Investigation of the optical properties of LiTi 2 O 4 and Li 4 Ti 5 O 12 spinel films by spectroscopic ellipsometry

The spinel lithium titanates materials Li4Ti5O12 and LiTi2O4 were fabricated by pulsed laser deposition. High quality and single phase thin films were successfully grown, thus opening the door for a systematic investigation of the optical properties of the spinel system Li1+xTi2-xO4 (0≤ x ≤1/3). The microstructure of Li1+xTi2-xO4 films were characterized by X-ray diffraction and atomic force microscope. The optical properties of the films were studied by spectroscopic ellipsometry at room temperature. The refractive index, extinction coefficient, and the thickness of the films were obtained by fitting the experimental data over the entire measured wavelength range. The results show that the two spinel oxides exhibit absolutely different dispersion trends in the visible region. The optical band gap of Li4Ti5O12 is about 3.14eV. 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Introduction
Transition-metal oxides crystallizing in the spinel structure have generated great interest due to rich physical phenomena such as high-temperature superconductor, ferrimagnetism, metalinsulator transition and so on [1][2][3][4].As one of those transition metal oxides, the spinel system Li 1+x Ti 2-x O 4 (0≤ x ≤1/3) has attracted much attention following the discovery by Johnston et al [5].The initial member LiTi 2 O 4 , the only known oxide spinel superconductor, has a superconducting transition temperature (T c ) of 13.7K for bulk materials [5] and display T c of about 11K for thin films [6,7].The ending member Li 4 Ti 5 O 12 is a most promising anode material for Li-ion battery due to its high reaction rate of lithium insertion and extraction [8][9][10].The disappearance of superconductivity with increasing x is correlated with anomalous changes in the lattice parameter with composition and is attributed to the occurrence of a composition-induced metal-semiconductor transition at x≈0.1 from electrical resistivity measurements [2].The metal-semiconductor transition is due to a disproportionation into Lirich and Li-poor compositions at the grain boundaries [11].Dalton et al [12] suggested that all members of Li 1+x Ti 2-x O 4 (LTO) have a cubic symmetry with the space group of Fd3m, where the 8a tetrahedral positions are occupied entirely by lithium ions whereas the 16d octahedral sites are randomly occupied by (x) lithium ions and (2-x) titanium ions per formula unit.LTO films were produced by means of various techniques, such as solid-state reaction, thermal processes, sol-gel method, RF magnetron sputtering method and pulsed laser deposition [13][14][15][16][17], and mostly LTO films are utilized in polycrystalline forms [18].The thermal, electrical and magnetic properties have been extensively investigated for decades.However, the optical research reports of LTO films are few, due to the lack of the single crystals and high quality thin films.In recent years, some researches have been reported on optical properties of Li 4 Ti 5 O 12 [19][20][21].But the analysis on the optical properties of LiTi 2 O 4 film still remain unreported.We have successfully grown high quality single crystalline-like epitaxial LTO thin films.Thus, we could systematic investigate and contrast the optical properties of the two kinds of Li 1+x Ti 2-x O 4 films for the first time.
In the present paper, LTO thin films were prepared by pulsed laser deposition (PLD) on MgAl 2 O 4 (001) substrates.X-ray diffraction (XRD) and atomic force microscopy (AFM) were performed to characterize the microstructure and the surface morphology of the films.We report on ellipsometric measurements of the LTO films in the visible region.Cauchy dispersion function and Drude-Lorentz dispersion function were succesfully used to describe the optical properties of Li 4 Ti 5 O 12 and LiTi 2 O 4 , respectively.The optical interband transitions of LiTi 2 O 4 have been explicated.The results show that the optical properties of the two LTO films are absolutely different.

