Oxygen vacancy-assisted recovery process for increasing electron mobility in n-type BaSnO₃ epitaxial thin films

Abstract

The scattering of charge carriers by line defects, i.e., threading dislocations (TDs), severely limits electron mobility in epitaxial semiconductor films grown on dissimilar substrates. The density of TDs needs to be decreased to further enhance electron mobility in lattice-mismatched epitaxial films and heterostructures for application in high-performance electronic devices. Here, we report a strategy for the post-treatment of epitaxial La-doped BaSnO₃ (LBSO) films by delicately controlling the oxygen partial pressure p(O₂), which achieved a significant increase in the room temperature (RT) electron mobility (μ_e) to μ_e = 122 cm² V⁻¹ s⁻¹ at a carrier concentration of 1.1 × 10²⁰ cm⁻³. This mobility enhancement is mostly attributed to an oxygen vacancy-assisted recovery process that reduces the density of TDs by accelerating the movement of dislocations in ionic crystals under a p(O₂)-controlled treatment despite an increase in the density of charged point defects. Our finding suggests that accurate control of the interactions between point defects and line defects can reduce dominant carrier scattering by charged dislocations in epitaxial oxide semiconductors that have dissimilar substrates. This method provides alternative approaches to achieving perovskite oxide heterostructures that have high RT μ_e values.

Introduction

Heteroepitaxial growth is the epitaxial growth of semiconductor films on dissimilar substrates (e.g., GaN on Al₂O₃); it has been widely used to obtain single-crystal films for electronic and photonic applications mostly because of the limited availability of single-crystal semiconductor substrates with identical lattice parameters for homoepitaxial growth^1,2. Inevitably, heteroepitaxial layers contain high densities of structural defects; because of the lattice mismatch between films and substrates, most of the defects are threading dislocations (TDs), which cross the epitaxial layers perpendicularly^2,3. TD cores consist of point defect complexes (e.g., impurities or vacancies) that have abundant dangling bonds, which form deep acceptors with a space-charge double Schottky barrier around dislocation lines; these acceptor-like negatively charged TDs generate an effective potential field that induces scattering of electrons by Coulombic interactions^4,5. This “charged TD scattering” severely reduces the number of free charge carriers and thus diminishes electron mobility (μ_e) in epitaxial semiconductor films (e.g., GaAs⁴, InN⁶, GaN^3,7). Therefore, the control of charged TD scattering is a key requirement for achieving heteroepitaxial semiconductor films with an electronic grade if homoepitaxy is not available^3,8,9.

Charged TD scattering also significantly affects electronic transport in epitaxial BaSnO₃ (BSO) films, which are new transparent and wide band-gap oxide semiconductors for transparent and power electronics^9,10,11,12. Although La-doped BSO (LBSO) single crystals have excellent an room temperature (RT) μ_e of ~320 cm² V⁻¹ s⁻¹ at a carrier concentration of n = 8.0 × 10¹⁹ cm⁻³ and excellent stability, even at high temperatures, heteroepitaxial LBSO films have much lower μ_e values (at best, ~70 cm² V⁻¹ s⁻¹ by pulsed laser deposition (PLD)¹¹ and ~124 cm² V⁻¹ s⁻¹ by molecular beam epitaxy (MBE)¹³) than single crystals¹¹. This low μ_e has been attributed to the abundance of TDs⁹ that inevitably form during epitaxial growth due to large lattice mismatch with the substrate, e.g., SrTiO₃ or MgO. Therefore, considerable effort has been devoted to decreasing the density of TDs by using substrates with a lattice constant that is similar to or even the same as that of BSO^13,14,15,16 or by inserting buffer layers between BSO epilayers and typical substrates^12,17,18,19 to release the lattice mismatch strain.

In this article, we report a new strategy to increase the μ_e of LBSO epitaxial films by exploiting a recovery process that is assisted by oxygen vacancies. By delicately adjusting both the oxygen partial pressure p(O₂) and the temperature during thermal treatment of LBSO epitaxial films, the density of TDs and the degree of mosaicity is significantly reduced, so a maximum RT μ_e value of 122 cm² V⁻¹ s⁻¹ at a carrier concentration of n = 1.1 × 10²⁰ cm⁻³ was achieved. This subtle introduction of an oxygen deficiency during post-treatment improves the crystal quality by decreasing the TD density, N_TD, which leads to an increase in mobility with a minimal increase in the number of oxygen vacancies as impurity scattering centers. This new strategy that exploits the interactions between point and line defects can be used to further reduce N_TD in heteroepitaxial thin films by using oxygen vacancies to lubricate TDs.

