Electron Transport at the TiO2 Surfaces of Rutile, Anatase, and

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Electron Transport at the TiO2 Surfaces of Rutile, Anatase, and Strontium Titanate: The Influence of Orbital Corrugation Tarapada Sarkar,†,‡ Kalon Gopinadhan,*,‡ Jun Zhou,† Surajit Saha,‡ J. M. D. Coey,⧧ Yuan Ping Feng,† Ariando,†,‡ and T. Venkatesan*,†,‡,∥,§ †

Department of Physics, National University of Singapore, Singapore 117542 NUSNNI-NanoCore, National University of Singapore, Singapore 117576 ∥ Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576 § Department of Materials Science and Engineering, National University of Singapore, Singapore 119077 ⧧ School of Physics and CRANN, Trinity College, Dublin 2, Ireland ‡

S Supporting Information *

ABSTRACT: The two-dimensional electron gas in SrTiO3 created by an overlayer of amorphous LaAlO3 is compared with those at the TiO2terminated surfaces of rutile and anatase. Differences in conductivity are explained in terms of the limiting Ti−O−Ti bond angles (orbital corrugation), band dispersion, and polaron formation. At 300 K, the sheet conductivity and mobility of anatase exceed those for SrTiO3 or rutile by one or two orders of magnitude, respectively. The electrons in rutile become localized below 25 K.

KEYWORDS: two-dimensional electron gas, rutile, anatase, strontium titanate, mobility, bond angles, anisotropic conductivity

1. INTRODUCTION Conductance in cubic s-band metals such as copper is isotropic, and the lattice manifests itself mainly through electron−phonon scattering. Conversely, the transport of electrons in metal oxides occurs through overlap of cation and anion orbitals. Because these orbitals are directional, the conductance and mobility can be quite anisotropic, and the bond angle may be a critical factor in determining the electronic mobility. To demonstrate this idea, we compare three different crystallographic TiO2 surfaces where we have been able to create a twodimensional electron gas (2DEG), which enables us to explore the differences in transport properties of the surfaces and correlate them with the natural orbital corrugation. In the TiO2 system, the Ti 3d t2g orbitals overlap with the oxygen 2p orbitals. As in superexchange, the Ti−Ti transfer integral is greatest for a bond angle of 180°. A 2DEG can be generated at the surface of SrTiO3 (STO) by covering it with a layer of material having a high affinity for oxygen. Shibuya et al.1 demonstrated metallic behavior at interfaces between amorphous CaHfO3 and STO single crystal substrates. Later, other groups characterized the metallic interfaces between STO substrates and other amorphous oxides.2,3 The forerunner of this work was the demonstration of a 2DEG by Ohtomo et al.4 at the interface of crystalline, polar LaAlO3 (LAO) and a nonpolar STO substrate, where the © XXXX American Chemical Society

2DEG arises in STO to avert a polar catastrophe. However, the amorphous oxides are not significantly polar, and therefore, it was found that the 2DEG arises from the gettering effect of the overlayer, which creates oxygen vacancies at the interface that donate an electron to the Ti conduction band.5 The limited diffusion of oxygen in these materials at room temperatures ensures that oxygen vacancies occur predominantly in the surface layer, although the electrons can be distributed within a few nm of the interface.3,6 Oxygen vacancies are known to introduce a shallow donor level close to the conduction band of SrTiO35,7 which controls the conductivity, thus making STO by far the favorite complex oxide for forming a 2DEG. However, Schladt et al.8 have recently found metallic behavior in rutile at the (101) and (001) surfaces, but not at the (100) and (110) surfaces, by applying an electric field using an ionic liquid gate. The metallization of an insulating oxide in this way opens new prospects for exploring the electronic structure. Furthermore, Minohara et al.9 have demonstrated a termination-dependent metal−insulator transition at the TiO2/LaAlO3 heterointerface. In both cases, the origin of conductivity was attributed to oxygen vacancies at the interface. Received: July 23, 2015 Accepted: October 19, 2015

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DOI: 10.1021/acsami.5b06694 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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ACS Applied Materials & Interfaces

Figure 1. Comparison of the crystal structures of strontium titanate, anatase, and rutile. The 001 axis is vertical, and the surface in each case is a plane with composition TiO2. The Sr, Ti, and O ions are colored in green, blue, and red.

Figure 2. A comparative overview of (a) sheet resistance, (b) carrier concentration, and (c) mobility of the two-dimensional electron gas created by an amorphous LaAlO3 overlayer on the 001 surfaces of strontium titanate, anatase, and rutile. Inset of (a) shows the measurement geometry.

