Inch‐Scale Freestanding Single‐Crystalline BiFeO3 Membranes for Multifunctional Flexible Electronics

Flexible electronics strongly demand the integration of flexible and large‐scale multifunctional oxides. BiFeO3 is one of the most essential multifunctional oxides that could be used in memories, logics, sensors, and actuators. Recently, freestanding single‐crystalline BiFeO3 membranes exhibited superior elasticity and flexibility. However, fabrication and integration of large‐scale freestanding BiFeO3 membranes into flexible electronics remain elusive. In this study, inch‐scale freestanding single‐crystalline BiFeO3 membranes are fabricated with assistance from a water‐soluble sacrificial layer. To transfer flat and crack‐free membranes, all the existing methods are first followed but fail. Then the study introduces a temporary supporting Cu layer on the surface of the as‐grown SiTiO3/Sr3Al2O6/(SrRuO3/)BiFeO3 heterostructure and successfully obtains full and crack‐free 5 mm × 5 mm freestanding membranes on various substrates. The residual strain within the heterostructure releases gradually under the protection of the Cu layer. The freestanding BiFeO3 membranes are relatively uniform among different regions and exhibit good dielectric, ferroelectric, and ferromagnetic properties. Finally, flexible ferroelectric photovoltaic devices are patterned based on those BiFeO3 membranes, and they have open circuit voltage and short circuit current density up to −0.25 ± 0.03 V and 0.82 ± 0.09 µA cm−2, respectively.


Introduction
Flexible electronics demand the integration of increasing multifunctional devices for sensing, actuation, signal processing, and information storage. [1]arge-scale and highly flexible thin films are fundamentals to fabricate those flexible devices.Usually, metallic thin films, polymers, and 2D materials have high flexibility and elasticity.[4] Oxide thin films are fundamentals of various conventional solid-state electronic devices, such as capacitors, sensors, actuators, memories, and so on. [5]Integration of those devices into flexible electronics will greatly enhance the functionality, and this depends on the availability of high-quality and highly flexible oxide thin films.Due to their relatively high crystallization temperature, large-scale oxide thin films are usually directly deposited on rigid substrates such as silicon and oxide substrates.8][9][10] Since oxides are not well-crystallized, their electrical performance is limited.Another improving method is depositing large-scale oxide thin films on mica substrates. [11]owever, the flexibility of thin films is limited by the mechanical properties of mica and not comparable to polymer substrates.Therefore, large-scale, highly flexible, and multifunctional oxide thin films that could be easily processed for flexible electronics are always desired.
Bismuth ferrite (BiFeO 3 ) is one of the most important multifunctional oxides.[14][15][16][17][18] Single-crystalline BiFeO 3 thin films are much more interesting than polycrystalline BiFeO 3 because those excellent properties always exist in the former one that close to perfect crystals and its anisotropy provides much freedom for designing devices.Conventional flexible and singe-crystalline BiFeO 3 thin films are usually deposited on mica substrate, [19] and they have limitations on flexibility as mentioned above.Besides, the epitaxy between mica and BiFeO 3 leads to thin films with specific orientation, [20] which limits the availability of single-crystalline BiFeO 3 with other orientations that have better performance.][23] They are fabricated by introducing a lattice-matched sacrificial layer during epitaxial growth and become freestanding after removing the sacrificial layer.
