of again a substrate temperature of 200 °C, TiO2 films were deposited with a constant growth rate of 2.0 nm/min. The vapor phase contains mainly TiO2 and TiO.36 Oxygen was admitted into the system to a partial pressure of 1 × 10-4 mbar to improve the TiO2 stoichiometry. After deposition, the samples were annealed in air for 2 h at 450 °C to further improve the stoichiometry and to obtain a crystalline phase. Structural characterization was performed using a Siemens F-Ω X-ray diffraction spectrometer using Cu KR radiation, and a Philips CM-30 transmission electron microscope. Electrochemical measurements were performed using a threeelectrode electrochemical cell, with a glassy carbon counter electrode and a Philips RE1 saturated calomel reference

Results and Discussion I. Structural Characterization. Figure 1 shows a cross section of a Ti|TiO2 film deposited on amorphous quartz. Two main regions can be distinguished: a titanium film with a thickness of 53 nm and a TiO2 film with a thickness of 135 nm. The surface roughness is approximately 0.3 nm at the quartz|Ti interface and less than 5 nm at both the Ti|TiO2 and TiO2|ambient interfaces. The titanium metal film determines the final surface roughness. During the 2 h annealing process, a fraction of the titanium is oxidized to TiO2, indicated by a small increase in optical transmittance and an increase in the sheet resistance of the titanium film from 36 to 56 Ω/0. The thermally oxidized part of the titanium film can be clearly recognized in Figure 1 as an intermediate layer between the titanium and the TiO2, with a thickness of 24 nm. The absence of contrast changes across a large part of the interface shows that the oxidized part of the titanium film has the same crystal structure and orientation as the evaporated TiO2 film on top of it. The fact that the intermediate layer can be discerned from the evaporated TiO2 film is caused by the presence of large voids. Understanding the formation of these voids requires detailed knowledge of the oxidation mechanism and is beyond the scope of this paper. The TiO2 grain sizes can be measured by tilting the substrate at various angles. The size of the mostly columnar grains ranges from 20 to 135 nm perpendicular to the surface and from 40 to 60 nm parallel to the surface. A significant fraction of the grains extends all the way from the titanium film to the sample surface. High-resolution transmission electron microscopy (TEM) analysis shows that the titanium metal film consists of an amorphous matrix with a few very small crystallites. The size

Figure 1. Transmission electron micrograph of a 135 nm TiO2 film on a 53 nm Ti film on amorphous quartz. The first 24 nm of the TiO2 film is thermally oxidized Ti formed during annealing of the sample.

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Figure 2. X-ray diffraction spectrum of an electron beam evaporated Ti/TiO2 multilayer: (A) as deposited; (B) after annealing at 450 °C in air for 2 h. The inset shows the integrated intensity of the TiO2 (004) peak while tilting the substrate, showing that the majority of the crystallites lie within 10° of the (004) orientation.

