Hetero-interfaces between epitaxial LaAlO3 films and SrTiO3 substrates can exhibit an insulator-metal transition at a critical film thickness above which a quasi-two-dimensional electron gas forms. This work aims to elucidate the significant role the defects play in determining the sources of non-mobile and mobile carriers, the critical thickness, and the dipolar field screening. A model is built based on a comprehensive investigation of the origin of charge carriers and the advanced analysis of structural factors that affect the electronic properties of these hetero-epitaxial interfaces.

In 2004, Ohtomo and Hwang1 demonstrated that at the interface between two bulk insulators, LaAlO3 (LAO) and SrTiO3 (STO), a conductive layer forms, depicted as a quasi-2D electron gas (q-2DEG). This sub-nanometer thickness conducting channel opened up the possibility of a new front in the miniaturization of electronic devices and expanding into oxide systems. The discovery gave rise to rapid multiplication of publications aiming to elucidate the observed behavior. A review of the literature reveals large variations in the electrical characteristics of the hetero-interface. This is mainly due to variations in the film growth conditions, indicating how important the control of these parameters is. Since then, many research groups have focused their effort on describing the origins of this surprising conduction. This first observation of metallic sheet formation was attributed to a decrease in the valence of Ti cations located in the first unit cell of SrTiO3 through a mechanism named “polar catastrophe.”2 However, this model was clearly undermined by many groups involved in experimental and theoretical studies,3–17 and the mechanisms of charge transfer and transport in this system are still not clearly established despite the large quantity of experimental results produced. Other structural and chemical changes have been revealed near the interface, including the expansion of SrTiO3 cells and polar distortions,4,7,18–27 cation intermixing,2,4,11,14,15,28–31 oxygen vacancies9,11,13,32–37 and cationic deficiency in the film.4,16,17,38–43 None of them was found exclusively responsible for the conduction, and a strong synergy is probably operating. The absence of consensus must also be understood as the consequence of a variety of deposition techniques and growth parameters used to synthesize the samples. An in-depth understanding of the link between the growth conditions and the atomic structure is a prerequisite for predicting and controlling the electron transport mechanism in this LAO/STO system. Here, we show that the defect population and the distribution need to be considered in order to understand the electrical behavior.

To address this issue, samples were grown by Pulsed Laser Deposition (PLD) with the following parameters: the deposition atmosphere was O2 at a partial pressure of 10−4 Torr, the target-to-substrate distance was fixed to 10.15 cm, and the growth was performed at 750 °C. The LAO target was ablated using a 248 nm KrF excimer (Coherent, Inc.) laser with a fluence of 1.2 J/cm2 and a repetition rate of 2 Hz. The growth rate of 15 pulses per layer was monitored in-situ by oscillations in Reflection High-Energy Electron Diffraction (RHEED) patterns (STAIB Instruments). After deposition, films were brought to room temperature maintaining the same O2 partial pressure as during the film growth. Following this protocol, LAO films with thicknesses of 3, 5, and 10 unit cells (u.c.) were grown on TiO2-terminated STO substrates.

We published in a previous report4 experimental results of two samples with film thicknesses just below (3 u.c.) and above (5 u.c.) the conduction-inducing critical thickness of four unit cells. That paper outlined various mechanisms known as possible triggers of the conduction at the LAO/STO hetero-interface. It was shown that none of them were individually sufficient to explain the electrical behavior of both samples. Three interrelated characteristics of these hetero-interfaces remained unclear and still need to be discussed in a comprehensive analysis of the observed behavior, namely (i) the origin of electrons and their contribution to conductivity, (ii) the compensation of the dipolar field across the thickness of the film, and (iii) the existence of the critical thickness. This present article aims to answer these three major questions, by adding a set of experimental results obtained for a 10 u.c.-thick sample.

