Surface-induced thickness limit of conducting La-doped SrTiO₃ thin films Free

In recent decades, there has been a growing interest in ABO₃ perovskite crystals due to a variety of physical properties arising in this material family, such as ferromagnetism, multiferroism, superconductivity, and novel topological states.^1,2 Functional perovskite oxides have been studied for a wide range of applications, including field effect transistors, nonvolatile memories, sensors and actuators, and optical waveguides.^3–8 Electron-doped strontium titanate (SrTiO₃ or STO), in particular, has occupied a central role in the development of oxide electronics. STO is a bandgap insulator with a gap of ∼3.2 eV. Introducing cationic dopants into STO forms hydrogenlike donor states that generate electrons in the STO conduction band, making the system metallic.^9–11 The conduction electrons show filling-dependent Fermi liquid behavior, enabling the robust control of the electron density by doping level^12,13 with a maximum electron density of up to 10²¹–10²² cm⁻³.^13–15 Low-temperature Hall mobility in excess of 10 000 cm²/(V s) has also been reported.^10,16,17 In addition to this semiconducting behavior, STO has a small lattice mismatch with other perovskite materials and exhibits intriguing physical properties, such as a large thermoelectric effect^15,18–20 and superconductivity,^21,22 making it an important building block for oxide electronics.

Thin film La-doped SrTiO₃ (LSTO) exhibits a low-temperature electron mobility exceeding 30 000 cm²/(V s).^23,24 The Ti valence change due to La³⁺ dopants affects the spin–orbit coupling of LSTO, resulting in a filling-dependent tunable effective electron mass.²⁰ The Ti valence change also turns LSTO into a polar compound, and as a result, LSTO can form a two-dimensional electron gas at an interface with nonpolar materials.²⁵ These remarkable features make LSTO an ideal candidate for a conducting channel in an all-oxide field effect transistor.^26–28 However, as the film thickness of LSTO is decreased, the effect of structural distortions, as well as interface and surface effects, is increased, degrading the electrical properties of LSTO.^25,29 This change of electrical properties not only hinders achieving the desired performance of the LSTO channel but also makes it difficult to control electrical properties via La-doping.

Here, we investigate the thickness dependence of LSTO's electrical properties with varying dopant concentration, reporting on the electrical properties of La_xSr_1−xTiO₃ (x = 0.15, 0.25, 0.5) thin films with thicknesses ranging from 8 unit cells (uc) to 20 uc grown on STO (001) substrates. Electrical transport measurements reveal that, within the measured doping levels and thickness ranges, the carrier density thickness-dependence is governed by a doping-independent insulating layer with a constant thickness and a constant trapped electron density. Atomic-scale structural analysis by surface X-ray diffraction (XRD) shows no significant structural or stoichiometric defects in the LSTO, excluding the possibility of a defect-driven insulating state inside the LSTO films. Adding a capping layer on our LSTO films counteracts the reduced carrier density. Based on these results, we attribute the degraded electrical properties found in our LSTO films to a strong surface effect.

High-quality single crystalline LSTO thin films are grown on STO (001) substrates by molecular beam epitaxy in a custom chamber operating at a base pressure of 1 × 10⁻¹⁰ Torr. Prior to deposition, the STO substrate is etched with a commercial 10:1 buffered oxide etch for 30 s and annealed at 950 °C for two hours in order to obtain an atomically smooth TiO₂-terminated surface. During LSTO growth, a molecular oxygen partial pressure of 1 × 10⁻⁶ Torr and a substrate temperature of 500 °C are used. After growth, the substrate temperature is cooled down at a rate of 20 °C/min to room temperature. During the cooling process, the oxygen partial pressure is maintained at what is used for LSTO growth in order to minimize the formation of oxygen vacancies. The desired La, Sr, and Ti cation flux ratios are achieved by calibrating the metal fluxes using a quartz crystal microbalance. The La concentration is chosen to be equal to or larger than 0.15, which is a composition we could reliably control. The thickness is monitored by observing intensity oscillations in reflection high-energy electron diffraction (RHEED), which show good agreement with the cation flux calibration to within 5%. The structural analysis of the LSTO films includes X-ray diffraction (XRD), atomic force microscopy (AFM), and synchrotron surface X-ray diffraction performed at the X-ray Science Division beamline 33-ID at the Advanced Photon Source, Argonne National Laboratory, using coherent Bragg rod analysis (COBRA). The transport properties of the films are measured in a conventional van der Pauw geometry at room temperature with sputtered Au electrodes. Ohmic contact between LSTO and Au electrodes is confirmed by the measurement of linear current–voltage curves up to ±30 μA, the maximum current range used for electrical transport study in this paper.

