Tailoring a two-dimensional electron gas at the LaAlO₃/SrTiO₃ (001) interface by epitaxial strain

Abstract

Recently a metallic state was discovered at the interface between insulating oxides, most notably LaAlO₃ and SrTiO₃. Properties of this two-dimensional electron gas (2DEG) have attracted significant interest due to its potential applications in nanoelectronics. Control over this carrier density and mobility of the 2DEG is essential for applications of these unique systems, and may be achieved by epitaxial strain. However, despite the rich nature of strain effects on oxide materials properties, such as ferroelectricity, magnetism, and superconductivity, the relationship between the strain and electrical properties of the 2DEG at the LaAlO₃/SrTiO₃ heterointerface remains largely unexplored. Here, we use different lattice constant single-crystal substrates to produce LaAlO₃/SrTiO₃ interfaces with controlled levels of biaxial epitaxial strain. We have found that tensile-strained SrTiO₃ destroys the conducting 2DEG, while compressively strained SrTiO₃ retains the 2DEG, but with a carrier concentration reduced in comparison to the unstrained LaAlO₃/SrTiO₃ interface. We have also found that the critical LaAlO₃ overlayer thickness for 2DEG formation increases with SrTiO₃ compressive strain. Our first-principles calculations suggest that a strain-induced electric polarization in the SrTiO₃ layer is responsible for this behavior. The polarization is directed away from the interface and hence creates a negative polarization charge opposing that of the polar LaAlO₃ layer. This behavior both increases the critical thickness of the LaAlO₃ layer, and reduces carrier concentration above the critical thickness, in agreement with our experimental results. Our findings suggest that epitaxial strain can be used to tailor 2DEGs properties of the LaAlO₃/SrTiO₃ heterointerface.

Strain has been used to engineer and enhance numerous properties of materials. For example, mobility in semiconductors (1,2), and transition temperatures in ferroelectric materials (3–6), and superconductors (7) have been controlled by strain. A recently discovered two-dimensional electron gas (2DEG) at the LaAlO₃/SrTiO₃ interface (8,9) has attracted great interest due to its unique application to nanoscale oxide devices (10). So far, most studies of 2DEGs at oxide interfaces were performed using TiO₂-terminated SrTiO₃ bulk single-crystal substrates. Despite the rich nature of strain effects on oxide materials properties, the relationship between the strain and electrical properties of the 2DEG at the LaAlO₃/SrTiO₃ heterointerface remains largely unexplored.

One important effect of strain arises from the constraint that integrating 2DEGs to other functional devices or substrates always involves strain. Understanding the effect of strain on a 2DEG at the LaAlO₃/SrTiO₃ interface is essential for these considerations. In addition, incorporation of strain might lead to unique functional properties. For example, strain can induce an electric polarization in otherwise nonpolar SrTiO₃ (11). It has been predicted that polarization can be used to control 2DEG properties at oxide heterointerfaces (12, 13). These effects provide tools to engineer the 2DEG behavior.

To address these issues, we explore the effect of epitaxial strain on transport properties of the LaAlO₃/SrTiO₃ interface. We create the 2DEG interface on strained single-crystal (001) SrTiO₃ templates grown on perovskite oxide substrates with various lattice mismatch. Pseudomorphic growth of the LaAlO₃/SrTiO₃ bilayer produces a continuously strained system, including the interface at which the 2DEG resides. This strained system allows us to add a new degree of freedom in the LaAlO₃/SrTiO₃ system and investigate the strain effect on its transport properties. We demonstrate that tensile strain makes the interface insulating, while compressive strain makes the interface metallic and allows modulating the critical thickness of LaAlO₃ and the 2DEG conductivity.