of these crystallites varies from 3 to 10 nm. Furthermore, some very small nanometer-sized voids are present in both the titanium metal and the TiO2, which are probably caused by clustering of vacancies. Figure 2 shows an X-ray diffraction spectrum of a TiO2 film before and after annealing for 2 h at 450 °C in air. Before the film is annealed, only a very small, broad peak is observed around 38°, 2θ. After it is annealed, the peaks are sharper and more intense and correspond to the (004) peak of anatase TiO2. No titanium peaks are visible, concordant with the presence of an amorphous titanium phase as observed with high-resolution TEM analysis. Considering the normal peak intensity distribution of anatase, also indicated in Figure 2, the TiO2 films appear to have a preferential (004) orientation, i.e. with the c axis perpendicular to the sample surface. This implies that the closepacked lattice planes are parallel to the surface. The presence of minor (103) and (105) peaks indicates small deviations from a perfect (004) orientation, which is to be expected for polycrystalline thin films. This is also evident from the presence of a small (101) peak, the most intense peak of randomly oriented anatase. To further investigate the extent of this deviation, the (004) peak area is plotted as a function of tilt angle of the sample, shown in the inset of Figure 2. This figure reveals that the deviation from the (004) orientation is limited to approximately 10° for the majority of the crystallites. The 10° deviation agrees with Debye-Scherrer photographs of the films (not shown) in which the dark spot on the (004) ring is smeared out approximately 10° to either side of the center. In an earlier paper37 we reported on electron beam evaporated TiO2 films on ITO-coated glass, deposited under identical conditions (substrate temperature, partial pressure, growth rate). XRD measurements showed that these TiO2 films had a randomly oriented polycrystalline structure, which indicates that the titanium metal film deposited prior to the TiO2 film is responsible for the preferential growth of the TiO2 crystals. It is interesting to note that no traces of rutile are observed. Photocurrent spectral responses of TiO2 films on titanium, grown via anodic oxidation38 and thermal oxidation at 400 °C,35 show that rutile is the preferred phase for TiO2 growth on titanium. However, the evaporated TiO2 films on amorphous Ti surfaces studied here prefer the anatase structure. Even the intermediate layer, which is thermally oxidized titanium, has the anatase structure. The explanation for this is that the density of the initially deposited amorphous phase (3.2-3.65 g/cm3) is comparable to that of anatase (3.84 g/cm3), while the density

Figure 3. (A) Cyclic voltammograms at various scan rates of anatase TiO2 in 1.0 M LiClO4 in PC. The scan rates are 20, 10, 5, 2, 1, 0.5, 0.2, and 0.1 mV/s, and the arrows indicate the direction of increasing scan rates. The inset of part A shows a linear relationship between the absolute anodic (O) and cathodic (b) peak currents of the voltammogram, and the square root of the scan rate. (B) Charge (solid) and transmission (dashed) as a function of potential, recorded during a cyclic voltammogram with a scan rate of 1 mV/s.

of rutile (4.26 g/cm3) is much larger. The conversion to rutile, although thermodynamically favored, does not occur because of the large amount of elastic energy required for densification.36 II. Optical and Electrochemical Characterization. In Figure 3A several cyclic voltammograms, recorded with different scan rates, are shown. The cathodic and anodic current peaks indicate the respective insertion and extraction of lithium ions. At potentials negative from the cathodic peak, side reactions cause an additional contribution to the total current. These side reactions can be reduction of traces of water and/or decomposition of the electrolyte. Figure 3B shows the potential dependence of the charge (solid line) and optical transmission (dotted line), which were simultaneously recorded during the 1 mV/s cyclic voltammogram of Figure 3A. At potentials negative of -1.0 V the amount of charge starts to increase followed by a decrease in optical transmission. The inserted lithium ions are extracted at potentials more positive than -1.3 V, followed by an increase in the transmission. At the end of the reverse scan, the transmission has reached the starting value of 100% again, indicating the excellent reversibility of the intercalation process. The amount of charge needed for extraction is less than that needed for insertion, which indicates the occurrence of side reactions. Analysis of the charge vs potential curves at various scan rates shows that the charge consumed by the side reactions is approximately 3.2 mC/cm2 and decreases with increasing scan rate. The charge contributions of the intercalation reaction and the side reactions are approximately equal at the lowest scan rate (0.1 mV/s), while at the highest scan rate (20 mV/s) the charge consumed by the side reactions is less than 30% of the total charge. The inset of Figure 3A shows that a linear relationship holds between the anodic and cathodic peak currents and the square root of the scan rate, indicating diffusion-controlled reaction kinetics. The large separation between the anodic and cathodic current peaks in Figure 3A and the often observed slow reaction kinetics indicate that the reaction can be classified as irrevers-

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ible.39 The diffusion coefficient can be calculated from the inset of Figure 3A, using eq 2.40

ip ) (2.99 × 105)n(RnR)1/2AD01/2C0*ν1/2

(2)

