Chris G. Van de Walle

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1 Complex oxide interfaces Chris G. Van de Walle Anderson Janotti, Lars Bjaalie, Luke Gordon, Burak Himmetoglu, K. Krishnaswamy Materials Department, University of California, Santa Barbara ES213 June 11-14, 213 Williamsburg, Virginia Acknowledgments NSF, ARO, ONR; XSEDE http// / d ll

2 Complex oxides ABO 3 perovskites Many interesting properties B O A SrTiO 3 A = Sr, B= Ti LaAlO 3 A = La, B= Al Complex oxides interfaces High-k dielectrics Colossal magnetoresistance Ferroelectricity Superconductivity Charge ordering Spin dependent transport Interplay of structural, electronic and transport properties Applications Sensors Electrodes in fuel cells Memory devices (memristors)

3 SrTiO 3 and LaAlO 3 Wide-band-gap oxides A two-dimensional electron gas (2DEG) STO LAO forms at the STO/LAO interface Conduction band Conduction band LAO 2DEG ~1 13 e - /cm ev ev STO Valence band Valence band A. Ohtomo and H. Y. Hwang, Nature 427, 423 (24). 2DEG appears only for LAO layers thicker than 4 unit cells S. Thiel et al. Science 313, (26).

4 The two-dimensional electron gas at the STO/LAO interface Where do the carriers come from? 1. Polar catastrophe/ surface 2. Oxygen vacancies (near the interface or in STO bulk) 3. Atomic intermixing (STO substrate, LAO surface, ) 3. Electronic reconstructions Ohtomo & Hwang, Nature 427, 423 (24). Mannhart et al., MRS Bull. Nov. 28. Mannhart et al., MRS Bull. Nov. 28. Brinkman et al., Nat. Matter. 6, 493 (27). Kalabukhov et al., Phys. Rev. B 75, 12144(R) (27). Siemons et al., Phys. Rev. Lett. 98, (27). Bristowe et al., Phys. Rev. B 83, 2545 (211). Li et al, Phys. Rev. B 84, (211). Nakagawa et al., Nat. Matter. 5, 24 (26). Qiao et al., Surf. Sci. 65, 1381 (211) Pentcheva and Pickett, Phys. Rev. B 74, (26) Popovic et al, Phys. Rev. Lett. 11, (28)

5 (1) STO/LAO interface [Al 3+ (O 2- )2] LaO [La 3+ O 2- ] LaO LaO TiO2 TiO2 TiO2 [Ti 4+ (O 2- )2 ] [Sr 2+ O 2- ] potential

6 (1) STO/LAO interface [Al 3+ (O 2- )2] LaO [La 3+ O 2- ] LaO LaO TiO2 TiO2 TiO2 [Ti 4+ (O 2- )2 ] [Sr 2+ O 2- ] potential Polar catastrophe

7 (1) STO/LAO interface [Al 3+ (O 2- )2] LaO [La 3+ O 2- ] LaO 5e.5e LaO Problem arises from ionic picture All layers originally neutral LaO ( donor ) layer donates.5 e to AlO 2 on either side At the interface extra.5 e!...

8 (1).5e STO/LAO interface [Al 3+ (O 2- )2] LaO [La 3+ O 2- ] LaO LaO TiO2 TiO2 TiO2 [Ti 4+ (O 2- )2 ] [Sr 2+ O 2- ] potential Polar Catastrophe

9 (1).5e STO/LAO interface LaO X X X X LaO LaO X TiO2 TiO2 TiO2 [Ti 4+ (O 2- )2 ] [Sr 2+ O 2- ] potential

10 (1).5e If take origins of electrons into account STO/LAO interface [Al 3+ (O 2- )2] LaO [La 3+ O 2- ] X X X X LaO LaO X TiO2 TiO2 TiO2 [Ti 4+ (O 2- )2 ] [Sr 2+ O 2- ] potential there is no Polar catastrophe!

11 (1) Free electrons bound to a plane of positive fixed charges.5e STO/LAO interface [Al 3+ (O 2- )2] LaO [La 3+ O 2- ] LaO LaO TiO2 TiO2 TiO2 [Ti 4+ (O 2- )2 ] [Sr 2+ O 2- ] Ideal interface.5e per unit cell area n=3x1 14 cm -2

12 (1) If free electrons leak away to the top surface, the 2DEG density decreases X.5e STO/LAO interface [Al 3+ (O 2- )2] LaO [La 3+ O 2- ] LaO LaO TiO2 TiO2 TiO2 [Ti 4+ (O 2- )2 ] [Sr 2+ O 2- ] potential

13 SrTiO 3, LaAlO 3, and STO/LAO from first principles -Density functional theory, hybrid functional (HSE) J. Heyd, G.E. Scuseria and M. Ernzerhof, J. Chem. Phys.118, 827 (23); 124, 21996(E) (26). Conduction band LaAlO 3 SrTiO 3 Valence band Conduction band Ti d (t 2g < e g ) Valence band O 2p bands Conduction band Al 3s, La 5d Valence band O 2p bands

14 First-principles calculations Total charge 5e.5 per interface! n=3x1 14 cm -2 A. Janotti, L. Bjaalie, L. Gordon, C. G. Van de Walle, Phys. Rev. B 86, 24118(R) (212).

