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Impact of lattice mismatch and stoichiometry on the structure and bandgap of (Fe,Cr)2O3 epitaxial thin films

This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 135005 (http://iopscience.iop.org/0953-8984/26/13/135005) View the table of contents for this issue, or go to the journal homepage for more

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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 135005 (12pp)

doi:10.1088/0953-8984/26/13/135005

Impact of lattice mismatch and stoichiometry on the structure and bandgap of (Fe,Cr)2O3 epitaxial thin films T C Kaspar1, S E Chamberlin1, M E Bowden2, R Colby2, V Shutthanandan2, S Manandhar2, Y Wang2, P V Sushko3 and S A Chambers1   Fundamental and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, WA 99354, USA 2   Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, WA 99354, USA 3   Department of Physics and Astronomy and London Centre for Nanotechnology, University College London, London WC1E 6BT, UK 1

E-mail: [email protected] Received 20 January 2014, revised 6 February 2014 Accepted for publication 11 February 2014 Published 13 March 2014 Abstract

The structural properties of phase-pure epitaxial (Fe1–xCrx)2O3 thin films deposited on α-Al2O3(0 0 0 1) substrates by oxygen-plasma-assisted molecular beam epitaxy are investigated across the composition range using x-ray photoelectron spectroscopy, high-resolution x-ray diffraction, scanning transmission electron microscopy and electron energy loss spectroscopy, and non-Rutherford resonant elastic scattering measurements. The films possess a columnar grain structure with uniform mixing of cations on the nanometer scale. Fe-rich films are relaxed and appear to be slightly oxygen-rich, while Cr-rich films remain partially strained to the Al2O3 substrate and are found to be oxygen deficient. A model is proposed to explain the oxygen stoichiometry results based on the energetics of oxygen defect formation and rate of oxygen diffusion in the corundum lattice, and the dependence on the cation composition. Deliberately introducing residual compressive biaxial strain into (Fe1–xCrx)2O3 thin films (x = 0, 0.41, 0.52) by employing a Cr2O3 buffer layer is shown to narrow the optical bandgap, from 1.80(1) eV for relaxed (Fe0.47Cr0.53)2O3 to 1.77(1) eV for partially strained (Fe0.48Cr0.52)2O3. The relationships which are elucidated between epitaxial film structure and optical properties can be applied to bandgap optimization in the (Fe,Cr)2O3 system. Keywords: hematite, eskolaite, oxygen non-stoichiometry, lattice strain, bandgap S Online supplementary data available from stacks.iop.org/J.PhysCM/26/135005/mmedia (Some figures may appear in colour only in the online journal)

1.  Introduction

potential to both reduce the bandgap [2] and improve the electron and hole transport properties [3, 4]. Recently, we reported experimental [5] and theoretical [6] results on the optical absorption properties of α-(Fe1–xCrx)2O3 epitaxial thin films deposited on α-Al2O3(0 0 0 1) substrates by oxygen-plasma-assisted molecular beam epitaxy (OPAMBE). Alloying Fe2O3 with Cr2O3 (bandgap of ~3.3 eV) results in substantial bandgap bowing, reducing the direct

Hematite (α-Fe2O3) and its alloys are of current interest as active materials in photovoltaic and photoelectrochemical water splitting applications [1]. Hematite’s natural abundance and stability in aqueous and oxidizing environments, as well as its bandgap of ~2.1 eV, make it an appealing choice for solar light harvesting applications. Doping hematite has the

0953-8984/14/135005+12$33.00

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© 2014 IOP Publishing Ltd  Printed in the UK

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J. Phys.: Condens. Matter 26 (2014) 135005

electron flood gun was utilized to compensate for charging effects in these insulating materials. Ex situ high-resolution x-ray diffraction (XRD) patterns were collected on a Philips X’Pert Materials Research Diffractometer (MRD) using Cu  Kα1 radiation monochromated with a hybrid mirror/4 crystal monochromator. High-resolution θ–2θ scans were collected with fixed-slit (‘rocking curve’) detector optics. In some cases, resulting patterns were fit utilizing the rads software program from Bede X-ray Metrology. High-resolution rocking curves and reciprocal space maps were collected utilizing a three-bounce Ge analyzer crystal at the detector (‘tripleaxis’ optics). High-resolution transmission electron microscopy (TEM) and scanning TEM (STEM) data were collected on a probe-corrected FEI Titan 80–300 operated at either 80 or 300 kV. High-angle annular dark-field (HAADF-STEM) images were acquired with an inner collection angle greater than 50 mrad, with a resolution better than 1 Å at 300 kV and 2 Å at 80 kV. Cross-sectional samples were prepared using a focused ion beam (FIB) liftout procedure [10]. Electron energy loss spectra (EELS) were recorded at 80 kV with a Gatan Quantum ER imaging filter, with an energy resolution between 0.7–0.9 eV. Portions of the EELS analysis employed the Cornell Spectrum Imager ImageJ plugin [11]. Rutherford backscattering spectrometry (RBS), non-Rutherford resonant elastic scattering (RES), and PIXE data were obtained with He+ of 2.0 MeV, 3.04 MeV, and H+ of 2.5 MeV, respectively, generated in a tandem electrostatic accelerator (National Electrostatics Corporation 9SDH-2). Density functional theory (DFT) calculations were performed using the Vienna ab initio Simulation Package (VASP) [12]. The projected augmented wave (PAW) method [13] was used to approximate the electron-ion potential, and exchange-correlation effects were treated within the PerdewBurke-Ernzerhoff (PBE) functional form [14] of the generalized gradient approximation (GGA). GGA + U was utilized in some cases to better describe the properties of the strongly correlated system, with U = 4.0 eV and J = 1 eV. Details of this approach are given in [5, 6].

optical bandgap approximately 0.3 eV below that of undoped Fe2O3, consistent with previous observations [7, 8]. This reduction arises from the electronic structure of the alloy, in which new, low-energy transitions occur from Cr 3d-derived states in the valence band to Fe 3d-derived states in the conduction band; hybridization in the alloy further reduces the energy difference between these states. Experimental photoconductivity measurements were promising in that photoinduced current could be obtained for transitions at or even below the direct optical bandgap for compositions x < ~0.4. While we now understand the electronic structure of stoichiometric, defect-free (Fe,Cr)2O3 alloys which leads to bandgap reduction, it is expected that the presence of strain and point and structural defects in real, imperfect specimens, such as epitaxial thin films, will play a substantial role in the material properties. For example, the effect of biaxial epitaxial strain on Ti-doped Fe2O3 was explored theoretically by Nabi and Pentcheva [9], and dramatic differences in cation ordering stability and bandgap were predicted for films strained to α-Fe2O3, FeTiO3 (ilmenite), and α-Al2O3. Once defensible structure-property correlations are made for (Fe,Cr)2O3, imperfections such as strain and defects can be utilized in a controlled manner to achieve the desired light harvesting properties. In this work, we report the detailed structural characterization of epitaxial (Fe1–xCrx)2O3 thin films deposited on α-Al2O3(0 0 0 1) by OPA-MBE across the composition range. We establish relationships between epitaxial film structure and optical properties which can be applied to bandgap optimization in the (Fe,Cr)2O3 system. As an example, we show that the bandgap of (Fe1–xCrx)2O3 thin films is reduced through the introduction of lattice strain. 2.  Experimental and computational methods Epitaxial thin films of α-(Fe1–xCrx)2O3 were deposited on α-Al2O3 substrates by OPA-MBE as described previously [5]. Briefly, substrate surfaces were pre-cleaned in situ by exposure to activated oxygen from an ECR microwave plasma source at an oxygen pressure of 2 × 10−5 Torr and room temperature for 30 min. The flow of activated oxygen continued as the substrate was heated to the deposition temperature of 700–50 °C. Cr was evaporated from an electron beam evaporator, and the flux was monitored by atomic absorption spectroscopy. Fe was co-evaporated from an effusion cell. The overall growth rate was 0.24 Å s–1 to a final film thickness of 500 Å. Except where noted, the plasma source was switched off at the end of the growth and the O2 flow immediately ceased, before the substrate temperature was decreased, so that the films were cooled in vacuum. Structural quality and morphology were monitored before, during, and after deposition with reflection high energy electron diffraction (RHEED). High-energy-resolution XPS data were collected in situ in an appended ultra-high vacuum chamber utilizing a monochromated Al Kα x-ray source (λ = 1486.6 eV) and a GammaData/ Scienta SES-200 hemispherical analyzer. The energy resolution of the SES-200 spectrometer is approximately 0.5 eV for the photoemission spectra reported here. A low-energy

