SrTiO3

PHYSICAL REVIEW B 74, 205416 共2006兲

Charge compensation and mixed valency in LaAlO3 / SrTiO3 heterointerfaces studied by the FLAPW method Min Sik Park, S. H. Rhim, and Arthur J. Freeman Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA 共Received 15 May 2006; revised manuscript received 17 August 2006; published 14 November 2006兲 The electronic structures and properties of heterointerfaces in the perovskite oxide superlattices LaAlO3 / SrTiO3 关001兴 are presented using the first-principles all-electron full-potential linearized augmented plane-wave 共FLAPW兲 method. Superlattices with three types of interfaces, 共i兲 electron-doped, 共ii兲 hole-doped, and 共iii兲 both electron- and hole-doped, are studied and compared. For the electron-doped interface, the mixed valency of Ti along with the Jahn-Teller effect are found to explain the metallicity, in agreement with experiment, whereas for the hole-doped interface metallicity is found, in contrast to experiment. Oxygen vacancies introduce an additional n-type carrier to compensate the holes present at the interface, which now becomes insulating and agrees well with experiment. For a system with both types of interfaces, the metallicity found for the unrelaxed structure is changed to insulating after relaxation is included. For all cases, the relaxation results in a complicated buckled geometry, which is a good indication of the adjustment due to polarity discontinuity. Our findings support recent experimental results, namely, 共i兲 the mixed-valence character of Ti at the electrondoped interface, and 共ii兲 the existence and importance of oxygen vacancies at the hole-doped interface. DOI: 10.1103/PhysRevB.74.205416

PACS number共s兲: 73.20.⫺r, 73.40.⫺c, 73.21.Cd

I. INTRODUCTION

Semiconductor heterostructures based on II–VI elements have been greatly studied because of their huge application for electronic devices, such as field-effect transistors, bipolar transistors, and light emitting diodes.1 Nowadays, the development of these electronic devices is reaching saturation as to high-integration, high-speed, and multifunctionality.2,3 As one of the ways for overcoming this, or for searching others, the heteroepitaxial structure of perovskite oxides has been studied intensively for practical applications as well as for understanding its rich physics, such as high-Tc superconductivity,4 colossal magnetoresistance,5 and ferroelectricity.6 In the study of devices from perovskite oxides, understanding the physics of heterointerfaces and their control at the atomic scale are indispensable for their stability and functionality.7,8 In making superlattices from different perovskite oxides, polarity discontinuity, or the mismatch between polar and nonpolar layers frequently arises. Thus understanding polarity discontinuities at the interfaces is essential in controlling the physical property of superlattices at the atomic scale and in exploring properties that are different from those in usual bulk materials. Recently, Ohtomo and Hwang9 reported that atomically controlled LaAlO3 / SrTiO3 关001兴 heterointerfaces exhibit different transport properties depending on the doping character of the interface. The hole-doped 共AlO2兲− / 共SrO兲0 interface is insulating, whereas the electron-doped 共LaO兲+ / 共TiO2兲0 interface is metallic with an extremely high carrier mobility. It is quite intriguing to have metallicity at the interface between two insulators with large band gaps— LaAlO3 共5.6 eV兲,9 and SrTiO3 共3.2 eV兲.9 The dominant mechanism behind these interesting properties is considered to be the polarity discontinuity of the interface. More recently, the microscopic distribution of charge and ions across the LaAlO3 / SrTiO3 关001兴 interface was determined using atomic-scale electron energy-loss spectroscopy. Nakagawa et 1098-0121/2006/74共20兲/205416共6兲

