Uniaxial strain induced anisotropic bandgap engineering in freestanding BiFeO₃ films

With the advances in thin-film epitaxy, biaxial strain has been widely employed in tuning the structures and properties of oxide materials,^1–4 largely enriching the phase diagrams of strain-driven emergent phases such as ferroelectricity in SrTiO₃,⁵ multiferroicity in EuTiO₃,⁶ and so on. In addition to the biaxial epitaxial strain, the recently developed freestanding film fabrication technique based on a water-soluble Sr₃Al₂O₆ sacrificial buffer layer provides unprecedented freedom to manipulate material properties.^7–12 The large tolerance of extreme uniaxial strain or strain gradients induces extraordinary properties in these freestanding films.^13–19 Moreover, by applying uniaxial strain along selective lattice orientations, we can realize the regulation of symmetry. For example, we can turn a square lattice into a rectangular or oblique lattice by stretching the film along the [100]_p or [110]_p directions, respectively. This tunability provides a new knob to engineer transition metal oxides for novel phases and phenomena.

Bismuth ferrite (BiFeO₃—BFO) has gained great interest for its potential application in photonics, by virtue of a relatively small bandgap (∼2.7 eV) in the visible range,²⁰ a strong photovoltaic effect,²¹ and sizable electro-optic coefficients.²² However, considering that solar energy absorption is ∼15% in BFO,²³ bandgap reduction is highly desired to further improve its photovoltaic performance. Common bandgap reduction methods such as Mn doping tend to form centrosymmetric structures in BFO while narrowing the gap,^24–26 sacrificing spontaneous polarization, which plays an important role in the separation of photoinduced carriers. Strain engineering is proven to be a possible method to tune the bandgap both theoretically and experimentally.^27–31 However, previous studies on strain-driven bandgap tuning in BFO show weak and even contradictory results, especially in rhombohedral-like structures.^32–36 For instance, BFO films grown on SrTiO₃(001), SrTiO₃(111), and (LaAlO₃)_0.3-(SrAl_0.5Ta_0.5O₃)_0.7 (LSAT) substrates show a relatively unchanged bandgap at 2.77 ± 0.04 eV,³² while another article reported a 50 meV difference in the gap deposited on SrTiO₃ and DyScO₃ substrates.³³ A recent article surprisingly found that the bandgap was insensitive to variations in out-of-plane lattice constants.³⁶ Note that the variations in strain states were obtained in different samples in these works. Considering the strong dependence of the bandgap on the exact crystalline structure and growth conditions,^37,38 it is of great importance to rule out sample-dependent extrinsic effects and study the strain effect on the bandgap by continuously tuning the strain state in the same sample.

Here, we investigate the in situ bandgap evaluation of freestanding BFO films as a function of strain and symmetry. We observe an opposite dependence of the bandgap by applying uniaxial tensile strain along the [100]_p and [110]_p directions, which is shown to be related to the distinct strain-driven antiferrodistortive (AFD) rotation patterns by first-principles calculations.

The water-soluble SAO films were grown 6-unit-cell thick on a (001) SrTiO₃ single-crystalline substrate, followed by the 16-unit-cell thick BFO films using MBE technique. This thickness of BFO is found to be suitable for stretching in Zang’s work,¹⁹ where they found that thicker BFO films crack more easily under strain. The growth of SAO films was in pure oxygen atmosphere with pressure of 1 × 10⁻⁶ Torr and at a substrate temperature T_substrate of 850 °C. The thickness of SAO films was monitored by reflection high-energy electron diffraction (RHEED) oscillations. The BFO films were grown in distilled O₃ atmosphere with pressure of 1 × 10⁻⁵ Torr and at T_substrate = 380 °C. Adsorption-controlled mode was used in film growth with a fixed Bi:Fe flux ratio of 3:1, and the thickness was controlled by the deposition time of iron.

After the growth of the BFO/SAO heterostructure on the substrate, we coated the BFO layers with epoxy at room temperature and heated them at 100 °C for 30 min to enhance adhesion to PET supporter. Then we immersed the samples into de-ionized (DI) water at room temperature for several days to make sure the SAO layer was completely removed, and finally we got the freestanding BFO layer transferred to the epoxy/PET supporter. We use micromanipulators to apply uniaxial strain, and strain tuning along a certain direction can be realized simply by changing the orientation of the BFO layer related to the epoxy/PET supporter.

XRD measurements were performed using a high-resolution x-ray diffractometer (Bruker D8). Utilizing x-ray reflectometry (XRR) technique and Laptos software, we confirm the thickness of 6.3 nm of our film, consistent with the 16-unit-cell design in growth [Fig. S3(a)]. The surface topography and ferroelectric domain structure of our freestanding BFO films were measured using an Asylum Research MFP-3D scanning probe microscopy. Nanoworld EFM-50 Pt/Ir -coated Si cantilevers were used in our measurements, and PFM images were taken in the Dual AC Resonance Tracking (DART) mode with driving voltage (0.5 V a.c.) applied at the tip.

