Polar Perovskite

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Creating Two-Dimensional Electron Gas in Polar/Polar Perovskite Oxide Heterostructures: First-Principles Characterization of LaAlO3/A+B5+O3 Yaqin Wang, Wu Tang, Jianli Cheng, Maziar Behtash, and Kesong Yang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b02399 • Publication Date (Web): 10 May 2016 Downloaded from http://pubs.acs.org on May 17, 2016

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ACS Applied Materials & Interfaces

Creating Two-Dimensional Electron Gas in Polar/Polar Perovskite Oxide Heterostructures: First-Principles Characterization of LaAlO3/A+B5+O3 Yaqin Wang,†,‡ Wu Tang,† Jianli Cheng,‡ Maziar Behtash,‡ and Kesong Yang⇤,‡ †State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China ‡Department of NanoEngineering, University of California, San Diego, 9500 Gilman Drive, Mail Code 0448, La Jolla, California 92093-0448, USA E-mail: [email protected];Tel:+1-858-534-2514

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Abstract By using first-principles electronic structure calculations, we explored the possibility of producing two-dimensional electron gas (2DEG) at polar/polar (LaO)+ /(BO2 )+ interface in the LaAlO3 /A+ B5+ O3 (A=Na and K, B=Nb and Ta) heterostructures (HS). Unlike the prototype polar/nonpolar LaAlO3 /SrTiO3 HS system where there exists a least film thickness of four LaAlO3 unit cells to have an insulator-to-metal transition, we found that the polar/polar LaAlO3 /A+ B5+ O3 HS systems are intrinsically conducting at their interfaces without an insulator-to-metal transition. The interfacial charge carrier densities of these polar/polar HS systems are in the order of 1014 cm

2,

much

larger than that of the LaAlO3 /SrTiO3 system. This is mainly attributed to two donor layers, i.e., (LaO)+ and (BO2 )+ (B=Nb and Ta), in the polar/polar LaAlO3 /A+ B5+ O3 systems, while only one (LaO)+ donor layer in the polar/nonpolar LaAlO3 /SrTiO3 system. In addition, it is expected that due to less localized of Nd 4d and Ta 5d orbitals with respect to Ti 3d orbitals, these LaAlO3 /A+ B5+ O3 HS systems can exhibit potentially higher electron mobility because of their smaller electron e↵ective mass than that in the LaAlO3 /SrTiO3 system. Our results demonstrate that the electronic reconstruction at polar/polar interface could be an alternative way to produce superior 2DEG in the perovskite-oxide-based HS systems.

Keywords Oxide heterostructures, two-dimensional electron gas, polar/polar, perovskite, KTaO3 , firstprinciples

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1

INTRODUCTION

With the rapid development of thin-film growth techniques like molecular beam epitaxy, 1 pulse laser deposition, 2 and atomic layer deposition, 3 , it has become possible to fabricate high-quality oxide heterostructures (HS), leading to novel interfacial properties. For instance, the HS based on wide-band-gap perovskite oxides can exhibit two-dimensional electron gas (2DEG), 4 superconductivity, 5 electric-field controlled conductivity, 6 and magnetism at the interface, 7,8 which are absent in their parent compounds. These intriguing interfacial physical properties are of great interest not only from the fundamental physics perspective but also because of their potential application in nanoelectronic devices. 4–8 A typical example is polar/nonpolar LaAlO3 /SrTiO3 HS system in which the LaAlO3 film is grown on the SrTiO3 substrate and the system shows the 2DEG at its n-type (LaO)+ /(TiO2 )0 interface. 4 Along the [001] direction, the SrTiO3 substrate can be considered as stacks of alternating neutral (SrO)0 and (TiO2 )0 , while the LaAlO3 film consists of charged sheets of (LaO)+ and (AlO2 ) . At the (LaO)+ /(TiO2 )0 interface, to avoid the polar discontinuity, about 0.5e are transferred from the charged (LaO)+ layer to the neutral (TiO2 )0 layer in SrTiO3 . 9 These transferred electrons partially occupy the Ti 3d orbitals, and form metallic states at the interface, corresponding to a theoretical charge carrier density of 3.3 ⇥ 1014 cm 2 . In contrast, a series of systematic experiments show that the LaAlO3 /SrTiO3 samples annealed under oxygen-rich condition have a sheet carrier density of about 1-2⇥1013 cm 2 , 10–14 which is about one order of magnitude smaller than the theoretical value. It is also important to note that a minimum thickness of 4 unit cells of LaAlO3 films is necessary to form the 2DEG in the LaAlO3 /SrTiO3 HS system. 11 Later theoretical studies based on first-principles simulations suggest that the critical thickness for forming the 2DEG is strongly correlated to the polar distortion (polarization) in the LaAlO3 film. 15,16 Our previous computational study based on the LaAlO3 /SrTiO3 HS-based slab model indicated that the polarization strength of the LaAlO3 film is strongly correlated to the film thickness, and the polarization decreases as the LaAlO3 film thickness increases. 16 When the LaAlO3 3