Here, ip is the peak current in the voltammogram, n and nR the number of electrons involved in the overall and rate-determining processes, A the electrode surface area, ν the scan rate, and D0 and C0* the diffusion coefficient and concentration of the active species, respectively. Both n and nR are taken as unity, and R is taken as 0.5.39 The diffusion of ions through the electrolyte is not taken into account, since ion diffusion in liquids (D0 ≈ 10-5 cm2 s-1)40 is generally much faster than in solid materials. The concentration of lithium ions in the electrolyte (1.0 mol/L) is much smaller than that in the expected endproduct (Li0.5TiO2, 24 mol/L),25 so transport across the interface is not determined by diffusion due to a concentration gradient. However, the current-voltage characteristics (Figure 3) indicate overall diffusion-controlled reaction kinetics. Hence, it is reasonable to assume that the lithium ions can readily cross the electrode|electrolyte interface and that diffusion through the TiO2 electrode is rate-limiting.39 The initial concentration of the active species, C0*, is then equal to the concentration of lithium ions inside the TiO2 close to the interface. Since transport across the interface is assumed to be fast, C0* is given by the maximal attainable lithium concentration in the TiO2, which is 24 mol/L (i.e., Li0.5TiO2, limit imposed by Li-Li repulsive interactions).25 For the cathodic reaction (Li+ insertion) a diffusion coefficient of 7.8 × 10-15 cm2 s-1 is obtained from eq 2. This value for the diffusion coefficient should be regarded as an upper limit, since no correction for the current due to side reactions has been made. An estimated average current contribution of 30% from side reactions would, according to eq 2, lead to a diffusion coefficient of 3.8 × 10-15 cm2 s-1, in good agreement with the value of 9 × 10-15 cm2 s-1 reported for planar TiO2 films made by chemical vapor deposition (CVD).41 In the case of the anodic reaction (Li+ extraction), the contribution of side reactions to the maximum peak current is negligible. The concentration C0* is again determined by the concentration of lithium ions in the host lattice, i.e., 24 mol/L for Li0.5TiO2. From this, the diffusion coefficient is calculated to be 2.4 × 10-15 cm2 s-1. However, since the extent of the Li0.5TiO2 region is not infinite, the value of C0* decreases during extraction (instead of being constant, as is assumed in eq 2). Hence, the actual value for the diffusion coefficient is expected to be significantly higher. To further investigate the rate of insertion and extraction of lithium ions, a potential step is applied to change from extraction to insertion conditions and vice versa. This method has the advantage that the influence of side reactions will be minor, since it is analogous to the potential sweep method with an infinitely high scan rate. Figure 4 shows a plot of i(t) vs (t - t0)-1/2, from the slope of which the diffusion coefficient of the lithium ions can be calculated using eq 3, the so-called Cottrell equation.40

i(t) )

nFAD01/2C0* π1/2t1/2

(3)

The cathodic part of the curve (insertion, I) appears to be linear, although the slope varies from -300 µA cm-2 s1/2 for the first few seconds to -150 µA cm-2 s1/2 after a few thousand seconds. With a lithium concentration C0* of 24 mol/L, this corresponds to a diffusion coefficient between 5.3 × 10-14 and

Figure 4. Current vs (t - t0)-1/2 after potential steps to insertion (I) and extraction (E) conditions. The potential step, applied at t ) t0 ) 1000 s, is from +4.0 to -1.5 V for insertion and vice versa for extraction. The inset shows the optical density at 650 nm vs time after the potential steps.