Many groups have obtained high-quality freestanding singlecrystalline BiFeO 3 membranes using this sacrificial layer. [12,18,22]hey still have piezoelectricity with thickness even down to the monolayer limit. [12]They could provide a platform to continuously control the photoconductance by the macroscopic flexoelectric effect. [18]They exhibit good exchange bias when combined with a magnetic layer. [21]Moreover, they show superior elasticity and flexibility that could be 180°folded and tolerate >5% bending strain without crack, comparable to polymer substrates. [22]he size of the available freestanding single-crystalline BiFeO 3 is usually small.How to transfer large-scale and crack-free BiFeO 3 , as well as other freestanding oxide membranes, is a critical issue in this field.Currently, there are three methods for transferring.1) Transferring without any supporting layer: [24][25][26][27][28][29] Once removing the sacrificial layer in the etchant solution, the freestanding membranes could float on the surface of the solution and then be picked up to other substrates.2) Transferring with soft polymer stamp: [30][31][32][33][34][35][36][37][38] The freestanding single-crystalline oxide membranes would be left on the soft polymer stamp after dissolving the sacrificial layer, further transferred and printed to the desired substrates.3) Transferring with hard polymer supporting layer: [39][40][41] A relatively "hard" polymer supporting layer is coated on the surface before removing the sacrificial layer, and this polymer is further removed in solvent after transferring the polymer/membranes on the desired substrates.[37][38]41] Currently, fabrication and integration of high-performance, large-scale, crack-free freestanding single-crystalline BiFeO 3 membranes into flexible electronics still remain elusive.
In this study, we fabricated one-inch scale freestanding singlecrystalline BiFeO 3 membranes by pulsed laser deposition with assistance from the water-soluble sacrificial layer.We checked the variation of microstructures, dielectric, ferroelectric, and magnetic properties over different regions.We tried to transfer flat and crack-free membranes onto other substrates by the reported methods.However, the transferred membranes always have flaws and defects.Then we introduce a new transferring method and obtain crack-free membranes on various substrates.Finally, a flexible photovoltaic device was demonstrated based on those high-quality freestanding single-crystalline BiFeO 3 membranes.

Results and Discussion
In the beginning, inch-scale SrTiO 3 (100)/Sr 3 Al 2 O 6 /BiFeO 3 heterostructures are epitaxially deposited, and the freestanding membranes are obtained following the process shown in Figure 1a.Although Sr 3 Al 2 O 6 has a complicate crystalline structure, its cubic lattice matches well with BiFeO 3 and SrTiO 3 substrate, [39] with a small lattice-mismatch of 1.41% and 1.43%, respectively.Figure 1b shows an optical image of one-inch SrTiO 3 (100)/Sr 3 Al 2 O 6 /BiFeO 3 heterostructures.We marked three regions as #1 to #3 from the center to the outside area to investigate the uniformity of microstructure and variation of electrical performance in the following.After epitaxial thin film deposition, we attach a soft supporting layer (e.g., PDMS, photoresist, PMMA) on the surface, immerse them into de-ionized water to remove water-soluble Sr 3 Al 2 O 6 , and obtain inch-scale freestanding BiFeO 3 membranes (Figure 1c). Figure 1d shows the XRD patterns of those freestanding BiFeO 3 membrane at three marked regions (Figure 1b) and one XRD pattern of as-grown SiTiO 3 /Sr 3 Al 2 O 6 /BiFeO 3 heterostructure in region #1.The XRD patterns of all the as-grown heterostructures are shown in Figure S4 (Supporting Information).Both as-grown heterostructures and freestanding membranes are perfectly (001)-oriented, and Sr 3 Al 2 O 6 has been entirely removed in the latter.The c-axis lattice constant of the freestanding BiFeO 3 membrane increases by ≈0.18% after releasing from the substrate.Table S1 (Supporting Information) gives the exact values of the c-axis lattice constants before and after transferring process (Supporting Information).