al.10 found a fundamental asymmetry between the two types of interface in their interfacial sharpness and charge density: the electron-doped 共LaO兲+ / 共TiO2兲0 interface is electronically compensated, while the hole-doped 共AlO2兲− / 共SrO兲0 interface is ionically compensated. If 0.5 electron per two-dimensional unit cell is transferred from LaAlO3共SrTiO3兲 to SrTiO3共LaAlO3兲 in the electron共hole兲-doped interface, the divergence of a potential catastrophe can be avoided. This 0.5 electron charge compensation for the n-type interface can be done by the mixed valency of Ti, whereas the p-type interface can be realized by oxygen vacancies. In this paper, a first-principles study on the LaAlO3 / SrTiO3 关001兴 superlattice is presented for three interfaces, namely the 共i兲 electron-doped, 共ii兲 hole-doped, and 共iii兲 both electron- and hole-doped interfaces. Metallic interface states are found to arise in all three cases, despite the fact that their bulk component materials are wide band-gap insulators. In all interfaces, atomic structure relaxation results in a complicated buckling geometry having a common tendency. For the electron-doped interface, Ti mixed valency at the interface plays an important role in its transport properties, which is also relevant to Jahn-Teller distortion. On the other hand, for the hole-doped interface, oxygen vacancies are critical to understanding its stability and transport properties—which agrees well with experiment. And last, for a superlattice with both types of interface, atomic relaxation alters the metallicity to an insulating state without oxygen vacancies. This is explained in terms of charge compensation between the two separated interfaces.

II. DETAILS OF THE CALCULATIONS

The geometry of the superlattices is schematically shown in Fig. 1 for the three kinds of interfaces. First, the electrondoped 共LaO兲+ / 共TiO2兲0 interface 关Fig. 1共a兲兴 has one and half unit cells of both LaAlO3 and SrTiO3 with a TiO2-layer ter-

205416-1

©2006 The American Physical Society

PHYSICAL REVIEW B 74, 205416 共2006兲

PARK, RHIM, AND FREEMAN

face 共space group P4 / mmm兲 and c = 15.388 Å 共=4 ⫻ a兲 for the superlattice with both types of interface 共space group P4mm兲, in which the c / a ratios of 3 and 4 are close to the theoretically optimized values 共within 1.7%兲. The atomic structure relaxation was also performed under a fixed c / a in all superlattices. For superlattices with oxygen vacancies, we used a 2a ⫻ 2a ⫻ c cell for 1 and 2 oxygen vacancies, and a 冑2a ⫻ 冑2a ⫻ c cell for four oxygen vacancies, respectively. III. RESULTS FIG. 1. Schematic diagrams for tetragonal unit cells of superlattices with 共a兲 共LaO兲+ / 共TiO2兲0 interfaces, 共b兲 共AlO2兲− / 共SrO兲0 interfaces, and 共c兲 both of them.

mination. On the other hand, the hole-doped 共AlO2兲− / 共SrO兲0 interface 关Fig. 1共b兲兴 has one and half unit cells of both SrTiO3 and LaAlO3 with an AlO2-layer termination. The superlattice with both types of interface consists of two unit cells of both SrTiO3 and LaAlO3, as depicted in Fig. 1共c兲. We employed the highly precise full-potential linearized augmented plan-wave 共FLAPW兲 method12,13 for the localdensity approximation 共LDA兲 calculations with the exchange-correlation potential formulated by Hedin and Lundqvist.14 For the treatment of extended core states in La, Sr, Al, Ti, the explicit orthogonalization 共XO兲 method15 was used. Since La 6p and Sr 5p states lie far above the Fermi energy 共EF兲, the La 5p and Sr 4p states were treated as valence states. The improved tetrahedron scheme was used16,17 for the k-point integrations. Since the difference between the experimental lattice constants of LaAlO3 and SrTiO3 is small,9,10 we use an average value 共3.847 Å兲 of the experimental lattice constants, which is very close to the theoretically optimized value 共within 0.3%兲 in our superlattices. All superlattices are tetragonal unit cells, so we use lattice constants, a = b = 3.847 Å for all superlattices and c = 11.541 Å 共=3 ⫻ a兲 for the superlattice with either the 共LaO兲+ / 共TiO2兲0 or the 共AlO2兲− / 共SrO兲0 inter-