Materials and methods

Synthesis of epitaxial LBSO thin films

Epitaxial La-doped BaSnO₃ (LBSO) thin films with a La-doping content of 0–5% and a thickness of ~100 nm were grown on (001)-oriented SrTiO₃(001) and MgO single-crystal substrates by using PLD with a KrF excimer laser in a chamber with an $\sim 10^{ - 6}$ Torr base pressure. The La-doping ratio was controlled by using targets with different La contents; the targets were synthesized by a conventional solid-solution reaction. A KrF excimer laser (λ = 248 nm, τ = 20 ns, Compex Pro 102F, Coherent Inc., Santa Clara, CA) was focused on rotating targets at a fluence of ~1.1 J/cm² and a repetition rate of 10 Hz. The as-grown LBSO layers were grown in a p(O₂) of 260 mTorr at 750 °C to optimize the structural and electrical properties of the as-grown LBSO films.

p(O₂) control of LBSO thin films during annealing

The degree of oxygen deficiency in the LBSO films was controlled by adjusting either the p(O₂) or the temperature post treatment. The p(O₂) post treatment was controlled by simultaneously applying pure Ar gas and 5% forming gas (Ar containing 5% H₂) and changing the flow ratio while maintaining a total flow rate of 500 sccm (Fig. S3). To further suppress the reducing ability of H₂ gas to achieve subtle control of the p(O₂), wet H₂ was used by passing H₂ gas through a Drechsel bottle that contained water. The H₂O ratio in the flowing gas was estimated to be ~3% from the water vapor pressure at RT, i.e., 3.17 kPa at 25 °C. A Yttria-stabilized Zirconia (YSZ) sensor accurately measured log p(O₂) as −3.91 in a flow of pure Ar gas, −20.0 in 5% H₂ mixed with Ar at 650 °C, and −16.6 in 0.5% wet H₂ mixed with Ar at 950 °C. The YSZ sensor measured the voltage difference between the inside of a YSZ cell that was exposed to air and the outside of the same cell that was exposed to flow gas. The measured voltage difference was converted to the p(O₂) in the flow gas by using the Nernst equation²⁰:

$$E = \left( {\frac{{{\mathrm{RT}}}}{{4F}}} \right)\log \left( {\frac{{p{\rm{O}}_2\left( {\rm{air}} \right)}}{{p{\rm{O}}_2\left( {{{\rm{flow}}\,{\rm{gas}}}} \right)}}} \right),$$

where E (mV) is the electromotive force, R = 8.3145 (J mol⁻¹ K⁻¹) is the universal gas constant, T (K) is the YSZ cell temperature, F = 96485 (C/mol) is the Faraday constant, pO₂(air) = 0.21 (bar) is the oxygen partial pressure of air, and pO₂(flow gas) is the oxygen partial pressure of flow gas.

Materials characterization

The crystallinity of the films was characterized using high-resolution X-ray diffraction (HRXRD, Bruker D8 Discovery X-ray diffractometer) with Cu K_α1 radiation (λ = 1.5406 Å) for θ–2θ scan, rocking curve (RC) scan, and reciprocal space mapping (RSM). The surface morphology of the films was observed using an atomic force microscope (AFM, VEECO Dimension 3100). Etching-pit analysis was performed by etching the thin films in 0.4 wt% nitric acid for 10 min before their surface morphologies were observed using AFM. Oxygen 1s X-ray photoemission spectroscopy (XPS) was performed with a synchrotron source in an ultrahigh vacuum chamber (base pressure of the analysis chamber ~5.3 × 10⁻¹⁰ Torr) at the 4D PES beamline at PLS-II of the Pohang Accelerator Laboratory, Pohang, South Korea, to quantify the oxygen deficiencies before and after H₂ treatment. The ratio of oxygen vacancies to lattice oxygens was estimated by the areal ratio of the O(II) peak (~531.6 eV) to the O(I) peak (530.1 eV). As a binding energy reference, the Au 4f^7/2 peak was set at 84.0 eV. Time-of-flight secondary ion mass spectrometry (TOF-SIMS) depth profiles were recorded by negative polarity with Cs⁺ sputtering at 3 keV–20 nA.

