Investigation of the optical properties of LiTi2O4 and Li4Ti5O12 spinel films by spectroscopic ellipsometry

Minglin Zhao; Jie Lian; Yanli Jia; Kui Jin; Liping Xu; Zhigao Hu; Xiulun Yang; Shishou Kang

doi:10.1364/OME.6.003366

1. Introduction

Transition-metal oxides crystallizing in the spinel structure have generated great interest due to rich physical phenomena such as high-temperature superconductor, ferrimagnetism, metal-insulator transition and so on [1–4]. As one of those transition metal oxides, the spinel system Li_1+xTi_2-xO₄ (0≤ x ≤1/3) has attracted much attention following the discovery by Johnston et al [5]. The initial member LiTi₂O₄, 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 Li₄Ti₅O₁₂ is a most promising anode material for Li-ion battery due to its high reaction rate of lithium insertion and extraction [8–10]. 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 Li-rich and Li-poor compositions at the grain boundaries [11]. Dalton et al [12] suggested that all members of Li_1+xTi_2-xO₄ (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 [13–17], 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 Li₄Ti₅O₁₂ [19–21]. But the analysis on the optical properties of LiTi₂O₄ 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+xTi_2-xO₄ films for the first time.

In the present paper, LTO thin films were prepared by pulsed laser deposition (PLD) on MgAl₂O₄ (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 Li₄Ti₅O₁₂ and LiTi₂O₄, respectively. The optical interband transitions of LiTi₂O₄ have been explicated. The results show that the optical properties of the two LTO films are absolutely different.

2. Experimental method

The Li₄Ti₅O₁₂ and LiTi₂O₄ thin films were epitaxially grown on (001)-oriented MgAl₂O₄ 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+xTi_2-xO₄ (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 LiTi₂O₄ 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 Li₄Ti₅O₁₂ was recorded with a GES5 Sopra made rotating polarizer spectroscopic ellipsometer, in the wavelength 300-800nm. The ellipsometric measurement of LiTi₂O₄ 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 $ψ$ . From the software Winelli, we can get $\tan (ψ)$ and $\cos (Δ)$ , as well as the ellipsometric parameters $\cos (2 ψ)$ and $\sin (2 ψ) \cos (Δ)$ , as 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 $ρ (= r_{p} / r_{s})$ of 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:

ρ = \tan (ψ) \exp (i Δ) = \frac{r_{1 p} + r_{2 p} \exp (- i δ)}{1 + r_{1 p} r_{2 p} \exp (- i δ)} \times \frac{1 + r_{1 s} r_{2 s} \exp (- i δ)}{r_{1 s} + r_{2 s} \exp (- i δ)} = f (n_{1}, n_{2}, n, λ, d)

By assuming a suitable optical model of the films and finding the best match via a least-square fitting calculation, the optical constants of LTO films, which is the function of wavelength, can be determined.

3. Results and discussion

3.1 Microstructure analyses of the LTO

The surface morphology of the MgAl₂O₄ substrate, LiTi₂O₄ thin film and Li₄Ti₅O₁₂ is shown in Fig. 1. Step and terrace structure is clearly observed in MgAl₂O₄ substrate. The grown LiTi₂O₄ thin film shows a rather smooth epitaxial thin film surface. While, rougher film morphology was seen in Li₄Ti₅O₁₂ thin film. As presented in Fig. 2, the XRD structure analysis indicated that both LiTi₂O₄ and Li₄Ti₅O₁₂ 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 LiTi₂O₄ and Li₄Ti₅O₁₂ 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 LiTi₂O₄ (2 $θ$ = 43.06°) clearly shifts to a lower 2 $θ$ angle compared with that of Li₄Ti₅O₁₂ (2 $θ$ = 43.48°). Which is due to the fact that spinel LiTi₂O₄ has a bulk room temperature lattice parameter of a = 8.405Å and Li₄Ti₅O₁₂ has a = 8.359Å, hence there is a larger compressive lattice mismatch with the spinel MgAl₂O₄ substrate (a = 8.08Å). As mentioned above, we can confirm that the quality of the two films is excellent.

Fig. 1 2D images of the LTO thin films and MgAl₂O₄ substrate surfaces performed by AFM, (a) MgAl₂O₄ substrate (b) LiTi₂O₄ thin film; (c) Li₄Ti₅O₁₂ thin film.