3.  Results 3.1.  Cation speciation and valence band structure

The cation composition of the (Fe1–xCrx)2O3 alloy films was determined by comparing the Fe 2p peak area from x-ray photoelectron spectroscopy (XPS) survey spectra collected at noralloy mal emission (IFe ) to the Fe 2p peak area in the Fe2O3 thin alloy Fe2O3 Fe2O3 / IFe [15]. Similarly, the composifilm (IFe ) as x = 1 − IFe tion can be calculated by comparing the Cr 2p area from the alloy Cr O alloy Cr 2O3 alloy (ICr ) and the Cr2O3 thin film (ICr ) as x = ICr / ICr2 3. The Cr composition values determined by both methods were averaged for each film. For three films, the compositions (Cr fraction x) were independently determined by proton-induced x-ray emission (PIXE, not shown) and found to be within a few percent of the values obtained by XPS (XPS : PIXE = 0.63 : 0.62, 0.81 : 0.81, and 0.23 : 0.25). High-resolution XPS data collected in situ at normal emission are presented in figure 1(a) for Fe 2p and figure 1(b) 2

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Multiplet splitting of the Cr 2p3/2 peak is well-defined for all films where complete charge compensation was achieved during data acquisition. Figure 1(c) presents the XPS valence band spectra for the same (Fe1–xCrx)2O3 films. As the Cr fraction increases, the cation d-states contribution at the top of the valence band (1–3 eV) increases in intensity relative to the O 2p states hybridized with cation 3d states (4–9 eV). This is consistent with the electronic structures of Fe2O3, which is a charge transfer insulator with predominantly O 2p character at the top of the valence band, and Cr2O3, which is intermediate between a charge transfer and Mott-Hubbard insulator with predominantly Cr 3d character at the top of the valence band [20]. As predicted [5], (Fe1–xCrx)2O3 alloys exhibit valence band structures intermediate between the end members. Up to x = 0.52, the VBM shifts upward, but as the alloy becomes more Cr2O3-like the VBM position becomes nearly constant, and any further bandgap changes ought to be attributed to the shift of the conduction band minimum. This behavior is fully consistent with the density of states of Fe2O3, (Fe0.5Cr0.5)2O3, and Cr2O3 calculated using density functional theory (DFT) [5]. 3.2.  Crystalline structure and strain

High-resolution θ–2θ x-ray diffraction (XRD) scans of the (Fe1–xCrx)2O3 films and α-Al2O3(0 0 0 1) substrate are presented in figure 2(a). Near the (0 0 0 6) reflection of corundum Al2O3, a reflection is observed corresponding to the film (0 0 0 6) plane. No corundum peaks other than (0 0 0 l), with l = 6 and 12, are present, indicating that the films possess a single out-of-plane orientation. In contrast to previous studies of ball-milled mixtures of metallic Fe and Cr2O3 [21], and (Fe,Cr)2O3 thin film deposition by PLD [7, 8], no reflections corresponding to spinel-structure chromite (FeCr2O4) or other secondary phases are detected. The strong finite thickness interference fringes flanking the film reflections further confirm the well-ordered crystal structure with sharp film/substrate interfaces and fairly flat film surfaces. For Cr2O3, some asymmetry is apparent on the lower-θ (larger d-spacing) side of the film reflection. This asymmetry originates from the presence of two distinct strain states in the film, which will be discussed in more detail below. In-plane epitaxy is verified by an azimuthal φ scan of the (104) reflection for (Fe0.13Cr0.87)2O3 (not shown), which consists of three sharp peaks separated by 120°, as expected for singledomain epitaxy. No evidence of peaks corresponding to 180° rotational domains [8] is observed. The reflection high energy electron diffraction (RHEED) patterns in figure 2(a) corroborate the conclusion that the films are crystalline and epitaxial. As expected from previous work on Fe2O3 and Cr2O3 epitaxial thin films [22], the RHEED streak modulation indicates that the surface morphology of Fe-rich (Fe1–xCrx)2O3 films is rougher than that of the Cr-rich films, due to the better lattice match between Cr2O3(0 0 0 1) and Al2O3(0 0 0 1), (afilm − asubstrate)/asubstrate = 4.2%, than that between Fe2O3(0 0 0 1) and Al2O3 (5.8%). The increased film roughness results in a decreased intensity of the finite thickness fringes flanking the θ–2θ (0 0 0 6) film reflection.

Figure 1.  High-resolution XPS spectra of (Fe1–xCrx)2O3: (a) Fe 2p,

(b) Cr 2p, (c) valence band region (M = Fe, Cr). Positions of valence band maxima are indicated by short vertical lines.

for Cr 2p core levels of several (Fe1–xCrx)2O3 films. Spectra were referenced to the O 1s peak at 530.0 eV, which is known to be correct for Cr2O3 [16]. The Fe 2p lineshape for pure Fe2O3 (x = 0) exhibits multiplet splitting and satellite structure consistent with Fe3+ [17]. The energy separation between the shake-up satellite and the Fe 2p3/2 peak, as well as the lack of a shoulder on the low binding energy (BE) side of the Fe 2p3/2 peak, indicates that the Fe2O3 film does not contain a detectable concentration of Fe2+. In the alloy films, the distinct multiplet splitting of the Fe 2p3/2 peak is not visible, which is likely due to cation disorder. However, the Fe3+ satellite is still present, confirming that the alloys also consist exclusively of Fe3+. Likewise, little change is observed in the Cr 2p spectra of Cr2O3 alloyed with Fe. The multiplet splitting and position of the Cr 2p3/2 peak for pure Cr2O3 (x = 1.0) indicates that Cr is present as Cr3+ [18], and this charge state is maintained over all alloy compositions. The feature at ~579 eV for (Fe0.59Cr0.41)2O3 corresponds to the film surface and arises from exposure to activated oxygen generated in the ECR plasma [19]; in this case, the film was cooled in O2, which preserved the plasma-treated surface generated during deposition. 3

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Figure 3.  (a) In-plane lattice parameter a, (b) out-of-plane lattice parameter c, and (c) unit cell volume as a function of x in (Fe1–xCrx)2O3. Experimental values from XRD (symbols) are plotted on the left axes, along with values for bulk powders [23] (dashed). Theoretical values calculated with DFT (crosses) are plotted on the right axes. (d) Strain relaxation values calculated from the XRD data (circles: in-plane, triangles: out-of-plane, left axis) and oxygen content from experimental RES data (inverted triangles, right axis). Dashed line represents both 100% relaxation to the bulk lattice parameters (left axis) and stoichiometric O content (right axis). The additional diamond symbols in all panels (left axes) correspond to films deposited on Cr2O3 buffer layers. The open symbols at x = 1.0 correspond to the second set of lattice parameters for pure Cr2O3.