2. EXPERIMENTAL METHODS

In this study, we have succeeded in creating a 2DEG at different surfaces with TiO2 stoichiometry by using an amorphous LAO overlayer. We have investigated transport at the three TiO2-terminated (001) surfaces, which are compared in Figure 1. It can be seen in the figure that the Ti−O−Ti and O−Ti−O bond angles are quite different at the three surfaces. It is reasonable to expect that the bond angle deviating most from 180° will be the limiting one in terms of electron transport. Also, these bonds may show significant anisotropy with respect to the in-plane axes. Hence, one would expect significant differences between the three systems in terms of inplane mobility and anisotropic transport. For strontium titanate and rutile, we have bulk single-crystal surfaces, whereas for anatase, we use high-quality single-crystal films grown by pulsed-laser deposition (PLD). We have studied the anisotropic transport properties of (110) oriented STO and rutile crystals, but in the case of anatase, we have no access to a crystal surface with built-in anisotropy. The 2D nature of the conductance is well-established in the case of STO.6,10 In anatase, we demonstrate the two-dimensional nature of the electron gas by means of the field-dependent magnetoresistance, which is well-fitted by a 2D weak localization model with a localization length of 50 nm (Supporting Information, Figure S2). In addition, the observed carrier density is ∼1 × 1014 cm−2, which is the carrier density typical of 2D systems as reported by many other groups on the LAO− STO system. The deposition is carried out at room temperature, which prevents oxygen vacancy diffusion deep inside. In addition, we calculate the depth of the oxygen vacancy possible with the measured carrier density, which also rules out any possibility of three dimensionality.

Rutile and SrTiO3 single crystals with (001) and (110) orientations were purchased from CrysTec GmbH, Berlin. Synthetic anatase crystals are not commercially available, and natural crystals are inevitably impure. The crystalline phase of (001) oriented anatase grown by PLD on LaAlO3 substrates at 700 °C in an oxygen pressure of 1 × 10−3 Torr using a TiO2 target was of excellent crystalline quality, as attested to by X-ray θ-2θ and ω-scans (Figure S1). The amorphous LaAlO3 thin film (20 nm) overlayers were grown by pulsed laser deposition on all three surfaces at room temperature at different oxygen partial pressures using a KrF excimer laser at a repetition rate of 1 Hz and a fluence of 2 J/cm2 on a LAO target. Temperature-dependent resistivity measurements were taken in the linear four-probe geometry. Hall coefficient and carrier concentration were determined by applying a magnetic field B perpendicular to the film plane in Hall bar geometry with Al wire bonding in a Quantum Design physical property measurement system equipped with a 9 T superconducting magnet. The magnetic field was swept from 9 to −9 T for both of the above measurements, which were performed at a constant current. To remove any inhomogeneity-related contributions, we performed measurements for both positive and negative currents, and the average of these two has been reported. In addition, the amorphous LaAlO3 was deposited at room temperature, which avoids any kind of temperature gradient in the samples. We therefore expect any inhomogeneity related to substrate temperature to be minimal.

3. RESULTS SrTiO3 is the benchmark material among oxides for electron mobility, which at low temperatures becomes comparable to that of silicon. The transport of electrons near the surface of STO is governed by the uppermost TiO2 layers. We show how this transport as a function of temperature compares with that in the uppermost TiO2 layers of rutile and anatase in Figure 2. B


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Figure 3. Temperature dependence of the (a) sheet resistance (Rs) and mobility and (b) the carrier concentration (ne) in SrTiO3. The inset is a plot of dRs/dT vs T, showing evidence for the cubic-tetragonal transition in SrTiO3 at 105 K.

Figure 4. (a) Hall resistance of anatase films and temperature-dependent (b) mobilities and (c) carrier concentrations deduced from the two-carrier model of eq 1.

Anatase. The Hall data are nonlinear (Figure 4a), implying two different carrier contributions to the transport. The inset shows fits of two representative data sets at 30 and 50 K to a two-carrier conduction model