First, for comparing the LDA and the generalized gradient approximation 共GGA兲,18 we optimized the lattice constants for both bulk LaAlO3 and SrTiO3 using the GGA and LDA. For LaAlO3, the calculated GGA lattice constant 共3.788 Å兲 gives better agreement with the experimental lattice constant 共3.789 Å兲 than does LDA 共3.712 Å兲; however, for SrTiO3, LDA gives a value 共3.878 Å兲 that is closer to experiment 共3.905 Å兲 than does GGA 共3.975 Å兲. Therefore both GGA and LDA well describe the experimental lattice constant— within a 2% deviation. Also since there is no difference between the LDA and GGA results in our superlattice calculations, we use LDA for our study. A. „LaO…+ / „TiO2…0 heterointerface

In agreement with experiment,9 the n-type metallic state is obtained for the fixed structure with the 共LaO兲+ / 共TiO2兲0 interface. This metallicity is not altered even after relaxation. The total density of states 共DOS兲 and the projected DOS of the interface Ti atom and O atoms in the relaxed structure are shown in Fig. 2共a兲. The state near EF is mainly comprised of Ti-3d states at the interface. This is well confirmed in the charge density around EF shown in Fig. 3共a兲, where the t2 orbital character of the Ti-3d state is clearly exhibited. The fact that the Ti 3d state is partially occupied implies that there is mixed valency of +3 and +4 in Ti. Comparison of the changes of valence electron charge inside the muffin-tin

FIG. 2. The total and projected DOS near EF of superlattices with 共a兲 共LaO兲+ / 共TiO2兲0 and 共b兲 共AlO2兲− / 共SrO兲0 relaxed interfaces.

205416-2

PHYSICAL REVIEW B 74, 205416 共2006兲

CHARGE COMPENSATION AND MIXED VALENCY IN…

FIG. 3. Charge density in the unit cell of relaxed structural superlattices with 共a兲 共LaO兲+ / 共TiO2兲0 interfaces and 共b兲 共AlO2兲− / 共SrO兲0 interfaces in an energy slice of 0.075 eV below EF. The starting density is 1 ⫻ 10−4 electrons/ a.u.3 and subsequent lines increase successively by a factor of 冑2.

共MT兲 spheres for Ti, Sr, La, and Al with those of their bulk counterparts shows that the MT charges of Ti and Sr increase by 0.19 and 0.08, respectively, whereas those of La and Al decrease by 0.07 and 0.06. As discussed in Ref. 10, the n-type metallicity in this superlattice is due to the charge transfer from the 共LaO兲+ layer to the 共TiO2兲0 layer. This can be realized by the Ti-mixed valency at the interface. After the atomic structure relaxation, the buckling of atoms occurs in a very complicated way with no in-plane

force, as illustrated schematically in Fig. 4共a兲 under the same space-group symmetry as in the fixed case. Hence we mainly focus on the buckling at the interface since the position changes of the atoms are largest there—the Ti is displaced from its fixed position by 0.11 Å. The Ti and O atoms in the 共LaO兲+ layer repel each other, while the La and O in 共TiO2兲0 attract each other. The octahedron around Ti is elongated along the c direction by 2.9% 共⬃0.11 Å兲; thus the threefold degenerate t2 states are split into single-fold 共dxy兲 and twofold 共dzx , dyz兲 states. This elongation of the octahedron is experimentally observed, and is explained by the Jahn-Teller effect.11 However, both the fixed and relaxed structures exhibit a high peak in the DOS at EF, indicating some instability in both cases. To simulate the growth situation in experiment, oxygen vacancies are introduced in the 共LaO兲+ and 共TiO2兲0 layers, because the oxygen vacancy at those interface layers is calculated to be more favorable than at the inner layers 关共AlO2兲− and 共SrO兲0兴. The high peak in the DOS around EF is slightly removed by an oxygen vacancy, which implies a stabilization of the superlattice. Indeed, a small number of oxygen vacancies at the n-type interface exist in experiment.10 There, Nakagawa et al.10 interpreted the role of oxygen vacancies as reducing the band offset at the heterointerface, in addition to avoiding a divergence by mixed-valent Ti ions. This oxygen vacancy is further discussed in the p-type interface in the next section. B. „AlO2…− / „SrO…0 heterointerface