15 Note First-principles calculations Charge is not on single Ti layer at the interface! Not Ti 3+! Total charge 5e.5 per interface! n=3x1 14 cm -2 A. Janotti, L. Bjaalie, L. Gordon, C. G. Van de Walle, Phys. Rev. B 86, 24118(R) (212).

16 Band alignments Density functional theory, hybrid functional Conduction band Quantum well with equivalent interfaces Subbands Valence band LaAlO 3 SrTiO 3 LAO STO LAO In agreement with experimental results of Chambers et al., Surface Science Reports (21).

17 First-principles calculations Subbands from (STO)8.5/(LAO)7.5 superlattice Popovic et al., Phys. Rev. Lett. 11, (28). Chen et al., Adv. Matter. 22, 2881 (21). La Sr Sr La

18 First principles versus Schrödinger-Poisson Schrödinger-Poisson simulations Input parameters Band offsets Dielectric constants Effective masses

19 First principles versus Schrödinger-Poisson

20 STO/LAO/STO Symmetric heterostructure n=3x1 14 cm -2 STiO SrTiO 3 LaAlO 3 STiO SrTiO 3 TiO 2 TiO 2 LaO AlO 2 LaO AlO 2 LaO TiO Flat potential across LAO 5e.5e per unit cell per interface charge density conduction band valence band

21 STO/LAO/STO Asymmetric heterostructure LaO-terminated on the left, AlO 2 -terminated on the right SrTiO 3 LaAlO 3 SrTiO 3 TiO 2 TiO 2 LaO + LaO AlO 2 TiO 2 TiO Potential increase across the LAO layer Low 2DEG density electrons leak to other interface charge density conduction band valence band

22 STO/LAO Surface LAO surface AlO 2 -terminated 2 n 1 13 cm -2 SrTiO 3 LaAlO 3 SrTi 3 TiO 2 TiO 2 LaO + LaO AlO potential increase across the LAO layer lower 2DEG density electrons leak to surface electrons go into surface states on LAO surface

23 (1) If free electrons leak away to the top surface, the 2DEG density decreases X.5e STO/LAO interface [Al 3+ (O 2- )2] LaO [La 3+ O 2- ] LaO LaO TiO2 TiO2 TiO2 [Ti 4+ (O 2- )2 ] [Sr 2+ O 2- ] potential

24 STO/LAO Surface LAO surface passivated SrTiO 3 LaAlO 3 TiO 2 TiO 2 LaO + LaO AlO Potential almost flat across the LAO layer High 2DEG density hydrogen passivation, or metal cap layer (work function!) R. Arras et al., Phys. Rev. B 85, (212).

25 Other materials combinations? STiO/GdTiO SrTiO3/GdTiO3 superlattices Schrödinger-Poisson simulations STO/GTO.5 e- per unit cell per interface P. Moetakef et al., Appl. Phys. Lett. 99, (211).

26 (1) STO/LAO STO/GdTiO 3 [Al 3+ (O 2- )2] LaO [La 3+ O 2- ] TiO 2 [Ti 3+ (O 2- )2] GdO [Gd 3+ O 2- ] TiO 2 GdO TiO 2 LaO TiO 2 LaO GdO TiO2 TiO2 TiO2 TiO2 TiO2 TiO2 n=1 13 cm -2 n=3x1 14 cm -2 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, (211).

27 Why is STO/GTO different from STO/LAO? Interface is not different Confirmed by first- principles i calculations l But STO can be grown with high quality on top of GTO! symmetric interfaces Superlattices Full 2DEG density GTO surfaces auto-passivated TiO 2 [Ti 3+ (O 2- )2] GdO [Gd 3+ O 2- ] TiO 2 GdO TiO 2 GdO TiO2 TiO2 TiO2 n=3x1 14 cm -2 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, (211).

28 Mott physics SrTiO 3 versus GdTiO 3 SrTiO 3 GdTiO 3 Conduction band Ti d states Valence band, O p states

29 2+ 3+ Mott physics SrTiO 3 versus GdTiO 3 SrTiO 3 GdTiO 3 Conduction band Ti d states Valence band, O p states

30 Mott physics SrTiO 3 versus GdTiO 3 SrTiO 3 GdTiO 3 GdTiO 3 Conduction band Ti d states Ti d states Valence band, O p states

31 GdTiO3 properties GTO a 3d 1 Mott insulator Mott/band insulator interface GTO unit cell 2-atom orthorhombic, Pnma space group STO GTO

32 U GdTiO3 properties

33 SrTiO3/GdTiO3 superlattices band offsets Calculating band offsets by using the (11) interface no electron transfer Macroscopic average x1 G Conti et al J Appl Phys 113 G. Conti et al. J. Appl. Phys. 113, (213).

34 Summary First-principles calculations Schrödinger-Poisson modeling Hybrid functional capable of capturing the physics of Mott insulators and the STO/GTO system Electrons in the 2DEG at STO/LAO and STO/GTO are intrinsic to the interface Asymmetry y of interfaces (or interface+surface) causes electrons to leak away in the STO/LAO case And so, my fellow theorists ask not where the electrons come from ask where the electrons disappear to. Reference A. Janotti, L. Bjaalie, L. Gordon, and C. G. Van de Walle, Phys. Rev. B 86, 24118(R) (212).

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