The films were characterized at room temperature using a rotating compensator-type spectroscopic ellipsometer (RC2, J. A. Woollam Inc.). The incidence angle was 65°, and the wavelength range was 210–2500 nm (0.49–5.9 eV). Since the optical properties of the epoxy/PET supporter were found insensitive to strain [Fig. S3(b)], we fitted the raw ellipsometry data to a two-layer model, including a semi-infinite substrate of epoxy/PET and a BFO layer (Fig. S2). With the exact thickness information from the XRR technique, point-by-point data inversion method under the correction of Kramers–Kronig consistency was used to extract the refractive index n and extinction coefficient k. The optical bandgaps were modeled following Tauc’s rule on band–edge transitions

with absorption coefficient α, photon energy E, the scaling constant A, the bandgap energy E_g, and the transition type n (n = 1/2 for direct-allowed, 3/2 for direct-forbidden, 2 for indirect-allowed, and 3 for indirect–forbidden transitions, respectively).⁴⁵ Since the direct bandgap behavior was found in BFO,^32–36 we took the value of n as 1/2 in the bandgap calculation. With the absorption coefficient α derived from ellipsometry data, Tauc plots of (αE)² vs E were constructed to obtain the optical bandgap of our sample, as the intersection extrapolated from the linear region to the E axis [Figs. 3(c) and 4(c)] yielded the gap value. Our PET had one side polished to reduce backside reflection.

Calculations were performed using density-functional theory within the Perdew–Burke–Ernzerhof functional,³⁹ using the Vienna ab initio simulation package^40,41 and projector augmented wave potentials.⁴² The strong onsite Coulomb interaction on the Fe was considered by including an effective Hubbard U parameter of 4 eV. Electrons taken to be valence are 6s²6p³ for Bi, 3d⁶4s² for Fe, and 2s²2p⁴ for O. A plane-wave cutoff of 550 eV is used throughout. The atomic structure relaxation was carried out until the force on each atom was less than 0.001 eV/Å. Supercells containing 20 atoms were used, and G-type antiferromagnetism from Fe ions was adopted, and a Γ-centered 7 × 7 × 5 k-point mesh was adopted.

Freestanding BFO films were synthesized using water-soluble Sr₃Al₂O₆ (SAO) as the sacrificing layer.^7–9 As illustrated in Fig. 1(a), the heterostructure of 16-unit-cell BFO thin films with a 6-unit-cell sacrificial SAO layer was epitaxially grown on a SrTiO₃ (001) substrate by molecular beam epitaxy (MBE) technique. Then the BFO layer was glued on polyethylene terephthalate (PET) tape by epoxy. Finally, the SAO layer was completely removed by immersing the samples into de-ionized (DI) water at room temperature, leaving the BFO layer attached to the epoxy/PET supporter. Uniaxial tensile strain in BFO was achieved by mechanically stretching the multilayer structure of BFO/epoxy/Pet along different in-plane directions. The surface topography and ferroelectric domain structure of freestanding single-crystalline BFO films were measured by piezoresponse force microscopy (PFM) (Fig. S1), showing a multidomain ferroelectric pattern.

XRD measurements were performed using high-resolution x-ray diffractometer (Bruker D8) to obtain the lattice parameter changes under strain. 2θ-ω scans around (002), (011), and (101) reflections of the freestanding BFO films with strain along [100]_p direction are shown in Figs. 2(a)–2(c). A comparison was made between the actual strain measured by XRD and nominal strain (elongation of PET) to estimate the actual strain value in the optical characterization [shown in Fig. 2(d)]. Note that the sample tends to crack under large strain (∼4%); so, the function between the strain measured by XRD and nominal strain deviates from the linear relationship. The slope of linear fit 0.85 is taken as the conversion factor between actual strain and nominal strain in the following optical measurements.

The 10 × 10 mm² sample was cut into four 5 × 5 mm² pieces after film growth and transferred for different optical experiments with strain applied along the [100]_p or [110]_p direction. Figure 3(a) presents the experimental energy dependence of the extinction coefficient with uniaxial tensile strain along the [100]_p direction, extracted from spectroscopic ellipsometry measurements (Fig. S2). Note that strain here corresponds to the actual lattice deformation along the [100]_p direction deduced from XRD measurements [Fig. 2(d)]. The variation in the refractive index n in response to strain and the corresponding experimental Tauc plots are shown in Figs. 3(b) and 3(c), respectively. As summarized in Fig. 3(d), a monotonic increase in the bandgap by applying uniaxial tensile strain along the [100]_p direction was observed, which raises the bandgap from 2.73 eV at 0% strain to 2.82 eV at 4% strain.