Figure 2.  (a) HRXRD (0 0 0 6) reflections of (Fe1–xCrx)2O3 films

and Al2O3 substrates. Insets show the final RHEED patterns in the [2 1 1 0] azimuth after growth. (b) (0 0 0 6) rocking curves for (Fe0.48Cr0.52)2O3 (solid) and Al2O3 substrate (dash-dot).

estimated error in the lattice parameter is ±0.001 Å, which is smaller than the symbol size in figure 3. The (Fe1–xCrx)2O3 system is known to deviate from a linear, Vegard’s law-type change in lattice parameters with composition, although the unit cell volume change is nearly linear with composition. The best fits to lattice parameters a and c derived from XRD measurements on bulk powder specimens [23], and the corresponding unit cell volumes, are plotted in figure 3 as dashed lines (left axes). Pure Fe2O3 and Fe-rich (Fe1–xCrx)2O3 film compositions exhibit lattice parameters reasonably close to the expected values for bulk powders, indicating that the films have relaxed nearly all the epitaxial strain. As the Cr content increases, the films become highly strained. The pure Cr2O3 film produced wide, asymmetric reflections that were best fit with two sets of lattice parameters, corresponding to two different strain states in the film (open and filled symbols for x = 1.0 in figure 3). However, even the highly strained films still exhibit unit cell volumes relatively close to the expected, strain-free values, indicating that the

The (0 0 0 6) rocking curve for the (Fe0.48Cr0.52)2O3 film and the associated Al2O3(0 0 0 1) substrate are shown in figure 2(b). The full width at half maximum (FWHM) of the substrate peak is 0.0018° (6.5 arcsec), and the film FWHM is nearly identical at 0.0017° (6.1 arcsec). The nearly identical FWHM values indicate comparable levels of crystallographic quality of the film and the substrate, despite the relatively large lattice mismatch. Similar results were obtained for other films in the (Fe1–xCrx)2O3 composition series. Comparable rocking curve measurements utilizing fixed-slit detector optics produced film peaks with much larger FWHM values (0.04°–0.06°) due to the large acceptance angle of the detector in this setup. In-plane (a) and out-of-plane (c) lattice parameters extracted from a least squares fit to (006), (116), (1 0 1 0), and (2 0 1 0) reflections for each film are plotted in figures 3(a) and (b), along with the resulting unit cell volumes (figure 3(c)) (left axes). The 4

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lattice compression in the a–b plane is compensated by expansion in the c direction. Deviation from the bulk lattice parameters is expected in thin films which have not fully relaxed the epitaxial strain induced by lattice mismatch with the substrate. In-plane lattice compression to accommodate the smaller in-plane spacing of Al2O3(0 0 0 1) (a = 4.7591 Å) is accompanied by a corresponding expansion in the out-of-plane direction, resulting in tetragonal distortion of the lattice. The degree of strain relaxation towards the bulk lattice parameters can be quantified by calculating the strain relaxation as [24]: dexpt – dstrain × 100% % strain relaxation = (1) d0 – dstrain where d is the lattice spacing of interest (in this case, the a or c lattice parameter), dexpt is the measured value, dstrain is the value assuming pseudomorphic lattice matching to the substrate, and d0 is the unstrained (fully relaxed) value [23]. For the XRD data summarized in figure 3, the strain relaxation can be calculated for both in-plane and out-of-plane lattice parameters. To calculate strain relaxation of the in-plane parameter a, astrain is held at the in-plane value for Al2O3 (a Al2O3 = 4.7591 Å) for all (Fe1–xCrx)2O3 compositions. For the out-of-plane parameter c, cstrain is calculated assuming astrain = a Al2O3 and the tetragonal distortion is governed by biaxial strain [25]: εc (cstrain − c 0 )/ c 0 −2ν = = (2) εa (astrain − a 0 )/ a 0 1−ν

where εc and εa are the strain along the out-of-plane and in-plane directions, respectively, and ν is the Poisson ratio for the alloy. The Poisson ratio is assumed to vary linearly with composition between the known values for Fe2O3 (ν = −s12/s11 = 0.23, where s12 and s11 are the elastic compliances of the material) [25, 26] and Cr2O3 (ν = −2 × c13 /c33 = 0.33, where c13 and c33 are the elastic constants of the material) [25, 27]. The resulting strain relaxation values are plotted at the bottom of figure 3. Error bars were estimated assuming the film composition x has an error of ±0.02, and found to be smaller than the symbol size in figure 3. The mismatch in the strain relaxation in-plane and out-of-plane indicates that the films are not responding to strain in a purely Poisson-like manner. The values of strain relaxation over 100% for 0 ⩽ x < 0.8 are also surprising, and indicate that the relaxed lattice parameters for the films differ from the bulk values [23] reported previously. The residual epitaxial strain observed in the lattice parameters as the film composition nears pure Cr2O3 reduces the strain relaxation. The highly strained component of the Cr2O3 film exhibits 60–65% strain relaxation. These trends of film strain and relaxation are reproduced in asymmetric reciprocal space maps (RSMs) of selected (Fe1–xCrx)2O3 films, as shown in figure S1 of the Supporting Information (stacks.iop. org/J.PhysCM/26/135005/mmedia). Also plotted in figure 3 are the calculated lattice parameters and unit cell volume resulting from (Fe1–xCrx)2O3 supercells which were relaxed with DFT/GGA + U to the lowest-energy configuration [6]. The magnitude of both a and c are overestimated with this procedure by ~1–2% [28]. Thus, the values from DFT are plotted independently of those determined experimentally (right axes in figures 3(a), (b), and (c)). The axes were

Figure 4.  STEM images of (Fe0.19Cr0.81)2O3/Al2O3. (a) Lowmagnification STEM image. (b) Fast Fourier transform (FFT) of a higher resolution TEM image (not shown). High magnification cross-sectional HAADF-STEM images along [1 1 0 0] (c) and [1 1 2 0] (d). Insets in (c) and (d) sketch the corundum crystal structure in the view direction. The radii of Fe (green), Cr (blue), Al (red), and O (gray) spheres approximate their contrast in STEM imaging. (e) Low-angle annular dark-field (ADF) STEM image (left) collected concurrently with EELS maps (center) at the O K-edge, Cr L-edge, and Fe L-edge. Right: Color overlay of EELS intensity (red: O; green: Cr; blue: Fe). (f) EELS linescans across the interface (interface = 0 nm). Fe and Cr concentrations have been arbitrarily scaled to the expected film stoichiometry. Solid lines are best fit sigmoid functions.