For the fixed and relaxed structures of the superlattice with the 共AlO2兲− / 共SrO兲0 interface, a p-type metallic state is obtained which is in contrast to the insulating state found in experiment.9 The total and projected DOS around EF, as seen in Fig. 2共b兲, is mostly from oxygen 2p states from all layers. However, in the fixed structure the contribution from the interface oxygen is larger than those from the other oxygens. In contrast, after atomic relaxation, the contribution of oxygen at the inner 共LaO兲+ layer is larger than those from the interface 共SrO兲0 layer oxygen. Furthermore, the oxygen 2p

FIG. 4. Schematic diagrams for the atomic buckling in the 关001兴 direction of superlattices with 共a兲 共LaO兲+ / 共TiO2兲0 interfaces, 共b兲 共AlO2兲− / 共SrO兲0 interfaces, and 共c兲 with both of them, and top views of 共d兲 the 共LaO兲+ 关or 共SrO兲0兴 layer and 共e兲 the 共AlO2兲− 关or 共TiO2兲0兴 layer; thick lines denote buckled layers, shaded areas denote interfaces.

205416-3

PHYSICAL REVIEW B 74, 205416 共2006兲

PARK, RHIM, AND FREEMAN

FIG. 5. The total and projected DOS near EF of superlattices with p-type 共AlO2兲− / 共SrO兲0 interfaces including 共a兲 25% and 共b兲 50% oxygen vacancies in the fixed structure. 共OVS: oxygen vacant site; NOVS: nearest neighbor of oxygen vacant site; NNOVS: next-nearest neighbor of oxygen vacant site.兲

character is clearly seen in the charge-density plot in Fig. 3共b兲, where hybridization occurs in plane for oxygen in the 共LaO兲+ and 共SrO兲0 planes, while it is out of plane for oxygen in the 共TiO2兲0 and 共AlO2兲− planes. In contrast to the n-type interface superlattice, the total valence electronic charge inside all MT spheres decreases by 0.2 per unit cell with respect to its bulk counterparts, which shows well the p-type character. This loss of charge at this interface is also consistent with the 0.5 electron transfer suggested in Ref. 10, if it is recognized that our value is only the charge in the MT sphere since the interstitial charge is not taken into account. As in the n-type interface, the p-type interface is metallic even after relaxation. The relaxation also results in buckling for this p-type superlattice with no in-plane force; thus all atom shifts are along the c direction, as illustrated in Fig. 4共b兲 共space-group symmetry P4 / mmm兲. The Sr atom moves toward the 共AlO2兲− plane, while oxygen in the 共AlO2兲− plane moves away from the 共SrO兲0 plane and the Al atom moves toward O in the 共SrO兲0 plane with the Al displaced from its fixed position by 0.08 Å. At the interface, however, unlike Ti in the n-type interface, Sr, Al, and O have a fixed valence 共+2, +3, and −2, respectively兲. In the p-type interface, there is no Jahn-Teller ion; hence the Jahn-Teller effect is excluded for producing a distortion upon relaxation. The role of oxygen vacancies at the p-type interface is discussed in Ref. 10. Further, an experiment on the epitaxial growth of SrTiO3 on LaAlO3 substrates show that the SrTiO3 growth on 共AlO2兲-terminated LaAlO3 exhibited lots of defects.19 To simulate this experiment, oxygen vacancies are introduced. Now, the oxygen vacancy can play a more important role in the p-type interface than in the n-type interface: oxygen vacancies increase the number of n-type carriers, mostly in the O-2p band; thus metallicity can be altered to insulating behavior. As in the n-type interface case, the total energy dependence on the position of the oxygen vacancy was calculated. The total energy of the oxygen vacancy at the 共SrO兲0 layer is lower than that of the oxygen vacancy at the 共AlO2兲− layer. First, one oxygen is removed