Experimental method
The Li 4 Ti 5 O 12 and LiTi 2 O 4 thin films were epitaxially grown on (001)-oriented MgAl 2 O 4 substrates via pulsed laser deposition technique in an ultrahigh-vacuum chamber.By controlling the oxygen partial pressure during deposition, we obtained the two end members of the spinel-phase system Li 1+x Ti 2-x O 4 (0≤ x ≤1/3) from a single target.The details of the preparation of the thin films can be found elsewhere [6,7,22].That is, starting with a Li:Ti ratio of 4:5 in the target, a ratio of 1:2 is obtained in the film at low oxygen partial pressures.This effect is discussed in Ref. 16.The LiTi 2 O 4 thin film used in this study show T c of ~11K with narrow transition widths of <0.5K.The microstructure analyses of the films were carried out by X-ray diffraction (D8 Advance, Bruker AXS with Cu-Kα radiation).The surface morphology was analysed by atomic force microscope (NaioAFM, Nanosurf, Switzerland) in taping mode.
Spectroscopic ellipsometry measurement of Li 4 Ti 5 O 12 was recorded with a GES5 Sopra made rotating polarizer spectroscopic ellipsometer, in the wavelength 300-800nm.The ellipsometric measurement of LiTi 2 O 4 was carried out using ultraviolet-near infrared spectroscopic ellipsometry (V-VASE by J. A. Woollam, Inc.), in the wavelength 300-2500nm.All the spectra were taken at an angle of incidence ( ) ϕ of 75° and all the calculations were performed using the Winelli software.Ellipsometry does not directly measure the optical constants or the film thickness, but two ellipsometric angels, Δ and ψ .
By assuming a suitable optical model of the films and finding the best match via a leastsquare fitting calculation, the optical constants of LTO films, which is the function of wavelength, can be determined.As mentioned above, we can confirm that the quality of the two films is excellent.and voids (50%).In order to determine the optical constants of LTO films, the MgAl 2 O 4 substrate was measured first by ellipsometry.The optical response of the substrate was described using a model of Cauchy to ensure the Kramer-Kronig consistency.Using the information of the substrate, the ellipsometric spectra were evaluated.A Cauchy dispersion model is adopted to describe the optical constants of Li 4 Ti 5 O 12 thin film.The expression is given by: ( )

Ellipsometry analysis of the LTO
( ) Where A, B, C, D, E, F are the model parameters.The best fitting parameters of the model is displayed in Table 1.The refractive index decreases slowly with the increase of wavelength according to the Cauchy model in Fig. 3(b).The thickness of the film and the roughness layer are 86.13nm and 4.61nm, respectively.The optical band gap Eg of the Li 4 Ti 5 O 12 film was determined using the extinction coefficient from the following Tauc expression: Where E is the photon energy ( hν ≡ ), B is a constant, 4 α πκ λ = is the absorption coefficient and κ is the extinction coefficient.The exponent n depends on the type of optical transition [23].Depending on the type of electronic transition in bulk semiconductors, the exponent is n = 1/2, 2, 1/3 and 2/3 for indirect allowed, direct allowed, indirect forbidden and direct forbidden transitions, respectively.Li 4 Ti 5 O 12 has a direct bandgap, we plotted the curve of ( ) α ν vs hν and extrapolated the linear segments of the curve to get the optical bandgap.As shown in Fig. 4, the optical bandgap is about 3.14 ± 0.12eV.Li 4 Ti 5 O 12 is an insulating nature material, in which the bandgap opens between the occupied O 2p valance states and empty Ti 3d conduction band.Li 4 Ti 5 O 12 is a wide band gap semiconductor and its bandgap value varies widely in the literature.Although our calculated bandgap value significantly exceed the theoretical bandgap values of 2.0eV [24] and 2.3eV [25], there are, nevertheless, reports that the bandgap value of Li 4 Ti 5 O 12 is about 3eV [26] and 3.1eV [27], which is in good agreement with our result.In contrast to Li 4 Ti 5 O 12 , the valence bands of LiTi 2 O 4 are mainly composed of the O 2p states, with partial contributions from Ti 3d orbits.The conduction bands are primarily assigned to the Ti 3d states, and the partially filled Ti 3d states cause LiTi 2 O 4 possessing metallic characteristics [28][29][30][31].Ellipsometry data of LiTi 2 O 4 from 0.496 to 4.13eV (300-2500nm) are shown in Fig. 5(a).By introducing the Drude-Lorentz dispersion model to describe the optical constants of LiTi 2 O 4 thin film, the simulated spectra are in excellent agreement with the measured spectra.The result of optical constants confirms that the spinel LiTi 2 O 4 is a metallic compound.The Drude-Lorentz dispersion model is given by: Drude: ) ) * ( 1 /( *  where P is the polarization; B and C are the mean free path and the inverse of the plasma wavelength, respectively; A, L 0 , γ introduce the intensity, the central wavelength and the width of the peak of Lorentz oscillator.A four-layer model (air/ roughness/ LiTi 2 O 4 / substrate) is used in this situation.To obtain more precise optical constants of LiTi 2 O 4 , the influence of the roughness layer is eliminated.The surface roughness layer was described by

