Stabilities of the Intrinsic Defects on SrTiO3 Surface and SrTiO3

Article pubs.acs.org/JPCC

Stabilities of the Intrinsic Defects on SrTiO3 Surface and SrTiO3/ LaAlO3 Interface Mingqiang Gu,† Jianli Wang,§ X. S. Wu,*,† and G. P. Zhang‡ †

Nanjing National Laboratory of Microstructures, Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China ‡ Department of Chemistry and Physics, Indiana State University, Terre Haute, Indiana 47809, United States § Department of Physics, China University of Mining and Technology, Xuzhou 221116, China ABSTRACT: Intrinsic defects are crucial to the electronic and magnetic properties in the SrTiO3/LaAlO3 (STO/LAO) system. With the first-principles simulation, we construct a formation energy phase diagram of different intrinsic defects on STO surfaces. The three most stable surface defects are Alsubstitution of Ti, La-substitution of Sr, and the oxygen vacancy at TiO2 surface. On STO, multiple defects are possible. When these defective surfaces form interfaces with LAO, the Al substitution of Ti atom is highly favored energetically. Defects of this type can change the n-type interface into p-type. The polar STO/LAO interface is found to effectively compensate the internal electric field, leading to a wider band gap in the system with both n- and p-type interfaces.

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INTRODUCTION With the advent of the state-of-the-art thin-film deposition techniques, such as molecular beam epitaxy and pulsed laser deposition, atomically sharp interfaces can be manufactured. SrTiO3 (STO) and LaAlO3 (LAO) surfaces and their interface are particularly interesting. Both Shubnikov-De Haas oscillations1 and superconductivity2 with a critical temperature of Tc = 0.3 K are observed in the quasi-two-dimensional electron gas (Q-2DEG) phase.3,4 The origin of this novel phase has attracted broad attentions,5−12 where the quantum nature of a metal-induced gap state was identified.13 The spin and orbital states are complicated in related interfaces.9,14−18 The whole picture for these unconventional properties is still under intensive debate. Of particular importance to the surfaces and interfaces are defects. Intrinsic defects, such as diffusive mixing or vacancies induced during the growing process, are common in thin-films. Such intermixing also induces the layered dipole moment in LAO. Systematic investigations on the intermixing have been performed by the experimental and theoretical efforts by Chambers et al.19,20 Other defects like oxygen vacancies (F centers) have been shown to be responsible for the intergap state and the space charge effects in STO.21−24 During fabrication, the formation of different defective interfaces must be controlled by the concentration of different species in the atmosphere. The investigation of the formation energy under different growing conditions is important but still missing. Recently, point defects on both sides of the LAO slab were proved to be stable energetically25 and be a possible candidate to compensate the build-in electric field. Since this combination of polar defects effectively avoids dielectric © 2012 American Chemical Society

breakdown, it is a natural idea to examine its impact on the STO/LAO interfaces. In this article, we carry out the firstprinciples calculations to investigate the formation energy of the intrinsic point defects on STO surfaces. We find that different combinations of defects can easily form on the STO surfaces, among which the Al-substitution of Ti, La-substitution of Sr, and the oxygen vacancy at TiO2 surface are most stable. After forming an interface, the Al-substitution of Ti defect will change the p-type interface into n-type. The polar defects can avoid dielectric breakdown in the STO/LAO superlattice, which can be used to obtain a wider band gap in this structure. This paper is arranged as follows. In Methodology, we first present the calculation methods and then the structure models. In Results and Discussion, we discuss the surface and interface stabilities, the relaxation of the atomic layers near the interface, and the electronic structure. We conclude this article in the last section.