The charge carrier density obtained from Hall measurements decreased by more than one order of magnitude for the 10 u.c.-thick film sample compared to the 5 u.c.-thick one (Fig. 1). To a lesser extent, the mobility was also decreased. These results are in agreement with Bell et al.10 who showed a systematic thickness-dependence of conduction above 4 u.c., with lower mobility, lower carrier density and higher resistance for thicker LAO films. However, the lower carrier density measured was not consistent with the change in Ti-valence, as determined experimentally by EELS (EELS experiments were done with a Nion UltraSTEM 200 microscope operating at 100 kV. The microscope was equipped with a spherical aberration corrector, which enabled obtaining a probe-size below 0.1 nm). We have estimated the Ti valence at the 10 u.c. LAO/STO interface to be 3.85+(±0.05) from its EELS Ti-L2,3 absorption edges (Fig. 2). This is lower than that at the 5 u.c. LAO/STO interface [Fig. 2(b) in Ref. 4]. In agreement with the published results using core-level photoemission spectroscopy,44 we have found that the Ti3+ contribution increases with the film thickness, but without reaching Ti3.5+. This contradicts once again the polar catastrophe model, for which a valence of +3.5 is predicted for any film thickness above the critical value. The extrinsic contribution of oxygen vacancies was ruled out as the source of additional carriers at the interface of the 10 u.c.-thick sample. Figure 3 displays the O-K EELS spectra of this sample. The spectrum recorded in the deepest part of STO in the thin foil (shown by green triangles in Fig. 3) revealed no clear signature of oxygen vacancies in agreement with expectations for bulk STO at this oxygen pressure (10–4 Torr). The spectrum recorded at the LaO/TiO2 interface (shown by red circles in Fig. 3) indicated a reduction of the Ti oxidation state and/or intermixing. No features characteristic of oxygen vacancies can be recognized around the interface. (A similar result was found for the 3 u.c. and 5 u.c. films.4) The concentration of oxygen vacancies does not increase with the duration of deposition in the PLD chamber at such O2 partial pressures. Thus, the higher density of electrons found by EELS at the interface of the thickest sample (10 u.c.) does not originate from oxygen vacancies.

FIG. 1.

Electrical measurements of the samples with film thicknesses of 5 u.c. and 10 u.c. Variation of (a) sheet resistance, (b) carrier density, and (c) Hall mobility, as a function of temperature. The thinner sample exhibits metallic conductivity with a carrier density larger than 1.2 × 1015 cm−2 at room temperature, while it was 6.5 × 1013 cm−2 for the thicker one. The 5 u.c.-thick sample exhibits better transport properties than the 10 u.c.-thick sample.

FIG. 1.

Electrical measurements of the samples with film thicknesses of 5 u.c. and 10 u.c. Variation of (a) sheet resistance, (b) carrier density, and (c) Hall mobility, as a function of temperature. The thinner sample exhibits metallic conductivity with a carrier density larger than 1.2 × 1015 cm−2 at room temperature, while it was 6.5 × 1013 cm−2 for the thicker one. The 5 u.c.-thick sample exhibits better transport properties than the 10 u.c.-thick sample.

Close modal
FIG. 2.

Ti-L2,3 edge EELS taken at the LaAlO3/SrTiO3 interface. (a) High-Angle Annular Dark-Field (HAADF) image of the region of interest. The interface is marked by a blue stripe. (b) EELS spectrum at the interface of the 10 u.c. sample. The contributions of Ti4+ and Ti3+ to the Ti edge were deduced from a linear combination of two reference spectra, a green one for Ti4+ (SrTiO3 away from the interface of the 10 u.c. sample) and a red one for Ti3+ (bulk Ti2O3) recorded on the same spectrometer. The blue dot spectra correspond to the experimental EELS measurement at the very first unit cell below the interface. The method of least squares has been used to fit the experimental and the simulated spectra. The black curve represents the best fit to the experimental spectrum. A valence of +3.85 was deduced. The error bars on the Ti valence were determined by varying the contribution of each reference spectra. EELS spectra were acquired with a Gatan Enfina spectrometer and a custom-made EELS camera. The beam convergence half-angle was in all cases 32 mrad. The spectrometer entrance half-angle was either 40 mrad for large dataset acquisitions or 15 mrad for the high resolution spectra. The probe current was around 50 pA. Spectral images used 0.05–0.1 nm pixel sizes and dwelling times of 100 ms or less, leading to doses of around 1–2 nC/nm2.

FIG. 2.

Ti-L2,3 edge EELS taken at the LaAlO3/SrTiO3 interface. (a) High-Angle Annular Dark-Field (HAADF) image of the region of interest. The interface is marked by a blue stripe. (b) EELS spectrum at the interface of the 10 u.c. sample. The contributions of Ti4+ and Ti3+ to the Ti edge were deduced from a linear combination of two reference spectra, a green one for Ti4+ (SrTiO3 away from the interface of the 10 u.c. sample) and a red one for Ti3+ (bulk Ti2O3) recorded on the same spectrometer. The blue dot spectra correspond to the experimental EELS measurement at the very first unit cell below the interface. The method of least squares has been used to fit the experimental and the simulated spectra. The black curve represents the best fit to the experimental spectrum. A valence of +3.85 was deduced. The error bars on the Ti valence were determined by varying the contribution of each reference spectra. EELS spectra were acquired with a Gatan Enfina spectrometer and a custom-made EELS camera. The beam convergence half-angle was in all cases 32 mrad. The spectrometer entrance half-angle was either 40 mrad for large dataset acquisitions or 15 mrad for the high resolution spectra. The probe current was around 50 pA. Spectral images used 0.05–0.1 nm pixel sizes and dwelling times of 100 ms or less, leading to doses of around 1–2 nC/nm2.