1.3 × 10-14 cm2 s-1, in fair agreement with the value of 3.8 × 10-15 cm2 s-1 found from the peak current method. The slope of the anodic part of Figure 4 (extraction, E) shows definite nonlinear behavior, which is caused by a decrease in concentration C0* as the lithium is extracted from the host lattice. As a rough approximation, the diffusion constant can be calculated from the slope in the first few seconds after the potential step. By use of a lithium concentration of 24 × 10-3 mol/cm3 (Li0.5TiO2), the diffusion coefficient is calculated to be 6.8 × 10-12 cm2 s-1 for the first few seconds of extraction, almost 3 orders of magnitudes faster than the insertion reaction. The marked difference between the insertion and extraction rates of the lithium ions is confirmed by the inset of Figure 4, where the change in optical density, i.e. free-electron absorption, is plotted as a function of time after the potential steps to insertion (I) and extraction (E) conditions. It should be noted that the diffusion coefficient for extraction, calculated from the potential step experiment, is much larger than that determined from the potential sweep method. The latter is of the same order of magnitude as that found for the insertion process, in clear contradiction to the observed time dependence of the optical absorption. An explanation for this is that the diffusion coefficient depends on the electric field strength; the maximal transport rate is reached directly after applying a potential step, whereas a potential sweep implies slowly accelerating ion transport. Figure 5 shows a linear relationship between optical density and charge, obtained from the same measurement as shown in Figure 4. From the slope of the curve, a coloration efficiency of 13 cm2 C-1 is obtained for both insertion and extraction. The coloration efficiency for evaporated anatase TiO2 films is significantly higher than for sputtered anatase TiO2 films, for which values of 6-7 cm2 C-1 (λ ) 633 nm) have been found.16,21 For comparison, coloration efficiencies as high as 20 cm2 C-1 have been reported for nanostructured electrodes.13,17 In Figure 6 a constant current discharge curve of lithiumintercalated TiO2 is shown, recorded after charging the sample with lithium ions at a potential of -1.5 V for 2.5 h. The horizontal plateau at -1.15 V, corresponding to 2.14 V vs the standard Li/Li+ redox potential, indicates a phase equilibrium between anatase TiO2 and anatase Li0.5TiO2. Accordingly, only a fraction of the film is transformed, leading to a two-phase system. Since the lithium ions are provided by the electrolyte, it is clear that the phase transformation starts at the surface and then gradually extends into the bulk of the material. It should

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Figure 5. Optical density (650 nm) as a function of charge for insertion and extraction of lithium after a potential step, showing identical coloration efficiencies for insertion and extraction. Higher intercalation levels result in deviations from linearity.

Figure 6. Constant current discharge curve of a 135 nm anatase TiO2 film. The discharge current is 0.14 µA cm-2. The constant potential plateau indicates a two-phase equilibrium.

be noted that the constant potential plateau is significantly higher than previously reported values of 1.78 V vs Li/Li+,2,5,23 which can be attributed to the (unknown) liquid junction potential between the saturated calomel electrode and the nonaqueous electrolyte. Although the liquid junction potential can, in principle, be calculated,40 this is nontrivial and beyond the scope of this study. It is well-known for many intercalation compounds that not all inserted ions can be extracted during the first few cycles.11,28 A small percentage remains in the host lattice, thereby changing the properties of the material. A convenient and accurate method to study the donor density in thin smooth films is the MottSchottky analysis.37 The Mott-Schottky equation reads40,42

(

)(

)

1 2 kT ) V - VFB 2 2 e CSC e0rNDA

(4)

where CSC is the differential capacitance of the space charge region, ND the donor density, 0 the vacuum permittivity, r the dielectric constant, V the applied potential, VFB the flatband potential, and other symbols have their usual meanings. To investigate intercalation-induced permanent changes in the sample, the sample is intercalated at a potential of -1.0 V for 2.5 h followed by extraction. Figure 7 shows several MottSchottky plots recorded at different times after starting lithium extraction with a potential step to +2.0 V. Electrochemical impedance spectroscopy results (not shown) confirm that at the applied frequency of 50 kHz, the measured capacitance can be entirely attributed to the space charge capacitance. Hence, little frequency dispersion is observed for these well-defined TiO2