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film thickness is below 5 unit cells, the LaAlO3 /SrTiO3 HS system exhibits an insulating behavior. This is because the polarization of the LaAlO3 film is strong enough, which neutralizes the polar-catastrophe-induced charge transfer. When the LaAlO3 film thickness increases up to 5 unit cells, the polarization in the LaAlO3 film becomes weakened so that the ability of transferring charges given by polar catastrophe can only be partially counteracted, and thus only few electrons (much less than 0.5e per unit cell) will be transferred to the SrTiO3 substrate, forming the interfacial metallic states. This slab model yields a calculated interfacial charge carrier density of about 1.6 ⇥ 1013 cm 2 , which is well consistent with the experimental values of around 1-2 ⇥ 1013 cm 2 . 10–14 Compared to the polar/nonpolar LaAlO3 /SrTiO3 HS system that generates 2DEG via the polar discontinuity, some nonpolar/nonpolar HS systems are also able to produce 2DEG but via polarization discontinuity. One example is the CaZrO3 /SrTiO3 HS system, 17,18 in which the CaZrO3 and SrTiO3 both consist of neutral layers and there is no polar discontinuity between the CaZrO3 and SrTiO3 . Chen et al. has observed the 2DEG at the interface of the CaZrO3 /SrTiO3 HS system for the first time. 17 Our consequent first-principles computational studies have revealed that the compressive strain induced by the lattice mismatch yields a strong polarization in the CaZrO3 film, and the CaZrO3 /SrTiO3 HS system exhibits an insulator-to-metal transition as the CaZrO3 film thickness increases. 18 This is in excellent agreement with the experimental observation. Moreover, the computational studies also indicate that the polarization direction in the CaZrO3 film and the critical thickness of forming interfacial conductivity strongly depends on the surface termination. These experimental and computational findings reveal a new avenue to produce 2DEG in the complex oxide HS system via polarization discontinuity. Besides the nonpolar/nonpolar and polar/nonpolar HS models, one can think of a third avenue to construct perovskite-oxide-based HS model, i.e., polar/polar HS system, simply from the mode of constructing an oxide HS system. To produce a 2DEG at the interface of a polar/polar HS system, it requires that the two terminations (consisting of the interface)

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from each perovskite oxide are both donor layers, i.e., cation layers, which donate electrons to the HS system. As a result, compared to the polar/nonpolar HS system, the polar/polar HS system is expected to produce higher interfacial charge carrier density because it has two donor layers while the polar/nonpolar system has only one. Similarly, to produce a two-dimensional hole gas (2DHG) at the interface, it requires that the two terminations are both anion layers, i.e., acceptor layers, which donate hole in the HS system. According to various types of combinations of the perovskite oxides, e.g., A+ B5+ O3 , A2+ B4+ O3 , and A3+ B3+ O3 , to form a polar/polar interface and meanwhile to keep the stoichiometry of the perovskite oxide interface (AO/BO2 ), the only one possible combination of the two cation layers is (AO)+ /(BO2 )+ . Consequently, this requires that the two polar perovskite oxides are A3+ B3+ O3 and A+ B5+ O3 . Among all the possible A+ B5+ O3 compounds, Nb- and Ta-based perovskite oxides are mostly known, 19–23 and the KTaO3 , in a cubic phase at room temperature, is a widely used substrate material. 19,20 Another reason to choose Nband Ta-based perovskite oxides as the substrate materials is because that, with respect to the localized Ti 3d states, the less localized Nd 4d and Ta 5d states in these substrate materials may result in a larger charge carrier mobility than that in the SrTiO3 -based HS systems. In fact, very recently, Zou et al. has grown a polar/polar perovskite oxide heterostructure, that is, LaTiO3 /KTaO3 HS system with (LaO)+ /(TaO2 )+ interface, and found that this HS system exhibits higher interfacial charge carrier density and electron mobility than that of the well-known LaAlO3 /SrTiO3 HS system. 24 In this work, we took the polar/polar LaAlO3 /KTaO3 HS as an model system and systematically explored the possibility of producing the 2DEG at the polar/polar LaAlO3 /A+ B5+ O3 (A = Na and K, B = Nb and Ta) HS systems. We analyzed their interfacial properties from the interfacial charge carrier density, electron e↵ective mass of the 2DEG, interfacial conductivity, and interfacial thermodynamics. The di↵erence between the LaTiO3 /KTaO3 and proposed LaAlO3 /A+ B5+ O3 structure is that LaTiO3 is a Mott insulator while the LaAlO3 is a wide-band-gap insulator. 25 The former tends to lead to metallic interface with another band insulator because of its partially

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occupied Ti 3d states at interface. 25,26 This work provides a clear picture for the formation of 2DEG in polar/polar perovskite-based HS systems, and opens a new avenue to prepare superior 2DEG with ultra high interfacial charge carrier density and mobility in such systems.

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COMPUTATIONAL AND STRUCTURAL DETAILS

In this work, all the density functional theory (DFT) calculations were performed using Vienna Ab-initio Simulation Package (VASP). 27,28 The projector augmented-wave (PAW) potentials were applied for electron-ion interactions. 29 The generalized gradient approximation (GGA) parameterized by Perdew-Burke-Ernzerhof (PBE) plus on-site coulomb interaction approach (GGA+U ) was used for exchange-correlation functional. 30 To appropriately describe the electronic states of strongly correlated Ti 3d electrons, the calculated on-site e↵ective U parameter of 5.8 eV from the constrained DFT calculations was employed for Ti 3d orbitals. 31,32 An empirical U value of 7.5 eV was used to describe La 4f orbitals, 33 and an U value of 5 eV was used for Nb 4d and Ta 5d orbitals. 34 After systematic energy convergence test, a cuto↵ energy of 450 eV was used for expanding plane-wave basis set, and a 10 ⇥ 10 ⇥ 1 Monkhorst-Pack k-space grid was used to appropriately converge the total energy. The electronic self-consistency calculation was assumed for a total energy convergence of less than 10