adjusted to align the Fe2O3 and Cr2O3 endpoints from DFT with the experimental bulk alloy lattice parameters and unit cell volumes (dashed lines). With this adjustment, the lattice parameters predicted by DFT closely follow the non-linear trend observed in the bulk alloy powders. As with the experimental data, the predicted unit cell volume exhibits a more linear dependence on alloy composition than do the lattice parameters. 3.3.  Film microstructure

Figure 4(a) presents a low-magnification scanning transmission electron microscopy (STEM) image of (Fe0.19Cr0.81)2O3/Al2O3, and 5

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ideal α-Al2O3 and (Fe0.19Cr0.81)2O3. Given the large standard deviation from such an analysis, the quantitative determination of oxygen deficiency is not particularly reliable. However, assuming the Al2O3 substrate is fully stoichiometric, the EELS data imply that, despite the substantial activated oxygen flux during deposition, the film is not fully oxidized.

high magnification cross-sectional high-angle annular dark-field (HAADF-STEM) images are presented along [1 1 0 0] and [1 1 2 0] in figures 4(c) and (d), respectively. The film is epitaxial, and the film/ substrate interface is fairly sharp in the Z-contrast images. Vertical intensity striations in the film, seen most clearly in figure 4(a), indicate that the film microstructure consists of narrow columnar grains separated by low-angle grain boundaries. In the high magnification images, the film appears less well resolved in regions containing overlapping grains, or in which single grains are slightly mis-aligned with respect to the Al2O3 substrate. The presence of a high concentration of defects and dislocations at the low-angle grain boundaries is fully consistent with the nearly relaxed lattice parameters measured by XRD (x = 0.81 in figure 3 above). Figure 4(b) displays a fast Fourier transform (FFT) of a higher resolution TEM image (not shown). Horizontal elongation of the spots in the pattern is due to the narrow grain size of the film in the in-plane direction. This same mechanism may be responsible for the elongated diffraction spots in the XRD RSMs (figure S1 of the supporting information (stacks. iop.org/J.PhysCM/26/135005/mmedia)) and asymmetry in the θ–2θ (0006) reflections (figure 2(a)). An alternative origin of the asymmetry in the XRD data is that different regions of the film are subjected to different levels of strain and thus have different lattice parameters. However, parallel-beam electron diffraction with a nanoscale beam (on the order of the grain size) collected in regions similar to those in figure 4, both along the interface and perpendicular to the interface through the film bulk, revealed no change in lattice spacing with spatial position over a region of a few hundred nanometers along the interface, and ~80 nm in the perpendicular direction. Electron energy loss spectroscopy (EELS) maps and line scans provide spatially resolved (~5 Å) information on atomic composition and intermixing. The STEM-EELS map in figure 4(e) probes the cation distribution in the (Fe0.19Cr0.81)2O3/Al2O3 sample. A low angle annular dark-field (LAADF) STEM image, sensitive to diffraction contrast and strain, is collected concurrently with the spectra to highlight the columnar structure of the film. Despite choosing a region with clear contrast from several columnar grains, no grain or grain boundary structure is observed in the EELS maps of O, Cr, or Fe. The Cr and Fe cations are uniformly mixed with no macroscopic correlation, with the exception of a very slight enrichment of Cr at the interface compared to Fe. The abruptness of the (Fe0.19Cr0.81)2O3/ Al2O3 interface can be estimated from the EELS linescans in figure 4(f) at 1.9 nm (Cr), 1.4 nm (Fe), and 1.1 nm (O), taken at 10% and 90% of the total intensity as determined from best fit sigmoid curves of the EELS linescans. The linescan data in figure 4(f) have been artificially normalized to the expected cation and anion concentrations for clarity. However, approximate quantification of the cation stoichiometry resulted in x ≈ 0.85, which compares well with x = 0.81 from XPS. Less O appears to be present in the film compared to the substrate, as indicated by the EELS map in figure 4(e) and the linescan in figure  4(f). The oxygen content in the film relative to that in the substrate can be estimated from EELS at ~90 ± 10% for the EELS linescan and ~80 ± 10% for the EELS map, after compensating for differences in the volumetric density of O and differing inelastic scattering cross-sections in

3.4.  Effect of film strain on optical properties

The films discussed above are relaxed (except for the very Cr-rich films), exhibiting little or no residual epitaxial strain. This relaxation is facilitated by the large lattice mismatch between the film and the sapphire substrate, defined as δf = (afilm − asubstrate)/asubstrate × 100%. The lattice mismatch values range from 5.8% for Fe2O3/Al2O3 to 4.7% for (Fe0.2Cr0.8)2O3. Films of 500 Å thickness appear to have exceeded the critical thickness [29], and epitaxial strain relaxation has occurred through the formation of misfit dislocations or other defects. Thus, the direct bandgap values reported in [5] correspond to the values for unstrained, bulk material. To investigate the effect of residual epitaxial film strain on optical properties such as the optical bandgap, several 250 Å thick films were deposited on 250 Å Cr2O3 buffer layers on doubleside-polished Al2O3(0 0 0 1) substrates. The nominal lattice mismatch between a relaxed buffer layer of Cr2O3 and bulk (Fe1–xCrx)2O3 is 1.5%, 1.1%, and 0.9% for compositions of x = 0, 0.41, and 0.52, respectively. With such small lattice mismatch values, the 250 Å thickness of the (Fe1–xCrx)2O3 film is below the critical thickness and thus is insufficient to fully relax the epitaxial strain. Instead, the films exhibit residual strain, as indicated by expanded out-of-plane lattice parameters. Due to the complexity of overlapping diffraction peaks from the (Fe1–xCrx)2O3 films and the Cr2O3 buffer layers in the XRD patterns, the out-of-plane lattice parameters for Fe2O3 and (Fe0.59Cr0.41)2O3 were determined by simulating the (0 0 0 6) peak envelope with two film layers, as shown in figure 5(a). The in-plane lattice parameters were then calculated from equation (2) above. This procedure increased the uncertainty in the lattice parameter determination to an estimated ± 0.01 Å. In contrast to the thicker Cr2O3 film discussed above, the buffer layers were nearly relaxed (93–97% strain relaxation). The (Fe0.48Cr0.52)2O3 film exhibited out-of-plane lattice spacings which were too similar to the Cr2O3 substrate to enable accurate simulation of the resulting pattern. As a rough estimate of the strain state in this film, the most intense peak in the (0 0 0 6) reflection was fit with a Gaussian function to determine the peak position, which was then taken as the out-of-plane lattice parameter for the (Fe0.48Cr0.52)2O3 film. Lattice parameters and strain relaxation (calculated from equation (1) relative to the Al2O3 substrate) for all three strained (Fe1–xCrx)2O3/Cr2O3 films are given in figure 3 (diamond symbols). The microstructure and interface abruptness of these films is expected to be somewhat similar to the Fe2O3/Cr2O3/ Fe2O3 heterostructure discussed in [30]. Figure 5(b) shows the resulting effect of lattice strain on the direct optical bandgap: the bandgap is reduced by 0.03–0.08 eV from the relaxed values [5] when the film possesses in-plane strain. The estimated error in the optical bandgap value is ±0.01 eV. The largest change in bandgap is observed for Fe2O3, with a reduction from 2.10 eV 6

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Table 1.  Formation energies of neutral oxygen vacancies and ­neutral

oxygen interstitials, as calculated using the PBE density functional. Positive (negative) values represent an energy gain (cost). The defect local environment indicates the number of Cr and Fe atoms near the corresponding oxygen defectsite..