The sheet resistance plotted in Figure 2a reveals delocalized behavior down to 2 K in STO and anatase, although there is an upturn below 100 K in anatase. Rutile, however, exhibits strong localization below 25 K, and the oxide is effectively insulating at low temperature. The carrier density plotted in Figure 2b shows a rapid carrier freeze out below 20 K, and almost constant values at low temperature for the other two oxides. The room temperature value for STO is ten times higher than the lowtemperature value; the behavior for anatase is more complex, reflecting the two-band nature of the transport. The mobility plotted in Figure 2c shows a three-orders-of-magnitude increase with decreasing temperature for STO with saturation below 10 K, whereas for anatase, the mobility increases down to approximately 100 K and then drops. Rutile shows a threeorders-of-magnitude increase in mobility with decreasing temperature, and it then begins to drop below 20 K as the carriers freeze out. At room temperature, the carrier concentrations are roughly 1014 per cm2 for all three oxides, but the mobilities are quite different, increasing in the order rutile < STO < anatase. We now examine each of the oxides in more detail. Strontium Titanate. Figure 3 shows the anisotropic transport properties of STO and the thermal activation of the carrier density. The ferrodistortive cubic to tetratgonal transition below 105 K has little effect on resistance and mobility, although it shows up in the temperature derivative (Figure 3a). There is negligible anisotropy in the transport in the (110) plane at any temperature. The activation energy for the oxygen vacancy-induced carriers is ∼7 meV.

⎛ B⎞ R xy = ⎜ ⎟ ⎝e⎠

( (

n1 μ1 1 + (μ1 B)2

+

n1 μ12 1 + (μ1 B)2 2

n2 μ 2 1 + (μ 2 B)2

)

+

n2 μ 22 1 + (μ 2 B)2

+ B2

(

)

n1 μ12 1 + (μ1 B)2

+

2 n2 μ12

1 + (μ 2 B)2

2

)

(1)

where Rxy is the Hall resistance, e is electronic charge, and B is the magnetic field. The fitted mobilities (μ1, μ2) and electron concentrations (n1, n2) were derived. A reasonable fit shows that one electron density (n1) decreases with a decrease in temperature whereas its mobility (μ1) increases; the other electron density (n2) increases with decreasing temperature with a decrease in mobility (μ2), which is shown in Figure 4b. The two densities in an Arrhenius plot in Figure 4c give activation energies of 10.4 meV for n1 and 4.8 meV for n2. It may be noted that the room-temperature mobilities of anatase, STO, and rutile are 50, 4, and 0.2 cm2 V−1 s−1, respectively. This can be understood in terms of the thermal occupancy of the two types of t2g sub-bands whose degeneracy is lifted by the slight elongation of the oxygen octahedra along the c-axis. Under this distortion, the lower level is the dyz, dzx doublet and the upper level is the dxy singlet.11 At low temperatures the doublet is occupied (heavy electrons), and with increasing temperature, the more mobile dxy orbitals are populated. The activation energy plot indicates that the energy separation of the conducting states is only ∼6 meV. C


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Figure 5. Temperature dependence of the (a) sheet resistance (Rs) and mobility and (b) the carrier concentration (ne) in rutile measured in two perpendicular directions on a (110)-oriented substrate.

Figure 6. Schematic illustrating the position of the donor level Vo. The donor level can accommodate up to one localized electron per oxygen vacancy (pink rectangle) relative to the bottom of the Ti (t2g) band in rutile, anatase, and SrTiO3. The Fermi level and the mobility edge(s) are shown by the blue and red dashed lines. The position of the mobility edge may be correlated with the occupancy of the V0 level.

Rutile. Figure 5 shows the anisotropic transport properties as a function of temperature of the rutile phase measured in two perpendicular crystallographic directions on a (110) substrate. Figure 5a shows the sheet resistance and mobility for the two different orientations. In both cases, the mobility rises substantially with decreasing temperature until localization has set in below 20 K. The carrier density drops off with temperature below 25 K with an activation energy of 8 meV.

d-band is in strontium titanate (Figure S3 and Table S1). However, the dispersion of the lowest d-bands in the bulk alone cannot explain the origin of strong localization in rutile and weak localization in anatase. The two-dimensional character of the conduction in the occupied states in a thin layer at the titanate interface is expected to be sensitive to the in-plane transfer integrals and bond angles. The limiting bond angle is 166° in tetragonal SrTiO3, 155° in anatase, and 81° in rutile. The bond angles are linked to the lattice deformations that give rise to polarons in anatase.18 It was proposed that large polarons are formed in anatase18,19 and small polarons20−23 in rutile. Although there is no small polaron formation in SrTiO3 according to the predictions of Janotti et al.,24 this could be the reason why there is strong localization in rutile but only a weak increase in resistance at low temperature in anatase and none in strontium titanate. In contrast, the high temperature conductivity (where polarons do not play a role) is highest in the case of anatase TiO2 owing to its lowest effective mass. The effective masses are 2−5me25−27 for SrTiO3, 0.6me28,29 for anatase, and 20me30 for rutile, which accounts for the observed differences in conductivity at room temperature. The (110) STO/amorphous LAO interface shows no appreciable anisotropy at any temperature, as expected for a cubic (or near-cubic) structure. This is in contrast with the 2DEG generated at a (110) STO/crystalline LAO interface,31 which may be attributed to interface strain effects in the latter case. However, large anisotropy is observed in rutile TiO2 that can be understood in terms of the limiting bond angle, which is different along the [110] and [001] directions as well as the direction-dependent d-band dispersion.10 The limiting bond angle along [110] is 81°. Along [001], the d-d overlap is direct,