5

eV. All the atomic positions were optimized until the inter-atomic forces

were smaller than 0.03 eV/˚ A. A sandwich type structural model, (LaAlO3 )m /(A+ B5+ O3 )12.5 /(LaAlO3 )m , was used to build LaAlO3 /A+ B5+ O3 (A = Na and K, B = Nb and Ta) HS slab systems by stacking the LaAlO3 film on the NbO2 - (TaO2 -) terminated [001]-oriented A+ B5+ O3 substrate, in which 12.5 unit cells of the A+ B5+ O3 were used as the substrate and m denotes the number of LaAlO3 unit cells. A 20˚ A vacuum layer was added above the AlO2 -terminated LaAlO3 film. At room temperature, KTaO3 crystallizes in a cubic phase with space no. 221 (P m¯3m), 19,20 and LaAlO3 , 35 KNbO3 , 21 NaNbO3 , 22 and NaTaO3 23 exhibit in an orthorhombic phase. To

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resemble the epitaxial film growth process in the experiment, we adopted an approximation of treating these non-cubic perovskite oxides as pseudo-cubic structures. The lattice parameters along the ab-plane were fixed, and all the ions are fully relaxed.

3

RESULTS AND DISCUSSION

3.1

Bulk Parent Compounds

To form a 2DEG at the interface of HS, the bulk compounds that form the HS must satisfy several necessary conditions that includes appropriate lattice mismatch, appropriate band gaps, relative band edge positions, and e↵ective charge accumulation at the interface. 36 Table 1 lists the bulk materials properties of the A+ B5+ O3 (A = Na and K, B = Nb and Ta) compounds, which include experimental and DFT equilibrium lattice constant a, lattice mismatch f with respect to LaAlO3 , and experimental and calculated band gaps Eg within the GGA and Heyd-Scuseria-Ernzerhof (HSE) formalism. 37 The calculated lattice constants from the GGA functional are well consistent with the experimental values. The lattice mismatch f is defined as f = (af

as )/as , where af and as are the lattice constants of the unstrained

film and substrate, respectively. 36 The negative value of f indicates that the LaAlO3 film undergoes a tensile strain from the substrate. The lattice mismatch f of the considered four HS models range from 2.6% for LaAlO3 /NaTaO3 to 5.8% for LaAlO3 /KNbO3 , comparable with that of Co3 O4 /SrTiO3 (3.46%) 38 and MgO/SrTiO3 (7.54%) 39 which have been successfully prepared in experiments. Besides an appropriate lattice mismatch f, another necessary condition for forming the 2DEG is that the conduction band minimum (CBM) of the electron donor oxide must be higher than that of the acceptor semiconductor, so that the charge transferred from the donor to the acceptor can be accumulated near the conduction band bottom of acceptor, forming n-type metallic states. 36 To justify whether LaAlO3 /A+ B5+ O3 HS systems satisfy this condition, we calculated the relative band edge positions between the LaAlO3 and 7



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Table 1: Structural and electronic properties of cubic (pseudo-cubic) LaAlO3 and A+ B5+ O3 (A = Na and K, B = Nb and Ta) perovskite oxides: experimental and DFT equilibrium lattice constants a (˚ A) and lattice mismatch f with the LaAlO3 film, calculated band gaps Eg (eV) from GGA and HSE methods. Compound LaAlO3 NaNbO3 KNbO3 NaTaO3 KTaO3

a (˚ A) 3.789 4 3.908 40 4.022 42 3.890 40 3.989 43

Experimental f Eg (%) (eV) 0.00 5.60 4 -3.05 3.08 41 -5.79 3.14 41 -2.60 3.96 41 -5.01 3.42 41

a (˚ A) 3.811 3.978 4.029 3.981 4.028

Theoretical f GGA (%) Eg (eV) 0.00 3.49 -4.20 1.62 -5.41 1.50 -4.27 2.27 -5.39 2.11

HSE Eg (eV) 4.89 3.37 2.86 4.08 3.52

Figure 1: (Color online) The estimated relative band edge positions of the A+ B5+ O3 (A = Na and K, B = Nb and Ta) oxides with respect to that of LaAlO3 . The red and blue lines indicate the valence band maximum and conduction band minimum, respectively. A+ B5+ O3 compounds by aligning their core energy levels of O 2s orbitals, 36 shown in Fig. 1. It is found that the valence band maximum (VBM) of these materials is approximately aligned, which is because the VBM of all the materials are mainly composed of O 2p states. In contrast, the CBM of all these I-V polar oxides, i.e. NaNbO3 , KNbO3 , NaTaO3 , and KTaO3 , are lower than that of the LaAlO3 , implying that electrons donated by the (LaO)+ and (NbO2 )+ [ or (TaO2 )+ ] layers will be accumulated at the interfacial (NbO2 )+ [or (TaO2 )+ ] layers of the I-V polar oxides.

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Figure 2: Calculated total density of states (DOS) for the (LaAlO3 )m /KTaO3 HS-based slab systems with di↵erent LaAlO3 unit cells (a) m=2, (b) m=4, (c) m=6, and (d) m=8. The Fermi level is indicated by the vertical dashed line at 0 eV in this and each subsequent DOS plot.