The resistivity ρ and carrier concentration n were obtained as functions of the temperature from RT (~300 K) to liquid nitrogen temperature (~80 K) using a Hall measurement system with a 0.56-T perpendicular magnetic field. Measurements were made in the van der Pauw geometry with square samples (5 × 5 mm²) and indium ohmic contacts (<1 × 1 mm²) in the sample corners. The four-terminal resistances were measured by a 1-mA current. For the Hall measurements, the magnetic field was varied between ±0.56 T. The carrier concentration was calculated as $n = 1/\left( {e \times R_{\mathrm{H}}} \right)$, where R_H is the measured Hall coefficient. The electron mobility was calculated as $\mu _e = R_{\mathrm{H}}/\rho$, where the resistivity (ρ = $R_{\mathrm{S}} \times t$) was determined by the van der Pauw method and is independent of any errors in determining the film thickness.

Theoretical estimation of the dislocation-limited mobility

The dislocation-limited mobility, $\mu _{e,{\mathrm{TD}}}$, was estimated by varying the TD density in the equation³:

$$\mu _{\mathrm{{e}},{\mathrm{TD}}} = \frac{{30\sqrt {2\pi } \varepsilon _0^2\varepsilon _{\mathrm{s}}^2a^2\left( {kT} \right)^{\frac{3}{2}}}}{{N_{{\mathrm{TD}}}e^3f^2{\mathrm{\lambda }}_{\mathrm{D}}\sqrt {m_{\mathrm{e}}^ \ast } }},$$

where

$${\mathrm{\lambda }}_{\mathrm{D}} = \left( {\frac{{\varepsilon _0\varepsilon _skT}}{{ne^2}}} \right)^2.$$

In these equations, $\varepsilon _0$ = 8.854 × 10⁻¹² (F/m) is the vacuum dielectric constant, $\varepsilon _{\mathrm{s}}$ = 21 is the relative dielectric constant¹², a =  4.116 (nm) is the lattice constant, k = 1.381 × 10⁻²³ (J/K) is the Boltzmann constant, T = 300 (K) is the temperature, N_TD (cm⁻²) is the TD density, e = −1.602 × 10⁻¹⁹ (C) is the electron charge, f = 1 is the fraction of occupied acceptor centers of each TD, $m_{\mathrm{e}}^ \ast$ = 0.1731 × 10⁻³¹ (kg) is the electron effective mass¹², and n (cm⁻³) is the carrier concentration.

Results and discussion

Epitaxial LBSO ([La] = 0–5%) thin films with a thickness of 100 nm were grown on (001)-oriented SrTiO₃ (STO) and MgO substrates by PLD at 750 °C. HRXRD θ–2θ scans of the as-grown films showed only the (00l) reflection; this result indicates that the films had (001) pseudomorphic epitaxy without secondary phases. However, the lattice mismatch of BSO (a = 0.4116 nm) is −5.4% with the (001)-oriented STO substrate (a = 0.3905 nm) and +2.2% with the (001)-oriented MgO (a = 0.4212 nm) substrate; these mismatches cause misfits and TDs to form in the epitaxial LBSO layers. The as-grown 1% LBSO epitaxial films exhibited the parameters n ~5.3 × 10¹⁹ cm⁻³ and RT μ_e ~15 cm² V⁻¹ s⁻¹ when grown on STO and n ~4.1 × 10¹⁹ cm⁻³ and RT μ_e ~16 cm² V⁻¹ s⁻¹ when grown on MgO (Fig. 1, Fig. S1); these values are comparable to those of other as-grown 1% LBSO epitaxial films produced by PLD (n ~6 × 10¹⁹ cm⁻³, μ_e ~20 cm² V⁻¹ s⁻¹)^11,21. When 1% La dopants are fully activated, n is expected to be ~1.5 × 10²⁰ cm⁻³, so the observed value of n ~6 × 10¹⁹ cm⁻³ indicates that approximately only one-third of the La³⁺ dopants provide conducting electrons. This low yield suggests that the donated electrons are trapped at the TDs.

Fig. 1: Increase in electron mobility of LBSO epitaxial thin films after precise H₂ treatment.