Figure 1e shows the typical surface morphology of the three marked regions on a one-inch freestanding BiFeO 3 membrane observed by atomic force microscopy.The freestanding membranes have dense microstructure over different regions.We could observe an apparent increase of roughness from #1 to #3 under the same scale.Both the average root roughness (R a ) and root-mean-square roughness (R q ) are shown in Figure 1f and Table S2 (Supporting Information).R a decreases from 2.77 to 1.25 nm, and R q decreases from 3.72 to 1.60 nm from center to outside.To obtain the thickness of the freestanding membranes, we transferred them to flat silicon substrates and measured the depth profile by AFM (Figure S5, Supporting Information).The film thicknesses are also presented in Figure 1f and Table S2 (Supporting Information), with a variation of ≈14%.The variation of surface roughness and film thickness is dominated by the growth dynamics of pulsed laser deposition. [42]Usually, the cone-shaped plasma determines that the closer to the rotation center of the sample station, the more and larger particles are sputtered.If deposited by magnetron sputtering, [43] spin coating, [44] or molecular number epitaxy, [12] the structure uniformity will be improved.In addition, the size of the freestanding single-crystalline BiFeO 3 membranes is also limited by the availability of large-scale single-crystalline oxide substrates (e.g., usually one-inch for SrTiO 3 substrates).We also fabricated freestanding SrRuO 3 /BiFeO 3 membranes, in which SrRuO 3 always acts as the bottom electrode to ensure electrical connection and modulate electrical performance in ferroelectric tunnel junction or ferroelectric photovoltaic devices. [45,46]fter obtaining inch-scale freestanding single-crystalline BiFeO 3 and SrRuO 3 /BiFeO 3 membranes on supporting layers, how to transfer crack-free membranes onto other arbitrary substrates is another challenge.At first, we tried the following existing methods we have mentioned above: i) Transferring without any supporting layer (Figure 2a): [24][25][26][27][28][29] This method does not use any supporting layer on top of the as-grown heterostructure and the heterostructure was directly immersed in etchant.Once removing the sacrificial layer, the freestanding single-crystalline membranes are supposed to keep their integrity and float on the surface of the fluid, then they could be picked up by a ring together with fluid and transferred to other substrates like silicon wafers.However, Our freestanding BiFeO 3 and SrRuO 3 /BiFeO 3 cracked easily and rolled up into micro-tubes (Figure 2d) once removing Sr 3 Al 2 O 6 .ii) Transferring with soft polymer stamp (Figure 2b): [30][31][32][33][34][35][36][37][38] This method is the most frequently used by attaching a polymer layer on the surface of as-grown heterostructures.The polymer could be PDMS, silicone rubber, and thermal tape.Once removing the sacrificial layer, freestanding membranes are supported by the soft polymer layer.They are transferred to other substrates (e.g., silicon) by transfer printing.However, we found that the freestanding BiFeO 3 and SrRuO 3 /BiFeO 3 form wrinkles naturally on PDMS (Figure 2f).iii) Transferring with a hard polymer supporting layer (Figure 2c): [39][40][41] Similar to method ii), a polymer supporting layer is also used while removing the sacrificial layer.Here, the polymer is relatively "hard" and has a larger Young's modulus, such as PMMA and photoresist.The relatively hard polymer supporting layer will avoid wrinkles during transferring.They could be further removed by another organic solvent.Here we use the positive photoresist as the temporary supporting layer, the freestanding BiFeO 3 or SrRuO 3 /BiFeO 3 supported by this relatively hard polymer could remain flat.Once transferred single-crystalline BiFeO 3 or SrRuO 3 /BiFeO 3 membranes on silicon, the photoresist was removed by acetone.However, the membrane still cracked easily after removing this hard polymer layer, especially for freestanding SrRuO 3 /BiFeO 3 membranes (Figure 2f).
Transferring large-scale and crack-free single-crystalline BiFeO 3 membranes on other substrates is still challenging based on the above methods.Considering method iii) could transfer relatively large-area membranes, we further improve it by introducing a temporary metallic layer to solve the crack problem, and Figure 3a shows the whole process of this new method.The transferring process started by depositing Cu thin films as a buffer layer on the as-grown SrTiO 3 /Sr 3 Al 2 O 3 /(SrRuO 3 /)BiFeO 3 heterostructures (the second picture of Figure 3b).The following process is similar to method iii): dissolving the sacrificial layer and transferring to other substrates.Once removing the relatively hard polymer layer (e.g., photoresist), the "SrRuO 3 /BiFeO 3 /Cu" bilayers remained flat and crack-free on silicon (the third picture of Figure 3b).The Cu thin films were further removed by FeCl 3 solution, leaving a 5 mm × 5 mm crack-free membrane (the last picture of Figure 3b).This method is highly reproducible, we present more cases of transferring crack-free BiFeO 3 membranes (Figure S6, Supporting Information) and SrRuO 3 /BiFeO 3 membranes (Figure S7, Supporting Information), both show enlarged observation of the whole membranes with nearly the same scale bar of Figure 2e,f.Therefore, comparing with the existed methods, our method improves the transferring process obviously.