4. DISCUSSION An oxygen vacancy in TiO2 (anatase12 or rutile13,14) or SrTiO315 is known to create a shallow donor level below the conduction band. Because the amorphous LaAlO3 is nonpolar, there is no polar discontinuity, and it is these shallow donor electrons that are responsible for the interface conduction. Furthermore, amorphous LAO, unlike crystalline LAO, does not strain the surface. The lifting of the degeneracy of the Ti t2g orbitals is significant for crystalline LAO, but one may assume that the band structure in the present case is close to bulk. Even though the dominant contribution to oxygen vacancies comes from the surface layer (which may be reconstructed because the LAO is deposited at room temperature), the resultant electrons are likely to travel in the uppermost few layers below the interface. Even if the top layer is reconstructed, the subsequent layers are epitaxial and unstrained; the bulk-like coordination of the Ti atoms in the rutile, anatase, and strontium titanate is preserved, justifying the assumption of the bulk band structure. The low-temperature conductivity is governed by the band structure along the conduction direction, which depends on the orbital overlap, bond length, and angles. Dispersion of the lowest d-band in the Γ-X direction in anatase is roughly twice as large as it is in rutile.16,17 The largest dispersion of the lowest D


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giving lower resistance and higher mobility. In the oxygen vacancy model for the 2DEG, the number of conductions electrons, 1014 per cm2 at room temperature, will be approximately equal to the number of oxygen vacancies. Because the number of oxygen ions on a TiO2 surface is 12 × 1014 cm−2, the vacancies should be distributed over a depth of a nanometer or more with the dominant contribution coming from the uppermost layer. This electron density of ∼1021 cm−3 in all the three cases will cause a Moss−Burstein shift of ∼0.5 eV and should be able to populate the bands beyond the parabolic part near the Γ-point. The donor level near the Fermi energy due to oxygen vacancies must occupy slightly different positions relative to the bottom of the Ti (t2g) band in each case, and there will be a mobility edge in the band due to the random potential fluctuations at Ti sites created by the vacancies. In rutile, the donor level must lie below the mobility edge, whereas in SrTiO3, it lies above it, and the donor levels are emptied. The situation in anatase is more complicated because of the splitting of the t2g band with possibly different mobility edges in the dxy and dyz/dzx bands. A schematic illustrating the proposed electronic structure near the interface in the three titanates is shown in Figure 6.

T.S. conducted the experiments with assistance from K.G., and K.G. and T.V. All authors contribute to the discussion and the writing of the manuscript. T.V. supervised the project. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Singapore National Research Foundation (NRF) under the Competitive Research Programs (CRP Award No. NRF-CRP 8-2011-06 and CRP Award No. NRF-CRP10-2012-02) and the NUS FRC (AcRF Tier 1 Grant No. R-144-000-346-112). We also acknowledge funding support from the Singapore NRF through the SingaporeBerkeley Research Initiative for Sustainable Energy (SinBeRISE) CREATE Programme.