Figure 7. Mott-Schottky plots of thin film anatase after one intercalation cycle to -1.0 V, recorded at various time intervals after the potential step at t ) 0 to extraction conditions (+2.0 V): (A) at t ) 190 s; (B) at t ) 425 s; (C) at t ) 1415; (D) at t ) 5505 s. After curve B was recorded, the potential was stepped to +4.0 V at t ) 1340 s. No more changes were observed after recording curve D. The perturbation was a 50 kHz sine wave with an amplitude of 5 mV, and the scan rate was 5 mV/s. The arrow indicates the scan direction.

films, as shown in detail in a previous paper.37 At the flatband potential, which lies at approximately -0.5 V, no band bending and, therefore, no space charge region are present in the TiO2. At potentials positive from the flatband potential, a depletion layer is formed, and CSC-2 increases. The slope of CSC-2 vs V is proportional to the reciprocal of the donor density, as given by eq 4. At a certain potential the depletion layer reaches the titanium metal back-contact, and the slope of CSC-2 vs V becomes virtually zero because of the high electron concentration in the metal. At higher potentials, say, V > 1.0 V, the system behaves as a parallel plate capacitor, with the fully depleted TiO2 film acting as a dielectric medium.37,43 From the curves of Figure 7 the following TiO2 donor densities are calculated, using r ) 50 (see below) and A ) 7.0 mm2: 8.7 × 1017 cm-3 (A), 5.3 × 1017 cm-3 (B), 2.7 × 1017 cm-3 (C), and 1.4 × 1017 cm-3 (D). Although the extraction current is too low to be measured (1000), the calculated thickness values reach limits of 7 and 17 nm for intercalation potentials of -1.0 and -1.2 V, respectively.

The decrease of the C-2 plateau can be fully explained by the presence of irreversibly trapped lithium ions in the outer part of the film, where the phase transition has occurred. The increase of the polarizability of the film, due to the trapped interstitial lithium ions, leads to a large increase of the dielectric constant. The system can then be described as two capacitors in series, one representing the phase-transformed surface layer with a large dielectric constant due to irreversibly trapped lithium, while the other represents the bulk of the TiO2 film where no phase transformation has occurred. The total capacitance of the system in full depletion, Ct, is given by

Ct )

0r,1r,2A d1r,2 + d2r,1

(6)

where the subscripts 1 and 2 denote the surface and bulk layers, respectively. To determine the thickness of the surface layer, we combined the experimental data from curves B and C in Figure 8 with eq 6. For Ct the value of the capacitance plateau in Figure 8 is taken, r,2 is 50, and d1 + d2 corresponds to the total TiO2 film thickness (135 nm). The results are shown in Figure 9 where the thickness of the surface layer, d1, is plotted as a function of the dielectric constant of the surface layer, r,1. The solid and dashed curves correspond to the capacitance plateaus of curves B and C in Figure 8, respectively. A quantitative calculation of the surface layer thickness requires knowledge of the dielectric constant and vice versa. The surface layer thickness can be estimated from the amount of charge used during extraction of the lithium ions. Assuming a surface layer composition of Li0.5TiO2 in the intercalated state,25,46 values of 4 and 12 nm are found after intercalation for 2.5 h at potentials of -1.0 and -1.2 V, respectively. However, these values should be regarded as lower limits, since the phase transition from TiO2 to Li0.5TiO2 can already occur at Li/Ti ratios significantly smaller than 0.5.23,46 Therefore, some fraction of the Li0.5TiO2 phase will have Li/Ti ratios smaller than 0.5, which results in a larger actual surface layer thickness. This is indeed observed in Figure 9, showing minimum values of 7 and 17 nm for intercalation potentials of -1.0 and -1.2 V, respectively. Assuming that the difference between the actual thickness and the thickness calculated from the amount of charge is limited to a few nanometers, the dielectric constant is estimated to be at least 500. The presence of a thin surface layer with a high dielectric constant results in a Mott-Schottky region with very small C-2