We further examined the change of lattice strain during transferring.Figure 3c 002) diffraction peaks remain relatively stable.Such behaviors indicate that the internal lattice strain in BiFeO 3 is entirely released while removing the sacrificial layer.We further quantitatively characterized such lattice strain by reciprocal space mapping (RSM), as shown in Figure 3d around the (103) plane and Figure S9 (Supporting Information) around the (002) plane.The in-plane lattice constant of BiFeO 3 decreases from 3.934 to 3.878 Å, while the out-of-plane lattice constant increases from 3.989 to 4.002 Å.The released in-plane lattice strain is ≈1.42% after transferring, and the released out-of-plane lattice strain is ≈0.33%, which is consistent with XRD observation (Figure 3c).The RSM results also indicate good single-crystallinity of freestanding BiFeO 3 membranes and good epitaxy relationship among SrTiO 3 substrate, Sr 3 Al 2 O 6 sacrificial layer and BiFeO 3 film.In addition, similar behavior was also observed during transferring single-crystalline BiFeO 3 membranes (Figure S8, Supporting Information) under the lattice strain up to 1.68% calculated from the crosssectional TEM images (Figure S10, Supporting Information) of the SrTiO 3 /Sr 3 Al 2 O 3 /BiFeO 3 heterostructure.
The Cu buffer layer is critical to protect freestanding singlecrystalline oxide membranes from cracking and curling based on the above observations.Although freestanding single-crystalline BiFeO 3 membranes have exhibited superior elasticity and flexibility that is considerable to metals and polymers, [22] imperfections such as point defects or dislocations still exist in those membranes, and their amount increases significantly when the area reaches the macroscopic scale, and this will inevitably result in cracks if not protected.The Cu layer in the BiFeO 3 /Cu composite could reduce the effective stress imposed on BiFeO 3 during removing the hard polymer layer (Figure 3a, photoresist in our study).Since Young's modulus of BiFeO 3 is larger than copper (Y(BiFeO 3 ) = 170 GPa [47] and Y(Cu) = 90 GPa), BiFeO 3 could deform freely to release the lattice strain, as observed by XRD and RSM.At the same time, Cu film deforms to absorb such elastic energy, and the induced strain is very small (0.04%).Therefore, the Cu layer assisted lattice strain releasing in BiFeO 3 during transferring.Moreover, the BiFeO 3 /Cu composite is relatively thick, with a total thickness of ≈600 nm.Such composite remains relatively flat and will have close contact with the transferred substrates, protecting freestanding BiFeO 3 from curling or rolling.Besides, the in-plane deformation of BiFeO 3 could be negligible during removing Cu.Therefore, the transferred BiFeO 3 membranes are crack-free.
