Instability, intermixing and electronic structure at the epitaxial ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3\left(001\right)$ heterojunction

Abstract

The question of stability against diffusional mixing at the prototypical LaAlO₃/SrTiO₃(001) interface is explored using a multi-faceted experimental and theoretical approach. We combine analytical methods with a range of sensitivities to elemental concentrations and spatial separations to investigate interfaces grown using on-axis pulsed laser deposition. We also employ computational modeling based on the density function theory as well as classical force fields to explore the energetic stability of a wide variety of intermixed atomic configurations relative to the idealized, atomically abrupt model. Statistical analysis of the calculated energies for the various configurations is used to elucidate the relative thermodynamic stability of intermixed and abrupt configurations. We find that on both experimental and theoretical fronts, the tendency toward intermixing is very strong. We have also measured and calculated key electronic properties such as potential energy gradients and valence band discontinuity at the interface. We find no measurable electric field in either the LaAlO₃ or SrTiO₃, and that the valence band offset is near zero, partitioning the band discontinuity almost entirely to the conduction band edge. Significantly, we find it is not possible to account for these electronic properties theoretically without including extensive intermixing in our physical model of the interface. The atomic configurations which give the greatest electrostatic stability are those that eliminate the interface dipole by intermixing, calling into question the conventional explanation for conductivity at this interface—electronic reconstruction. Rather, evidence is presented for La indiffusion and doping of the SrTiO₃ below the interface as being the cause of the observed conductivity.

Introduction

As a class of materials, complex oxides exhibit an exceedingly wide range of structural, compositional, and functional properties. The working definition of a complex oxide is an inorganic solid consisting of more than one metal cation and oxygen anions. The simplest of the complex oxides contain (only) two metal cations in distinct, well-defined sublattices. For example, the perovskites have the formula ABO₃, where twelve-coordinate A-site cations are at the corners of the unit cell (u.c.), six-coordinate B-site cations are at body center positions, and six-coordinate O anions are at face-center positions. The structural and compositional diversity of complex oxides is realized by the ease with which different metal cations that can be placed within the A- and B-site sublattices. For instance, the A sites can be populated by mixtures of alkaline earth and rare earth cations, and the B sites can be occupied by first and second row transition metal cations, in addition to several of the Group IIIA, IVA and VA cations, giving rise to a wide range of compositions, many of which are achieved via solid solution formation. The formal charge degree of freedom on the B-site when transition metal cations are used allows mixing and matching of A-site cations to achieve a range of charge configurations. As the chemical identities of A and B sites are varied, the resulting structures change in response to variable cation radii. Complex oxides can be characterized by useful metrics such as the tolerance factor $\left(f\right)$ for perovskites, defined as $f=(r_A+r_O)/\sqrt{2}(r_B+r_O)$ [1]. Cubic perovskite structures result when $f$ is near unity. Distorted perovskites with rhombohedral and eventually orthorhombic structures occur as the size of the A-site cation drops, and the B–O–B bond angle deviates from 180°. B–O–B bond angle distortion in turn results in a decrease in the one-electron bandwidth due to a drop in the $d$-electron transfer amplitude between adjacent B sites associated with changes in B–O 3d–2p hybridization. The functional impact of this kind of structural distortion is a change in the metal–insulator transition temperature.

The wide range of functional properties exhibited by complex oxides is then a direct consequence of the chemical identity of the constituent cations and the associated structural distortions. Perhaps the best know example of this phenomenon is the occurrence of high-$T_c$ superconductivity in the layered cuprates (La_2−xSr_xCuO₄), brought about by Sr-induced hole doping of the formally charge-neutral (Cu–O) state to Cu^(2+x)+(Cu–O)^x+ [2], [3], [4]. A less well-known example is that of doped SrTiO₃ (STO), a cubic, diamagnetic band insulator with an optical gap of 3.2 eV. Doping the A site with La(III) or the B site with Nb(V) at the ∼1 at.% level transforms STO into an n-type oxide semiconductor [5]. Conversely, doping LaTiO₃, an antiferromagnetic Mott insulator, with Sr(II) at the ∼5 at.% level results in a phase transition to a paramagnetic metal ground state. [6].