Supercell

x in (Fe1-xCrx)2O3

1 Cr12O18 Fe1Cr11O18 0.92 Fe2Cr10O18 0.83 Fe10Cr2O18 0.17 Fe11Cr1O18 0.08 Fe2O3

0

Vacancy Interstitial O­ Defect formation formation local energy e­ nergy environment (eV) [eV] Cr4 Cr4 Fe1C3 Cr4 Fe1C3 Fe2C2 Fe2C2 Fe3C1 Fe4 Fe3C1 Fe4 Fe4

–5.0 –5.0 –4.6 –5.0 –4.6 –4.1 –4.0 –3.9 –3.5 –3.9 –3.5 –3.5

0.1 0.6 1.4 0.7 1.2 1.5 1.5 1.5 1.7 1.5 1.7 1.7

order of magnitude compared to RBS [32, 33]. Thus, RES is one of the few techniques which can non-destructively quantify the oxygen content in oxide thin films [34, 35]. A representative RES profile for (Fe0.48Cr0.52)2O3/Al2O3 and fits to the data are shown in figure S2 of the supporting infor­ mation (stacks.iop.org/J.PhysCM/26/135005/mmedia). The O content determined for several films, expressed as atomic %, is plotted in figure 3(d) (right axis). Error bars on these data points are the standard deviation in oxygen content determined from independent data fitting of two separate RES measurements on each sample. Interestingly, a compositional dependence on the oxygen content is observed in figure 3: Fe-rich films exhibit a slight excess of oxygen, while the Cr-rich alloy film (x = 0.87) is oxygen deficient and Cr2O3 is nearly stoichiometric. Figure 5.  (a) HRXRD (0 0 0 6) reflections of (Fe1–xCrx)2O3 films,

3.6.  Energetics of oxygen vacancies and oxygen excess

Cr2O3 buffer layers, and Al2O3 substrates (thick lines). Fits to the data are shown (thin lines), as described in the text. (b) Direct bandgap as a function of composition for nominally relaxed [4] and strained (this work) (Fe,Cr)2O3 thin films. For c­ omparison in this plot, the stoichiometry of strained films in this work has been determined as described in [4]. Inset: direct bandgap ­determination (dashed lines) from optical absorption data (solid lines) for relaxed x = 0.37 from [4] and strained x = 0.41 (x ~ 0.38) from this work.

The formation energy of a neutral oxygen vacancy in (Fe1–xCrx)2O3 alloys was investigated with DFT/GGA calculations of a 30 atom corundum supercell, as sketched in figure S3(a) of the supporting information (stacks.iop.org/ J.PhysCM/26/135005/mmedia). We considered O vacancies in pure Fe2O3 and Cr2O3 as well as in the most stable structures corresponding to two Fe:Cr ratios for both Fe-rich (x < 0.17) and Cr-rich (x > 0.83) solid solutions. As summarized in table 1, neutral oxygen vacancies are energetically less favorable in Cr2O3 than in Fe2O3: the corresponding vacancy formation energies calculated with respect to half of the O2 molecule are 5.0 and 3.5 eV, respectively. Since the two electrons associated with the neutral O vacancy tend to fill unoccupied 3d states of the nearest metal ions, this difference in vacancy formation energy is attributed to the difference in the position of the lowest unoccupied 3d states of the Fe3+ and Cr3+ ions with respect to the top of the valence band [5, 6]. In (Fe1–xCrx)2O3 alloys of intermediate composition, the vacancy formation energy tends to decrease with increasing Fe concentration, and oxygen vacancies are more likely to occur near Fe sites than near Cr sites. To explore the effect of lattice strain on the thermodynamic stability of the oxygen vacancies, the Cr2O3 supercell was held

at 103% strain relaxation to 2.02 eV at 90% strain relaxation. A smaller, but still significant, change is observed for x ~ 0.5, with a reduction from 1.80 eV at 107% strain relaxation to 1.77 eV at 81% strain relaxation. 3.5.  Oxygen stoichiometry

To more accurately quantify the oxygen stoichiometry of the films, non-Rutherford resonant elastic scattering (RES) was employed. RES is similar to traditional Rutherford backscattering spectrometry (RBS), except that the He+ ions are incident on the sample with sufficient energy, in this case 3.04 MeV, to cause an 16O(α,α)16O nuclear interaction. Because the resulting compound nucleus 20Ne possesses a resonance at this energy [31, 32], the scattering cross section at certain scattering angles is enhanced by more than an 7

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in a strained configuration analogous to the experimental Cr2O3 film in figure 3, with astrain = −0.0089 × aDFT and cstrain = 0.0095 × cDFT (where aDFT and cDFT are the relaxed lattice parameters for Cr2O3 determined by relaxation of the supercell). The formation energy of a neutral oxygen vacancy was found to barely depend on lattice strain, decreasing from 4.985 to 4.97 eV. Including electron correlation effects via GGA + U calculations produced a similarly negligible decrease in the formation energy. To determine whether an excess of oxygen is favorable in a given alloy, we investigated the stability of interstitial oxygen atoms. Generally, interstitial O atoms in oxides are known to bind with the lattice O2− ions and form peroxy species O22−. In low-symmetry structures such as the corundum-type cell of (Fe1–xCrx)2O3, there can be several nonequivalent geometric configurations that O22− molecular ions can adopt. Their relative stability is governed primarily by steric hindrance and lattice distortion effects, and less by electronic structure differences. As above, we considered interstitial O atoms in pure Fe2O3 and Cr2O3 as well as in the most stable structures corresponding to two Fe:Cr ratios for both Fe-rich (x < 0.17) and Cr-rich (x > 0.83) solid solutions. In each case we selected a set of the lattice O2− ions coordinated with all possible nonequivalent configurations of Fe and Cr atoms. Then 13 nonequivalent orientations of an O22− molecular ion at each of those sites were considered and the corresponding energies were minimized with respect to the coordinates of all atoms. While the peroxy species preserves its chemical identity in all cases, we identified three distinct configurations of O22− orientation and bonding to the neighboring cations. Two examples of fully relaxed O22− configurations are shown in figure S3(b) and S3(c) of the supporting information (stacks.iop.org/J.PhysCM/26/135005/mmedia). The energy gain of adding an interstitial O to stoichiometric (Fe1–xCrx)2O3 in each of these configurations is plotted in figure S4 of the Supporting Information. The energy calculation is referenced to oxygen atoms, not O2 molecules, which is appropriate in this case since the films were deposited in an O/O2 mixture generated in the ECR plasma source [36]. The resulting energy gains for the most stable configurations are listed in table 1. Interstitial oxygen is more stable than the stoichiometric material for all alloy compositions, but more energetically favored for Fe2O3 than for Cr2O3. The intermediate alloy compositions follow a rough trend between these endpoints, with interstitial oxygen more stable in Fe-rich regions than in Cr-rich regions of the alloy. As shown in figure S5 of the supporting information (stacks.iop.org/J. PhysCM/26/135005/mmedia), inclusion of interstitial oxygen expands the corundum lattice by 2–5%, with the largest changes occurring for interstitial oxygen located in Fe-rich regions.