3.2

2DEG in LaAlO3 /KTaO3 HS systems

Next, we took the LaAlO3 /KTaO3 HS as an example to study its electronic property at the (LaO)+ /(TaO2 )+ interface. It is well-known that there exists a critical thickness of 4 unit cells for LaAlO3 to form the interfacial conducting states in the polar/nonpolar LaAlO3 /SrTiO3 HS system. 11 As a consequence, one might speculate whether the same phenomenon will occur in the LaAlO3 /KTaO3 HS system. To check this assumption, we modeled the LaAlO3 /KTaO3 HS by stacking various LaAlO3 unit cells on the TaO2 - terminated KTaO3 substrate along the [100] direction, and studied its electronic state evolution as a function of the LaAlO3 film thickness. For convenience, these models are referred to as (LaAlO3 )m /KTaO3 , in which m denotes the number of the LaAlO3 unit cells. The calculated total density of states (DOS) for these HS models are shown in Fig. 2. Unlike the LaAlO3 /SrTiO3 HS model, our results show that all the LaAlO3 /KTaO3 HS models are metallic, indicating that there does not exist a critical thickness to lead to an insulator-to9



metal transition. At m = 2 and 4, our calculations clearly show that the HS models exhibit a band gap, and the Fermi level is pinned near the bottom conduction bands, indicating a typical n-type conductivity. At m

6, the band gap vanishes, and the HS models are

conducting. As discussed below, this is because, in the (LaAlO3 )m /KTaO3 HS models with m = 6 and 8, the O 2p states in the LaAlO3 film shift significantly toward higher energy, leading to a overlap between O 2p states and Ta 5d states, and thus there is no band gap.

PDOS (states/eV)

(a) 2 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 -4

O 2p

Al 3p

La 5d

Ta 5d

Vacuum

K 4s

(AlO2)-1 (LaO)+1 (AlO2)-1 (LaO)+1 (TaO2)+1

IF-I

-1

(KO)

IF-III

(TaO2)+1 -1

(KO)

IF-V

(TaO2)+1 -2

0

2

E-EF (eV)

(b) PDOS (states/eV)

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Ta 5d IF-I

Ta 5d IF-III

2.0

dxy

1.2 0.8

dyz

1.5

dxz

1.0

0.4 0.0

O 2p (surface layer) px py pz

0.5 -2

-1

0

1

2 -2

-1

0

1

E-EF (eV)

2

0.0

-4

-3

-2

-1

0

Figure 3: (Color online) (a) Calculated layer-resolved partial DOS for (LaAlO3 )2 /KTaO3 HS model, along with the charge density projected on bands forming the 2DEG. (b) Orbitalresolved partial DOS for Ta atom at the 1st (IF-I) and 3rd (IF-III) TaO2 layers, and for O atom at surface AlO2 layer. To understand the origin of the conducting states and the associated electron transfer in the polar/polar LaAlO3 /KTaO3 HS system, we calculated the layer-resolved DOS for (LaAlO3 )2 /KTaO3 model (see Fig. 3) and (LaAlO3 )6 /KTaO3 (see Fig. 4), respectively. For a direct view of the each layer’s contribution to the conducting states, we also calculated the 10


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charge density projected on the bands forming the conducting states for each model. For convenient discussion, the first, third, and fifth layers of TaO2 were defined as IF-I, IF-III, and IF-V, respectively. For the (LaAlO3 )2 /KTaO3 model, the layer-resolved DOS and the charge density plots show that the metallic states mainly come from the Ta 5d states at the interfacial IF-I TaO2 layer, along with a small contribution from the IF-III and IF-V TaO2 layers, while the LaAlO3 film has no contribution to the metallic states. The calculated orbital-resolved partial DOS in Fig. 3b indicates that the metallic states at the interfacial IF-I TaO2 layer is solely contributed by Ta 5dxy orbitals, while the metallic states at the IF-III TaO2 layer come from both the dxy and dyz orbitals. This conductive property in the LaAlO3 /KTaO3 model is significantly di↵erent from that in the LaAlO3 /SrTiO3 HS system, in which (LaAlO3 )m /SrTiO3 HS models are insulating for m  4. 11,16,44 For the LaAlO3 /SrTiO3 model, at m  4, the strong polarization in the LaAlO3 film induces the charge transfer from the interfacial (LaO)+ layer to the surface (AlO2 ) layer, which neutralizes the polar (AlO2 ) surface and the polar catastrophe at the (LaO)+ /(TiO2 )0 interface and thus leads to the insulating state. 16 For the LaAlO3 /KTaO3 HS system, similar to the case of the LaAlO3 /SrTiO3 HS system, there also exists a polarization in the LaAlO3 film (see Fig. 3), which leads to the charge transfer from the interfacial (LaO)+ layer to the surface (AlO2 ) layer, and the system does not exhibit conducting surface states, see Fig. 3a. However, unlike the LaAlO3 /SrTiO3 HS with a polar/nonpolar interface, the LaAlO3 /KTaO3 HS has a polar/polar (LaO)+ /(TaO2 )+ interface, which means that the LaAlO3 and KTaO3 are both electron donors. Hence, although the electrons in the (LaO)+ layer is transferred to the surface (AlO2 ) layer, the electrons in the interfacial (TaO2 )+ layer contribute to the interfacial metallic states. It should be noted that the polarization e↵ects in the LaAlO3 film significantly influence the electronic property of the LaAlO3 /KTaO3 HS model, particularly the surface electronic property. To have a clear comparison, we presented the layer-resolved DOS and the charge density projected on the metallic states for the unrelaxed (LaAlO3 )2 /KTaO3 HS model, see Fig.S1 of the Supporting Information. For the unrelaxed HS model, besides