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values. This region extends from the flatband potential to the potential at which the surface layer is fully depleted, after which the depletion layer enters the unmodified TiO2 and a rapid increase of C-2 is observed. Hence, this region results in an apparent increase of the flatband potential. The potential drop across the fully depleted surface layer can be calculated from eq 7, which can obtained by combining eqs 4 and 5:

LD )

( )( 20r eND

1/2

V - VFB -

)

kT e

1/2

(7)

Here, LD is the thickness of the depletion layer, corresponding to d in eq 5. With representative values of LD ) 10 nm, r ) 500, and ND ) 1017 cm-3, (V - VFB) is ≈ kT/e, much too small to explain the observed shift in Figure 8. Such a small potential drop also explains that the shifts of curves B and C in Figure 8, corresponding to surface layers of 7 and 17 nm, are identical, whereas eq 7 predicts a quadratic dependence of the magnitude of the shift on the surface layer thickness. A more likely explanation for the observed shift is the generation of surface states at potentials negative from the flatband potential, i.e. during intercalation. Preliminary cyclic voltammetry measurements (not shown) indeed indicate that surface states are created at V < VFB, resulting in a positive shift of the flatband potential. Further work is in progress to elucidate the exact nature of this effect. Weber et al.43 have reported a large increase of the dielectric constant, up to r ) 880, after proton intercalation in sputtered TiO2 films. They suggested that there are three modes of electrochemical hydrogen incorporation in TiO2: (i) irreversible filling with hydrogen, (ii) filling with hydrogen that can be removed at anodic potentials under illumination, (iii) reversible filling with hydrogen under potential control. The hydrogen is probably trapped at dangling bonds, in a similar way as in amorphous silicon, and its polarizability results in a large increase of the dielectric constant. Another effect observed for hydrogen termination of the dangling bonds is an increase of the photocurrent due to passivation of these bonds, which can act as electron-hole recombination centers. In contrast, Boschloo et al. explain the observed C-V characteristics for hydrogendoped anatase films in terms of a high donor density, without considering changes in the dielectric constant.47 In the present work, illuminating the sample did not result in the extraction of extra lithium ions. However, evidence does exist for lithium intercalation in TiO2 according to modes i and iii. Although lithium is present throughout the film, as shown by Figure 7, the dielectric constant only increases in that part of the film where the phase transformation has taken place. The transformation to Li0.5TiO2 and back can introduce structural disorder in the film, resulting in dangling bonds. Apparently, lithium ions can be irreversibly trapped at these bonds, analogous to the case of hydrogen trapping. Here, the polarizability of the trapped lithium ions causes a large increase of the dielectric constant. However, since lithium is heavier than hydrogen, the dielectric constant of lithium-doped TiO2 will be less than that of hydrogen-doped TiO2. Therefore, the value for the dielectric constant of TiO2 after a lithium insertion/extraction cycle is estimated to range between 500 and 900. An alternative explanation for the decrease of C-2 can be given in terms of a high donor density caused by trapped ionized lithium. If a sufficient number of ionized lithium ions remains in the thin, phase-transformed surface layer under extraction conditions, this layer can become degenerate. Its conductivity will then be very high, almost metallic, and the

Figure 10. Schematic drawing of the intercalation process. Panel A shows the lithium concentration at various stages of intercalation. The critical concentration needed for a phase transition from TiO2 to Li0.5TiO2 is indicated by x*. The length over which the phase transition has occurred is indicated by ∆d. Panel B shows the expected lithium concentration profile during extraction for the case where the lithium ions closest to the electrolyte are extracted first. This implies a second phase front, which moves from the surface toward the existing phase front.

