Band alignments between SmTiO 3, GdTiO 3, and SrTiO 3

Transcription

1 Band alignments between SmTiO 3, GdTiO 3, and SrTiO 3 Running title: Band alignments between SmTiO 3, GdTiO 3, and SrTiO 3 Running Authors: Bjaalie et al. L. Bjaalie 1, A. Azcatl 2, S. McDonnell 2,a, C. R. Freeeze 1, S. Stemmer 1, R. M. Wallace 2, and C. G. Van de Walle 1,b 1 Materials Department, University of California, Santa Barbara, CA Department of Materials Science and Engineering, The University of Texas at Dallas, Richardson, Texas, a) Present address: Department of Materials Science and Engineering, University of Virginia, Charlottesville, Virginia b) Electronic mail: vandewalle@mrl.ucsb.edu The generation of a two-dimensional electron gas (2DEG) with unprecedented high density at the interface between two complex oxides has spurred interest in the growth and characterization of these materials. Interfaces between SrTiO 3 and the rare-earth titanates SmTiO 3 and GdTiO 3 exhibit 2DEG densities of 3x10 14 cm -2. Band alignments are key descriptors of these interfaces, and we report a joint experimental/computational investigation. Photoemission spectroscopy was used to measure the band alignments at the SmTiO 3 /GdTiO 3 (110) o interface. In parallel, hybrid density functional calculations were performed. The measured and calculated band alignments for both the top of the O 2p band and the Ti 3d lower Hubbard band agree to within 0.13 ev. Our results also shed light on the position of the lower Hubbard band with respect to the O 2p valence band.. 1

2 I. INTRODUCTION Interfaces between perovskite oxides can give rise to a high-density twodimensional electron gas (2DEG), which may enable novel electronic device applications. 1,2 In particular, interfaces between SrTiO 3 (STO) and rare-earth titanates such as LaTiO 3 (LTO), 3,4 GdTiO 3 (GTO), 5 or SmTiO 3 (SmTO) 6 give rise to the maximum 2DEG density (½ electron per unit cell area, or cm 2 ) expected from the polar discontinuity at the interface. 7 The rare-earth titanates are Mott insulators, in which the energy band gap (Mott-Hubbard gap) arises from strong intra-atomic Coulomb electron-electron interactions that split the partially filled Ti 3d bands, separating an occupied lower Hubbard band (LHB) from an unoccupied upper Hubbard band (UHB). The band alignment between the materials in the heterostructure is a key descriptor of the interface, since it determines on which side of the interface the 2DEG will reside, as well as the degree of confinement. In this paper we report a joint experimental/theoretical study of the band alignment between SmTO and GTO. X-ray photoemission spectroscopy (XPS) is used to determine core-level alignments and valence-band positions. In parallel, first-principles calculations based on hybrid density functional theory are used to determine the band alignment. The agreement between measured and calculated alignments for both the top of the O 2p band and the Ti 3d lower Hubbard band is to within 0.13 ev. We also computationally investigate interfaces with STO. The STO/SmTO band alignment is within 0.1 ev of those for STO/GTO, as might be expected based on the similarity in electronic structure between SmTO and GTO. 2

3 II. Experiment A. Growth GTO and SmTO films were grown by hybrid MBE (Veeco GEN 930) using solid source effusion cells for Gd and Sm and a metalorganic precursor to supply titanium and oxygen (titanium tetraisopropoxide, TTIP) as described elsewhere. 8 Films were grown on cubic, single crystalline (001) LSAT substrates at 950 C. All films are epitaxial and single crystalline. The orientation relationship is such that the orthorhombic (110) plane is parallel to the (001) LSAT plane: (110) o // (001) LSAT. There are two domain orientations in the GTO and SmTO films, due to the fact that the substrate is cubic and the films are orthorhombic: [110] o // <100> LSAT and [001] o // <100> LSAT. The presence of these domains does not affect the determination of the alignments. To measure the band offsets ex-situ by XPS, a heterostructure of 4 nm GTO was grown on 10 nm SmTO. A 8 nm GTO film and a 9 nm SmTO film were also grown as a reference (reference sample thicknesses were confirmed by X-ray diffraction and used to calibrate the heterostructures thicknesses). B. XPS XPS data acquisition was performed ex-situ using a monochromatic Al K X-ray source (h = ev), using a take-off angle of 45 and pass energy of 15 ev in apparatus described elsewhere. 9 For XPS peak analysis and deconvolution, the software AAnalyzer was employed, where Voigt line shapes and an active Shirley background were used for peak fitting. 10. The XPS spectrometer was calibrated according to standard ASTM procedures. 11 No charging effects were detected on the survey spectra for all the 3