Although a permanent supporting layer, e.g., amorphous Al 2 O 3 [38] or Au, [48] could help obtain crack-free freestanding membranes, such an additional layer will not only change the mechanical boundary conditions of the membrane but also introduce additional processing steps for further micro-fabrication.In contrast, our method offers truly "freestanding" membranes that are ready for further operation like stacking and twisting. [49]esides, the Cu layer is completely removed, and the surface morphology of the BiFeO 3 membrane does not change much (Figure S11, Supporting Information).We further examined the electrical properties of freestanding BiFeO 3 membranes and their variation in different regions at room temperature.Figure 4a shows the frequency-dependent dielectric constant and dielectric loss from regions #1 to #3.The dielectric constants are 226 ± 2, 224 ± 3, and 223 ± 2 at 10 5 Hz from regions #1 to #3, indicating that the large-scale freestanding single-crystalline BiFeO 3 membrane remain stable dielectric properties.This is a typical value as compared to previous report. [50]Their dielectric loss is relatively small and < 1% at 10 5 Hz. Figure 4b S13 (Supporting Information), which showed an increasing trend from region # 1 to region # 3 in remnant polarization.The average P r is close to 56 μC cm −2 , similar to what was reported. [51]The variation in P r from the center area to the outside is likely related to the slight increase of the out-of-plane lattice constant (Figure S4, Supporting Information).Usually, P r is proportional to the distance between positive and negative ion centers in perovskite.BiFeO 3 is a typical multiferroic material at room temperature.Figure 4c shows the magnetic hysteresis loops along out-of-plane in different regions.All have a slim and nearly hysteresis-free magnetization response.The saturation magnetization in #1, #2, and #3 is ≈1.69, 1.75, and 1.68 emu cc −1 , respectively, within the same order of magnitude of impurity-free BiFeO 3 thin films. [52]The in-plane hysteresis loops at different regions and the in-plane/out-of-plane hysteresis loops at region #1 are shown in Figure S14 (Supporting Information).Freestanding single-crystalline BiFeO 3 membranes have good dielectric, ferroelectric, and ferromagnetic properties, making them useful for lead-free capacitors, ferroelectric or multiferroic memories as well as piezoelectric devices.
In addition, BiFeO 3 epitaxial thin films usually have excellent photovoltaic properties.Figure 5a schematically shows the mechanism of the ferroelectric photovoltaic effect based on the Pt/BiFeO 3 /SrRuO 3 capacitor.Photogenerated carriers can be separated and transported to the electrodes on either side to generate an electrical signal by multiple forces in single-crystalline BiFeO 3 membranes.The forces could be generated by bulk photovoltaic effect, depolarization field, ferroelectric domain wall, and Schottky barrier. [53]Here, we explored such functionality in freestanding single-crystalline BiFeO 3 membranes.Figure 5b shows an optical image of the flexible photovoltaic sensors based on freestanding BiFeO 3 membranes and a closer observation of the patterned device with small round top electrodes.Figure 5c shows their current density-voltage (J--V) curves under the illumination of 30 mW cm −2 and the dark environment, with BiFeO 3 polarized up and down at −7 and +10 V.The open-circuit voltage (V oc ) and short-circuit current density (J sc ) are −0.25 ± 0.03 V and 0.82 ± 0.09 μA cm −2 , respectively.The I-V curves measured from ten capacitors are shown in Figure S15 (Supporting Information).The overlapped lines indicate the stable photovoltaic effect of freestanding BiFeO 3 membranes.Those parameters are considerable to previous reports. [18]And the power conversion efficiency and fill factor are 1.64 × 10 −6 and 0.25, respectively calculated by the basic formula. [54]The photovoltaic behaviors of the freestanding BiFeO 3 membrane before and after transferring are very close, as shown in Figure S16 (Supporting Information), indicating the membranes maintain good functionality after transferring.In this ferroelectric photovoltaic effect dominated by the Schottky junction effect, the change in spontaneous polarization caused by lattice changes does not significantly affect the photovoltaic response. [55]Figure 5c,d shows the photovoltaic current intensity and photovoltaic voltage under different illumination with the light turned on and off sequentially.Both photovoltaic current and voltage increase with the increase of illumination density, as reported before. [18]Figure 5e shows time-dependent short-circuit current and open-circuit voltage over seven days.Both J sc and V oc remain relatively stable over a long time.This provides a device basis for a new generation of flexible photodetectors or light sensors in integrated flexible electronics.