Experimental Methods

LaAlO₃/SrTiO₃ thin film heterostructures were grown on various single-crystal substrates using pulsed-laser deposition (PLD) with in situ high-pressure reflection high-energy electron diffraction (RHEED) (14). Fig. 1A shows the schematic of the thin film heterostructure. Table 1 shows substrates that were used in this study to vary the SrTiO₃ strain state from biaxial compressive to biaxial tensile in the plane. As shown in Fig. 1, (001) SrTiO₃ thin films were grown on (110) NdGaO₃ (NGO), (001) (LaAlO₃)_0.3 - (Sr₂AlTaO₆)_0.7 (LSAT), (110) DyScO₃ (DSO), and (110) GdScO₃ (GSO) substrates. The varying lattice parameters result in an average biaxial strain ranging from -1.21% (compressive) to +1.59% (tensile) in a fully commensurate SrTiO₃ deposited film. All grown single-crystal (001) SrTiO₃ templates were fully coherent with the substrates. (001) SrTiO₃ films were also grown on (001) silicon (Si) substrates using Molecular Beam Epitaxy. Thickness of these quasi-single-crystal (001) SrTiO₃ templates on Si was 100 nm, and the films were almost fully relaxed. The measured SrTiO₃ lattice parameters on Si correspond to an average biaxial strain of 0.15% (15, 16). The biaxial strain state and lattice parameters of the strained (001) SrTiO₃ templates are summarized in Table 1. The full width at half maximum (FWHM) values of 002 rocking curves for the strained SrTiO₃ template are much narrower than that of the bulk SrTiO₃ single crystal (17). The single-crystal (001) SrTiO₃ templates were also etched using buffered hydrofluoric acid solution to maintain Ti-termination after the growth. The atomic percent of Sr, Ti, and O in the films were determined with wavelength dispersive X-ray spectroscopy. The chemical ratio of grown templates was the same as that of SrTiO₃ bulk single crystal within experimental error. This result confirms that the quality of SrTiO₃ templates is comparable with the bulk single-crystal SrTiO₃ substrate, ruling out extrinsic effects in our experiments.

Fig. 1.

Structural characterization of heterostructures. (A) Schematic diagram of grown structures. Thickness of LaAlO₃ layer was varied from 1 to 30 unit cells on STO on LSAT, NGO, Si, DSO, and GSO substrate, (B) RHEED intensity oscillations for the growth of LAO and STO on LSAT substrate. The insets show the RHEED pattern at the end of the LAO and STO growth. (C) High-resolution TEM image of LAO on STO on LSAT. Clear intensity differences between separate LaAlO₃ and SrTiO₃ layers in both cases and images showing distinctly the individual La and Sr atoms. (D) AFM images of LAO on STO on DyScO₃, substrates.

Table 1.

Results from high-resolution X-ray diffraction measurements on the films at room temperature are given

	a (Å)	c (Å)	Biaxial lattice mismatch
LaAlO3 (10 uc) on SrTiO3 (50 uc) on NdGaO3
SrTiO3	3.860	3.964	−1.21%
NGO	3.859	3.866
LaAlO3 (10 uc) on SrTiO3 (100 uc) on LSAT
SrTiO3	3.868	3.940	−0.96%
LSAT	3.869	3.867
LaAlO3 (10 uc) on SrTiO3 (120 nm) on Si
SrTiO3	3.911	3.985	0.15%
Si	3.840	3.840
LaAlO3 (10 uc) on SrTiO3 (20 uc) on DyScO3
SrTiO3	3.944	3.939	1.11%
DyScO3	3.944	3.939
LaAlO3 (10 uc) on SrTiO3 (20 uc) on GdScO3
SrTiO3	3.964	3.875	1.59%
GdScO3	3.963	3.967

The in-plane (a) and out-of-plane (c) lattice constants and lattice mismatch between the SrTiO₃ films and single-crystal substrates on average of two orthogonal directions. The a- and c-lattice parameters of single-crystalline SrTiO₃ are 3.905 Å. All SrTiO₃ templates were fully coherent except STO/Si (12). (002), (101) of SrTiO₃ and cubic substrates, LSAT, Si (200)_pseudo-cubic of (101)_pseudo-cubic of orthorombic substrate, GdScO₃ and DyScO₃, NdGdO₃ were observed to determined in-plane and out-of-plane lattice parameters. Biaxial strain of SrTiO₃ templates

LaAlO₃ overlayers were deposited using PLD on these variously strained Ti-terminated single-crystal SrTiO₃ templates. RHEED intensity oscillations of the specular spots show layer-by-layer growth mode (Fig. 1B), similar to those observed for LaAlO₃ films on SrTiO₃ single-crystal substrates. High-resolution transmission electron microscopy (TEM) cross-sectional image in Fig. 1C shows that the LaAlO₃/SrTiO₃ film on LSAT has high crystalline quality and an atomically sharp interface. For all substrates, surfaces of LaAlO₃ and SrTiO₃ films were atomically smooth with single unit cell high steps measured by atomic force microscopy (AFM), as seen in Fig. 1D. As a result, we confirmed that all biaxial strained heterostructures in this report were atomically controlled and grown epitaxially. More details about growth are described in ref. 11 and Materials and Methods.