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(a)

PDOS (states/eV)

O 2p 2 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0

Al 3p

La 5d

Ta 5d

K 4s

Vacuum

(AlO2)-1 (LaO)+1 (AlO2)-1 (LaO)+1 (AlO2)-1 (LaO)+1 (AlO2)-1 (LaO)+1 (AlO2)-1 (LaO)+1 (AlO2)-1 (LaO)+1

IF-I

(TaO2)+1 (KO)-1

IF-III

(TaO2)+1 (KO)-1

IF-V

(TaO2)+1 -2

0

2

E-EF (eV)

(b) Ta 5d IF-I

PDOS (states/eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Ta 5d IF-III

2.0

dxy

1.2 0.8

dyz

1.5

dxz

1.0

0.4 0.0

O 2p (surface layer) px py pz

0.5 -2

-1

0

1

2 -2

-1

0

1

E-EF (eV)

2

0.0

-2

-1

0

1

2

Figure 4: (Color online) (a) Calculated layer-resolved partial DOS for (LaAlO3 )6 /KTaO3 model, along with the charge density projected on bands forming the 2DEG. (b) Orbitalresolved partial DOS for Ta atom at the 1st (IF-I) and 3rd (IF-III) TaO2 layers, and for O atom at surface AlO2 layer. the interfacial metallic states at the interfacial (TaO2 )+ layers, the surface (AlO2 )

layer

exhibit p-type conductive property because of its intrinsic polar character. Moreover, the electrical field caused by the asymmetrical polar layers, i.e., interfacial (LaO)+ and surface (AlO2 ) layer, leads to an evident shift of the electrostatic potential in the LaAlO3 film. For the (LaAlO3 )6 /KTaO3 model, similar to the case of the unrelaxed (LaAlO3 )2 /KTaO3 , it shows the n-type conducting states from the interfacial (TaO2 )+ layers and p-type conducting state from the surface (AlO2 ) layer, along with an evident shift of the electrostatic potential in the LaAlO3 film, see Fig. 4. This is because the LaAlO3 film exhibits a weaker 12


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polarization than that in the (LaAlO3 )2 /KTaO3 model, which is not capable of driving enough charge transfer from the interfacial (LaO)+ layer to the surface (AlO2 )

layer to

neutralize the surface hole states, and thus there exists an electrostatic potential shift in the LaAlO3 film and p-type conducting states on the surface. Similar electronic property also appears in the unrelaxed (LaAlO3 )6 /KTaO3 model in which there is no polarization in the LaAlO3 film, see Fig. S2 of the Supporting Information. This from another side indicates that the polarization in the relaxed LaAlO3 film is relatively weak. In short, as m increases, (LaAlO3 )m /KTaO3 HS models show the trends: at m < 6, the conducting state is only from the Ta 5d orbitals at the interface; while at m

6, the p-type conducting states from O 2p

orbitals on the surface and the n-type conducting states from Ta 5d states at the interface co-exist in the LaAlO3 /KTaO3 HS-based slab model.

Figure 5: (Color online) Calculated interfacial charge carrier density for the LaAlO3 /KTaO3 and LaAlO3 /SrTiO3 HS-based slab systems as a function of the number of LaAlO3 unit cells. It is important to note that, in addition to the absence of the critical thickness to form insulator-to-metal transition in the polar/polar LaAlO3 /KTaO3 model compared to the polar/nonpolar LaAlO3 /SrTiO3 HS system, another important di↵erence is that the po-

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lar/polar system has a significantly higher interfacial charge carrier density than that in the polar/nonpolar system. To have a qualitative comparison regarding this point, we calculated the interfacial charge density for the (LaAlO3 )m /KTaO3 and (LaAlO3 )m /SrTiO3 HS systems by integrating the partial DOS of the occupied Ta 5d (Ti 3d) orbitals from the interfacial TaO2 (TiO2 ) layers, and plotted it as a function of the number of the LaAlO3 unit cells (m=2, 4, 6 and 8) in Fig. 5. For the (LaAlO3 )m /SrTiO3 HS models, at m  4, the system is insulating and the interfacial charge carrier density is zero; at m

5, the interfacial

charge carrier density increases as m increases. For the (LaAlO3 )m /KTaO3 HS models, there does not exist a critical thickness and thus all the models exhibit a charge carrier density in the order of 1014 cm 2 , which is about three times larger than that in the corresponding LaAlO3 /SrTiO3 HS systems with the same LaAlO3 unit cells (>4 unit cells). This is because in the polar/polar LaAlO3 /KTaO3 HS model, its interfacial (LaO)+ and (TaO2 )+ layers are both electron donors, while in the polar/nonpolar LaAlO3 /SrTiO3 HS model, there is only one electron donor layer, i.e., (LaO)+ layer. In addition, it is interesting to note that the interfacial charge carrier density increases dramatically at m = 6 for LaAlO3 /KTaO3 and at m = 5 for LaAlO3 /SrTiO3 . This di↵erence is attributed to the di↵erent polarization strength in the two systems. To show this clearly, we plotted their average polarization in the LaAlO3 film as a function of the number of LaAlO3 unit cells (m) (see Fig. S3 in Supporting Information), and the computational details can be found in our previous work. 16 At m  4, the average LaAlO3 polarization is nearly same for these two systems. At m

5, the

average LaAlO3 polarization in the LaAlO3 /KTaO3 HS system is much larger than that in the LaAlO3 /SrTiO3 system for the same m. As revealed in our previous work, there exists a critical LaAlO3 polarization around 38 - 40 µC cm

2

below which the donated electrons from

the (LaO)+ layer can stay at the interface and contribute to the interfacial metallic states. 16 Accordingly, for the LaAlO3 /KTaO3 HS system, the interfacial charge carrier density can only increase dramatically when the LaAlO3 polarization is less than this critical value, that is, at m

6.