Figure 6.  Relaxed lattice parameters calculated for (Fe1–xCrx)2O3

by DFT with lowest-energy magnetic spin arrangement (). Also included are lattice parameters for Fe2O3 with Cr2O3-like spins (), and Cr2O3 with Fe2O3-like spins (). Dashed lines extrapolate the Fe-rich alloy parameters to the Cr2O3 endpoint, and dash-dot lines extrapolate the Cr-rich alloy parameters to the Fe2O3 endpoint. Insets schematically illustrate the magnetic spin ordering in Fe2O3 and Cr2O3. Dashed lines represent O layers, buckled solid lines represent cation layers, and arrows indicate cation spin orientation.

interactions between cations. One example of superstructure ordering is the formation of a layered R3 structure in (Fe0.5Cr0.5)2O3, analogous to ilmenite FeTiO3. However, neither in this work nor in other investigations of (Fe1–xCrx)2O3 [23] have superstructure peaks corresponding to ordering of the Fe and Cr cations been observed by XRD, and the lack of ordering has been confirmed by neutron diffraction [23]. Thus, the deviation in lattice parameters is likely due to magnetic interactions. Although Fe2O3 and Cr2O3 are both antiferromagnetic (AFM) oxides with the corundum crystal structure, the details of their AFM ordering differ [6]. The corundum structure consists of closely spaced bilayers (or buckled layers) of cations in (0 0 0 1) planes, separated by planar layers of oxygen. In Fe2O3 between the Morin (262 K) and Néel (948 K) temperatures, each bilayer of Fe is ferromagnetically coupled with spins lying in the (0 0 0 1) bilayer, and antiferromagnetically coupled between bilayers (a slight canting of the ferromagnetic spins out of the (0 0 0 1) plane leads to ferrimagnetism). In contrast, the Cr cations in each bilayer of Cr2O3 are antiferromagnetically coupled with spins perpendicular to the (0 0 0 1) plane; coupling between bilayers is also antiferromagnetic. These two AFM ordering schemes are sketched in figure 6. (Fe1–xCrx)2O3 solid solutions may in principle adopt the magnetic ordering schemes of either

4.  Discussion 4.1.  Lattice parameter deviation from Vegard’s law

The lattice parameters for bulk [23] (Fe1–xCrx)2O3 deviate strongly from the linear relationship with composition expected from Vegard’s law, in contrast to similar systems such as (Fe1–xTix)2O3 solid solutions [9]. Such non-linear behavior has been hypothesized to be due to either superstructure cation ordering in the material, or to magnetic 8

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although no Fe valence state changes are observed in this work (figure 1(a)). Experimentally determining the oxygen stoichiometry in oxide thin films is challenging. The EELS line scan of (Fe0.19Cr0.81)2O3 in figure 4(f) indicates that approximately 10–20 ± 10% of the lattice oxygen is missing. RES measurements of a film with similar stoichiometry suggests an oxygen deficiency of about 2–9%, which is within the error of the EELS measurement. Qualitatively, it appears that very Cr-rich alloy films possess a substantial concentration of oxygen vacancies. In contrast, the RES data for (Fe1–xCrx)2O3 films with x ⩽ 0.52 hints at the presence of excess oxygen, accompanied by a concurrent lattice expansion, as shown in figure 3. At first glance, the DFT results for oxygen vacancy formation energies given in table 1 contradict the experimental findings of oxygen deficiency in Cr-rich alloys, since oxygen vacancy formation becomes less thermodynamically stable as the concentration of Cr increases. To reconcile the experimental findings with the theoretical predictions, we propose that oxygen vacancies form near Fe sites at the growth front during deposition for all Fe-containing compositions of (Fe1–xCrx)2O3 (0 ⩽ x < 1). Fewer, if any, oxygen vacancies form in pure Cr2O3. As the oxygen vacancies in Fe-containing alloys are buried by subsequent film deposition, their annihilation is governed in part by the rate of diffusion of interstitial oxygen through the overlayer and the rate of vacancy migration to the surface. Interstitial oxygen diffusion and vacancy migration cannot be easily distinguished experimentally, and hence the generic term ‘oxygen diffusion’ is employed in the following discussion to represent the cumulative effects of all oxygen transfer channels. At high temperatures, the rate of oxygen diffusion in Fe2O3 single crystals [43] is approximately twice that of Cr2O3 single crystals [44]. Extrapolating the high temperature diffusion data down to the deposition temperature, the oxygen diffusion rate in Fe2O3 is estimated to be roughly three times that of Cr2O3. The higher rate of oxygen diffusion in Fe2O3, combined with the predicted propensity of oxygen vacancies to migrate to the Fe2O3 film surface [45], can be expected to lead to the annihilation of a substantial fraction of oxygen vacancies in Fe-rich films. In contrast, in highly Cr-rich films, the percolation paths which would allow diffusion through Fe-rich regions cannot form, and oxygen diffusion through the film is significantly reduced. Presumably, oxygen vacancy migration rates are also reduced compared to those in Fe2O3, since migration requires the vacancy to leave the proximity of the neighboring Fe and move into energetically less favorable Cr-rich regions. As sketched in figure 7, these factors lead to a ‘freezing-in’ of the vacancies introduced at the growth front, and a resulting film with a higher concentration of oxygen vacancies than found in Fe-rich films. Post-growth annealing in air at elevated temperature may be sufficient to overcome the oxygen diffusion barriers in Cr-rich films and annihilate the oxygen vacancies, but was not investigated in this study. In an overpressure of oxygen atoms, as occurs during deposition in an O/O2 mixture from the ECR plasma source, the incorporation of oxygen interstitials is more favorable than the alloy remaining stoichiometric, as shown in table 1. Thus, the oxygen diffusion postulated above which fills oxygen vacancies in Fe-rich material can also be expected to incorporate oxygen

crystal, or alternatives, depending on the energetics of the system [20, 37]. Figure 6 shows the a and c lattice parameters calculated for bulk (Fe1–xCrx)2O3 (from figure 3), together with the predicted relaxed lattice parameters for Fe2O3 with a Cr2O3-like AFM structure imposed (circles), and, likewise, for Cr2O3 with an Fe2O3-like AFM structure imposed (triangles). Clearly, the change in the magnetic ordering strongly impacts the structural parameters of the crystal. By fitting lines to the compositions near the endpoints of Fe2O3 and Cr2O3, and extending them across the composition range, it is evident that the linear extrapolations fall closer to the artificially constrained magnetic structure of the opposite end member than to the energetically more favorable magnetic configuration. This implies that much less deviation from Vegard’s law would be observed if the magnetic ordering of the solid solutions remained constant with composition, and provides direct theoretical confirmation that the majority of the deviation from Vegard’s law occurs due to the magnetic structure of the alloys. Interestingly, the a lattice parameter is strongly influenced by the Cr composition when the magnetic structure is constrained to be Cr2O3-like, but shows little change with composition when it is Fe2O3-like. Conversely, the c lattice parameter exhibits a more substantial change with a Fe2O3-like magnetic structure than with a Cr2O3-like structure. These results suggest that solid solutions of materials that satisfy the Hume-Rothery rules [38], but possess different magnetic structures, can result in novel magnetic-strain-induced phenomena such as strong deviations from Vegard’s law in the absence of external stress. 4.2.  Strain and point defects