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METHODOLOGY Theoretical Formalism. We employ the Vienna ab initio simulation package (VASP) code26 to calculate structural stabilities and the electronic properties. Projector augmented wave (PAW) method is used to treat the valence−core interaction. We optimize the structure until the forces on each ion are less than 0.02 eV/Å. The energy cutoff for the planewave basis set is 500 eV, which is sufficient to converge our results. A (12 × 12 × 12) Monkhost-Pack k-point mesh is used Received: September 24, 2012 Revised: November 1, 2012 Published: November 5, 2012 24993

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Figure 1. Model structures used in the calculations. (a) In-plane 2 × 2 slabs of 11 atomic layers simulate the SrO (left) and TiO2 (right) surfaces. The vacuum layer is ∼20 Å. (b) In-plane √2 × √2 models contain totally 4.5 ucs of LAO and 7.5 ucs of STO, with two n-type (left) and p-type (right) interfaces along the z-direction. Only halves of these models are shown. The entire structure can be obtained by the mirror symmetry. (c) Inplane 2 × 2 unsymmetric superlattice model, which contains 4 ucs of LAO and 7 ucs of STO in the z-direction. There are two different interfaces in this structure: the lower one is n-type and the upper one is p-type.

in the bulk calculation. A (6 × 6 × 1) k-point mesh is used for the (2 × 2) surface and polar np-type interfaces, while a (8 × 8 × 1) k-point mesh is used for the (√2 × √2) geometry for ntype and p-type interfaces. We optimize the lattice constants for bulk STO and LAO under both local-density approximations (LDA) and generalized gradient approximations (GGA).27 The Perdew−Burke− Ernzerhof (PBE) functional is used for the GGA calculation. LDA calculations for STO are found to underestimate by 1.1%, while GGA calculations overestimate by about 1% in comparison to the experimental value (3.905 Å).28 PBE functionals have been shown to give reliable accuracy in calculation of the formation energy in this system (only 0.1 eV deviation compared to the B3LYP hybrid functionals20). In the following calculations, we use the PBE functionals. The lattice constant of LAO is calculated to be 3.823 Å in the cubic phase, which is in good agreement (only a 0.8% deviation) with the experimental data of 3.791 Å.29 These theoretical lattice constants will be used in the following calculations. Structural Models. To investigate the defective surfaces, we use slab models (see Figure 1). The slab consists of 11 atomic layers and ∼20 Å of vacuum layer (see Figure 1a). For the calculation of interfaces, a thick STO layer is necessary to reflect the metal induced gap state (MIGS) in the n-type interface.30 Here, we use 4.5 unit cells (ucs) of LAO and 7.5 ucs of STO to simulate the n-type and p-type interfaces, as shown in Figure 1b. The in-plane dimension of these two supercells is (√2 × √2). Our previous study31 showed that both SrO and TiO2 terminated surfaces in STO are available. It is necessary to investigate different defects on surface of both types. The properties of SrO or TiO2 surfaces can be easily modified by substituting a small fraction of Sr with Nb, La, or Ta.32−34 In the current work, we focus on the intrinsic defects in the LAO/

STO system, i.e., no additional chemical elements involved. Specifically, we consider the following defects in the (2 × 2) surface (Figure 2): (a) Sr vacancy, VSr, where one Sr atom is removed from SrO surface, (b) O vacancy, VO, where one O atom is removed from SrO surface, (c) La substitution at Sr site, LaSr, (d) Ti vacancy, VTi, where one Ti atom is removed from TiO2 surface, (e) O vacancy at TiO surface, VO′ , and (f) Al substitution at Ti site, AlTi.

Figure 2. Geometries for the intrinsic defects. (a−c) Defects on the SrO surface. (d−f) Defects on the TiO2 surface. The dashed circles denote the vacancies, while the arrows denote the substitutional atoms. Vacancies: (a) a Sr vacancy, (b) an oxygen vacancy on the SrO plane, (d) a Ti vacancy, and (e) an oxygen vacancy on the TiO2 plane. Substitutional defects: (c) Sr is substituted by La, and (f) Ti is substituted by Al. 24994

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Figure 3. Phase diagrams when the chemical potentials ΔμSr and ΔμO change for (a) the most stable surface defect with the lowest formation energy and (b) the possible combinations of surface defect(s), which have negative formation energies.

where EfSTO = 18.09 eV is the formation energy of STO, with respect to the bulk Sr, Ti, and gas O2 energies (−1.70, −5.63, and −9.84 eV, respectively).