system would behave as a capacitor with the bulk TiO2 as the dielectric medium, while the titanium back-contact and the degenerate surface layer serve as electrodes. The thickness of the dielectric medium is then given by the total TiO2 film thickness minus the thickness of the degenerate layer; the thickness decrease of the dielectric medium would explain the observed decrease of the C-2 plateau. However, depletion of the bulk TiO2 without also depleting the degenerate surface layer is only possible if there is a Schottky barrier at the interface of the degenerate TiO2 surface layer and the bulk TiO2. Formation of a Schottky barrier is very unlikely, since there is no apparent reason for local charge buildup at the interface. Furthermore, one would expect to be able to extract ionized lithium donors with the applied electric field. For these reasons, the interpretation in terms of a degenerate surface layer is rejected. On the basis of the preceding results, the proposed mechanism of lithium intercalation in thin films of anatase TiO2 is shown in Figure 10. Panel A schematically shows the lithium concentration at different times during intercalation. At t ) t1 some lithium is inserted, but the critical concentration x* needed to induce a phase transition from TiO2 to Li0.5TiO2 has not yet been reached. At t ) t2 some TiO2 has been converted to Li0.5TiO2, but the lithium concentration is still less than the maximum Li/Ti ratio of 0.5. At t ) t3 the phase transition has taken place along a distance ∆d, a large part of which has reached the maximum Li/Ti ratio of 0.5. At equilibrium conditions the electrochemical potential of both phases is the same, although their lithium concentration differs. The actual lithium concentration profile depends on the ratios of the lithium diffusion coefficients for TiO2 and Li0.5TiO2. The lithium concentration profile presented in Figure 10A does not obviously correspond to equilibrium conditions but may represent the situation at a certain moment in time after a potential step from extraction to insertion conditions.

7158 J. Phys. Chem. B, Vol. 103, No. 34, 1999 General Discussion The coexistence of two separate phases implies that in describing lithium intercalation kinetics, the lithium diffusion rates in TiO2 and Li0.5TiO2 should both be taken into account. At the beginning of the insertion process, the overall diffusion rate will be determined by the TiO2. Shortly thereafter, part of the outer layer has been transformed into Li0.5TiO2, which will then determine the overall insertion rate. For extraction, two different mechanisms are possible. One mechanism is that the TiO2/Li0.5TiO2 phase front moves back toward the surface, i.e., exactly the reverse of the insertion process. Alternatively, the Li0.5TiO2 to TiO2 phase transformation can start at the surface, resulting in a new Li0.5TiO2|TiO2 phase front moving toward the existing front, as illustrated in Figure 10B. In the first case, the diffusion constant will be determined by the Li0.5TiO2 until this phase has completely disappeared. The extraction rate of the second mechanism will be determined by lithium ions moving through TiO2. Although no conclusive evidence is yet available, the inset of Figure 4 supports the second model, since there is a considerable difference in the rates of insertion and extraction. Specifically, extraction is faster than insertion, indicating a much faster lithium ion diffusion in anatase TiO2 than in Li0.5TiO2. This can be explained by the number of unoccupied octahedral sites per unit cell available for Li+ transport, which is four for TiO2 versus two for Li0.5TiO2. Alternative explanations for the difference in insertion and extraction rates involve the energy barriers associated with the phase transformation,24 loss of solvation energy of the lithium ions in the electrolyte, and the electric field strength, which might be different when going from insertion to extraction conditions. The overall distortion accompanying the phase transformation is not very large, since the unit cell volume increases only by 4% and actually yields less distorted TiO6 octahedra.25,46 The effect of the total electric field has a pronounced influence on the intercalation kinetics. Specifically, in a potential step experiment lithium ion extraction is much faster than in a potential sweep experiment. Furthermore, a 200 mV more negative intercalation potential, applied during the same time, results in the formation of a 2-3 times thicker Li0.5TiO2 layer. The effect of the internal electric field is included in the overall apparent diffusion coefficient, which is a result of the coupled motion of the lithium ions and electrons inside the electrode in the absence of a local space charge.48 Strictly speaking, diffusion coefficients should only be determined for single-phase systems, where the ion concentration profile and ion transport are governed by Fick’s law. In a two-phase system, ion transport is also determined by the velocity at which the phase front moves, which in turn depends on the activation energy of the phase transformation. Most of the equations used with standard techniques to measure ionic diffusivities are derived under the assumption of a Fickian diffusion process. Examples are the Cottrell equation, eq 3, for potential step methods and eq 2 for linear sweep voltammetry. Hence, the values calculated from these equations should be considered as apparent diffusion coefficients and can be significantly different from the chemical diffusion coefficients. Interestingly, Canta˜o et al.15 reported that lithium diffuses only into a thin surface layer of a TiO2 film. The calculated extent of lithium diffusion in their sputtered TiO2 films ranges from 7 to 18 nm, in close agreement with our values for the thickness of the layer in which a phase transformation occurs. They suggested that this limitation was imposed by the thickness of the accumulation layer needed to preserve (local) electroneutrality. However, their interpretation does not explain the