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(1) Shibuya, K.; Ohnishi, T.; Lippmaa, M.; Oshima, M. Metallic Conductivity at the CaHfO3/SrTiO3 Interface. Appl. Phys. Lett. 2007, 91, 232106. (2) Chen, Y. Z.; Bovet, N.; Trier, F.; Christensen, D. V.; Qu, F. M.; Andersen, N. H.; Kasama, T.; Zhang, W.; Giraud, R.; Dufouleur, J.; Jespersen, T. S.; Sun, J. R.; Smith, A.; Nygård, J.; Lu, L.; Büchner, B.; Shen, B. G.; Linderoth, S.; Pryds, N. A high-mobility TwoDimensional Electron Gas at the Spinel/Perovskite Interface of γAl2O3/SrTiO3. Nat. Commun. 2013, 4, 1371. (3) Lee, S. W.; Liu, Y.; Heo, J.; Gordon, R. G. Creation and Control of Two-Dimensional Electron Gas Using Al-Based Amorphous Oxides/SrTiO3 Heterostructures Grown by Atomic Layer Deposition. Nano Lett. 2012, 12, 4775−4783. (4) Ohtomo, A.; Hwang, H. Y. A High-mobility Electron gas at the LaAlO3/SrTiO3 Heterointerface. Nature 2004, 427, 423−426. (5) Lin, C.; Demkov, A. Electron Correlation in Oxygen Vacancy in SrTiO3. Phys. Rev. Lett. 2013, 111, 217601. (6) Liu, Z. Q.; Li, C. J.; Lü, W. M.; Huang, X. H.; Huang, Z.; Zeng, S. W.; Qiu, X. P.; Huang, L. S.; Annadi, A.; Chen, J. S.; Coey, J. M. D.; Venkatesan, T.; Ariando. Origin of the Two-Dimensional Electron Gas at LaAlO3/SrTiO3 Interfaces: The Role of Oxygen Vacancies and Electronic Reconstruction. Phys. Rev. X 2013, 3, 021010. (7) Kan, D.; Terashima, T.; Kanda, R.; Masuno, A.; Tanaka, K.; Chu, S.; Kan, H.; Ishizumi, A.; Kanemitsu, Y.; Shimakawa, Y.; Takano, M. Blue-light Emission at room Temperature from Ar+-Irradiated SrTiO3. Nat. Mater. 2005, 4, 816−819. (8) Schladt, T. D.; Graf, T.; Aetukuri, N. B.; Li, M.; Fantini, A.; Jiang, X.; Samant, M. G.; Parkin, S. S. P. Crystal-Facet-Dependent Metallization in Electrolyte-Gated Rutile TiO2 Single Crystals. ACS Nano 2013, 7, 8074−8081. (9) Minohara, M.; Tachikawa, T.; Nakanishi, Y.; Hikita, Y.; Kourkoutis, L. F.; Lee, J.-S.; Kao, C.-C.; Yoshita, M.; Akiyama, H.; Bell, C.; Hwang, H. Y. Atomically Engineered Metal−Insulator Transition at the TiO2/LaAlO3 Heterointerface. Nano Lett. 2014, 14, 6743−6746. (10) Wang, Z.; Zhong, Z.; Hao, X.; Gerhold, S.; Stöger, B.; Schmid, M.; Sánchez-Barriga, J.; Varykhalov, A.; Franchini, C.; Held, K.; Diebold, U. Anisotropic Two-Dimensional Electron Gas at SrTiO3 (110). Proc. Natl. Acad. Sci. U. S. A. 2014, 111, 3933−3937. (11) Nuspl, G.; Yoshizawa, K.; Yamabe, T. Lithium Intercalation in TiO2 Modifications. J. Mater. Chem. 1997, 7, 2529−2536. (12) Kumar, P. M.; Badrinarayanan, S.; Sastry, M. Nanocrystalline TiO2 studied by Optical, FTIR and X-ray Photoelectron Spectroscopy: Correlation to Presence of Surface states. Thin Solid Films 2000, 358, 122−130. (13) Stausholm-Møller, J.; Kristoffersen, H. H.; Hinnemann, B.; Madsen, G. K. H.; Hammer, B. DFT+U Study of Defects in Bulk Rutile TiO2. J. Chem. Phys. 2010, 133, 144708.

5. CONCLUSIONS We have demonstrated that the oxygen-vacancy-induced 2DEG that has been extensively studied in SrTiO3 can also be created in rutile and anatase. By comparing the distinct properties of the 2DEG SrTiO3 and the two TiO2 polymorphs, which have quite different Ti−O−Ti bond angles, we are able to highlight important differences in metallic conduction in a metallic metal oxide compared to that in a normal metal. High quality (001) anatase grown by pulsed-laser deposition on LaAlO3 substrates shows the highest mobility and lowest sheet resistance at roomtemperature: each of them is an order of magnitude better than for STO. However, its mobility below 50 K is inferior to that of STO because of the formation of large polarons and splitting of the Ti t2g-derived conduction band by the noncubic crystal field. In rutile, the electrons form small polarons, and they are localized below 25 K. The temperature variation of the mobility for the different interfaces has been further rationalized in terms bond angles and the dispersion of the lowest t2g bands. The room temperature mobility of anatase, which is comparable to that of thin layers of MoS232 or WS2,33 may be of interest for low-loss plasmonics.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.5b06694. Detailed discussion about the X-ray diffraction pattern of grown samples, theoretical band structure, and angledependent magnetoresistance along with the 2D weak localization fit (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*E-mail:[email protected]. *E-mail:[email protected]. E


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Electron Transport at the TiO2 Surfaces of Rutile, Anatase, and

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