Figure 1c shows a superlattice structure with both n- and ptype interfaces. This system is used to simulate the combined polar point defect.25 In such a structure, an oxygen vacancy exists at the AlO2/SrO interface, while a La vacancy exists at the LaO/TiO2 interface (VLa,O). Defect Formation Energy. We use the following method to compute the formation energies of the surface defects within the above models. The chemical potential of La (Al) is calculated from the total energy of thermal equilibrium bulk La (Al). In a compound such as STO, the formation energy should be estimated with respect to the total energy of the stoichiometric unit. The formation energy of the surface defects, Edef, is defined as Edef =

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RESULTS AND DISCUSSION Stabilities of Defects. The stabilities of surface defects can be estimated by the formation energy calculated with eq 3. The most stable defect has the lowest formation energy. The results are plotted in Figure 3. The AlTi and V′O defects have the lowest formation energy when the sample is grown in an oxygen-poor and Sr-rich atmosphere; the LaSr defect is favored in a Sr-poor atmosphere; while a stoichiometric STO surface (no defects) is favored when it is rich in oxygen and poor in Sr (see Figure 3a). This agrees with the experimental observation that oxygen vacancies are the most common point defect during the growth of perovskites. Figure 3b shows the energetically possible defect combinations, i.e., all the defects with negative formation energies, under different conditions. For instance, in the shaded area, the formation energies for both VO′ vacancy and AlTi substitution defects are lower than zero, meaning that these defects can coexist under this condition. The most common coexisting defect combinations are VO′ −AlTi, AlTi−LaSr, and LaSr−VO. The lone LaSr defect is also common in this system. The ranges of defect formation energies are listed in Table 1, which can be compared with other works (e.g., from ∼7.25 to 8.5 eV for the oxygen vacancy in bulk STO in ref 21).

1 (Etot − NSrμSr − NTiμTi − NOμO − NLaE La 2 − NAlEAl)

(1)

where NSr, NTi, NLa, NAl, and NO are the numbers of Sr, Ti, La, Al, and O atoms in the slab. Etot is the total energy of the system. The factor of 1/2 is due to the two symmetric surfaces in our slab model. The chemical potential μSTO of a stoichiometric phase of strontium titanate is a sum of the chemical potential of the Ti, Sr, and O atoms (μTi, μSr, and μO) μSTO = μSr + μTi + 3μO

(2)

Since the surface is in equilibrium with the bulk STO, we have μSTO = Ebulk (the bulk energy per formula unit of the cubic STO structure). By introducing the relative chemical potentials with respect to the atomic energy of oxygen gas or bulk Sr (ΔμO = bulk μO −1/2Emol O2 , and ΔμSr = μSr − ESr , respectively), we obtain Edef =

Table 1. Range of Formation Energies for the Intrinsic Defects on Termination of STO Surfaces As Chemical Potential Changes and the Work of Separation for Different Defective Interfaces

⎡ EOmol 1⎢ 2 Etot − NTiE bulk − (NO − 3NTi) 2 ⎢⎣ 2

range of the formation energies SrO termination

− ESrbulk (NSr − NTi) − NLaE La − NAlEAl ⎤ − ΔμO(NO − 3NTi) − ΔμSr (NSr − NTi)⎥ ⎥⎦

(3)

Here, Etot is the total energy of the slab with a specific defect. The values for the VSr, VO, LaSr, VTi, VO′ , and AlTi defective structures are calculated to be −831.68, −829.34, −856.34, −861.33, −886.41, and −890.93 eV, respectively. The boundaries of the Sr, Ti, and O chemical potentials are determined following refs 31 and 35. We have f ΔμSr + 3ΔμO > −ESTO

VSr

Edef (eV) TiO2 termination Edef (eV)

VO

LaSr

(−2.50, 15.59) (−4.55, 31.63) VTi VO′ (−3.54, 20.57) (−15.39, 20.80) work of separation