Temperature-dependent (a) electrical resistivity ρ, (b) carrier concentration n, (c) and electron mobility μ_e of 1% La-doped BaSnO₃ thin films: as-grown (black-filled squares), Ar-annealed at 950 °C (green-hollow squares), 5% H₂-annealed at 650 °C (red-filled circles), and wet 0.5% H₂-annealed at 950 °C (blue-hollow circles). (d) μ_e as a function of n at room temperature (RT) in LBSO films with different La-doping contents: as-grown (black-filled squares), 5% H₂-annealed at 650 °C (red-filled circles), and wet 0.5% H₂-annealed at 950 °C (blue-hollow circles). Dashed lines: theoretically calculated μ_e limited by charged-dislocation scattering as a function of threading dislocation density, N_TD. Note that the RT μ_e maximum of the H₂-treated LBSO films shifts toward the upper left corner and is located near 10²⁰ cm⁻³ (orange arrow)

The $\mu _e$ of the as-grown epitaxial layer was optimized using various post-treatments to tune the oxygen chemical potential of the samples. As an initial attempt, the samples were annealed under inert Ar at 650 or 950 °C. Annealing at 650 °C did not change n or μ_e, but annealing at 950 °C increased μ_e to ~30 cm² V⁻¹ s⁻¹ at RT with an almost constant n; this result is consistent with previous reports that μ_e can be increased by annealing in inert N₂ at 1000 °C²¹.

To further modulate the degree of oxygen deficiency during the thermal treatment of as-grown LBSO epitaxial films with large TD densities, the LBSO films were thermally annealed at 650 °C under a reducing atmosphere with 5% H₂-mixed forming gas (denoted 5% H₂); both n and the RT μ_e increased (μ_e ~90 cm² V⁻¹ s⁻¹ at n ~1.2 × 10²⁰ cm⁻³). The increase in n under a reducing atmosphere may be related to the introduction of carrier-generating point defects such as oxygen vacancies or interstitial hydrogen^22,23,24. Treatment under excessively reducing conditions at high temperature (i.e., 5% H₂ at 950 °C) to increase the diffusivity of the point defects led to a significant suppression of the (001) XRD peak and insulating properties of the LBSO epitaxial films; these changes can be attributed to the collapse of the BSO crystal structure due to excessive formation (or incorporation) of oxygen vacancies in BSO (Fig. S2). Therefore, to exploit the high ionic mobility at high temperature without causing the collapse of the BSO crystal structure, the concentration of generated oxygen vacancies should be regulated to maintain the lattice framework during H₂ treatment.

To achieve this balance, the p(O₂) was precisely controlled in the following way. By flowing 0.5% H₂ gas through a Drechsel bottle that contained water, H₂O gas was added to the H₂ gas in the furnace (i.e., wet H₂) (Fig. S3)²⁵. The effects of this experimental setup could be predicted from the following reaction equation:

$${{{\rm{BaSnO}}_3}}\left( {\mathrm{s}} \right) + {{{\rm{H}}_2}}\left( {\mathrm{g}} \right) \rightleftharpoons {\rm{BaSnO}}_{3 - \delta }\left( {\mathrm{s}} \right) + {{{\rm{H}}_2O}}\left({\mathrm{g}}\right).$$