From
output.These angles describe the amplitude and phase of the light, which were changed after reflection from a sample.This change is measured as the ratio () the p (parallel) and s (perpendicular) field components of the light beam defined with respect to the plane of incidence of the sample.The relation between ρ and the optical constants is given by:

Fig. 2 .
Fig. 2. XRD spectra (Cu Kα radiation = 1.5418Å) of the LTO thin films grown on (001) MgAl 2 O 4 substrate, Left: Li 4 Ti 5 O 12 thin film; Right: LiTi 2 O 4 thin film.The surface morphology of the MgAl 2 O 4 substrate, LiTi 2 O 4 thin film and Li 4 Ti 5 O 12 is shown in Fig. 1.Step and terrace structure is clearly observed in MgAl 2 O 4 substrate.The grown LiTi 2 O 4 thin film shows a rather smooth epitaxial thin film surface.While, rougher film morphology was seen in Li 4 Ti 5 O 12 thin film.As presented in Fig. 2, the XRD structure analysis indicated that both LiTi 2 O 4 and Li 4 Ti 5 O 12 thin films were single phase, and the spinel phase reflections were epitaxially matched to the spinel single phase substrate.The full width at half maximum of (004) peaks for LiTi 2 O 4 and Li 4 Ti 5 O 12 are about 0.142 degree and 0.181 degree, respectively, which reveals that both thin films exhibit good orientation.The XRD patterns of the two materials look similar, but the (004) peak of LiTi 2 O 4 (2θ = 43.06°)clearly shifts to a lower 2θ angle compared with that of Li 4 Ti 5 O 12 (2θ = 43.48°).Which is due to the fact that spinel LiTi 2 O 4 has a bulk room temperature lattice parameter of a = 8.405Å and Li 4 Ti 5 O 12 has a = 8.359Å, hence there is a larger compressive lattice mismatch with the spinel

Fig. 3 .
Fig. 3. (a) Measured (dotted) and fitted (lines) ellipsometric spectra cos(2 ψ ) and sin(2ψ )cos( Δ ) of Li 4 Ti 5 O 12 thin film at the incident angle of 75° (b) Refractive index and extinction coefficient for Li 4 Ti 5 O 12 thin film.The measured ellipsometric angles and corresponding fitting results of Li 4 Ti 5 O 12 thin film are shown in Fig. 3(a).According to the analysis of AFM, Li 4 Ti 5 O 12 thin film has a rougher surface.The ellipsometric data are very sensitive to surface condition, so a surface roughness layer was added in the model.A four-layer model (air/ roughness/ Li 4 Ti 5 O 12 / substrate) is utilized to describe the Li 4 Ti 5 O 12 thin film itself.The surface roughness layer was modeled byBruggeman effective-medium approximation (EMA) with a mixture of the material (50%) and voids (50%).In order to determine the optical constants of LTO films, the MgAl 2 O 4 substrate was measured first by ellipsometry.The optical response of the substrate was described using a model of Cauchy to ensure the Kramer-Kronig consistency.Using the information of the substrate, the ellipsometric spectra were evaluated.A Cauchy dispersion model is adopted to describe the optical constants of Li 4 Ti 5 O 12 thin film.The expression is given by:

Fig. 5 .
Fig. 5. (a) Measured (line-dots) and fitted (lines) ellipsometric spectra cos(2 ψ ) and sin(2ψ )cos( Δ ) of LiTi 2 O 4 thin film at the incident angle of 75°(b) Refractive index and extinction coefficient shown for LiTi 2 O 4 thin film at room temperature, the inset shows the second derivative of extinction coefficient.