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Figure 6: (Color online) Calculated total DOS and layer-resolved partial DOS projected on Nb 4d or Ta 5d near the interface region for (a) LaAlO3 /NaNbO3 , (b) LaAlO3 /KNbO3 , (c) LaAlO3 /NaTaO3 , and (d) LaAlO3 /KTaO3 HS systems, respectively. IF-I, IF-III, and IF-V represent the 1st, 3rd, and 5th NbO2 (TaO2 ) layer of A+ B5+ O3 .

3.3

2DEG in LaAlO3 /A+ B5+ O3 HS Systems

Next we carried out comparison studies for the interfacial electronic properties of the other three LaAlO3 /A+ B5+ O3 HS systems, i.e., LaAlO3 /NaNbO3 , LaAlO3 /KNbO3 , and LaAlO3 /NaTaO3 . The calculated total DOS and partial DOS projected on the Nb 4d and Ta 5d orbitals from three consecutive interfacial NbO2 (TaO2 ) layers for the (LaAlO3 )2 /A+ B5+ O3 HS systems are shown in Fig. 6. In these HS models, two unit cells of LaAlO3 are stacked on the A+ B5+ O3 substrate. To have a comparison with the prototype LaAlO3 /KTaO3 HS system, we plotted total and layer-resolved partial DOS in Fig. 6d. It shows that the Fermi level crosses the CBM in all the systems, showing n-type conductivity. The layer-resolved DOS was also plotted to show the contribution from the interfacial NbO2 and TaO2 layers. To clearly show the spatial distribution of 2DEG, we plotted three-dimensional charge density projected on the bands forming the 2DEG, see Fig. 7. It shows that 2DEG is confined within the IFV NbO2 (TaO2 ) layers for the LaAlO3 /NaNbO3 (Fig. 7a) and LaAlO3 /KTaO3 (Fig. 7d) systems, and within the IF-VII NbO2 (TaO2 ) layers for the LaAlO3 /KNbO3 (Fig. 7b) and LaAlO3 /NaTaO3 (Fig. 7c) systems. Moreover, it also shows that, for the LaAlO3 /NaNbO3 15



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(a)

(b)

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(c)

(d)

(AlO2)-1 (LaO)+1 (AlO2)-1 (LaO)+1 (NbO2)+1 -1

(NaO) (NbO2)+1

(TaO2)+1 (TaO2)+1

(NaO)-1

(KO)-1

(NbO2)+1

(TaO2)+1

IF-III

-1

(KO)

-1

(KO)

IF-I

(KO)-1

(KO)-1

(NaO)-1 (NbO2)+1

(TaO2)+1

(TaO2)+1

(TaO2)+1

IF-V

(KO)-1 (TaO2)+1

(TaO2)+1

IF-VII

Figure 7: (Color online) Charge density projected on the bands forming the 2DEG near the interfacial region for (a) LaAlO3 /NaNbO3 , (b) LaAlO3 /KNbO3 , (c) LaAlO3 /NaTaO3 , and (d) LaAlO3 /KTaO3 HS systems, respectively. The same isovalue of 0.0018 e/bohr3 is used to produce the charge density plots. (Fig. 7a) and LaAlO3 /NaTaO3 (Fig. 7c) HS system, the IF-I, IF-III, and IF-V NbO2 and TaO2 layers almost contribute equally to the interfacial conducting states, while for the LaAlO3 /KNbO3 (Fig. 7b) and LaAlO3 /KTaO3 (Fig. 7d) HS systems, the conducting states largely come from the interfacial IF-I NbO2 (TaO2 ) layer, along with relatively small contributions from the IF-III and IF-V layers.

3.4

Evaluation of E↵ective Mass

To have a qualitative comparison of the electron transport property for these four polar/polar HS systems, i.e., LaAlO3 /A+ B5+ O3 (A = Na and K, B = Nb and Ta) HS systems, we evaluated the electron e↵ective masses of the bottom conduction band for each system. To this end, we calculated the electronic band structures for these four LaAlO3 /A+ B5+ O3 HS systems along the path M- -X of the interfacial Brillouin zone in Fig. 8. Our results show that the highly dispersed bottom conduction band (marked by red lines) resides below the Fermi level in all these four HS systems, showing n-type conductivity. Although not shown here, the orbital-projected DOS analysis indicates that these bottom conduction bands are mainly comprised of Nb 4d (Ta 5d) orbitals, and these orbitals are divided into two parts: 16


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light dxy bands (parallel to the interfacial plane) and heavy dxz and dyz bands (perpendicular to the interfacial plane), similar to the case of LaAlO3 /SrTiO3 HS system. 45 The light band is mainly along the -M path and is parabolic centered at , which plays a major role in the electron transport property. The heavy band extends along the -X direction, with a small dispersion.