Close modal
FIG. 3.

EELS fine structure of the O-K absorption edge in the thicker LaAlO3/SrTiO3 heterostructure. Experimental spectra recorded at the 10 u.c. thick sample hetero-interface (red dots) and deeper into the SrTiO3 substrate of the same sample (green triangles).

FIG. 3.

EELS fine structure of the O-K absorption edge in the thicker LaAlO3/SrTiO3 heterostructure. Experimental spectra recorded at the 10 u.c. thick sample hetero-interface (red dots) and deeper into the SrTiO3 substrate of the same sample (green triangles).

Close modal

La doping of STO can act as donor doping and thus can release charge carriers. However, these extra carriers in the 10 u.c. sample do not come from La donor doping either, since the intermixing level was found to be similar to that of the conducting 5 u.c.-thick sample (data not shown here).

The growth of the LAO polar film on a TiO2-terminated substrate induces the development of a dipolar field across the film. The greater number of polar unit cells deposited in the 10 u.c.-thick film is expected to significantly increase the electrostatic potential. The valence band of LAO is projected to cross the conduction band of STO. However, experimentally, the Ti valence decreased only slightly compared to the 5 u.c. system. The transfer of electrons from the film surface to the interface by band bending was not significantly favored indicating that the polar field was weaker than predicted, as it will be explained later in this paper. Thus, the mobile charges observed in these conductive samples do not originate from the valence band of LAO.

Besides the three potential sources of mobile carriers at the interface of our conductive samples (oxygen vacancies in STO, La doping and LAO valence band) that have been excluded, another mechanism remains unexplored: charge transfer from the surface. Donor defects at the surface of a polar film, such as oxygen vacancies or hydrogen adsorbed onto surface oxygen, see their formation energy modified by the potential build-up. Oxygen vacancy formation on the LAO surface should not be favored at the partial pressure used. However, calculations showed that their formation energy decreases with increasing film thickness and polarity. Yu and Zunger45 have determined that positively charged oxygen vacancies, VO··, become stable at and above the film thickness of 4 u.c. These donor defects at the LAO surface have a higher energy level than the bottom of the STO conduction band and can transfer electrons to the interface. The dipolar field can be cancelled for ¼ VO·· per LAO unit cell of the surface. Similar conclusions have been established for H+ adsorbates.18,46 The contribution of these defects to the electronic reconstruction is enhanced in the 10 u.c.-thick film compared to the thinner one of 5 u.c.-thickness.

We emphasized earlier that there is no crossing between the LAO valence band and the STO conduction band of STO by band bending. The potential slope in the film is already reduced, contrary to the first model proposed by Nakagawa et al.,2 even below the critical thickness by two simultaneous mechanisms, namely intermixing and buckling:

  • Ti ↔ Al intermixing forms AlTi (acceptor, below the interface)-TiAl (donor, in the film) pairs. As the donor level is higher than the acceptor level, a transfer of electrons is possible from the film to the substrate's first layers. It must be added that the donor defects cannot inject electrons into the conduction band and acceptor defects cannot accept electrons from the valence band, since their energy levels are too deep in the band gap.45 This electron transfer reduces the polar field but cannot make the interface conductive as the carriers are not mobile. It explains the presence of carriers detected at the interface of the insulating sample.4 

  • In LaO and AlO2 layers, the displacement of the cations toward the surface relative to the anions produces counter-dipoles that reduce the dipolar field. The displacement of Ti observed by High-Angle Annular Dark-Field (HAADF) in the film (Fig. 1 in Ref. 4) and the first-principles calculations proposed in Ref. 18 showed a clear buckling in a 3 u.c.-thick film.