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Fig. 2 XRD spectra (Cu Kα radiation = 1.5418 Å) of the LTO thin films grown on (001) MgAl₂O₄ substrate, Left: Li₄Ti₅O₁₂ thin film; Right: LiTi₂O₄ thin film.

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3.2 Ellipsometry analysis of the LTO

The measured ellipsometric angles and corresponding fitting results of Li₄Ti₅O₁₂ thin film are shown in Fig. 3(a). According to the analysis of AFM, Li₄Ti₅O₁₂ 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/ Li₄Ti₅O₁₂/ substrate) is utilized to describe the Li₄Ti₅O₁₂ thin film itself. The surface roughness layer was modeled by Bruggeman 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 MgAl₂O₄ 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 Li₄Ti₅O₁₂ thin film. The expression is given by:

n (λ) = A + B / λ^{2} + C / λ^{4}

k (λ) = D / λ + E / λ^{3} + F / λ^{5}

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.

Fig. 3 (a) Measured (dotted) and fitted (lines) ellipsometric spectra cos(2 $ψ$ ) and sin(2 $ψ$ )cos( $Δ$ ) of Li₄Ti₅O₁₂ thin film at the incident angle of 75° (b) Refractive index and extinction coefficient for Li₄Ti₅O₁₂ thin film.

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Table 1. The best fitting parameters in Cauchy model for the Li₄Ti₅O₁₂ film.

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The optical band gap Eg of the Li₄Ti₅O₁₂ film was determined using the extinction coefficient from the following Tauc expression:

E - E_{g} = {(\frac{4 π κ}{λ}) \frac{h ν}{B}}^{n}

Where E is the photon energy (

\equiv h ν

), B is a constant,

α = 4 π κ / 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. Li₄Ti₅O₁₂ has a direct bandgap, we plotted the curve of

{(α h ν)}^{2}

vs

h ν

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. Li₄Ti₅O₁₂ is an insulating nature material, in which the bandgap opens between the occupied O_2p valance states and empty Ti_3d conduction band. Li₄Ti₅O₁₂ 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 Li₄Ti₅O₁₂ is about 3eV [26] and 3.1eV [27], which is in good agreement with our result.

Fig. 4 The relationship between ${(α h ν)}^{2}$ and photon energy $(h ν)$ known as the Tauc plot for Li₄Ti₅O₁₂ thin film.

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In contrast to Li₄Ti₅O₁₂, the valence bands of LiTi₂O₄ 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 LiTi₂O₄ possessing metallic characteristics [28–31]. Ellipsometry datas of LiTi₂O₄ 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 LiTi₂O₄ thin film, the simulated spectra are in excellent agreement with the measured spectra. The result of optical constants confirms that the spinel LiTi₂O₄ is a metallic compound. The Drude-Lorentz dispersion model is given by:

(5) Drude:

(6)

(7) Lorentz:

(8)

where P is the polarization; B and C are the mean free path and the inverse of the plasma wavelength, respectively; A, L₀,

γ

introduce the intensity, the central wavelength and the width of the peak of Lorentz oscillator. A four-layer model (air/ roughness/ LiTi₂O₄/ substrate) is used in this situation. To obtain more precise optical constants of LiTi₂O₄, the influence of the roughness layer is eliminated The surface roughness layer was described by Bruggeman effective-medium approximation (EMA) with a mixing fraction of 50%, and the thickness of roughness layer is fixed as 1.3nm (originated from AFM test). The best fitting parameters are listed in Table 2, and the thickness of LiTi₂O₄ thin film is 194.8nm. Fig. 5(b) displays the optical constants of LiTi₂O₄ at room temperature as a function of energy, and the inset shows the second derivative spectra of extinction coefficient derived from the numerical calculation of the corresponding optical constants. In the spectrum of the second derivative of extinction coefficient, we can observe that optical transitions labeled X1, X2 and X3 are located at about 0.74eV, 1.17eV and 3.26eV, respectively.

Fig. 5 (a) Measured (line-dots) and fitted (lines) ellipsometric spectra cos(2 $ψ$ ) and sin(2 $ψ$ )cos( $Δ$ ) of LiTi₂O₄ thin film at the incident angle of 75°(b) Refractive index and extinction coefficient shown for LiTi₂O₄ thin film at room temperature, the inset shows the second derivative of extinction coefficient

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Table 2. The best fitting parameters in the Lorentz oscillators and Drude model for the LiTi₂O₄ film.