Conclusion
We obtained one-inch freestanding single-crystalline BiFeO 3 membranes by a water-soluble sacrificial layer method.We tried the three existing methods to transfer freestanding membranes to other substrates but faced up with rolled-up, wrinklepattern, or cracked membranes.By introducing a copper layer, combined with a removable polymer layer, on the as-grown

Experimental Methods
Film Deposition and Sample Preparation: At first, Sr 3 Al 2 O 6 and BiFeO 3 targets were prepared by the solid-state reaction method.Both the Sr 3 Al 2 O 6 sacrificial layer and the BiFeO 3 layer were epitaxially grown on a one-inch scale single-crystalline SrTiO 3 substrate by pulsed laser deposition technique using a KrF excimer laser with a wavelength of 248 nm.The Sr 3 Al 2 O 6 layer was deposited at the temperature of 760 °C with an oxygen pressure of 15 Pa, and the energy density was ≈1.4 J cm −2 .Following the growth of Sr 3 Al 2 O 6 , BiFeO 3 was deposited at 650 °C with an oxygen pressure of 5 Pa, and the laser energy density used for the BiFeO 3 film growth was fixed at 0.8 J cm −2 .The laser repetition rate for the deposition of Sr 3 Al 2 O 6 and BiFeO 3 thin films was 5 and 3 Hz, respectively.The SrRuO 3 layer was deposited at 650 °C with an oxygen pressure of 10 Pa as the bottom electrode, and the energy density was ≈0.8 J cm −2 .
After the preparation of SrTiO 3 /Sr 3 Al 2 O 6 /SrRuO 3 /BiFeO 3 heterostructures, photolithography was conducted to prepare the top electrodes (point electrodes with a radius of 50 μm).The sample surface was first coated with a layer of positive photoresist (AR-P 3510T, Allresist GmbH) using a spin coater at 4000 r.p.m., followed by baking at 115 °C for 15 min.The sample was then attached to a photomask for UV light exposure for 8 s using a UV exposure machine.The desired patterns were obtained by developing in developer solution for 60 s to remove the exposed photoresist.After the photolithography, Pt (20 nm in thickness, 25/50 μm in diameter) electrodes were deposited by magnetron sputtering.The remaining photoresist was removed by acetone.
Transfer of Large-Scale Membranes: For a part of SrTiO 3 /Sr 3 Al 2 O 6 / SrRuO 3 /BiFeO 3 heterostructures, following the fabrication of top electrodes, 100 nm Cu was deposited on the surface by magnetron sputtering as a buffer layer.A soft dissolvable supporting layer was coated to the surface of the Cu buffer layer, and this supporting layer could be polymethyl methacrylate (PMMA) or photoresist (AR-P 3510T, Allresist GmbH).They were then immersed in deionized water at room temperature for a few hours until the Sr 3 Al 2 O 6 layer was entirely dissolved and SrRuO 3 /BiFeO 3 /Pt electrodes/Cu/photoresist heterostructures were separated from the substrates.To transfer SrRuO 3 /BiFeO 3 /Pt electrodes devices on any desired substrates, the "SrRuO 3 /BiFeO 3 /Pt electrodes/Cu/photoresist" stack was first transferred to a substrate such as glass, and then the photoresist could be removed entirely by acetone, and the Cu buffer layer could be removed by 5% mass fraction FeCl 3 solution.
Characterization of Microstructure and Electrical Properties: Highresolution x-ray diffraction measurements (−2 scan) were conducted with a Bruker D8 Advance diffractometer.The XPS measurements were conducted with a Thermo Fisher ESCALAB Xi+.The surface morphology was characterized by atomic force microscopy (AFM) on Bruker Icon.For all the electrical measurements, the capacitors had a sandwich structure, using Pt (20 nm in thickness, 25/50 μm in diameter) as the top electrode and SrRuO 3 as the bottom electrode (20-30 nm in thickness).Those Pt electrodes were precisely defined by photolithography and deposited by the magnetron sputtering (Phase II, AJA International), with a base pressure <1 × 10 −7 Torr, a working Ar pressure of 3 mTorr, and a DC power of 20 W. A quartz crystal microbalance could monitor the deposition rate.Therefore, the thickness of Pt could be precisely controlled by deposition time.A probe station and beryllium copper probes (5 μm in tip diameter) were used to connect capacitors and instruments.The dielectric response was carried out via a commercial precision LCR meter (E4980A, Keystight).A ferroelectric analyzer (TF Analyzer 2000, aixACCT) was used to measure the polarization of BiFeO 3 thin film at 2k Hz.M-H hysteresis loops were measured on a vibrating (Lake Shore 7404).I-V curves, I-t response, and V-t response were measured using a pA meter/direct current (DC) voltage source (B2901A, Keysight) on a low noise probe station.The light source was a Halogen lamp, and the illumination energy density used in this study ranged from 0 to 100 mW cm −2 .