The observation of in-plane biaxial strain in the Cr-rich (Fe1–xCrx)2O3 epitaxial thin films is fully expected and indi­ cates that the films have not completely relaxed the epitaxial strain to the Al2O3 substrate. What is unexpected, however, is the strain relaxation values greater than 100% for intermedi­ ate composition and Fe-rich films. In addition, the films exhibit non-Poisson-like elastic properties, with out-of-plane lattice parameters inconsistent with a single, reasonable Poisson-like relation to the in-plane parameters. This is in sharp contrast to epitaxial thin film systems such as metallic CrxMo1-x and CrxV1-x alloys deposited on MgO(001) [39, 40]. In both of these material systems, the relationship between the in-plane and outof-plane lattice parameters closely followed a Poisson-like relationship. The key difference between metallic alloys such as CrxMo1-x and CrxV1-x, and oxide alloys such as (Fe1–xCrx)2O3, is the high concentration of point defects in the latter. Point defects induce additional stress in the lattice, and the resulting strain can be approximated as a hydrostatic term which must be included in equation (2) [25]. In particular, oxygen stoichiometry can strongly influence the crystalline structure of the material. This phenomenon has been long recognized; for example, YBa2Cu3O7-δ epitaxial thin films exhibit an expansion in the out-of-plane c lattice parameter as δ increases [41]. For systems such as the iron oxides, the effect of oxygen vacancies on lattice parameters is further complicated by the ability of Fe to alter its valence state as the oxygen stoichiometry changes [42], 9

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conduction band minimum. From the position of the VBM for (Fe0.48Cr0.52)2O3 in figure  1(c) (0.69 eV) and the measured direct optical bandgap (1.80 eV [5]), the relative position of the CBM can be placed at −1.11 eV. This value is shifted 0.81 eV higher in energy than the CBM of Fe2O3 (CBM = −0.30 eV). Raising the CBM relative to the position for Fe2O3 may reduce or eliminate the overpotential required for photoelectrochemical water splitting applications [1, 46]. The epitaxial strain present in the Cr2O3 film appears to affect the optical bandgap. The optical bandgap was measured as 3.07 eV [5], which is reduced from the bulk value [5, 47] of 3.3–3.4 eV. In contrast, the measured optical bandgap of the fully relaxed Fe2O3 film, 2.10 eV, is consistent with the bulk value [1, 20] of 1.9–2.2 eV. The effect of strain on the optical properties of semiconductors has been established previously. For example, the lowest exciton transition energy in the photoluminescence spectrum of ZnO has been observed to shift to lower values with increasing biaxial strain, decreasing ~0.04 eV when the in-plane strain εin-plane = −1.3% [48]. For comparison, the in-plane strain for Cr2O3 is εa = (astrain − a0)/a0 × 100% = −0.9%. Although the same trend of reduction in the optical transition energy is observed, the results cannot be quantitatively compared to those for ZnO, given the differences in electronic band structure: the lowest optical transitions for II-V compounds, such as ZnO, are valence band p to conduction band s orbitals, while for Cr2O3 the lowest transitions are from hybridized p-d orbitals in the valence band to d orbitals in the conduction band. Nabi and Pentcheva [9] have calculated via DFT the band structure of Fe1.67Ti0.33O3 [x = 0.167 in (Fe1–xTix)2O3] biaxially strained to FeTiO3 (tensile lattice strain), Fe2O3 (slight compressive strain), and Al2O3 (large compressive strain). The bandgap was predicted to decrease by as much as 25% with increasing biaxial compressive strain, from 1.90 eV for α-FeTiO3 and 1.79 eV for α-Fe2O3 to 1.43 eV for α-Al2O3. A simple calculation for the epitaxial Cr2O3 film in this work, assuming a linear decrease in bandgap with increasing compressive strain from 3.3 eV at 100% strain relaxation (bulk value) to 3.07 eV at 77% strain relaxation, predicts a bandgap of 2.3 eV for Cr2O3 fully strained in-plane to Al2O3. This decrease in bandgap of 30% is similar to the reduction predicted by Nabi and Pentcheva [9] Thus, the reduced bandgap for Cr2O3 epitaxial thin films is potentially a result of residual in-plane compressive strain. As illustrated in figure 3, (Fe0.13Cr0.87)2O3 also exhibits residual strain which may contribute to its lower bandgap. Figure 5 illustrates the utility of deliberately engineering strain in (Fe,Cr)2O3 thin films to modify the bandgap. Employing a Cr2O3 buffer layer to reduce the lattice mismatch and increase the critical thickness for relaxation in the (Fe,Cr)2O3 overlayer results in 250 Å thick (Fe,Cr)2O3 films which exhibit residual in-plane strain. This in-plane strain, although small (80–90% strain relaxation), is sufficient to decrease the direct optical bandgap of the material by 0.03– 0.08 eV. Interestingly, the magnitude of change in the direct optical bandgap decreases with increasing Cr content in the film. The (Fe,Cr)2O3 films also possess greater strain than the pure Fe2O3 film (see figure 3(d)), which is a consequence of the reduced lattice mismatch, and thus a reduced degree of epitaxial strain relaxation, with increasing Cr content. The

Figure 7.  Schematic corundum crystal structures for Fe-rich (left) and Cr-rich (right) (Fe1-xCrx)2O3 alloys. Representative oxygen vacancies (Ovac) introduced during deposition are included. Dashed lines indicate percolation pathways through Fe-rich regions in which O diffusion and O vacancy migration are more facile, increasing the likelihood of vacancy annihilation.

atoms as interstitials in the lattice. Note that this would not be the case in an overpressure of O2. Interstitial oxygen is a more stable defect in Fe-rich alloys than in Cr2O3, which corroborates the experimental finding of excess oxygen for x ⩽ 0.52. Further, the incorporation of interstitial oxygen is predicted to expand the lattice by 2–5%. This magnitude of expansion is likely to be overestimated due to the relatively small size of the supercell used in the calculations. Importantly, it is consistent with the expansion observed experimentally (~0.3–0.6%), considering that only a small fraction of volume in the film will possess interstitial oxygen. For example, RES measurements of (Fe0.48Cr0.52)2O3 estimated the oxygen content as 61.7 at %, which is equivalent to interstitial oxygen present in approximately 3% of the unit cells in the lattice. 4.3.  Effect on electronic structure and optical properties