from the 共SrO兲0 layer, which corresponds to 共SrO0.75兲0.5+ / 共AlO2兲−. In a simple ionic model, there is no free electron at this interface; however, in contrast to expectation, metallicity is obtained for one oxygen vacancy. For this interface with a single oxygen vacancy to change to insulating, it is necessary for additional n-type carriers to compensate for the hole around the O-2p band. As seen in Fig. 5共a兲, the Ti-3d state in the octahedral site with an oxygen vacancy strongly hybridizes with the O-2p near EF. Therefore the n-type carriers from the oxygen vacancy cannot exactly compensate for holes at the p-type interface. This is consistent with experiment: very few Ti3+ ions were observed near oxygen vacancies at the p-type interface.10 For two oxygen vacancies in the 共SrO兲0 layer, which corresponds to 共SrO0.5兲+ / 共AlO2兲−; this p-type interface becomes insulating—as shown by the DOS presented in Fig. 5共b兲. This insulating property of two oxygen vacancies agrees with experiment,9 and indicates that additional n-type carriers compensate for holes at the p-type interface. The difference in transport properties between 25% and 50% oxygen vacancies indicates that the interface with 25– 50 % oxygen vacancies is insulating. Indeed, the experiment by Nakagawa et al.10 found for nearly 32% oxygen vacancies that the p-type interface was insulating. Our finding suggests that the p-type interface is insulating due to the oxygen vacancy. This finding supports previous experiments, where lots of defects can exist at the 共AlO2兲− / 共SrO兲0 interface. The p-type interface behaves differently from the n-type 共LaO兲+ / 共TiO2兲0 interface, where nearly defect-free layers can be grown as a result of the multivalency of Ti. C. Both „LaO…+ / „TiO2…0 and „AlO2…− / „SrO…0 heterointerfaces

For the fixed structure of a superlattice with both interfaces, the metallic state is obtained. The total and projected DOS in Fig. 6共a兲 show that most states near EF are comprised of Ti-3d and O-2p states, each from the interface 共TiO2兲0 and 共AlO2兲− plane, respectively. However, the

205416-4

PHYSICAL REVIEW B 74, 205416 共2006兲

CHARGE COMPENSATION AND MIXED VALENCY IN…

FIG. 6. The total and projected DOS near EF of the superlattice with both types of interfaces in the 共a兲 fixed structure and 共b兲 relaxed structure 共IF: interface兲.

atomic structure relaxation changes this metallic superlattice to insulating, with a band gap of 1.7 eV, which means induced interfacial charges are removed by relaxation. There are reports of similar charge redistribution 共broadening兲 by relaxation in the LaTiO3 / SrTiO3 superlattice,20,21 even though there is no p-type interface—different from the LaAlO3 / SrTiO3 superlattice. In both systems, the relaxation plays an important role in the charge distribution. The atomic relaxation also results in buckling, as in the previous superlattices 共space group P4mm兲, as the average positions of both n-type 共LaO兲+ and p-type 共AlO2兲− interfacial layers come close to the inner polar layers 关Fig. 4共c兲兴, which reduces the polarity discontinuity at both interfaces. In Sec. III B, we discussed the p-type 共AlO2兲− / 共SrO兲0 interface with many oxygen vacancies. From the results above, we may expect for both types of interfaces that charge compensation without oxygen vacancies helps the growth of the oxygen defect-free p-type interface. IV. CONCLUSIONS

We investigated the electronic structures and properties of the LaAlO3 / SrTiO3 关001兴 superlattice with 共i兲 the electrondoped 共LaO兲+ / 共TiO2兲0 interface, 共ii兲 the hole-doped 共AlO2兲− / 共SrO兲0 interface, and 共iii兲 both the electron- and hole-doped interfaces. For the electron-doped interface, the superlattice is still metallic even after relaxation. The DOS analysis and charge density show that the states near EF are

mostly of Ti 3d character. Further analysis on the change of charge in the MT spheres indicates that Ti shows mixed valency, +3 / + 4, indicating a Jahn-Teller distortion which induces the charge compensation in the electron-doped interface. For the hole-doped interface, the superlattice is also metallic before and after relaxation. This metallicity is different from experiment; introducing 25– 50 % oxygen vacancies at the interface changes the superlattice to insulating, in agreement with experiment. Unlike the electron-doped interface, there is no ion like Ti with mixed valency; thus the charge compensation can occur through oxygen vacancies. Finally, for the superlattice with both interfaces, metallicity is found for the fixed structure, whereas it becomes insulating after relaxation. With both types of interfaces, charge compensation occurs between two layers separated by 7.694 Å. This understanding for the mechanism of charge compensation in the heterointerface of perovskite oxide— mixed valency, oxygen vacancies, and atomic structure relaxation—is expected to contribute to the useful control of physical properties at the atomic scale in applications.22 ACKNOWLEDGMENTS