(−11.07, 7.02) AlTi (−14.59, 9.53)

type of interface

n

p

np

VO′

AlTi

LaSr

VLa,O

Wsep (eV)

−6.05

−4.42

−4.76

−5.33

−8.31

−6.87

−4.07

When defective surfaces form the interfaces, we use the work of separation to estimate the stabilities of the interfaces. The work of separation is defined as Wsep = (E1 + E2 − E12)/A, where E12, E1, and E2 are the total energy of the LAO/STO supercell, the isolated STO slab, and the LAO slab, respectively. On the basis of the above results, we simply pick up three most

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Figure 4. Changes in interplanar distances Δd for oxygens and cations at different layers. (a−c) Clean n-, p-, and np-type interface structures, respectively. (d−g) Interfaces with AlTi, VO′ , LaSr, and VLa,O defects, respectively. The interfaces are shown with dashed lines.

stable defective surfaces (AlTi, LaSr, and V′O) to construct the interfaces. We compare these interfaces with the pure n-type, ptype, np-type, and VLa,O-type interfaces. The results are shown in the lower panel of Table 1. It is clear that both the LaO/TiO2 and SrO/AlO2 interfaces are stable, while the former one is ∼0.82 eV/2D unit cell more stable than the latter one. The substitution defects (AlTi and LaSr) can stabilize both interfaces. This is expected since the substitutional atoms represent the diffusion across the interface, which provides excessive adhesion energy through diffusion. However, the oxygen vacancy (VO′ ) and the combined vacancies VLa,O in the LAO slab tend to weaken the adhesion of the two materials. Interface Relaxations. To see the local structure of the interfaces, we examine the atomic relaxations and interplanar separation of the interfaces. The relaxed interplanar spacings Δd along the z-axis are shown in Figure 4. Here, Δd is defined as

undergo a nearly constant expansion far from the interface, while, in the LAO layer, they show the zigzag type feature among layers. In all of these clean interface structures, the oxygens planes in STO layer do not vary a lot, and the biggest deviations from the bulk interplanar distance are found at the cation planes. When defects set in, the rumplings and interplanar distances change substantially. For the single-point defect structures (LaSr, VO′ , and AlTi), the defect eliminates the zigzag feature in LAO layer. The interplanar distance for oxygen planes undergo constant expansion at the STO layer and constant compression at the LAO layer. The combined VLa,O defects suppress and reverse the direction of the dipole in the np-type structure. This slightly reduces the zigzag-type feature of the cation in the LAO layer and flips the sign of Δd(M) at the LaO/TiO2 interface. Furthermore, the oxygens at the layer close to the SrO/AlO2 plane deviate from their ideal positions, which raises the total energy. This explains why the structure with this type of interfaces has the lowest work of separation. Electronic Structure. We further investigate the defectinduced effects on the electronic properties. The n-type (LaO/ TiO2) interface has a band gap of 1.85 eV.36 The electronic structure agrees with the metal induced gap state.13 When the oxygen vacancy sets in this interface, a lack of O2− ions slightly lowers the conduction band minimum and enhances the n-type behavior. The carrier concentration is increased. However, the Al substitution defect highly suppresses the n-type behavior. This is because the Al3+ ion acts as an acceptor. Such suppression effect obviously depends on the defect concentration C. At C = 0%, it forms the n-type LaO/TiO2 interface; at C = 100%, all the Ti atoms at the interface are replaced by Al, giving an excessive AlO2 plane, and thus leads to the p-type SrO/AlO2 interface; at C = 50%, the 0.5e per 2D unit cell can be precisely counteracted by the half layer Al3+ ions. For the same reason, in the p-type (SrO/AlO2) interface, the LaSr defect suppresses the p-type behavior with the La3+ ion acting as a donor (Figure 5). The structure with np-type interfaces has the lowest band gap (see Table 2). This attributes to the broken inverse symmetry. When the symmetry is broken, a nonzero net