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The interband transitions in spinel material are very complex, mainly originate from three types of electronic transition process: intervalence charge transfer (IVCT) transitions, intersublattice charge transfer (ISCT) transitions, crystal field (CF) transitions. IVCT transitions are transitions in which an electron, through optical excitation, is transferred from one cation to a neighboring cation. When the two cations are on different crystallographic sites, IVCT transitions are traditionally called ISCT transitions. CF transtions is a single-ion transition, while the former two transitions involve two cations. For normal spinel materials CoFe₂O₄, the absorption feature at 0.83eV corresponds to a CF transition within the spin state of tetrahedrally coordinated Co²⁺ ions, namely between ⁴A₂ and ⁴T₁ bands, Co²⁺ on A site, as reported by Fontijn et al [32]. The tetrahedral sites in LiTi₂O₄ are occupied by lithium ions. The behaviour of Li⁺ is similar to Co²⁺, so we attribute the X1 feature located below ~1eV to the CF transitions between ⁴A₂ and ⁴T₁ bands, which represent the ground state and the excited states, respectively, according to standard crystal-field theory [33]. The broad structures X2 and X3 are interpreted as being contributed by two similarly transitions, namely CT transitions involving O^2- and octahedral Ti³⁺/Ti⁴⁺ ions, ie., O^2-(2p) →Ti³⁺/Ti⁴⁺(3d) for 1.17 (t_2g) and 3.26eV (e_g) structures, similar to spinel LiNi_xMn_2-xO₄ reported by Kim [34]. The Ti_3d orbitals are split by the cubic component of the crystal field into t_2g orbitals and e_g orbitals. The t_2g band is half-filled while the higher-lying e_g band is empty. The broader nature of the t_2g energy-band width compared to the e_g band [30] is reflected in the broader Lorentz oscillator parameter $γ$ shown in Table 2. From the difference between the energies of the CT transitions (X2, X3), the energy splitting between the t_2g and the e_g orbitals was calculated to amount to 2.09eV. For the ideal cubic spinel structure, the splitting energy gap between t_2g and the e_g orbitals is about 1.36eV [29]. However, for the real structure, a small octahedral distortion leads to a broadening of the gap and the value extends to 2.28eV [30]. Our calculated value of the gap is a little smaller than the theoretical reported value. The difference is in the acceptable range.

4. Summary

Li_1+xTi_2-xO₄ with x = 0 and x = 1/3 thin films were deposited onto MgAl₂O₄ substrates by plused laser deposition, and their optical constants were derived using spectroscopic ellipsometry. Good model fits for Li₄Ti₅O₁₂ and LiTi₂O₄ were achieved using Cauchy dispersion model and Drude-Lorentz dispersion model, respectively. The analysis of the extinction coefficient of Li₄Ti₅O₁₂ indicates a wide bandgap of about 3.14eV. To the best of our knowledge, the optical constants of LiTi₂O₄ was observed for the first time, and we try to explain interband transtitions of normal state of LiTi₂O₄. The crystal-field splitting between the e_g and the t_2g states of the octahedral Ti³⁺/Ti⁴⁺ ion estimated from the assigned charge transfer transitions is about 2.09eV.

Funding

National Key Basic Research Program of China (2015CB921003) and the Fund grants No.2016JC027.

Acknowledgments

M. L. Zhao acknowledges the assistance from Ge He and Yujun Shi for proofreading and useful discussion.

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Lorentz		A	L₀ (um)	ϒ
	Peak 1	4.018705	1.655550	1.573365
	Peak 2	0.674966	1.057313	0.633824
	Peak 3	0.331477	0.379688	0.064937
	Peak 4	0.856379	0.286395	2.6694E-3
Drude		P	B	C
		2.332912	0.176578	1.696921

Lorentz		A	L₀ (um)	ϒ
	Peak 1	4.018705	1.655550	1.573365
	Peak 2	0.674966	1.057313	0.633824
	Peak 3	0.331477	0.379688	0.064937
	Peak 4	0.856379	0.286395	2.6694E-3
Drude		P	B	C
		2.332912	0.176578	1.696921

Investigation of the optical properties of LiTi₂O₄ and Li₄Ti₅O₁₂ spinel films by spectroscopic ellipsometry

Abstract

1. Introduction

2. Experimental method

3. Results and discussion

3.1 Microstructure analyses of the LTO

3.2 Ellipsometry analysis of the LTO

4. Summary

Funding

Acknowledgments

References and links

Cited By

Figures (5)

Tables (2)

Equations (4)

Optical Materials Express