4 as-received samples, with the adventitious C 1s peak detected at a binding energy of ev for all samples. The valence-band offset for the GTO/SmTO heterostructure was determined as described in section IV B, where the envelopes of the core level Gd 3d 5/2 and Sm 3d 5/2 spectral regions from the GTO and SmTO films were fit until the fit residual was minimized, and the resultant binding energy at the peak fit maximum intensity was recorded. III. MODELLING The first-principles calculations are based on density functional theory 12,13 using the screened hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE) 14 as implemented in the Vienna Ab initio Simulation Package (VASP). 15,16 In the HSE functional, the exchange potential is separated into a long- and short-range part, and Hartree Fock exchange is mixed with the exchange potential from the generalized gradient approximation (GGA) 17 in the short-range part. The extent of this short-range part is determined by a range separation parameter, for which we use the standard value of 0.2 Å 1. The amount of Hartree-Fock exchange mixed with the short-range GGA exchange potential is determined by a mixing parameter, which we also set to the standard value of 25%. The long-range part of the exchange potential and electronic correlation is represented by the GGA functional. The HSE functional yields structural parameters in very good agreement with experiment and provides a reliable description of the electronic structure both for band insulators 18 and Mott insulators. 19 In the rare-earth titanates, HSE correctly produces a gap separating the lower and upper Hubbard bands, 20 in contrast to conventional exchange-correlation functionals such as GGA, which predict these compounds to be metals. The bulk calculations were performed using a 4x4x2 4

5 Monkhorst-Pack k-point mesh. We use projector augmented wave potentials (PAW) 21 and a 500 ev energy cutoff for the plane-wave expansions. All calculations include spin polarization; the exchange interaction is essential to open up the Mott-Hubbard gap in the rare-earth titanates. The band alignments between various materials are calculated using the following procedure. 22 The alignment at an interface A/B is obtained by first performing calculations for bulk materials A and B separately, in which the band positions are determined with respect to the average electrostatic potential in the bulk. Subsequently, the average electrostatic potentials in the two materials are aligned by performing a calculation for an interface, effectively in a superlattice that contains layers of both materials. This calculation allows us to determine the difference in the average electrostatic potential in the bulk-like regions of the superlattice (i.e., far enough from the interface). Obviously this requires that the thickness of each material in the superlattice is large enough to contain a bulk-like region and obtain a converged value for the electrostatic potential alignment. For STO/SmTO and STO/GTO superlattices, we used five layers of each material, and we use the (110) c interface plane (subscript c referring to the coordinate system being that of the cubic 5-atom cell). Overall, the process is analogous to that in the photoemission experiments, except that average electrostatic potentials are used instead of core levels. The superlattice geometry implies that the interfaces are pseudomorphic, i.e., that the in-plane lattice constants of both materials are the same; if the materials have different lattice constants, strain will necessarily be present. The layers in the experimental structure are indeed strained, and we will address those strain effects. 5

6 However, we also want to determine the natural band alignment between the materials at their equilibrium volume. To obtain this alignment, we have to account for the effect of volume change in the interface calculation. This is done by performing another superlattice calculation to calculate the alignment of the electrostatic potential between strained and unstrained volumes of the same material 23 at a homojunction with equilibrium in-plane lattice parameters. Here we used six layers of each material, and we used the (001) c interface plane. The volume change applied was 2%, which is in the linear regime (i.e., we observe a linear dependence of the average electrostatic potential with strain, and the same numbers are found using positive or negative strain). We have previously used this methodology to predict natural band alignments between candidate complex oxides, 7 including alignments between STO and the rare-earth titanate Mott insulators GTO and YTiO 3 (YTO). 24 Starting from the natural band alignments, we can obtain alignments for the materials in arbitrary strain configurations. In the experiments reported here, the SmTO and GTO are strained to match the in-plane lattice constant of LSAT. The lattice parameters of SmTO and GTO are listed in Table I. We determine the band-edge positions from calculating a unit cell of each material in the specific strain state, and perform a homojunction calculation between unstrained and strained material to obtain the shift in the electrostatic potential. 6