Δdi(K) = {Zi̅ + 1(K) − Zi̅ (K)}relax − {Zi̅ + 1(K) − Zi̅ (K)}ideal K = O or M

(5)

K represents the ion type: oxygen (O) or metal cation (M). Z̅ is the average z-coordinate of those ions within one layer, and i is the atomic layer index. The presence of interface leads to bucklings of the AO and BO2 planes due to different bonding environment from the bulk. The relaxations of cations and oxygens are different (see Figure 4). In the STO layer of the p-type interface, the interplanar distance between oxygens is nearly unchanged, while that between cations first shrinks and then expands from the interface, alternatively. In the LAO layer of the p-type interface, the interplanar distances for both cations and oxygens are generally shortened, with different magnitudes. For the ntype interface, both cations and oxygens planes in the LAO layer are under compression, while, in the STO layer, the distance between oxygen planes slightly expands. For the superlattice consisting of both p- and n-type interfaces, the oxygens and cations behave similarly: in the STO layer, they 24996

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Figure 6. Planar- (black solid) and macroscopic-average (red dashed) of the internal potential of the [STO]7/[LAO]4 superlattice without (upper panel) and with (lower panel) the VLa,O defect. The red solid lines are the linear fittings of the internal field in the STO or LAO layer.

that, within the whole range of the Sr and O chemical potential, three types of point defect, AlTi, LaSr, and VO′ , are most stable. These defects usually coexist on the STO surface. We have investigated several STO/LAO interfaces comprising these point defects. The interfaces with substitutional AlTi and LaSr defects are shown to be energetically favored. This indicates that the intermixing diffusion is common in the interface. These two defects suppress the original n-type and p-type features of the interfaces, respectively. The polar combined defect VLa,O compensates the internal field and increases the band gap in such system.

Figure 5. Density of states for the structures with AlTi, V′O, LaSr, and VLa,O defects, respectively. The density of states for the clean nondefective interface structures are shown with shaded areas. The Fermi level is set to zero and denoted with a dashed line. It is clear that the LaO/TiO2 interface is changed from n-type into p-type when the Ti is substituted by the Al atom.

Table 2. Band Gap of the Structure with Different Defects type of interface

n

p

np

V′O

AlTi

LaSr

VLa,O

band gap (eV)

1.85

1.81

1.36

1.78

1.75

1.59

1.94

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internal electric field is established, pointing from the n-type interface to the p-type. The valence band minimum is gradually pushed to higher energy by the internal field. This mechanism is universal in the superlattice systems with asymmetric upper and lower interfaces, for instance, the PbTiO 3 /SrTiO 3 system.37 The net effect is to reduce the band gap as the thickness of the superlattice period increases. Bristowe et al.38 have predicted that the band gap will vanish when there are 12 STO and LAO ucs within one superlattice period. The combined polar defect VLa,O, however, provides an inverse electric field. This compensates the dipole moment in the LAO layer. In this way, it leads to the largest band gap among all the structures examined. To see the impact of the polar defect, we investigate the internal electric field. It is clear in Figure 6 that the direction of the internal field within the LAO layers of the superlattice reverses when the VLa,O defect exists, from 9 × 10−5 to −8 × 10−5 V/Å. Within the STO layer, the change in the internal field is remarkable, from −1 × 10−5 to 7 × 10−7 V/Å, a reduction by more than 1 order. This is the reason for the wider band gap. Also, the change of the macroscopic-average potential at the interface becomes less sharp in the defective structure (denoted by the arrow in Figure 6). The effect induced by such polar defect consists with the electrostatic model in ref 39.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by NKPBRC (2010CB923404) and NNSFC (10974081, 10979017, 11147126, and 11274153). We are grateful to the High Performance Computing Center of Nanjing University and the High Performance Computing Center of China University of Mining and Technology for the award of CPU hours to accomplish this work. M.G. thanks China Scholarship Council and Indiana State University for all the resources provided during the exchange period.

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CONCLUSIONS We have examined the formation energies for the intrinsic defects on the STO surface. The surface phase diagram shows 24997

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