Results and Discussion

It is known experimentally that a conducting 2DEG forms at the LaAlO₃/bulk SrTiO₃ interface only after the LaAlO₃ overlayer thickness exceeds a critical value of four unit cells (18). We have found that this critical thickness depends on the strain of the system. We determined this critical thickness by measuring the conductivity of strained LaAlO₃/SrTiO₃ bilayers for different thickness of the LaAlO₃ layer. As shown in Fig. 1, the LaAlO₃ overlayer thickness was changed from 0 to 30 unit cells while the thickness of SrTiO₃ template on NGO, LSAT, DSO, and GSO substrates was fixed at 50 unit cells. We also checked the critical thickness of LaAlO₃ on Ti-terminated (001) SrTiO₃ bulk single crystal and on quasi-single-crystal (001) SrTiO₃ templates on Si (19) as a reference.

In the case of the two samples with unstrained SrTiO₃ layers (LaAlO₃ on bulk single-crystal SrTiO₃ substrate and LaAlO₃ on relaxed SrTiO₃ templates on Si), the critical thickness was in agreement with that previously reported, i.e., four unit cells. However, in the compressive strain states, (SrTiO₃ templates on LSAT and NGO), the critical thickness of LaAlO₃ increased to 10 unit cells and 15 unit cells, respectively, as shown in Fig. 2A. In all the cases, the conductivity saturated above the critical thickness of the LaAlO₃ overlayer. However, unlike the nonstrained state, the conductivity vs. thickness of LaAlO₃ had a gradual rather than an abrupt change at the critical thickness. For instance, in the case of LaAlO₃/SrTiO₃/LSAT measurable conductivity was detected at 10 unit cells (u.c.) LaAlO₃ thickness, but it did not saturate until 20 unit cells. There is however a clear trend of increasing LaAlO₃ critical thickness with increasing compressive biaxial in-plane strain.

Fig. 2.

Effect of strain on 2DEG. (A) Critical thickness of LaAlO₃ under biaxial strain. While other samples had 50 unit cell-thick SrTiO₃ layer, LAO/STO/Si had 100 nm-thick STO to get nominally unstrained STO layer on Si. Conductivity vs. thickness of LaAlO₃ in LAO/STO interface on various substrates was represented in inset. (B) Room-temperature carrier concentration at the LAO/STO interface under various biaxial strains. Carrier concentrations in tensile strain state were below our measurement limit.

Fig. 2B shows the room-temperature carrier concentration at each strain state above the critical thickness of LaAlO₃. Similar to the critical thickness of LaAlO₃ layer, we find nearly the same carrier concentration at both near-zero strain states, LaAlO₃ on SrTiO₃ bulk single crystal and LaAlO₃ on quasi-single crystal (001) SrTiO₃ template on Si. The saturation carrier concentration (above the critical thickness) decreased with increasing compressive strain. Although LaAlO₃/SrTiO₃ interfaces on DSO and GSO were grown and treated in the same manner, the interfaces were not conducting within our measurement limit at any thickness of LaAlO₃ overlayer in these tensile-strained films.

Our experimental results indicate that tensile-strained SrTiO₃ destroys the conducting interfacial 2DEG, while compressive-strained SrTiO₃ preserves the 2DEG, but with decreased interfacial carrier concentration. The maximum carrier concentration at the SrTiO₃ unstrained state suggests that it is the strain-dependence of SrTiO₃ properties that control the 2DEG. It has been predicted theoretically that free-standing biaxially strained SrTiO₃ under electrical short-circuit boundary conditions can develop an electric polarization (20, 21). Compressive strain is predicted to produce an [001] (out-of-plane) polarization, and tensile strain to produce a [110] (in-plane) polarization. Experimental evidence suggests a more complex picture, with many strain-states resulting in a relaxor behavior at room temperature (11, 22) without a stable switchable polarization.