Figure 8: (Color online) Electronic band structures for (a) LaAlO3 /NaNbO3 , (b) LaAlO3 /KNbO3 , (c) LaAlO3 /NaTaO3 , and (d) LaAlO3 /KTaO3 HS systems, respectively. The red line indicates the bottom conduction band that is used to evaluate the electron e↵ective mass. Table 2 lists the calculated electron e↵ective mass, m⇤ /me , along two of the highestsymmetry directions, -X and -M directions. It was calculated by using parabolic approximation for the bottom conduction band according to the following formula: 1 1 @ 2 ECB = m⇤ ~2 @k 2

17


(1)


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where i represents the interfacial Brillouin zone path of the bottom conduction band, ~ is the reduced Planck constant, ECB the energy of the minimum conduction band, and k the wave vector corresponding to the conduction bands. For a comparison, we also calculated the electron e↵ective mass for LaAlO3 /SrTiO3 HS system using the same sandwich-type HS-based slab model. The calculated value of m⇤ /me for the LaAlO3 /SrTiO3 HS system is 0.545 along -X direction and 0.564 along -M direction, which is in agreement with previous theoretical results. 46 It is noted that the calculated e↵ective mass of the HS-based slab model is slightly di↵erent from that of the periodic superlattice model. 47 This is because the local TiO6 structures at the interface are di↵erent in the superlattice and HS-based slab models, which leads to the di↵erence of the Ti 3d band characters at the interface. Interestingly, the calculated m⇤ /me agrees well with the experimental value of about 0.5 for the surface bands forming the 2DEG in the SrTiO3 , measured from the angle-resolved photoemission spectroscopy. 48 This implies that the e↵ective mass of the 2DEG in the LaAlO3 /SrTiO3 and SrTiO3 surface mostly inherits the intrinsic feature of the Ti 3d bands of the parent bulk material, i.e., SrTiO3 . However, it is also realized that there exist various experimental values for the electron e↵ective mass such as 0.7, 49 1.45, 50 and 3.2, 51 for the LaAlO3 /SrTiO3 systems, which is di↵erent from the theoretical value. This discrepancy may result from more complex interfacial correlation e↵ects such as the site dislocation and defects in the experiments, which was neglected in the ideal interfacial models. The estimated m⇤ /me along -X direction are 0.319, 0.339, 0.317, and 0.334 for the LaAlO3 /NaNbO3 , LaAlO3 /KNbO3 , LaAlO3 /NaTaO3 , and LaAlO3 /KTaO3 HS systems, respectively. These values are much lower than that of the LaAlO3 /SrTiO3 HS system, which is mainly because Nb 4d (Ta 5d) orbitals are less localized than Ti 3d orbitals. Hence, our results suggest that replacing SrTiO3 with NaNbO3 , KNbO3 , NaTaO3 and KTaO3 as the substrate can potentially reduce the electron e↵ective mass and improve the electron mobility.

18


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Table 2: Calculated relative electronic e↵ective mass m⇤ /me along the -X and -M path. m⇤ /me

Systems

-X 0.545 0.319 0.339 0.317 0.334

LaAlO3 /SrTiO3 LaAlO3 /NaNbO3 LaAlO3 /KNbO3 LaAlO3 /NaTaO3 LaAlO3 /KTaO3

3.5

-M 0.564 0.340 0.341 0.328 0.336

Charge Carrier Density and Conductivity

As discussed above, the polar/polar LaAlO3 /A+ B5+ O3 (A=Na and K, B=Nb and Ta) HS system has a higher interfacial charge carrier density than that in the polar/nonpolar LaAlO3 /SrTiO3 HS system because the former has one more electron donor layer than the later. To have a quantitative comparison among these HS systems, we estimated their interfacial orbital occupations and charge carrier densities by integrating the DOS of occupied Nb 4d (Ta 5d) orbitals at the interfacial NbO2 (TaO2 ) layers for the (LaAlO3 )6 /A+ B5+ O3 HS systems, see Fig. 9a. The estimated interfacial charge carrier densities are 5.3⇠10.4 ⇥1013 cm

2

for LaAlO3 /NaNbO3 , LaAlO3 /KNbO3 , LaAlO3 /NaTaO3 , and LaAlO3 /KTaO3 HS sys-

tems, which, as expected, are much larger than that of the LaAlO3 /SrTiO3 HS system. 52 Among the four considered polar/polar systems, the LaAlO3 /KTaO3 HS system shows the largest orbital occupation number and charge carrier density. The interfacial conductivity of the HS systems is determined by both the interfacial charge carrier density and the carrier mobility. To have a direct comparison of the interfacial conductivity among these four HS systems, we calculated their normalized charge carrier mobility (µ/µo ) and conductivity ( / o ) with respect to that of the LaAlO3 /SrTiO3 system, see Fig. 9b. µo and

o

refer to the charge carrier mobility and conductivity of

the LaAlO3 /SrTiO3 HS system, respectively. To this end, we employed the following two equations: 53 µ = e /m⇤ and constant. e, , m⇤ , n, and

= neµ, along with an assumption that the is a

are the fundamental charge, average scattering time, electron

e↵ective mass, charge carrier density, and electrical conductivity, respectively. Our results 19



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Figure 9: (Color online) (a) Calculated interfacial orbital occupation and interfacial charge carrier density (n) for LaAlO3 /SrTiO3 and LaAlO3 /A+ B5+ O3 HS systems. (b) Normalized interfacial electron mobility (µ) and electrical conductivity ( ) of LaAlO3 /A+ B5+ O3 HS systems with respect to the LaAlO3 /SrTiO3 HS system. clearly show that the polar/polar LaAlO3 /A+ B5+ O3 systems have a much higher electron mobility and electrical conductivity than that of the polar/nonpolar LaAlO3 /SrTiO3 system. In particular, the electrical conductivity of the LaAlO3 /KTaO3 system is about five times than that of LaAlO3 /SrTiO3 system, which is attributed to the increased interfacial charge carrier density and enhanced mobility. These results suggest a new avenue to prepare superior 2DEG with ultra high interfacial charge carrier density and mobility using Nb- and Ta-based polar/polar perovskite oxide HS systems.