Based on Le Chatelier’s principle, both the introduction of H₂O and a decrease in the H₂ content would suppress the formation of H₂O and oxygen vacancies in BaSnO₃, even at high temperature. Measurements using an oxygen sensor based on YSZ detected a higher p(O₂) in wet H₂ at 950 °C (log p(O₂) = −16.6) than in 5% H₂ at 650 °C (log p(O₂) = −20.0)²⁰. This difference confirms that the utilization of wet H₂ is an effective method for slightly suppressing the reducing ability at high temperature; this suppression cannot be achieved using 5% H₂ alone. With the accurate tuning of the oxygen chemical potential, the wet H₂ process at 950 °C gave the maximum RT μ_e of LBSO (~122 cm² V⁻¹ s⁻¹ at n ~1.1 × 10²⁰ cm⁻³) without collapsing the lattice framework of LBSO, even at high temperature. Therefore, the optimized thermal treatment with subtle p(O₂) control could remarkably increase the RT μ_e in LBSO thin films with a minimal increase in the number of oxygen vacancies as impurity scattering centers. The thermal H₂ treatment also increased μ_e and n in the LBSO epitaxial films on MgO substrates (Fig. S1: μ_e and n increased from 16 cm² V⁻¹ s⁻¹ and 4.1 × 10¹⁹, respectively, in as-grown LBSO to 76 cm² V⁻¹ s⁻¹ and 7.3 × 10¹⁹ in wet H₂ LBSO at 950 °C (50 cm² V⁻¹ s⁻¹ and 8.1 × 10¹⁹ in 5% H₂ LBSO at 650 °C) despite the severe crystal mosaicity in LBSO on MgO (Fig. S4); this result indicates that the wet H₂ process is very effective for increasing the RT μ_e regardless of the substrate. To confirm the chemical origin of the point defects and generate more carriers after the H₂ treatments, we performed TOF-SIMS and XPS on the as-grown and H₂-treated BSO epitaxial films (Fig. S5). The hydrogen anion (H⁻) signal increased very little after the H₂ treatments (Fig. S5a)^26,27, so hydrogen interstitials are unlikely to be the main origin of mobile carriers. Instead, deconvolution of the O 1s XPS spectra of both films indicates that the areal ratio of the O(II) peak (~531.6 eV) to the O(I) peak (~530.1 eV), which are related to oxygen vacancies and lattice oxygens²³, respectively, increased from 0.588 in as-grown BSO to 1.42 in the 5% H₂ BSO films (Fig. S5b, c); this result reveals the formation of oxygen vacancies, which can be additional sources of mobile electrons in the LBSO films after H₂ treatment. However, oxygen vacancies usually scatter carriers and thus cannot be the origin of the RT μ_e increase. Indeed, the formation of oxygen vacancies decreases the RT μ_e of the LBSO thin film due to increased scattering by the charged point defects²⁸, which is contrary to our present result in which RT μ_e increased even with the formation of oxygen vacancies after H₂ treatment; this contradiction suggests that a different origin induces the increase in μ_e after H₂ treatment.

To exclude the possibility of electrical conduction through the STO substrate after our precise H₂ treatment, the substrate conductance was indirectly estimated from the linear extrapolation of the sheet conductance and (Fig. S6) directly measured with respect to the H₂ treatment at different p(O₂) values and temperatures (Fig. S7). Unlike in the typical reducing conditions for producing oxygen-deficient SrTiO_3−δ, the STO substrates showed negligible conduction comparable to that of the pristine STO substrate after our delicate thermal treatment (i.e., 5% H₂ LBSO at 650 °C and wet H₂ LBSO at 950 °C). Therefore, it can be inferred that our mild reducing conditions produced oxygen vacancies in only the LBSO epitaxial layers and are not sufficient to produce oxygen deficiency in the STO substrates. This selective formation of oxygen vacancies in LBSO/STO can be explained by the fact that the formation energy of oxygen vacancies in STO (~3.1 eV)²⁹ is considerably higher than that in BSO (~1.7 eV)²⁴.

To gain further insight into electron transport in the LBSO epitaxial films, we measured the temperature dependence of n and μ_e for 1% La-doped LBSO films treated under different conditions (Fig. 1b, c). n was almost constant with varying temperature in all samples (Fig. 1b), indicating that the films are degenerately doped. In contrast, the temperature dependence of μ_e was affected by the p(O₂) used during post-treatment (Fig. 1c); this relationship indicates that the dominant carrier scattering mechanism changed. Samples without H₂ treatment showed no temperature dependence of μ_e (e.g., 15 cm² V⁻¹ s⁻¹ at 300 K and 17 cm² V⁻¹ s⁻¹ at 80 K for as-grown LBSO), but those subject to H₂ treatment showed a significant increase in μ_e as the temperature decreased (e.g., 122 cm² V⁻¹ s⁻¹ at 300 K and 197 cm² V⁻¹ s⁻¹ at 80 K for the LBSO film annealed in wet H₂ at 950 °C).

To understand the significant increase in μ_e after the H₂ treatment, the resulting μ_e can be expressed according to Matthiessen’s rule^3,12,17:

$$\mu _{\rm e}(T)^{ - 1} = \mu _{{\rm e},{\rm{LO}}}(T)^{ - 1} + \mu _{{\rm e},{\rm{CI}}}(T)^{ - 1} + \mu _{{\rm e},{\rm{TD}}}(T)^{ - 1},$$

where μ_e,LO is μ_e governed by LO phonon scattering, μ_e,CI is μ_e governed by charged impurities, and μ_e,TD is μ_e governed by TDs. The dominant scattering factor changes with N_TD, as previously reported in the plot of the temperature dependence of $\mu _{\mathrm{e}}(T)$^12,17: when N_TD is high, the contribution of weakly temperature-dependent μ_e,TD is dominant over the contribution of μ_e,LO and μ_e,CI, so the resultant μ_e exhibits negligible change with temperature. However, if N_TD is low, μ_e,TD is negligible compared to μ_e,LO and μ_e,CI, so the resultant μ_e shows a strong temperature dependence due to LO phonon-limited scattering, charged-impurity-limited scattering, or both. Our analysis of the dominant scattering mechanisms suggests that the precise tuning of oxygen vacancies in our LBSO films induces a change in the scattering processes from charged-dislocation-limited scattering to ionized impurity- or LO phonon-limited scattering (or both) by reducing N_TD.