The basic characteristics of the LSTO films are addressed in Fig. 1. During the growth of LSTO, the intensity of the RHEED specular spot shows clear oscillations, indicating that the films grow in a layer-by-layer manner. As shown in Fig. 1(a), the RHEED oscillations remain up to 20 uc, the maximum thickness we study, with the appearance of streaky lines in the RHEED patterns confirming the two-dimensional nature of our LSTO surface. Atomically flat surfaces are observed by AFM. Figure 1(b) shows a typical AFM topographic image of a 20-uc-thick LSTO film, showing a root mean square roughness of less than 5 Å and a clear step-and-terrace structure with a single unit cell step height. The structural properties of the LSTO films are further confirmed by XRD. Figure 1(c) shows XRD θ-2θ scans of La_0.25Sr_0.75TiO₃ films with 8, 14, and 20 uc thicknesses. Within the measured scan angles, only (00l) reflections of LSTO and STO are shown without any secondary phases. Thickness-dependent fringe oscillations near the (00l) reflections confirm sharp interfaces and flat surfaces, with the periodicity matching the film thickness expected from RHEED intensity oscillations. The dependence of the LSTO structure on La-doping levels is also investigated. Figure 1(d) shows XRD θ-2θ scans of 20-uc-thick LSTO films with x = 0.15, 0.25, and 0.5. In the figure, the (002) Bragg reflections of the LSTO films appear at decreasing q_z with increasing La-doping levels, showing the expansion of the c-axis lattice parameter due to the atomic size difference between La and Sr and impurity-induced changes in the electronic structure.³⁰ 

We investigate the effect of La-dopants and film thickness on the electrical transport properties of our LSTO films. For the ideal case, substituting Sr²⁺ with La³⁺ generates one free electron per unit cell, uniformly distributed over the entire volume. As a result, for film thickness t, the sheet electron density n_s can be expressed by a linear equation

However, the experimentally measured n_s, shown in Fig. 2(a), reveals distinct departures from Eq. (1). While n_s plots for all doping levels show the expected linear relation with film thickness, each linear fit has a nonzero thickness intersecting n_s = 0 (approximately 11, 8, and 6 uc for x = 0.15, 0.25, and 0.5, respectively). Below these thicknesses, the resistivity exceeds the measurement limit. This indicates the existence of an insulating layer inside our LSTO films. From the slopes of linear fitting for n_s, we estimate electron densities for the conducting part of the LSTO films. As shown in Fig. 2(b), the number of electrons per unit cell volume estimated from the slopes in Fig. 2(a) matches well with the intended La-doping levels, showing fully activated La³⁺ dopant states in the conducting region. The electrical conductivity of LSTO films is also observed to exhibit a similar dependence on film thickness and x, but because of the difference in electron mobility between samples, the trends are less clear. Figure 2(c) shows the electron mobility of the LSTO films, estimated from the measured n_s and sheet conductivity. All LSTO films exhibit a room temperature electron mobility ranging from 2–7 cm²/(V s), consistent with the previously reported mobility values for ∼100 nm thick LSTO films,^31,32 but showing no clear dependence on film thickness or x. Therefore, we conclude that the variation of electron mobility of the samples is due to differences in the microstructure between the films.