7 TABLE I: Calculated and experimental 25 lattice parameters and bond angles, and calculated energy differences between key electronic bands. SmTiO 3 GdTiO 3 HSE Exp. HSE Exp. a (Å) b (Å) c (Å) Vol. (Å 3 ) Ti I -O-Ti II ( ) Ti I -O-Ti III ( ) LHB width (ev) LHB-top O 2p top (ev) UHB-bottom O 2p top (ev) IV. RESULTS AND DISCUSSION A. First-principles results for bulk SmTO and GTO In the Mott insulators SmTO and GTO the valence band (VB) and conduction band (CB) are both derived from the Ti 3d states, with the Ti atoms in the 3+ oxidation state (a Ti 3d 1 electron configuration). This one d electron per Ti atom causes the degenerate Ti bands to split in an occupied lower Hubbard band (LHB) and an empty upper Hubbard band (UHB), forming a Mott-Hubbard gap. Both compounds are stable in the distorted GdFeO 3 -type orthorhombic structure, described by a 20-atom unit cell [Figs. 1(a) and (b)], which corresponds approximately to a 2a x 2a x 2amultiple of the simple cubic 5-atom perovskite unit cell with lattice parameter a. This is in contrast to STO, 7

8 which has a Ti 3d 0 electron configuration and band gap between the O 2p and Ti 3d states, and is stable in the 5-atom unit cell. The calculated lattice parameters, listed in Table I, are in good agreement with experiment. 25 The deviation from experiment is systematic between the compounds: the a parameter for SmTO (GTO) is underestimated by 0.04 Å (0.04 Å), the b-parameter overestimated by 0.07 Å (0.03 Å), and the c-parameter underestimated by 0.11 Å (0.04 Å). For STO our calculated lattice parameter (3.903 Å) is in excellent agreement with experiment (3.905 Å). 26 SmTO and GTO display large deviations from the perfect cubic perovskite structure, with Ti O Ti angles of 144 and 146 in the (001) plane, and 140 and 143 in the perpendicular c direction. In GTO the Ti 3d 1 spins are aligned ferromagnetically [Fig. 1(a)], in agreement with experiment. 27 In SmTO, the various possible magnetic orderings are all very close in energy. Our calculations show the ferromagnetic spin configuration of the Ti 3d 1 moments to be lowest in energy, but it is less than 10 mev per Ti atom lower in energy than the experimentally observed G-type antiferromagnetic order. 27 We therefore perform our bulk and band-alignment calculations using this antiferromagnetic configuration, as shown in Fig. 1(b). 8

9 FIG. 1. (Color online) Atomic structure of (a) antiferromagnetic SmTO and (b) ferromagnetic GTO calculated with the HSE hybrid functional. The Ti 3d orbitals making up the lower Hubbard bands are shown, with spin-up in red and spin-down in blue. The roman numerals I, II, and III indicate the atomic positions listed in Table I, used to define the Ti-O-Ti angles in the compounds. 9

10 The calculated electronic band structures of bulk SmTO and GTO are shown in Fig. 2, and the density of states in Fig. 3. Even though SmTO has an antiferromagnetic alignment of the 3d 1 electrons, the electronic structure of SmTO is very similar to that of GTO. The Mott-Hubbard gap in SmTO is slightly larger than that of GTO, 2.21 ev vs ev. These values are larger than what has been inferred from photoconductivity measurements; 28 the calculated gap value in GTO has been confirmed by photoluminescence measurements. 29 The top of the LHB occurs at T and the bottom of the UHB at Γ, and both the LHB and UHB display small dispersions. Table I lists the widths of the LHBs, the energy difference between the top of the LHB and the top of the O 2p band, and the energy difference between the UHB and the top of the O 2p band. FIG. 2. (Color online) Band structure of (a) SmTiO 3 and (b) GdTiO 3 calculated with the HSE functional. Red corresponds to spin-up bands, and blue to spin-down. 10