The change in the dominant scattering mechanism upon H₂ treatment can be readily seen in the plot of the RT μ_e of the LBSO films ([La] = 0–5%) as a function of n at RT (Fig. 1d). Due to competition between charged-dislocation scattering and charged-impurity scattering, the plot of the RT μ_e vs. n is bell-shaped^3,9,12,17. In the as-grown and Ar-treated LBSO films, μ_e was maximized at high n (~5 × 10²⁰ cm⁻³) and then decreased with decreasing n; this relationship demonstrates the strong influence of charged dislocations as charge traps, scattering centers for carriers, or both, and also shows that this influence reduces n and μ_e simultaneously. After H₂ treatment of the LBSO films, both n and μ_e increased simultaneously in all the LBSO films; this change led to a shift in each data point of n vs. μ_e toward the upper right corner. This shift indicates that the H₂ treatment causes a decrease in the intensity of charge TD scattering despite the increase in the number of charged point defects. In the overall bell-shaped curves, the maximum μ_e of the H₂-treated LBSO films shifted toward the upper left corner (Fig. 1d, orange arrow) and is located near 10²⁰ cm⁻³. In GaN epitaxial films with a high N_TD, the shift in the maximum μ_e toward the upper left corner indirectly represents a decrease in N_TD³, which again confirms that our subtle H₂ treatment reduces N_TD and the contribution of charged-dislocation scattering.

As a further check of our model, various X-ray diffraction techniques, e.g., RSM around the (103) Bragg reflection and RC of the (002) reflection, were used to explore the structural origin of the RT μ_e increase induced by the p(O₂)-controlled thermal treatment (Fig. 2). At first glance, the (103) Bragg reflections of the precisely H₂-treated LBSO films (Fig. 2c, d) had higher peak intensities and narrower peak widths than those of the as-grown (Fig. 2a) LBSO films (Fig. 2b). Ar treatment of the LBSO films had almost no effect on the full-width half maximum (FWHM) in both the RSM and RC, but both H₂ treatments caused significant reductions in the FWHMs in the in-plane direction (ΔQ_x) and the out-of-plane direction (ΔQ_z). In particular, ΔQ_x decreased considerably more than ΔQ_z and the RC Δω in the H₂-treated LBSO films (Fig. 2e) (e.g., ΔQ_x = 0.0172 Å⁻¹$\to$0.0111 Å⁻¹, ΔQ_z = 0.0099 Å⁻¹$\to$0.0088 Å⁻¹, Δω = 0.033°$\to$0.026° in the wet 0.5% at 950 °C H₂ samples). In contrast to the increase in the number of oxygen vacancies in the BSO films after H₂ treatment, the distinct narrowing of the RSM (i.e., ΔQ_x) peaks after thermal treatment under a controlled p(O₂) should be related to structural improvement by the reduction in the density of line defects (e.g., $N_{{\rm{TD}}}$) in the films, which is likely to be the main origin of the increase in the RT μ_e.

Fig. 2: Structural improvement of LBSO epitaxial films after H₂ treatment.

Reciprocal space mapping (RSM) around (103) reflections from LBSO epitaxial films: (a) as-grown, (b) Ar-annealed at 950 °C, (c) 5% H₂-annealed at 650 °C and (d) wet 0.5% H₂-annealed at 950 °C. e Full-width at half-maximum of the (103) RSM peak along the x direction (ΔQ_x) and z direction (ΔQ_z) and of the (002) rocking curve (Δω) for the LBSO films in a–d. The RSM peak width narrowed substantially along the Q_x direction after H₂ treatment of the LBSO films