van de Krol et al. observed dependence of the thickness on the intercalation potential, since they showed that the accumulation layer thickness is independent of the applied potential when (V VFB) < -0.25 V. We explain the limited intercalation region by the small diffusion coefficient of lithium ions in Li0.5TiO2, which slows down the diffusion as the Li0.5TiO2 thickness increases, i.e., a self-limiting diffusion process. Of particular interest is the valence state of the trapped lithium species and the nature of the chemical bonding with the surrounding atoms. The large dielectric constant suggests a strongly ionic character of this bond. Hence, the lithium ions may act as electron trapping and/or recombination centers. Since electronic trap levels can have a significant influence on the charge carrier transport and optical properties, more research on the optoelectronic properties of intercalated ions is necessary. Summary and Conclusions Thin, smooth anatase TiO2 films have been prepared with electron beam evaporation of reduced TiO2 followed by oxidation at 450 °C in air. The surface roughness of these films is less than 5 nm. The crystallographic orientation of the TiO2 can be controlled by the choice of substrate. When an amorphous titanium metal film is used as a substrate, anatase TiO2 with a preferential (004) orientation is formed. From Mott-Schottky analysis of the (004) oriented TiO2 films, values of 1.4 × 1017 cm-3 for the donor density and 50 for the dielectric constant are found. Electrochemical insertion of lithium ions into anatase TiO2 results in a phase transformation to Li0.5TiO2 (anatase).23 The transformation starts at the surface of the TiO2 film, after which the phase front gradually moves into the bulk. After extraction, a certain fraction of the lithium ions is irreversible trapped in that part of the film that has been phase-transformed. This trapping probably occurs at dangling bonds, which are a manifestation of disorder introduced during the phase transformation to Li0.5TiO2 and back. The polarizability of the trapped lithium ions causes a large increase of the dielectric constant. The thickness and dielectric constant of the transformed layer can be determined by combining coulometric and capacitance measurements. Thickness values of approximately 7 and 17 nm are found for 2.5 h of intercalation at -1.0 and -1.2 V vs SCE, respectively, while the dielectric constant is estimated to range between 500 and 900. On the basis of these observations, a scheme is proposed that describes the mechanism of lithium intercalation in anatase TiO2. It implies that a simple Fickian diffusion process is inadequate to describe the intercalation kinetics accurately. The striking difference between insertion and extraction rates can be explained by a larger Li+ diffusion coefficient of TiO2 compared to that of Li0.5TiO2, providing an additional explanation to those based on energy barriers accompanying the phase transformation. Acknowledgment. The authors thank Dr. F. D. Tichelaar and Mr. T. R. de Kruijff of the Dutch National Center for High Resolution Electron Microscopy in Delft for the TEM analysis. A.G. expresses his gratitude to the Royal Netherlands Academy of Arts and Sciences for his fellowship. R.v.d.K. thanks Dr. E. M. Kelder for helpful discussions. References and Notes (1) Huang, S. Y.; Kavan, L.; Exnar, I.; Gra¨tzel, M. J. Electrochem. Soc. 1995, 142, L142. (2) Macklin, W. J.; Neat, R. J. Solid State Ionics 1992, 53-56, 694.

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