Previously reported optical absorption data and associated theoretical calculations for these (Fe1–xCrx)2O3 films indicated that new transitions from occupied Cr 3d t2g to unoccupied Fe 3d t2g orbitals were responsible for substantial bandgap bowing in the alloy system, resulting in a minimum bandgap of 1.8 eV for x ≈ 0.5 [5]. This bandgap is less than that for Fe2O3 (~2.1 eV) or Cr2O3 (3.3–3.4 eV), making the (Fe1–xCrx)2O3 alloy system appealing as a photoactive material. The new Cr 3d t2g → Fe 3d t2g transitions only occur when the Cr3+ and Fe3+ cations are in close proximity, and are not detectable in well-defined Fe2O3/Cr2O3 heterojunctions [8]. The nanometer-scale cation mixing deduced from the EELS map of (Fe0.19Cr0.81)2O3 (see figure 4(f)) facilitates these transitions, resulting in a low optical bandgap (~1.9 eV) at this composition despite its proximity to pure Cr2O3. In addition to lowering the bandgap, alloying Fe2O3 with Cr2O3 also raises both the valence band states and the 10

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Acknowledgments

bandgap data in figure 5 suggests that there may be an optimum level of strain which will produce the largest change in the optical bandgap. All the films, regardless of strain state, exhibited an exponential tail in the optical absorption spectrum at photon energies < ~1.5 eV [5], precluding the determination of indirect bandgap values. This exponential tail is likely related to the defect structure of the films, originating in the columnar microstructure observed by STEM. Defect states at the lowangle grain boundaries between columns may result in localized optical transitions at low photon energies. Overall, these results suggest several promising avenues of investigation to optimize the bandgap of (Fe,Cr)2O3 for efficient solar energy harvesting. Tuning the strain state in (Fe1–xCrx)2O3 epitaxial films, for example by varying the substrate or employing buffer layers, is expected to significantly impact the bandgap. This may be particularly fruitful near a composition of x ~ 0.5, where a minimum in the bandgap of ~1.8 eV is observed [5]. Strain engineering and process optimization can also be utilized to reduce undesired structural defects in the film, such as columnar grain boundaries. A decrease in the areal density of columnar grain boundaries will suppress undesired IR wavelength absorption, and improve the photogenerated electron-hole pair separation and carrier transport properties of the films.

TCK, VS, SM, and SAC were supported by the US DOE, Office of Science, Office of Basic Energy Sciences (BES), Division of Materials Sciences and Engineering; SEC and YW were supported by BES, Division of Chemical Sciences, Geosciences, and Biosciences. PVS acknowledges support by the Royal Society. RC was supported by the EMSL William Wiley Postdoctoral Fellow program. This work was performed using EMSL, a national scientific user facility sponsored by the US DOE’s Office of Biological and Environmental Research and located at the Pacific Northwest National Laboratory (PNNL). PNNL is a multiprogram national laboratory operated for DOE by Battelle. References [1] Sivula K, Le Formal F and Gratzel M 2011 ChemSusChem 4 432–49 [2] Pozun Z D and Henkelman G 2011 J. Chem. Phys. 134 224706 [3] Sanchez C, Sieber K D and Somorjai G A 1988 J. Electroanal. Chem. 252 269–90 [4] Zhao B, Kaspar T C, Droubay T C, McCloy J, Bowden M E, Shutthanandan V, Heald S M and Chambers S A 2011 Phys. Rev. B 84 245325 [5] Chamberlin S E, Wang Y, Kaspar T C, Cohn A W, Gamelin D R, Sushko P V and Chambers S A 2013 J. Phys.: Condens. Matter 25 392002 [6] Wang Y, Lopata K, Chambers S A, Govind N and Sushko P V 2013 J. Phys. Chem. C 117 25504−12 [7] Mashiko H, Oshima T and Ohtomo A 2011 Appl. Phys. Lett. 99 241904 [8] Mashiko H, Oshima T and Ohtomo A 2012 Japan. J. Appl. Phys. 51 11PG 11 [9] Nabi H S and Pentcheva R 2009 J. Appl. Phys. 106 073912 [10] Giannuzzi L A, Drown J L, Brown S R, Irwin R B and Stevie F 1998 Microsc. Res. Tech. 41 285–90 [11] Cueva P, Hovden R, Mundy J A, Xin H L L and Muller D A 2012 Microsc. Microanal. 18 667–75 [12] Kresse G and Joubert D 1999 Phys. Rev. B 59 1758–75 [13] Blöchl P E 1994 Phys. Rev. B 50 17953 [14] Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 [15] Gao Y and Chambers S A 1996 Mater. Lett. 26 217–21 [16] Chambers S A and Droubay T 2001 Phys. Rev. B 64 075410 [17] Gao Y, Kim Y J, Chambers S A and Bai G 1997 J. Vac. Sci. Technol. A: Vac. Surf. Films 15 332–9 [18] Chambers S A 2000 Surf. Sci. Rep. 39 105 [19] Kaspar T C, Chamberlin S E and Chambers S A 2013 Surf. Sci. 618 159–66 [20] Moore E A 2007 Phys. Rev. B 76 195107 [21] Biondo V, de Medeiros S N, Paesano A, Ghivelder L, Hallouche B and da Cunha J B M 2009 Solid State Sci. 11 1444–50 [22] Chambers S A, Liang Y and Gao Y 2000 Phys. Rev. B 61 13223–9 [23] Grygar T, Bezdicka P, Dedecek J, Petrovsky E and Schneeweiss O 2003 Ceram. Silik. 47 32–9 [24] Gazquez J, Bose S, Sharma M, Torija M A, Pennycook S J, Leighton C and Varela M 2013 APL Mater. 1 012105 [25] Kisielowski C, et al 1996 Phys. Rev. B 54 17745–53 [26] Hearmon R F S 1946 Rev. Mod. Phys. 18 409–40 [27] Wang Y, Fang H Z, Zacherl C L, Mei Z G, Shang S L, Chen L Q, Jablonski P D and Liu Z K 2012 Surf. Sci. 606 1422–5 [28] Lutfalla S, Shapovalov V and Bell A T 2011 J. Chem. Theory Comput. 7 2218–23

5.  Conclusions Epitaxial thin films of α-(Fe1–xCrx)2O3 were deposited on α-Al2O3(0 0 0 1) by OPA-MBE. High crystalline quality films are achieved, with uniform cation mixing on the nanometer scale. Films with 0 ⩽ x < 0.8 exhibit relaxation of in-plane biaxial strain, with in-plane lattice parameters somewhat larger than expected. This lattice expansion, as well as the non-Poisson-like relationship between the in-plane and outof-plane lattice parameters, results from a slight excess of oxygen in the lattice. In contrast, films with x > 0.8 remain partially strained to the Al2O3 substrate, with stoichiometric or slightly deficient oxygen content. The in-plane compressive strain for Cr2O3 accounts for the reduction in bandgap from the bulk value. Engineering strain in (Fe1–xCrx)2O3 films is a promising avenue to decrease the bandgap further. As an example, the bandgap of (Fe0.48Cr0.52)2O3 is reduced from 1.80(1) eV to 1.77(1) eV when the film possesses a small amount of residual in-plane strain. The low-angle grain boundaries present in the columnar film structure of (Fe1–xCrx)2O3 films likely contain localized defect states which contribute to the exponential optical absorption tail observed at low photon energies. Comparison of lattice parameters for corundum Fe2O3 and Cr2O3 supercells relaxed via DFT with fixed antiferromagnetic ordering confirms that the lattice parameter deviation from linearity with composition is due to the magnetic structure of the alloys. The relationships established for (Fe,Cr)2O3 between strain state, defect structure, and optical properties such as bandgap can be utilized to further optimize the material for solar energy applications. 11

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