11 FIG. 3. (Color online) Density of states of (a) SmTiO 3 and (b) GdTiO 3 calculated with the HSE functional. Gaussian broadening with a width of 0.2 ev was included. B. XPS results X-ray photoelectron spectroscopy was employed to determine the valence-band offset (VBO) for the GTO/SmTO heterostructure. Following the standard methodology, 30,31 the VBO was calculated according to the following equation: Δ = / / / / (1) where the valence-band maximum (VBM) values (E VBM ) were obtained from the linear regression 32 of the (LHB) Ti 3d or the O 2p edge features from reference bulk GTO and SmTO sample spectra, as shown in Fig. 4. The core-level binding energy peak separation for the GTO/SmTO heterostructure was measured to be (E Gd 3d5/2 - E Sm 3d5/2 )= ev. 11

12 FIG. 4. (Color online) Valence-band structure for GTO and SmTO bulk samples showing extrapolated VBM values by linear regression of the spectra edge. Figure 5 summarizes the E VBO values deduced from Eq. (1), where the measured core-level peak maximum intensities were determined from the GTO and SmTO reference samples to occur at the following binding energies: BE max,gd 3d = ev and BE max,sm 3d = ev. It is seen that the O 2p edge for GTO is offset ev relative to SmTO, and similarly that the Ti 3d (LHB) is offset ev relative to SmTO. Also, the energy gap between the LHB and the O2p edge is 3.84 ev (3.85 ev) for SmTO (GTO). 12

13 FIG. 5. (Color online) Measured band alignments between GTO and SmTO, grown on LSAT in the (110) o plane.. C. Calculated band alignments and comparison We now apply the first-principles methodology outlined in Section III to obtain the natural band alignments. We first compute the alignments between STO/SmTO and STO/GTO, and take advantage of the observation that band offsets for lattice-matched nonpolar interfaces exhibit transitivity 33,34 : If the offsets A/B and B/C are known, the offset A/C can be derived. From our separate calculations of STO/SmTO and STO/GTO, we can thus obtain the alignment between SmTO and GTO. The results for the STO/SmTO/GTO band alignments are shown in Fig

14 FIG. 6. (Color online) Calculated natural band alignment (in the absence of any strain) between SrTiO 3, SmTiO 3, and GdTiO 3. The sign convention is such that an offset at interface A/B (going from left to right) is positive if the band in B is higher in energy than the band in A. The width of the LHB in this figure reflects energies directly obtained from band-structure calculations, and hence appears narrower than in Fig. 3, where additional broadening was included in the DOS calculations. Next, we assess the impact of strain on the measured SmTO/GTO band alignment, since the SmTO/GTO thin film is coherently grown on LSAT. These perovskite oxides grow in the (110) o plane (subscript o referring to the coordinate system being that of the orthorhombic 20-atom cell), and we therefore strain the SmTO and GTO unit cells to reproduce the in-plane strain that is imposed experimentally while allowing the lattice parameter (and hence the volume) in the perpendicular direction to relax. Doing so, we obtain a volume that is 0.04% smaller for GTO and 0.97% smaller for SmTO. As described in Section III, we start from the natural band alignments and determine the shifts in the band-edge positions from the strained unit cells and 14

15 homojunction calculations between the unstrained and strained material. The natural band alignments, and the alignments for SmTO and GTO strained to LSAT, are given in Table II. TABLE II: Calculated band alignments (in ev) for SmTO and GTO with respect to STO. Offsets are given for the O 2p edge, the top of the lower Hubbard band (both referenced to the VBM of STO), and for the bottom of the upper Hubbard band (referenced to the CBM of STO). Material O 2p LHB top UHB SmTO GTO SmTO on LSAT GTO on LSAT Table II shows that when strain to LSAT is taken into account, the offset in the O 2p band edges at the SmTO/GTO interface is calculated to be 0 ev; the measured value (Fig. 5) is 0.13 ev. For the top of the LHB, the calculated offset is 0.08 ev, while the measured value is 0.14 ev. The agreement between theory and experiment is satisfactory. Finally, we comment on the energy difference between the LHB and the O 2p band, which seemingly is a lot larger in experiment (Fig. 5, 3.84 ev in SmTO, 3.85 ev in GTO) than in the calculations (Table II, 3.34 ev in SmTO, 3.42 ev in GTO). These values can be reconciled as follows. 15