We thank I. G. Kim for helpful discussions about the XO method. This work, initiated at the suggestion of C. W. Chu, was supported by a Korea Research Foundation Grant funded by the Korean Government 共MOEHRD兲 共Grant No. KRF-2005-214-C00035兲 and by the U.S. Department of Energy 共Grant No. DE-FG02-88ER 45372/A021兲.

205416-5

PHYSICAL REVIEW B 74, 205416 共2006兲

PARK, RHIM, AND FREEMAN Kroemer, Rev. Mod. Phys. 73, 783 共2001兲. D. A. Muller, T. Sorsch, S. Moccio, F. H. Baumann, K. EvansLutterodt, and G. Timp, Nature 共London兲 399, 758 共1999兲. 3 L. B. Kish, Phys. Lett. A 305, 144 共2002兲. 4 J. G. Bednorz and K. A. Müller, Z. Phys. B: Condens. Matter 64, 189 共1986兲. 5 S. Jin, T. H. Tiefel, M. McCormack, R. A. Fastnacht, R. Ramesh, and L. H. Chen, Science 264, 413 共1994兲. 6 C. Kittel, Introduction to Solid State Physics, 7th ed. 共Wiley, New York, 1995兲, Chap. 13. 7 G. Hammerl, A. Schmehl, R. R. Schulz, B. Goetz, H. Bielefeldt, C. W. Schneder, H. Hilgenkamp, and J. Mannhart, Nature 共London兲 407, 162 共2000兲. 8 H. Yamada, Y. Ogawa, Y. Ishii, H. Sato, M. Kawasaki, H. Akoh, and Y. Tokura, Science 305, 646 共2004兲. 9 A. Ohtomo and H. Y. Hwang, Nature 共London兲 427, 423 共2004兲. 10 N. Nakagawa, H. Y. Hwang, and D. A. Muller, Nat. Mater. 5, 204 共2006兲. 11 J.-L. Maurice, C. Carretero, M.-J. Casanove, K. Bouzehouane, S. Guyard, É. Larquet, and J.-P. Contour, Phys. Status Solidi A 203, 2209 共2006兲. 12 E. Wimmer, H. Krakauer, M. Weinert, and A. J. Freeman, Phys. Rev. B 24, 864 共1981兲.

J. F. Jansen and A. J. Freeman, Phys. Rev. B 30, 561 共1984兲. L. Hedin and B. Lundqvist, J. Phys. C 4, 2064 共1971兲. 15 M. Weinert 共unpublished兲. 16 O. Jepsen and O. K. Andersen, Solid State Commun. 9, 1763 共1971兲. 17 P. E. Blöchl, O. Jepsen, and O. K. Andersen, Phys. Rev. B 49, 16223 共1994兲. 18 J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 共1996兲. 19 D. W. Kim, D. H. Kim, B. S. Kang, T. W. Noh, D. R. Lee, and K. B. Lee, Appl. Phys. Lett. 74, 2176 共1999兲. 20 D. R. Hamann, D. A. Muller, and H. Y. Hwang, Phys. Rev. B 73, 195403 共2006兲. 21 S. Okamoto, A. J. Millis, and N. A. Spaldin, Phys. Rev. Lett. 97, 056802 共2006兲. 22 We learned of the appearance of a recent interesting paper 关R. Pentcheva and W. E. Pickett, Phys. Rev. B 74, 035112 共2006兲兴 reporting results obtained using density-functional theory within the LDA+U approach on the same interface system. Among other results, these authors show how strong correlations in the oxygen 2p states may be necessary to account for observed insulating behavior at the p-type 共AlO2兲− / 共SrO兲0 interface without oxygen defects.

1 H.

13 H.

2

14

205416-6