A reduction in N_TD for a specific type of TD can explain the reduction in the RSM FWHM in ΔQ_x after H₂ annealing. Dislocations cause local lattice displacement, u(r), which influences the X-ray scattering intensity I(q) as follows:

$$I\left( q \right) \propto \left| {{\int} {e^{ - iq \times u\left( r \right)}e^{ - iq \times r}dr} } \right|^2,$$

where q is a diffraction vector that corresponds to the Bragg reflection plane (hkl)³⁰. Therefore, if lattice distortion is induced in the in-plane direction (u₁ = (x, 0, 0)), then I(q + $\Delta$q_x) increases but I(q+$\Delta$q_z) does not, so peak broadening occurs along the x direction. In the case of TDs, in-plane distortion, u₁, can be induced by edge-type dislocations but not by screw-type dislocations^30,31. Therefore, the type of TD in the epitaxial layers affects the direction of lattice distortion, so the RSM FWHMs change asymmetrically. For example, in GaN epitaxial films with a high density of TDs, edge-type TDs widen the in-plane FWHMs and screw-type TDs widen the out-of-plane FWHMs^30,31,32,33.

Likewise, the observed reduction in the in-plane FWHMs in our LBSO epitaxial films should be related to a decrease in the edge-type N_TD rather than the screw-type N_TD after the H₂ treatment. Therefore, the H₂ atmosphere at high temperature accelerated the elimination of edge-type TDs, which are expected to be the dominant TD type in the as-grown LBSO epitaxial films. Indeed, a Burgers vector of <010>_a was mostly observed in the as-grown LBSO thin films by two-beam dark-field transmission electron microscopy (TEM) imaging (Fig. S8); this observation confirms that edge-type TDs were the dominant TD type. The reduction in N_TD after the H₂ treatment was confirmed by etching-pit analysis using AFM (Fig. S9). Etching with 0.4% nitric acid creates pits near the cores of the TDs because etching is faster near defective and deformed atomic structures than nearly ordered ones^21,34. The H₂-treated film with a narrow ΔQ_x had far fewer etching pits than the as-grown film, i.e., N_TD was lower in the H₂-treated epilayers than in the as-grown epilayers.

The importance of the precise p(O₂) control for inducing the structural improvement responsible for the increases in the RT μ_e can be demonstrated by the changes in the structural and electrical properties of undoped BSO films after systematically controlling the p(O₂) to change the percentage of H₂ gas (0–10 %) at 650 °C during thermal treatment for 1 h (Fig. 3). As the amount of H₂ gas increased (p(O₂) decreased) during post-annealing, ΔQ_x and the RT resistivity of the annealed BSO drastically decreased and almost saturated when the H₂ content was 1%; this trend indicates that the improvement in the in-plane structural quality (ΔQ_x), not ΔQ_z, seems to be strongly correlated with the increase in electrical transport. The best structural quality can be observed in the range 0.4 ≤ H₂ content < 1% H₂, but an H₂ gas content >5% H₂ caused ΔQ_x to increase again; this result confirms that the excessive generation of oxygen vacancies degrades the overall crystal quality. Therefore, simultaneous increases in both the structural and electrical properties require that the p(O₂) be precisely controlled. This conclusion may explain why the RT μ_e can be increased using the wet H₂ process to slightly improve the precision of the p(O₂) control. If this is the case, the increase in μ_e after H₂ treatment may occur because the improvement imparted by the contribution of μ_TD dominates the degradation caused by the contribution of μ_CI.

Fig. 3: The importance of the precise control of the p(O₂) for increasing the RT μ_e through structural improvement.

a Electrical resistivity (black square), carrier concentration (red circle), electron mobility (blue triangle) and (b) corresponding RSM FWHM ΔQ_x and ΔQ_z of BSO thin films H₂-annealed at 650 °C with changing H₂/Ar ratio. Note that careful control of the p(O₂) is essential for achieving simultaneous increases in the structural and electrical properties, which can explain the further improvement in the RT $\mu _{\rm{e}}$ at the small expense of point defect generation by precise p(O₂) control

The electrical and structural results both suggest that the formation of oxygen vacancies by the precise H₂ treatment reduces the density of TDs and thereby increases the RT μ_e. Dislocation annihilation assisted by point defects has been traditionally considered an effective recovery process in physical metallurgy³⁵: This recovery process is exploited in single-crystal-like materials to release strain energy concentrated around dislocations by removing or rearranging structural defects during the annealing of highly deformed samples at high temperature. The recovery process during heat treatment is kinetically limited by atomic migration, so point defects (e.g., oxygen vacancies in the present study) facilitate dislocation motion and efficiently increase the release of deformed strain^35,36,37. In our case, the LBSO epitaxial films grown by PLD contain extended defects, e.g., TDs, which are either in equilibrium or non-equilibrium; the films also contain local deformations near the TD cores due to lattice/thermal mismatch, high-energy growth processes, or both.