The observed electrical properties of our LSTO films can be explained by introducing an insulating layer (or dead layer) with a constant thickness and a constant trapped electron density. Assuming an insulating layer thickness, t_DL, that traps electron density, n_trapped, from the conducting LSTO region, Eq. (1) can be rewritten as

By comparing Eq. (2) with Fig. 2(a), we determine that t_DL = 4 uc, and n_trapped = 0.9 electrons per uc⁻². We note that the dopant-independent insulating layer thickness and the amount of trapped charge observed in our LSTO films cannot be explained by general depletion theory for semiconductors.^33–35 This means that the insulating layer and the trapped charge have a complex origin that is related to the detailed structural and electronic properties of LSTO films.

For insight into the origin of the insulating layer, we first consider the effect of a local stoichiometry change or defects. Changes in stoichiometry and defects can form an insulating phase in several different ways. Examples include (i) the formation of structurally ordered insulating phases, such as La₂Sr_n-2TiO_3n+1 during growth,³⁶ (ii) the migration of La-dopants that can form a local insulating STO or LaTiO₃ phase, and (iii) the formation of oxygen vacancy clusters that can localize free electrons, as reported in a highly oxygen-deficient STO.^37,38 We investigate the atomic-scale structure of our LSTO films, measuring integer-order crystal truncation rods with surface X-ray diffraction (Fig. S1). We analyze these rods with COBRA to obtain a three-dimensional electron density map.³⁹ Vertical cuts along the [110] direction of the electron density map for a 7-uc-thick La_0.5Sr_0.5TiO₃ film are shown in Fig. 3(a) on the left. Atomic-scale structural details of the topmost LSTO layer are obscured by a disorder at the surface. (See the supplementary material, Fig. S2.) We therefore concentrate our study on the structure of the inner six layers. The composition for each layer of LSTO is estimated based on the integrated peak intensity for each site in the perovskite structure. Away from the interfaces, the scattering strength is uniform throughout the thickness of the film with a magnitude consistent with the as-grown composition [Fig. 3(b)]. Near the LSTO/STO interface, the scattering strength changes gradually, suggesting intermixing at the LSTO/STO interface.⁴⁰ An estimate of the carrier concentration from these data {the total [La³⁺] concentration} is estimated to be around 2.44 electrons per uc⁻², which is still higher than the measured electron density for a 7-uc-thick La_0.5Sr_0.5TiO₃ film (∼0.67 electrons per uc⁻²). Based on these results, we conclude that the formation of a local insulating phase by local stoichiometry change or defects is not the origin for the observed dead layer. We also note that there is a significant lattice expansion and polar distortions of the LSTO [Figs. 3(c) and 3(d)], whose origins require further investigation.

The growth of insulating BaTiO₃ with a thickness of 20 nm is observed to counteract the reduction of n_s from the insulating layer, with an n_s value (∼0.5 uc⁻²) five times higher than that of the bare LSTO film (∼0.1 uc⁻²). A similar result is obtained with an STO capping layer, showing that the increased n_s does not depend on the specific choice of the capping material. Figure 4 shows the electron sheet density n_s of an 8-uc-thick La_0.25Sr_0.75TiO₃ film with and without a capping layer. To investigate the structure of LSTO when it is capped, we measure crystal truncation rods for a La_0.5Sr_0.5TiO₃ film with a 3-uc-thick BTO capping layer (Fig. S3). Figure 3(a) shows the results from a COBRA analysis of the atomic-scale electron density map of BTO-capped La_0.5Sr_0.5TiO₃ film on the right. The integrated peak scattering strength for each site in the perovskite structure is consistent with the magnitude expected for the as-grown film, again with intermixing at the LSTO/STO interface [Fig. 3(b)].