16 The zero of energy in the experimental data is set to the Fermi-level position, which is determined as a part of the spectrometer energy calibration process. The coincidence of the zero of energy with the LHB edge is therefore accidental. The width of the LHB observed in experiment (Fig. 4) is significantly larger than the theoretical width. We do not have a solid explanation for why this additional broadening is observed in experiment; one can speculate that it is related to some variations in octahedral rotation/tilting near the interface. But this additional broadening complicates the determination of the experimental value of the top of the LHB; the standard straightforward extrapolation procedure (leading to the blue vertical lines and values in Fig. 4) will significantly overestimate this value. We can actually more accurately determine the top of the LHB (in the absence of broadening) by invoking information about the expected position of the Fermi level in the band structure. The rare-earth titanates commonly exhibit unintentional p-type conductivity [Zhou 2005], 27 with holes forming small polarons. 35,36 The polaron level is 0.55 ev above the top of the LHB, and the Fermi level will tend to be pinned at this value. The position of the top of the LHB is therefore expected to be about 0.55 ev below the measured Fermi level. Using this information combined with the experimental numbers for the position for the O 2p band, we estimate the top of the LHB to lie at ( )=3.32 ev above the top of the O 2p band in GTO, and ( )=3.31 ev above the top of the O 2p band in SmTO. These values agree very well with the calculated numbers (3.42 ev in GTO, 3.34 ev in SmTO), thus resolving the apparent discrepancy between the measured and calculated energy difference between the top of the O 2p and LHB bands. 16

17 . V. SUMMARY AND CONCLUSIONS We have reported a combined experimental/computational study of the band alignments between SmTiO 3, GdTiO 3, and SrTiO 3. Effects of strain (due to pseudomorphic growth on LSAT) were taken into account, but are found to cause shifts in the band edges of less than 0.05 ev. The results indicate the offset between the O 2p bands in SmTO and GTO is small, on the order of 0.1 ev. The same result applies to the offset between the top of the LHB. The position of the LHB within the band structure of these Mott insulators was clarified. ACKNOWLEDGMENTS This work was supported by the NSF MRSEC program (DMR ) and by the Center for Low Energy Systems Technology (LEAST), one of six SRC STARnet Centers sponsored by MARCO and DARPA. Computational resources were provided by the Extreme Science and Engineering Discovery Environment (XSEDE), supported by NSF (ACI ), and the Center for Scientific Computing at the CNSI and MRL (an NSF MRSEC, DMR ) (NSF CNS ). 1. A. Ohtomo and H. Y. Hwang, Nature 427, 423 (2004). 2. A. Brinkman, M. Huijben, M. Van Zalk, J. Huijben, U. Zeitler, J. C. Maan, W. G. Van der Wiel, G. Rijnders, D. H. A. Blank, and H. Hilgenkamp, Nature Mater. 6, 493 (2007). 17