The range of functional properties that can be achieved in bulk complex oxides by mixing and matching cations generates tantalizing possibilities when considering single layers and superlattices prepared by epitaxial thin-film growth techniques. By combining a high degree of stoichiometric control with the reduced dimensionality in the growth direction achievable by ultrathin film and small-period superlattice growth, it is in principle possible to create artificially structured materials with novel properties not realized in the bulk. An excellent example of this phenomenon is recent work by Santos et al. [7] in which ozone-assisted molecular beam epitaxy (MBE) was used to grow small-period superlattices consisting of alternating unit cells (u.c.) of SrMnO₃ and LaMnO₃ on SrTiO₃(001), and then comparing the resulting electronic and magnetic properties with those of random alloys of MBE-grown La_0.5Sr_0.5MnO₃. Differences were observed in the saturation magnetization and resistivity between superlattices and the solid solution of the same overall composition, particularly at low temperatures, and novel tuning of the magnetic properties could be achieved by injected an extra u.c. of SrMnO₃ and LaMnO₃. However, the same forces of nature that allow us to generate a wide range of compositions in complex oxides in the first place can also promote solid solution formation at interfaces that we intend to be abrupt. These forces include mutual solubility and structural similarity, both of which can readily homogenize an otherwise abrupt interface at the junction of materials with different compositions. The problem is exacerbated by the thermal energy available to the system from substrate heating which is in turn required to achieve epitaxial growth, as well as the sometimes high ion energies of species within the laser plume generated during pulsed laser deposition (PLD), an exceedingly popular method for complex oxide film growth. It is thus of considerable interest to engineer the deposition conditions so that intermixing is kinetically constrained at the interface, giving rise to metastable structures that retain a high degree of abruptness.

Against this backdrop, we consider the LaAlO₃/ SrTiO₃(001) (LAO/STO) interface. This material system has attracted widespread interest over the past several years because of the common, but not universal, observation of conductivity near the interface under certain deposition conditions, despite the fact that both constituent materials are band insulators. Starting with seminal work by Ohtomo and Hwang [8], soon thereafter reproduced and built upon by Thiel et al. [9], several experimental groups worldwide have synthesized this interface in various forms and have made a common set of observations. These include the following: (1) when using on-axis PLD (the most commonly used growth method for LAO/STO interface preparation), layer-by-layer growth and conductive interfaces occur only when the oxygen partial pressure is between $\sim 10^{-4}$ and $\sim 10^{-6}$ Torr, (2) interface conductivity is unambiguously observed only when LAO is grown on TiO₂-terminated STO(001), which can be realized by a buffered HF etch followed by a tube furnace anneal in oxygen, (3) in the absence of external perturbations, conductivity occurs at and above a threshold LAO thickness of 4 u.c., (4) the measured carrier concentration is less than that expected based on electronic reconstruction arguments involving transfer of half an electron per unit cell from LAO into the STO, unless the film is not grown and/or annealed in sufficient oxygen to prevent reduction of the STO, and, (5) the interface appears to be abrupt when examined using high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM), as reviewed recently by Muller [10]. In HAADF-STEM images, the high degree of atomic number (Z) contrast realized by collecting scattered electrons at high angles, in conjunction with a highly focused beam and aberration correction in the lenses, results in La cations “lighting up” relative to Sr cations, giving the appearance of a high degree of interfacial abruptness. Imaging alone is not sufficient to rule out cation disorder at the LAO/STO interface, as high resolution electron energy loss measurements in conjunction with HAADF-STEM have shown [11]. However, a majority of experimentalists and theorists who have published on this system to date tend to model the interface as if it were abrupt. If cation disorder (intermixing) is considered at all, it is thought to be limited approximately at most one unit cell on either side of the interface.

The presumed cause of LAO/STO interface conductivity is alleviation of the so-called “polar catastrophe”, which results from forming a junction between a polar material (LAO) and a nonpolar material (STO). STO consists of alternating layers of (Sr²⁺O²⁻)⁰ and (Ti⁴⁺O²⁻₂)⁰ along [001]. Both constituent layers are formally charge neutral. In contrast, LAO consists of alternating (La³⁺O²⁻)⁺ and (Al³⁺O²⁻₂)⁻ layers, and thus exhibits a polarity along [001]. Atomically abrupt interface formation between LAO and STO thus gives rise to a polar discontinuity which extends to the LAO’s surface. Elementary electrostatic considerations suggest that layer-by-layer growth of LAO on STO and abrupt interface formation will lead to a diverging electric potential as a result of the accumulation of dipoles within the LAO film — the so-called “polar catastrophe”. This unstable situation can in principle be mitigated by transfer of half an electron per unit cell from (La³⁺O²⁻)⁺ to (Ti⁴⁺O²⁻₂)⁰ at the interface for TiO₂-terminated STO, or half a hole per unit cell from (Al³⁺O²⁻₂)⁻ to (Sr²⁺O²⁻)⁰ for SrO-terminated STO. Electronically, these two interfaces are formally n-type and p-type, respectively, and are routinely referred to as such in the literature. In principle, both interfaces should exhibit some degree of conductivity, albeit with opposite majority carriers. Moreover, the carriers should be confined to the interface to form a two-dimensional electron or hole gas (2DEG or 2DHG) if there is sharp band bending there. However, conductivity has been observed only at the n-type interface, and it is routinely ascribed to the presence of a 2DEG.