20


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3.6

Interface Energetics

Finally, we evaluated the cohesive strength of the polar/polar interfaces in these LaAlO3 /A+ B5+ O3 (A = Na and K, B = Nb and Ta) HS systems by calculating their cleavage energies using the following equation: 54–56 LaAlO3 ABO3 Ecleav = (Eslab + Eslab

EHS )/2A

(2)

LaAlO3 ABO3 where Eslab , Eslab , and EHS are the total energy of LaAlO3 slab, A+ B5+ O3 slab

and LaAlO3 /A+ B5+ O3 HS systems, respectively. A is the interface area and the factor 2 indicates two symmetrical interfaces in the HS systems. To minimize the error, the LaAlO3 and A+ B5+ O3 slab models are built in the same LaAlO3 /A+ B5+ O3 HS system with the other part replaced by vacuum. The physical meaning of the cleavage energy is the energy required to separate the HS system into two parts, and thus its value determines the strength of the interfacial cohesion between the LaAlO3 film and the A+ B5+ O3 substrate, which can characterize the thermodynamically stability of the interface. The calculated cleavage energies are in the following order: 0.175, 0.155, 0.111, and 0.096 eV/˚ A2 for LaAlO3 /NaTaO3 , LaAlO3 /NaNbO3 , LaAlO3 /KTaO3 and LaAlO3 /KNbO3 HS systems, respectively. This indicates that the (LaO)+ /(TaO2 )+ interface of the LaAlO3 /NaTaO3 HS system has the strongest interfacial cohesion, while (LaO)+ /(NbO2 )+ interface of the LaAlO3 /KNbO3 system has the weakest interfacial cohesion. The relative values of the cleavage energies can be attributed to the interfacial bonds length for Nb-O, and Ta-O. Moreover, it is worth mentioning that the cleavage energies of these HS systems are comparable to that of the LaAlO3 /SrTiO3 HS system (0.19 eV/˚ A2 56 ). This implies that it is likely to grow the LaAlO3 film on these A+ B5+ O3 substrates and to form the polar/polar (LaO)+ /(BO2 )+ n-type interfaces. The conclusion is supported by an recent experiment reported by Zou et al. 24 in which the n-type (LaO)+ /(TaO2 )+ interface is formed in LaTiO3 /KTaO3 system.

21



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4

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CONCLUSION

In summary, we study the possibility of producing high-mobility 2DEG at n-type polar/polar (LaO)+ /(BO2 )+ interfaces in the LaAlO3 /A+ B5+ O3 (A = Na and K, B = Nb and Ta) HS systems using first-principles density functional theory calculations. All these polar/polar HS systems show interfacial metallic states mainly contributed by Nb 4d and Ta 5d orbitals, independent of the LaAlO3 film thickness, indicating that there does not exist a critical thickness for the insulator-to-metal transition, unlike the case of LaAlO3 /SrTiO3 HS system. Moreover, they exhibit much higher interfacial charge carrier densities than that in the LaAlO3 /SrTiO3 system. This is because there are two donor layers, i.e., (LaO)+ and (BO2 )+ , in the polar/polar interface while only one donor layer of (LaO)+ in the polar/nonpolar LaAlO3 /SrTiO3 system. In addition, as compared to the prototype LaAlO3 /SrTiO3 system, these polar/polar LaAlO3 /A+ B5+ O3 systems have a smaller e↵ective mass because of the less localization of Nd 4d and Ta 5d states with respect to Ti 3d states, and thus they are expected to show higher electron mobility and conductivity. Hence, we propose an alternative way to produce superior 2DEG via electronic reconstruction at polar/polar interface in the perovskite oxide HS systems.

Supporting Information Available Calculated layer-resolved DOS for the unrelaxed (LaAlO3 )2 /KTaO3 and (LaAlO3 )6 /KTaO3 HS systems, along with the charge density projected on bands forming the metallic states (Figure S1 and S2); and calculated average polarization in LaAlO3 film for the LaAlO3 /KTaO3 and LaAlO3 /SrTiO3 HS-based slab systems as a function of the number of LaAlO3 unit cells (Figure S3).

This material is available free of charge via the Internet at http:

//pubs.acs.org/.

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5

Acknowledgement

This work was supported by the start-up funds from the University of California, San Diego and a Department of Defense National Security Science and Engineering Faculty Fellowship (under the ONR contract no. N000141510030). KY thanks Dr. Jian Luo for useful discussions. YW is grateful for a visiting graduate student fellowship from University of Electronic Science and Technology of China. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number OCI-1053575.

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Table of Contents

Nonpolar Perovskite

Polar Perovskite (LaO)+ (TiO2 )0

2DEG

Polar Perovskite

Ferroelectric/ Piezoelectric

(CaO)0 (TiO2 )0

2DEG

(LaO)+ (BO2 )+

2DEG

Paraelectric

Nonpolar Perovskite

Nonpolar Perovskite

LaAlO3 /SrTiO3

CaZrO3 /SrTiO3

30


Polar Perovskite LaAlO3 /A+B 5+O3 (A=Na, K; B=Nb, Ta)

Polar Perovskite

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