18 3. A. Ohtomo, D. A. Muller, J. L. Grazul, and H. Y. Hwang, Nature 419, 378 (2002). 4. S. S. A. Seo, W. S. Choi, H. N. Lee, L. Yu, K. W. Kim, C. Bernhard, and T. W. Noh, Phys. Rev. Lett. 99, (2007). 5. P. Moetakef, T. A. Cain, D. G. Ouellette, J. Y. Zhang, D. O. Klenov, A. Janotti, C. G. Van de Walle, S. Rajan, S. J. Allen, and S. Stemmer, Appl. Phys. Lett. 99, (2011). 6. C. A. Jackson and S. Stemmer, Phys. Rev. B 88, (R) (2013). 7. L. Bjaalie, B. Himmetoglu, L. Weston, A. Janotti, and C. G. Van de Walle, New J. Phys 16, (2014)]. 8. P. Moetakef, J. Zhang, S. Raghavan, and A. Kajdos, J. Vac. Sci. Technol. A 31, (2013). 9. R. M. Wallace, Electrochem. Soc. Trans. 16, 255 (2008) 10. A. Herrera-Gómez, A. Hegedus, and P. L. Meissner, Appl. Phys. Lett., 81, 1014 (2002). 11. ASTM E Standard Practice for Calibration of the Electron Binding-Energy Scale of an X-Ray Photoelectron Spectrometer, ASTM International, West Conshohocken, PA, DOI: /E P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964). 13. W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). 14. J. Heyd, G. E. Scuseria, and M. Ernzerhof,J. Chem. Phys. 118, 8207 (2003). Erratum: J. Chem. Phys. 124, (2006). 15. G. Kresse and J. Furthmüller, Phys. Rev. B 54, (1996). 16. G. Kresse and J. Furthmüller, Comput. Mater. Sci. 6, 15 (1996). 18

19 17. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). 18. P. Rivero, I. P. R. Moreira, G. E. Scuseria, and F. Illas, Phys. Rev. B 79, (2009). 19. J. He and C. Franchini, Phys. Rev. B 86, (2012). 20. B. Himmetoglu, A. Janotti, L. Bjaalie, and C. G. Van de Walle, Phys. Rev. B 90, (R) (2014). 21. P. E. Blöchl, Phys. Rev. B 50, (1994). 22. C. G. Van de Walle and R. M. Martin, J. Vac. Sci. Technol. B 4, 1055 (1986). 23. C. G. Van de Walle and R. M. Martin, Phys. Rev. Lett. 62, 2028 (1989). 24. A. Janotti, L. Bjaalie, B. Himmetoglu, and C. G. Van de Walle, Phys. Status Solidi RRL 8, 577 (2014). 25. D. A. MacLean, H.-N. Ng, and J. E. Greedan, J. Solid State Chem. 30, 35 (1979). 26. J. Brous, I. Fankuchen, and E. Banks, ActaCrystallogr. 6, 67 (1953). 27. H. D. Zhou and J. B. Goodenough, J. Phys.: Condens. Matter 17, 7395 (2005). 28. D. A. Crandles, T. Timusk, J. D. Garrett, and J. E. Greedan, Physica C 201, 407 (1992). 29. L. Bjaalie, A. Verma, B. Himmetoglu, A. Janotti, S. Raghavan, V. Protasenko, E. H. Steenbergen, D. Jena, S. Stemmer, and C. G. Van de Walle, Phys. Rev. B 92, (2015). 30. E. A. Kraut, R. W. Grant, J. R. Waldrop, and S. P. Kowalczyk, Phys. Rev. B 28, 1965 (1983) 31. G. Conti, A. M. Kaiser, A. X. Gray, S. Nemšák, G. K. Pálsson, J. Son, P. Moetakef, A. Janotti, L. Bjaalie, C. S. Conlon, D. Eiteneer, A. A. Greer, A. Keqi, A. Rattanachata, A. 19

20 Y. Saw, A. Bostwick, W. C. Stolte, A. Gloskovskii, W. Drube, S. Ueda, M. Kobata, K. Kobayashi, C. G. Van de Walle, S. Stemmer, C. M. Schneider, and C. S. Fadley, J. Appl. Phys. 113, (2013) 32. R. S. List and W. E. Spicer, J. Vac. Sci. Technol. B 6, 1228 (1988). 33. A. Franciosi and C. G. Van de Walle, Surf. Sci. Rep. 25, 1 (1996). 34. C. G. Van de Walle, Phys. Rev. B 39, 1871 (1989). 35. L. Bjaalie, A. Janotti, K. Krishnaswamy, and C. G. Van de Walle, Phys. Rev. B 93, (2016). 36. L. Bjaalie, D. G. Ouellette, P. Moetakef, T. A. Cain, A. Janotti, B. Himmetoglu, S. J. Allen, S. Stemmer and C. G. Van de Walle, Appl. Phys. Lett. 106, (2015). 20