However, we expect the strain-induced SrTiO₃ (STO) properties to be altered by the LaAlO₃ overlayer. Observations from TEM (23, 24), synchrotron radiation X-ray scattering (25, 26), and tunneling (27), indicate that in strain-free SrTiO₃ a few unit cells near the LaAlO₃ interface have ferroelectric-like structural distortions with local polarization pointing away from the interface, and decreasing in magnitude with distance from the interface (28). Biaxial compressive strain induces a tetragonal distortion along 001, which would enhance this polarization, potentially uniformly polarizing the SrTiO₃ throughout its thickness (29).

Fig. 3 schematically compares the strained and unstrained systems. In the unstrained system positively charged (LaO)⁺ atomic layers and negatively charged (AlO₂)^- atomic layers create an average polarization whose positive bound charge resides at the interface, as shown schematically in Fig. 3A (left). This polarization charge is responsible for the intrinsic electric field E₀ in LaAlO₃ (shown by arrow in Fig. 3A) resulting in an electric potential difference between the LaAlO₃ surface and the LaAlO₃/SrTiO₃ interface that increases with LaAlO₃ layer thickness. Above the LaAlO₃ critical thickness, charge is transferred to the LaAlO₃/SrTiO₃ interface (shown by a blue filling) to avoid this polarization catastrophe.

Fig. 3.

Calculated atomic structure of unstrained (A) and compressively strained (B) LaAlO₃(3u.c.)/SrTiO₃ system. In B Ti-O and Sr-O displacements are amplified by a factor of eight as compared to the calculated results for visual comprehension. Left and right columns show schematically the 2DEG formation and the effect of the polarization P in the strained SrTiO₃ on the 2DEG as described in text.

The compressively strained SrTiO₃ layer contains polar displacements of the Ti⁴⁺ ions with respect to the O^2- ions, shown in Fig. 3B for the case of uniform polarization. These displacements are responsible for a polarization P pointed away from the interface [indicated by an arrow at the bottom of Fig. 3B (left)]. The polarization orientation is determined by the presence of the LaAlO₃ layer and is likely not switchable. The polarization produces a negative bound charge at the LaAlO₃/SrTiO₃ interface [indicated in Fig. 3B (left)] that creates an additional electric field in LaAlO₃ equal to P/ε_LAO, where ε_LAO is the dielectric constant of LaAlO₃, that opposes the intrinsic electric field E₀. The presence of polarization in the compressively strained SrTiO₃ layer reduces the total electric field in LaAlO₃ and hence enhances the critical thickness necessary to create a 2DEG at the LaAlO₃/SrTiO₃ interface due to the polarization catastrophe effect. Above this critical thickness, the mobile interfacial carrier concentration would be reduced by the interfacial bound charge (12,13).

In order to quantify these effects we have completed first-principles calculations of the LaAlO₃/SrTiO₃ bilayer under various strain states based on density functional theory (DFT), as described in Materials and Methods. Fig. 4 shows calculated ionic displacements for unstrained and 1.2% compressively strained (LaAlO₃)₃/(SrTiO₃)₅ structures. It is seen that in the unstrained case polar Ti-O displacements in the SrTiO₃ layer are very small, consistent with the previous calculations (30). The in-plane 1.2% compressive strain produces sizable ionic displacements, polarizing the SrTiO₃ layer. The calculation predicts that the induced polarization is oriented away from the interface and is not switchable. The magnitude of the polarization is P ≈ 0.18 C/m², as found from the known polar displacements in the strained SrTiO₃ layer using the Berry phase method (31, 32).

Fig. 4.

B (Ti, Al) cite atom—oxygen (O) atom displacements in the unstrained (squares) and 1.2% compressively strained (circles) (LaAlO₃)₃/(SrTiO₃)₅ structure.