Furthermore, negatively charged defects can also contribute to potential screening. A wide range of defects can form in LAO/STO heterostructures, among which cationic vacancies have barely been experimentally evidenced. Strontium vacancies, VSr, could be formed by the annealing of STO in an oxidative atmosphere,47 as well as during PLD by the energetic plume or by a defect equilibrium reaction induced by Sr ↔ La intermixing. At the oxygen partial pressure and the growth temperature used, any electronic disequilibrium is partially compensated by ionic compensation through the formation of VSr.40,48–50 The direct observation of Sr vacancies in bulk STO was recently presented by Kim et al.,51 showing the displacement of the surrounding Ti columns away from the vacancy. The strontium vacancies play a crucial role in the expansion of the parameter c and can explain the distinct strain profiles of conducting and insulating samples (Fig. 7 in Ref. 4). The different distributions of Sr vacancies highlighted are explainable by the difference in the polar fields developed. The lower dipolar field in the thinnest film induces a weaker VSr attraction toward the interface than in the 5 u.c. sample, explaining the deeper region with c/a > 1 in the 3 u.c. assembly and the higher in-plane compression below the interface of the 5 u.c. sample. This statement provides the first explanation for the existence of a critical thickness. Indeed, the presence of VSr has two consequences on the electron conductivity. Firstly, on the charge carrier density: since the interfacial charge can be partially compensated by these charged defects, the density of carriers injected from the surface is lowered. Secondly, on the charge carrier mobility: in-plane compression induces significantly lighter effective electron masses for transport along the [001] direction compared to unstrained STO,52 whereas a 2D confinement of the charges would require a heavier effective mass along [001] and a lighter one on (001). Several reports underlined the dilution of carriers due to the expansion of lattice c.24,52–54 We explain the dilution of the charge carriers in the substrate region by a thermally activated charge carrier transport in the direction of lighter masses, normal to (001). The model of conduction strictly confined to the LAO/STO hetero-interfaces, advanced as a paradigm when the high electron mobility was discovered, is thus ruled out.

The carrier mobilities and densities, measured in Hall configuration, are lower in the LAO(10 u.c.)/STO sample than in the LAO(5 u.c.)/STO one, despite a higher Ti3+ concentration being measured by EELS at the interface of the thickest film. Once again, the mechanisms involved in the compensation of the dipolar field must be responsible for reduced electrical conductivities. The intermixing was found to be similar for the two conductive samples, minimizing its possible role in counteracting the higher electrostatic potential. Neither does the slightly higher concentration of carriers measured by EELS at the interface of the 10 u.c.-thick film sample playing in favor of electronic reconstruction to preferentially screen the potential. That leaves two factors that might reduce the electrostatic field: buckling and strontium vacancies. These two factors imply structural distortions. Therefore, the higher dipolar field developed within the thicker film will induce higher structural distortions, resulting in lower conduction.

We conclude that carrier mobility, rather than density, is the critical parameter driving the insulating/conducting transition. The literature10,20,53,55 confirms a link between the carrier mobility and structural distortions. With the growth conditions chosen in the present work, structural distortions are concluded to be the critical mechanism governing the conduction of the LAO/STO heterostructure above the critical thickness. Hence, in this configuration, film thicknesses just above the conduction threshold must be chosen to optimize the performances of the LAO/STO system.

In summary, the growing LaO+/AlO2 layers on the TiO2 surface stores dipolar energy and creates a positively charged interface. In view of the defect population we have highlighted, a model of compensation for the dipolar field and the interfacial charge is proposed, involving the interplay of several mechanisms (Fig. 4):

FIG. 4.

Model of the dipolar field compensation. This illustration gathers all the mechanisms involved in the model, explaining the screening of the electrostatic field developed within the LaAlO3 film.

FIG. 4.

Model of the dipolar field compensation. This illustration gathers all the mechanisms involved in the model, explaining the screening of the electrostatic field developed within the LaAlO3 film.

Close modal
  1. The relaxation of the ionic layers that buckle to produce counter-dipoles with oxygen anions moving toward the interface and cations toward the film surface.

  2. The presence of negatively charged strontium vacancies at the interface.

  3. The interdiffusion of B cations and the electron transfer to the interface: TiAlfilmAlTiint. These electrons are trapped and do not participate in the conduction.

  4. The formation of donor defects at the film surface such as surface oxygen vacancies or surface hydrogen. Their formation energy is reduced with the potential build-up. Their energy level allows electron transfers to the STO conduction band.

When the first unit cells are deposited, mechanism #4 is not activated and the interface is insulating. This was the case for the 3 u.c.-thick sample. Above the critical thickness, the dipolar potential allows the formation of donor defects at the surface. The interfacial charge can be partially compensated with mobile electrons, and the interface is conducting. This was the case for the 5 u.c.- and 10 u.c.-thick samples. The conduction threshold is between 3 and 5 u.c. The electron transfer by mechanism #3 or #4 only partially compensates the positive charge. The strontium vacancies proposed in mechanism #2 are responsible for an elongation of parameter c in the substrate below the interface. The in-plane compressive strain reduces the in-plane transport properties since it does not allow a strict 2D confinement of the charges; they are diluted over several unit cells below the interface resulting in a higher valence charge than the theoretical value due to the polar catastrophe hypothesis.

The prediction of the properties of the LAO/STO heterostructure is only possible if defect distributions can be controlled during the process and if the synergy of their actions on charge carriers is understood.

We acknowledge financial support from the CNRS-CEA “METSA” French network (FR CNRS 3507) for the USTEM experiments conducted on the LPS (Université Paris-Sud) platform, and this work was supported by the Air Force Office of Scientific Research (AFOSR) Grant No. FA 9550-12-1-0441.

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