BTO capping affects the structural distortion of LSTO in two significant ways. First, with the BaTiO₃ capping layer, the lattice expansion observed in uncapped-LSTO is suppressed. Figure 3(c) shows layer-by-layer c-axis lattice parameters estimated by the spacing between each cation peak. The c-axis lattice parameters for the BTO-capped LSTO layers are around 3.95 Å, which is consistent with the expected value estimated using the bulk La_0.5Sr_0.5TiO₃ lattice constant and Poisson's ratio for SrTiO₃.⁴¹ In contrast, the uncapped-LSTO film exhibits lattice expansions of 1.60–3%. Second, BTO capping suppresses polar distortions in the LSTO. Figure 3(d) shows the layer-by-layer polarization along LSTO- and BTO-capped LSTO, estimated from the displacement between each cation and oxygen in the same plane and the Born effective charges for STO.⁴² Without the BTO capping layer, the polarization inside the LSTO layer changes sign and is as large as −30 μC cm⁻² at the LSTO/STO interface and 20 μC cm⁻² at the surface. Adding the BTO capping layer reduces the polarization to ∼10 μC cm⁻² at the LSTO/STO interface and becomes almost zero at the BTO/LSTO interface. We also observe larger oxygen octahedral rotations in the LSTO layer for the BTO-capped films (Fig. S4). We speculate that these differences may be due to the changes in the elastic boundary conditions and possible oxygen vacancy concentration.

The effect of the capping layer on the structural and electrical properties of LSTO implies that the insulating layer originates from the top surface, not from the bottom interface or from the bulk of the interior of the film. We first notice that typical surface-induced depletion mechanisms, such as a stoichiometric change near the surface, surface Fermi pinning, and electron trapping by charged surface adsorbates, cannot explain our observations. As briefly mentioned above, Fermi pinning-induced surface depletion exhibits a depletion layer thickness proportional to x^−0.5,³³ while our LSTO films exhibit a constant insulating layer thickness of 4 uc. In addition, assuming that the reduced n_s observed in Fig. 1(a) comes solely from the trapped carriers at the surface, a maximum of three electrons per unit cell area is needed for x = 0.5, which cannot be achieved by typical adsorbates present in the air. We speculate that the surface-induced insulating LSTO layer and trapped electrons may originate from structural distortions, accompanied by changes in the electronic structure of LSTO.

One possible explanation for the insulating layer in LSTO is a filling-controlled Mott transition, driven by a locally varying carrier density. Strong correlations in STO can give rise to a Mott–Hubbard type bandgap opening on the STO conduction band when a high-electron density is achieved on a single Ti site.⁴³ This filling-controlled Mottlike behavior has been observed in rare-earth titanate/STO heterostructures.^44–46 In our LSTO films, strong polarization possibly acts as a source for electron trapping, giving rise to a locally enhanced electron density near the surface region.⁴⁶ The increased electron density may cause a Mottlike metal-to-insulator transition in the surface layers, explaining the dead layer and trapped charge inside the LSTO film. Another possible explanation is oxygen vacancy formation or migration, which can induce additional electrons to the LSTO layer. The significant increase in the c-axis lattice parameter for uncapped-LSTO might be a result of such oxygen vacancies in the LSTO layer. We believe that the surface structure distortion is a result of an uncompensated electric field and changes in surface stoichiometry during cooling. Modifications to the growth process and termination layers at both interface and surface should allow us to further understand and control surface contributions to electrical transport.

In summary, we have investigated the electrical properties of LSTO films as a function of film thickness and La-doping level and the nature of the dead layer effect in this material. Within the measured range of La-doping and film thickness, n_s can be quantitatively determined by introducing a constant insulating layer of thickness 4 uc and a constant trapped electron density of 0.9 electrons per unit cell. COBRA atomic-scale structural analysis shows no significant nonstoichiometric or defect states in our LSTO films. Growing a BaTiO₃ or an STO capping layer is observed to counteract the effect of the insulating layer. Based on these results, we conclude that the insulating layer and trapped electron states originate from an LSTO surface effect. Our findings suggest a guiding principle for controlling the electrical properties of ultrathin LSTO films and provide future directions on determining the microscopic origin of the LSTO surface effect. In future work, we plan to perform detailed studies of the atomic and electronic structures of the LSTO surface.

See the supplementary material for the details of atomic-scale structural analysis on studied La-doped SrTiO₃ films.

Characterization work was supported by AFOSR Grant No. FA9550-15-1-0472 and synthesis work was supported by ONR Grant No. N000144-19-1-2104. The use of the Advanced Photon Source at Sector 33-ID-D was supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.