The critical thickness t_c in the presence of a SrTiO₃ polarization can be estimated as follows:

[1]

where , ε_g is the band gap of SrTiO₃, and are the valence band maxima (VBM) of SrTiO₃ and LaAlO₃ respectively, and E is the electric field in LaAlO₃. The latter is reduced from the intrinsic value of E₀ due to polarization P of SrTiO₃ so that

[2]

where ε_LAO is the dielectric constant of LaAlO₃. Due to the reduced electric field in LaAlO₃ in the presence of the SrTiO₃ polarization, the critical thickness [1] is enhanced. The intrinsic electric field E₀ can be estimated from the experimentally measured critical thickness for the unstrained system. Taking into account the experimental band gap of SrTiO₃ ε_g = 3.2 eV and the VBM offset between SrTiO₃ and LaAlO₃ , (33) we find that δε = 3.55 eV. Using the relationship

[3]

we obtain that E₀ ≈ 0.23 V/Å which is consistent with our first-principles calculation predicting E₀ ≈ 0.22 V/Å, and with calculations by others (30, 34, 35). Using Eqs. 1–3 we obtain

[4]

Using the calculated polarization value P ≈ 0.18 C/m² for 1.2% compressive strain in the SrTiO₃ layer, and the calculated electric fields in the LaAlO₃ and SrTiO₃ layers in the strained LaAlO₃/SrTiO₃ system, we estimate the dielectric constant of the LaAlO₃ grown on 1.2% compressively strained SrTiO₃ to be ε_LAO ≈ 18ε_o. This value is consistent with that obtained from the induced polarization of 0.34 C/m² in the LaAlO₃ layer, as is estimated from the calculated ionic displacements using the Berry phase method. [We note that the estimated value of the dielectric constant of the unstrained LaAlO₃ is ε_LAO ≈ 24ε_o which is consistent with the previously found result (36)]. Using. Eq. 4 and the dielectric constant ε_LAO ≈ 18ε_o we obtain t_c ≈ 9 u.c.. This value is higher than the critical thickness (4 u.c.) for the unstrained system, and is consistent with the experimental result for the 1.2% strained LaAlO₃/SrTiO₃ structure. In the structural model used in our DFT calculation the SrTiO₃ polarization is screened by charge transferred to the SrTiO₃ surface.

For the case of tensile strain in the SrTiO₃ layer, our experiments indicate that there is no conducting 2DEG for biaxial tensile strains above 1.1%. Free-standing SrTiO₃ at zero temperature has been predicted to develop an in-plane polarization in the (110) direction under biaxial tensile strain. Experiment suggests that relaxor behavior, with nanoscale polar regions that can be aligned in an electric field, occurs in many tensile-strained SrTiO₃ samples at room temperature. Stabilization of a uniform in-plane polarization by the LaAlO₃ layer does not seem likely. If such nanoscale regions near to the interface were present in our samples, bound charge at polarization discontinuities between random nanopolar regions would tend to be locally screened by carriers at the 2DEG interface. This behavior would lead to localization of these carriers, preventing us from observing conduction in these samples.

Another aspect is strain in the LaAlO₃ overlayer. The bulk pseudocubic lattice constant of LaAlO₃ is 3.791 Å, so that coherent LaAlO₃ even on unstrained SrTiO₃ has a 3% tensile strain. Growing the bilayer on a GSO substrate results in 4.5% tensile strain in the LaAlO₃ layer. An NGO substrate reduces the LaAlO₃ strain to 1.8% tensile, but for all substrates used the LaAlO₃ layer is under tensile strain. Our TEM analysis of these samples indicates that the LaAlO₃ layer on SrTiO₃ is fully coherent when grown on LSAT (2% LaAlO₃ tensile strain) and SrTiO₃, but that growth on DSO (leading to 4% LaAlO₃ tensile strain) results in partial relaxation of the LaAlO₃. Such defect incorporation might alter the conduction properties of the interface. However, the SrTiO₃ layer on Si (grown by Molecular beam epitaxy) is almost fully relaxed, and the bilayer shows a fully conducting interfacial 2DEG, but with lower mobility. This observation suggests that such defects do not destroy the 2DEG. Large tensile strain in LaAlO₃ has been predicted (37) to alter the Al-O bond lengths, which could affect the electronic structure.

We have demonstrated that properties of the 2DEG formed at the LaAlO₃/SrTiO₃ interface can be controlled by epitaxial strain. Both the critical thickness of the LaAlO₃ overlayer required to generate the 2DEG and the carrier concentration of the 2DEG depend on the strain of the SrTiO₃ layer. Compressive strain increases the critical thickness and decreases the saturated carrier concentration. Our DFT calculations indicate that a strain-induced polarization stabilized by the LaAlO₃ overlayer is responsible for these changes. Changes in critical thickness and carrier concentration estimated from the DFT calculations are in agreement with the experimental data.