Along the dislocation lines, the columns of grown films are slightly tilted or mis-oriented relative to each other, forming mosaic-like structures with local deformation⁹. Once sufficient thermal energy is supplied, the deformation energy can be released in a recovery process that entails dislocation annihilation, thereby reducing N_TD and decreasing the lattice distortion induced by the TDs. Because dislocation movement is a prerequisite for dislocation annihilation, point defects such as oxygen vacancies accelerate the movement of dislocations along and across the slip plane, e.g., dislocation climb^35,36. This climb occurs by the absorption or emission of vacancies, which are thermally activated processes³⁵, so the rate of climb is directly proportional to the vacancy concentration in ionic crystals. Therefore, dislocation movement that is assisted by oxygen vacancies without creating excessive oxygen deficiencies appears to be very important for improving the structural and electrical properties of the LBSO epitaxial layer by reducing N_TD. A similar improvement in the structural quality by vacancy-dislocation interaction has been reported in cold-worked Al, in which the presence of vacancies significantly increased the mobility of dislocations³⁶.

Finally, Fig. 4 shows a comparison of the variation in μ_e with n at RT for our H₂-treated LBSO/STO films with various La concentrations and previously reported LBSO/STO films. With the exception of the bulk LBSO crystals, in which μ_e increased a relatively small amount as n decreased, all the LBSO films showed bell-shaped curves in the plot of μ_e vs. n at RT. This curve represents charged-dislocation-limited scattering at low n and ionized impurity scattering at high n, at which charge screening at high n suppresses dislocation scattering as a dominant scattering mechanism. The maximal RT μ_e as a function of n was significantly shifted toward the upper left corner in our wet H₂-treated LBSO films compared to the other as-grown LBSO films prepared by PLD. This shift indicates that our precise H₂ treatment significantly reduced N_TD. This reduction in N_TD induced by the optimized control of the interactions between point defects and line defects achieves a maximal RT μ_e in our LBSO (~122 cm² V⁻¹ s⁻¹ at ~n = 1.1 × 10²⁰ cm⁻³) that is comparable to the RT μ_e of other LBSO films whose properties were improved by buffer layers, homoepitaxial growth, or different growth methods (e.g., MBE). However, at a high n > 10²⁰ cm⁻³, μ_e significantly decreased with increasing n in our case, but the LBSO thin films grown by MBE with controlled cation stoichiometry¹⁷ maintained a relatively high RT μ_e in spite of the increase in n and thus achieved a low resistivity <10⁻⁴ Ω cm by minimizing the impurity scattering induced by the cation off-stoichiometry. Therefore, a further improvement in the RT μ_e of our H₂-treated LBSO through the precise control of the residual point defects and line defects as scattering centers is possible.

Fig. 4

Comparison of the room temperature electron mobility vs. carrier concentration for our optimized LBSO films wet 0.5% H₂-annealed at 950 °C (red stars) and previously reported LBSO films, i.e., PLD-grown LBSO thin films on an STO substrate¹¹ (black squares), and on a single-crystal BSO substrate¹⁶ (green circles), MBE-grown LBSO thin films on an STO substrate¹³ (blue triangles, orange diamonds), and single-crystal LBSO³⁸ (pink hexagons)

Conclusion

The precise control of the oxygen partial pressure p(O₂) and temperature during post-treatment with H₂ increased n and μ_e simultaneously in epitaxial La-doped BaSnO₃ (LBSO) films and thereby achieved a significant increase in the RT μ_e (122 cm² V⁻¹ s⁻¹ at a carrier concentration of 1.1 × 10²⁰ cm⁻³). Despite the possibility that the H₂ treatment could increase the number of scattering centers caused by charged point defects (i.e., oxygen vacancies), the precise control of the p(O₂) enabled an increase in the mean free path of electrons in the LBSO thin films. This change is mostly attributed to a reduction in the number of TDs and the mosaicity by the accelerated dislocation movement that occurs due to oxygen vacancy-assisted recovery in ionic crystals. These results suggest that precise control of the interactions between point and line defects can be used to switch the dominant carrier scattering centers in heteroepitaxial oxide films. This strategy using defect chemistry may provide new approaches for achieving perovskite oxide heterostructures that have a high RT μ_e.