Nakagawa et al. [11] carried out cross-sectional HAADF-STEM measurements on PLD-grown LAO/STO(001) heterojunctions of both polarities (n- and p-type). These authors found that cation disorder in the form of La and Ti cross diffusion exists at both kinds of interfaces, as seen in Fig. 1(a) and (b). However, the p-type interface was found to be somewhat more abrupt than the n-type interface, with the interface width being slightly less than 2 nm for the p-type interface and slightly greater than 2 nm for the n-type interface. Additionally, the presence of Ti(III) within a few nm of the n-type interface was deduced by fitting Ti L-edge spectra to linear combinations of appropriate reference spectra (Fig. 1(a)). Likewise, O vacancies $\left(V_O\right)$ were deduced at both interfaces by fitting O K-shell spectra to those of bulk LAO, bulk STO and O-deficient STO (SrTiO_3−δ, where $\delta =0.25$), as seen in Fig. 1(c) and (d). Ironically, more $V_O$ were found at the p-type interface, despite the virtual absence of Ti(III). The electrical asymmetry between n- and p-type interfaces was rationalized as follows. Extra electrons from the LaO’s interfacial layer result in the partial reduction of Ti ions near the interface where $V_O$ would normally be found. The absence of free holes at the p-type interface was ascribed to the presence of compensating $V_O$ with the attendant pair of electrons per vacancy. Intrinsic to this argument is the claim that oxygen vacancies at this interface are qualitatively different in origin and effect than those in bulk oxides. Moreover, these authors argue that the electrical and roughness asymmetries are related in the following way. The increase in interface dipole energy resulting from the spread of electrons from the LaO’s interfacial layer across several TiO₂ layers near the n-type interface is compensated by enhanced Sr–La exchange, which reduces the dipole energy and roughens the interface. They suggest that the absence of itinerant charge at the p-type interface eliminates the need for cation exchange, resulting in a sharper interface.

Jia et al. [12] also used STEM to investigate the LAO/STO interface prepared by high-oxygen-pressure radio-frequency sputtering, but did not carry out EELS measurements. These authors observed an increase (decrease) in HAADF intensity as the interface was approached from the STO (LAO) side and interpreted this finding as being due to Sr–La intermixing over a few u.c.

Willmott et al. [13] used surface X-ray diffraction (SXRD) to deduced atom profiles and displacements across the PLD-grown n-type LAO/STO interface by fitting the experimental data to simulations. The results are summarized in Fig. 2. These authors concluded that intermixing occurs and extends over greater distances for Sr and La than for Ti and Al. Their model of the interface includes a few u.c. of predominantly LaTiO₃ and a region of La_1−xSr_xTiO₃ on the STO side of the interface. Such a structure would contain a significant quantity of Ti(III) with the resulting effect of lattice dilation in the $Z$ direction by virtue of the larger ionic radius of Ti(III) compared to Ti(IV), which was consistent with the diffraction data. Density functional theory (DFT) calculations based on the interface composition extracted from SXRD led to the prediction of a significant enhancement in band bending in both the LAO and STO relative to those in the abrupt n- and p-type interfaces. These authors note that La_1−xSr_xTiO₃ is conductive for a wide range of $x$, and at least imply that the La doping of the underlying STO may be at least partially responsible for electron conduction at the n-type interface.