The dependence of 2DEG properties at the LaAlO₃/SrTiO₃ interface on the strain state opens a new correlation between strain-induced polarization and the electrical properties of oxide interfaces. We believe that such strain engineering can be very useful for oxide 2DEG device applications, and the relation between strain and 2DEG properties provides a new tool in the manipulation of oxide interfacial 2DEGs.

Materials and Methods

Epitaxial LaAlO₃ and SrTiO₃ thin films were grown on (001) LSAT, (110) NdGaO₃, (110) GdScO₃, and (110) DyScO₃ substrates by PLD. To grow heterostructures by PLD, substrates were attached to a resistive heater and positioned 5.0 ∼ 6.0 cm from the target. A KrF excimer laser (248 nm) beam was focused on a stoichiometric LaAlO₃ and SrTiO₃ single-crystal target to an energy density of 2.0 ∼ 2.5 J/cm² and pulsed at 3 ∼ 5 Hz. SrTiO₃ templates were grown at substrate temperatures ranging from 650 to 850 °C and oxygen pressures of 10–100 mTorr. Before deposition, low miscut (< 0.05°) LSAT, NGO, DSO, and GSO substrates were treated by a modified buffered hydrofluoric acid etch and annealed in oxygen at 1,000 ∼ 1,100 °C for 2 ∼ 12 h to create atomically smooth surfaces with unit cell step. The PLD system is equipped with high-pressure RHEED, which enabled atomic layer controlled growth and in situ monitoring during the growth. SrTiO₃ templates were etched using buffered hydrofluoric acid for 30 ∼ 90 s to maintain Ti-termination after growth SrTiO₃ layer. LaAlO₃ films were grown at 550 °C at oxygen pressures of 10^-3 mbar and cooled down to room temperature at the same oxygen pressure.

The three-dimensional strain state of the films was determined using high-resolution four-circle X-ray diffraction (Bruker D8 advance). The microstructure and interfacial structure of the samples were characterized by cross-sectional TEM. Film surfaces were imaged by AFM (Veeco).

After the growth, Al contacts were made by wire bonding near the four corners of the sample for van der Pauw electrical characterization. A Keithley 2700 sourcemeter combined with a 2400 switch matrix multimeter was used for the van der Pauw measurements of conductance and carrier concentration. The sheet resistance was calculated by fitting slopes to the four point IV curves measured between the four combinations of contacts. The nominal sheet carrier concentration was determined from the Hall coefficient as n_2D = -t/R_He where t is the film thickness, R_H is the Hall coefficient, and e is the charge of an electron. The mobility was determined from the sheet resistance R_□ and sheet carrier concentration n_2D as μ = 1/en_2DR_□.

Density functional calculations were performed within the local density approximation using the plane-wave pseudopotential method (38, 39), similar to the calculations performed previously (40). In the calculations we neglected the effect of strong correlations which is justified due to both LaAlO₃ and SrTiO₃ being band insulators. We considered a LaO/TiO₂-interfaced (LaAlO₃)_n/(SrTiO₃)_m bilayer (where n and m are the numbers of unit cells of LaAlO₃ and SrTiO₃ respectively), as a model system. The LaAlO₃/SrTiO₃ bilayer was placed in a LaAlO₃/SrTiO₃/vacuum/SrTiO₃/LaAlO₃/vacuum supercell, where the doubled bilayer was used to avoid an unphysical electric field in vacuum which otherwise would occur due to the potential step within the LaAlO₃ layer and periodic boundary conditions of the supercell calculations. The in-plane lattice constant of the unstrained superlattice was fixed to the calculated bulk lattice constant of SrTiO₃, i.e., a = 3.871 Å. For the strained systems the in-plane lattice constant was constrained to be a certain percentage smaller than the bulk one. To reduce the effect of the SrTiO₃ surface on atomic structure and ionic displacements within the SrTiO₃ layer we used a boundary condition according to which the atomic positions within one unit cell on the SrTiO₃ surface were fixed to be the same as in the respectively strained bulk SrTiO₃. The latter were computed separately for the unstrained and strained bulk SrTiO₃. All the other atoms in the superlattices were relaxed.