Figure 1 .
Figure 1.Fabrication of inch-scale freestanding single-crystalline BiFeO 3 membranes.a) Schematics of the fabrication process for the inch-scale freestanding BiFeO 3 membrane.b) Optical image of a one-inch SrTiO 3 (100)/Sr 3 Al 2 O 6 /BiFeO 3 heterostructure with marked regions.c) Optical image of a one-inch freestanding BiFeO 3 membrane.d) XRD pattern of the one-inch freestanding BiFeO 3 membrane in three different regions and as-grown SiTiO 3 /Sr 3 Al 2 O 6 /BiFeO 3 heterostructure in region #1.e) Surface morphology of one-inch freestanding BiFeO 3 membrane measured at three regions by AFM.f) Variation of the film thickness and surface roughness over three regions.

Figure 2 .
Figure 2. Transferring freestanding single-crystalline BiFeO 3 or SrRuO 3 /BiFeO 3 membranes by the existing methods.a) Method i: transferring without any supporting layer.b) Method ii: transferring with soft polymer stamp.c) Method iii: transferring with hard polymer supporting layer.d-f) Optical images of cracked freestanding BiFeO 3 membranes corresponding to methods i to iii.

Figure 3 .
Figure 3.A temporary metallic layer supported crack-free transferring process.a) Schematic illustration of the whole transferring process, including deposition of SrTiO 3 /Sr 3 Al 2 O 6 /SrRuO 3 /BiFeO 3 heterostructure, coating temporary Cu layer and hard polymer supporting layer, removing Sr 3 Al 2 O 6 sacrificial layer, transferring membranes to other substrates, and removing temporary Cu layer.b) Optical images of the as-grown heterostructure, asgrown heterostructure with Cu, transferred membranes on Si with Cu, and transferred single-crystalline BiFeO 3 membrane after removing Cu. c) XRD patterns of the films and membranes throughout the transferring process.d) RSM around (103) peak of as-grown SrTiO 3 /Sr 3 Al 2 O 6 /SrRuO 3 /BiFeO 3 heterostructure and the final freestanding SrRuO 3 /BiFeO 3 membrane.

Figure 4 .
Figure 4. Dielectric, ferroelectric, and ferromagnetic properties of freestanding BiFeO 3 membranes.a) The frequency-dependent dielectric constant and dielectric loss in different regions.b) Polarization hysteresis loops in different regions.c) Out-of-plane magnetic hysteresis loops in different regions.
compares the polarization hysteresis loops at different regions.The remnant polarization values measured at 2k Hz are ≈40.6 ± 4.6, 51.5 ± 1.6, and 57.1 ± 2.8 μC cm −2 , respectively.The I-E loops accompanying the P-E loops during testing are shown in Figure S12 (Supporting Information), and the calculated conductivity is ≈265 nS•cm −1 .Hysteresis loops measured from multiple capacitors in different regions are shown in Figure

Figure 5 .
Figure 5. Ferroelectric photovoltaic performance of freestanding single-crystalline BiFeO 3 membranes.a) Schematic diagram of the mechanism of ferroelectric photovoltaic.b) Optical image of the single-crystalline BiFeO 3 membranes based photovoltaic devices.c) J--V curve of freestanding singlecrystalline BiFeO 3 membrane under illumination and in the dark.d) I-t and e) V-t response of freestanding single-crystalline BiFeO 3 membrane under different illuminations.f) V oc and I sc of freestanding single-crystalline BiFeO 3 membrane based photovoltaic devices versus rest time.