We chose another piece of sample and apply the uniaxial tensile strain along the [110]_p direction (Fig. 4). In contrast to the increase in the bandgap by applying strain along the [100]_p direction, we observed an unexpected decrease in the bandgap by applying strain along the [110]_p direction, indicating different microscopic mechanisms in these two cases. Interestingly, compared to the [100]_p direction, BFO films are more brittle by applying strain along this [110]_p diagonal direction, which starts to form small cracks when the strain is larger than 2%. Nonetheless, the bandgap evolution is clear, and even the 2.8% strain state fits in the trend, although it contains some small cracks in the film.

To explain the strain induced anisotropic bandgap engineering in BFO films, we performed first-principles calculations based on Density Functional Theory (DFT) within the generalized gradient approximation (GGA). The rhombohedral phase as the zero strain possesses same oxygen octahedral tilting of 8.2° along the [100], [010], and [001] directions. In the calculations of strain along the [100] direction, we fixed the strained lattice parameter along the[100] direction and relaxed the lattice parameters along the [010] and [001] directions. In the calculations of strain along the [110] direction, the strained lattice parameter along [110] direction is fixed and the lattice parameters along [−110] and [001] directions are relaxed. As shown in Fig. 5(a) [(c), respectively], the calculated bandgaps of BFO thin films under [100] ([110], respectively) strain increase (decrease, respectively) when increasing strain. The [100] and [110] strain induced changes of gaps exhibit opposite evolution with strain, which agrees well with our experiments. Note that the discrepancy between calculated bandgaps and experimental values comes from the derivative discontinuity of the exchange-correlation energy in DFT calculations, which is a general phenomenon.⁴³ 

We further investigated the effects of lattice and oxygen octahedral tilting separately [see red triangles and blue circles in Figs. 5(a) and 5(c)]. In the calculation of lattice deformation effect on bandgap, the structures have the same lattice as the strained lattice, but without atomic relaxation. In the calculation of the effect on bandgap from oxygen octahedral tilting, the structures adopt the same oxygen octahedral tilting with the considered strained structure, but without the lattice strain comparing to the bulk structure. From Figs. 5(a) and 5(c), we find that pure lattice expansion narrows the bandgap in both cases, while AFD rotations raise the bandgap in the [100]_p stretched state and narrow the gap in the [110]_p stretched state. Clearly, the AFD rotations under strain are the main reason for the anisotropic bandgap engineering in our films. For a deeper understanding of the AFD rotation changes induced by strain, we calculated the impact on bandgap from the AFD components around the x, y, and z axes [Fig. 5(f)]. As shown in Fig. 5(e), the bandgap decreases with increasing AFD rotations, no matter around which direction the rotation takes place. Further calculations show that the variation of AFD components strongly depends on how the strain is applied [Figs. 5(b) and 5(d)]. When uniaxial strain is applied along the [100]_p direction, the rotation angle around the x axis increases, while the rotation angles around the y and z axes decrease. In contrast, in the [110]_p case, the angle of rotations increase around the x and y axes, but decrease around the z axis with increasing strain. Now we can explain our anisotropic bandgap engineering from different AFD rotations in two strain states. When the uniaxial tensile strain is applied along the [100]_p direction, the AFD rotations around two axes decreases and one axis increases, which effectively increases the bandgap. In contrast, when the strain is applied along the [110]_p direction, the AFD rotations around two axes increases and one axis decreases, resulting in a bandgap narrowing.

In summary, we observed an anisotropic bandgap variation in BiFeO₃ films under uniaxial tensile strain. The bandgap increases and decreases when uniaxial tensile strain is applied along the [100]_p and [110]_p directions, respectively. This phenomenon can be understood on the selective tuning of AFD rotations by uniaxial strain along different lattice orientations. Moreover, the regulation on symmetry by applying uniaxial strain along selective lattice orientations broadens the horizon of materials design, providing a new knob to engineer transition metal oxides for novel phases and phenomena.

See the supplementary material for the intrinsic ferroelectric polarization, process of spectroscopic ellipsometry measurement, calculation of the actual strain in the stretching experiment, XRR measurement of BFO films, and optical properties of epoxy/PET supporter under strain.

This work was supported by the National Key R&D Program of China (Grant No. 2021YFA1400400), the National Natural Science Foundation of China (Grant Nos. 11861161004 and 11874207) and the Fundamental Research Funds for the Central Universities (Grant No. 0213-14380221).

The authors have no conflicts to disclose.

Xingyu Jiang: Formal analysis (equal); Investigation (equal); Writing – original draft (lead). Yuefeng Nie: Conceptualization (equal); Project administration (equal); Writing – review & editing (equal). Yiren Liu: Formal analysis (equal). Yipeng Zang: Investigation (supporting). Yuwei Liu: Methodology (supporting). Tianyi Gao: Investigation (supporting). Ningchong Zheng: Formal analysis (supporting). Zhengbin Gu: Conceptualization (supporting). Yurong Yang: Formal analysis (supporting). Di Wu: Methodology (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.