Kalabukhov et al. [14] have used medium energy ion scattering (MEIS) along with atomic force and scanning Kelvin probe (SKP) microscopies to probe atom profiles, morphology and electrostatic potential at PLD-grown n-type LAO/STO(001) interfaces of various thicknesses. The MEIS spectra and associated modeling in the channeling and random directions yield clear evidence for La indiffusion and both Sr and Ti outdiffusion to the surface for LAO thicknesses of up to 4 u.c. Fig. 3 shows the results for 1 u.c. LAO/STO(001) in the random geometry in which the incident beam is not aligned along a low-index direction. Simulations reveal that only ∼50% of the A sites within the top u.c. are populated with La and that significant La atomic fractions must be included in the A sites of the first three u.c. of STO to account for the measured yield. Moreover, SKP measurements reveal inhomogeneities in the surface potential with characteristic sizes of 100–1000 nm which are suggestive of compositional inhomogeneities and, thus, “filamentary” interdiffusion. These authors suggest that fully stoichiometric LAO nucleates on an intermixed phase that forms during nucleation of the first 3 u.c., giving rise to an insulator-to-metal transition at 4 u.c., perhaps as a result of the formation of a La_xSr_1−xTiO₃ conductive layer. It is not clear why the threshold for conductivity should be 4 u.c. unless this thickness of LAO is required to drive enough La diffusion into the STO to form a continuous, conductive doped layer.

While the experiments discussed above were well conceived and well executed, the associated results are often ignored, particularly by those who carry out first principles calculations of electronic structure at the LAO/STO interface. For example, a recent topical review by Pentcheva and Pickett [15] states, “Layer-by-layer growth allows synthesis of phases that are not thermodynamically stable. Recent development of growth techniques like PLD and MBE have enabled the synthesis of oxide superlattices with atomic precision”. The theoretical work reviewed thereafter and, indeed, the vast majority of all theoretical modeling of this interface, starts with a completely abrupt and structurally perfect interface. Similarly, while the possibility of intermixing is sometimes admitted, an abrupt interface paradigm tends to dominate the thinking of experimentalists [16]. However, what Refs. [11], [12], [13], [14] unambiguously show is that at the very least, interfacial intermixing can occur when LAO/STO is prepared by PLD and reactive sputtering, and perhaps also by MBE as well, although very little MBE growth of this system has been reported [17]. The fundamental unanswered question is whether intermixing at the LAO/STO interface is the exception or the rule. Is intermixing an unfortunate consequence of non-optimized growth conditions or ion induced diffusion, or is it a natural result of the thermodynamics of interface formation?

In light of the potential importance of intermixing at the LAO/STO interface in determining electronic structure, and the need to find reliable ways to characterize intermixing at complex oxide interfaces in general, we have undertaken a multi-technique, multi-institutional investigation of interface composition using samples prepared in the pioneering laboratories of Professors Jochen Mannhart and Harold Hwang at the Universities of Augsburg and Tokyo, respectively. This report summarizes our investigation. The analytical techniques we have brought to bear on the problem include Rutherford backscattering spectrometry (RBS), time-of-flight secondary ion mass spectrometry (ToF-SIMS), high-angle annular dark field scanning transmission electron microscopy and electron energy loss spectroscopy (HAADF STM/EELS), angle-resolved X-ray photoelectron spectroscopy (ARXPS) and medium energy ion scattering (MEIS). We have also undertaken first principles DFT as well as classical force field calculations in which interfacial intermixing is explicitly included in our structural models in order to determine the energetics of intermixing, as well as the effect of intermixing on key electronic properties such as valence band offsets and internal electric fields, or band bending. The Report is organized as follows. Section 2 discusses details of film growth. Sections 3 Film and interface composition — 25 unit cell LAO films, 4 Film and interface composition — 4 unit cell LAO films cover interface composition in thicker (25 u.c.) and thinner (4 u.c.) films, respectively. For each thickness, we utilize techniques well suited to the thickness — RBS, ToF-SIMS and HAADF-STEM/EELS for 25 u.c. films, and ARXPS, MEIS and theory for 4 u.c. films. Moreover, we used these different techniques on the same samples from the two laboratories in order to directly compare data from the different methods on a given sample. Section 5 presents results on the determination of band offsets and band bending at the interface of 4 u.c. films based on high-energy resolution XPS along with theoretical prediction of these quantities, and Section 6 summarizes the report. Our purpose is not to write a comprehensive review of the LAO/STO field; other recent reviews can be found [15], [16], [18]. Rather, we focus specifically on interfacial composition and its relationship to electronic structure, a topic that is inadequately dealt with in the LAO/STO literature in our view.