Ferroelectric and Electrical Properties Optimization of Mg-doped BiFeO 3 Flexible Multiferroic Films

: Bi 1-x Mg x FeO 3 (BMFO, x = 0, 0.02, 0.04, 0.06 and 0.08) multiferroic ﬁlms were directly synthesized on ﬂexible stainless steel (FSS), save the bottom electrode process, by means of sol–gel spin-coating technology. The e ﬀ ects of di ﬀ erent bending conditions on ferroelectric, dielectric and leakage-current properties of BMFO ﬁlms were investigated. The leakage-current densities of BiFeO 3 (BFO, x = 0) and BMFO (x = 0.06) ﬁlms were 5.86 × 10 − 4 and 3.73 × 10 − 7 A / cm 2 , which shows that the BMFO (x = 0.06) has more than three orders of magnitude lower than that of BFO ﬁlm. The residual polarization (2 Pr) can be enhanced from 120 to 140 µ C / cm 2 . The proper doping of Mg in BiFeO 3 ﬁlm could provide an e ﬀ ective method for reducing the leakage-current values as well as boosting the ferroelectric properties. In this study, the leakage-current mechanism of low electric ﬁeld and high electric ﬁeld of BMFO ﬁlm is analyzed and established. In addition, the ﬂexible BMFO ﬁlm maintains practical ferroelectric and leakage-current properties at retention time of 10 6 s under di ﬀ erent symmetry bending conditions. These results indicate that the BFMO ﬁlm will be very practical in opto-electronic and storage device applications. FSS at a spin rate of ﬁlms were pyrolyzed on a hot plate at 300 ◦ C for 2 ﬁnal annealing. multilayer the BMFO ﬁlms were annealed at 450 ◦ C, 500 ◦ C, 550 ◦ C and ◦ C by rapid thermal annealing (RTA) in the ambient atmosphere at a heating rate of 100 ◦ C / min for 2 min. In this the BMFO ﬁlms annealed at 500 ◦ C have the best ferroelectric lowest leakage-current properties. Hereafter the will be on the BMFO ﬁlms (thickness 300 nm) annealed at 500 ◦


Introduction
Nowadays, many new technologies in science have created amazing and rapid development in the miniaturization of devices, and electronic products have made humans an important driving force for the quality of life. The rise of flexible electronic products, with excellent flexibility, portability and lightness, is currently actively entering the electronics market [1][2][3][4]. Considering ergonomics to make it easier for users to carry, when the appearance of electronic products begins to bend, the structure and various characteristics and functions of the internal components will also change accordingly. Therefore, the current electronic products on the market are gradually becoming flexible, which has led many researchers to invest in flexible film research [5][6][7].
Ferroelectric materials not only have more superior characteristics in memory element applications, but also have a wide range of applications including sensors, actuators, piezoelectrics, spin electrons and microelectronic devices. There are many kinds of ferroelectric materials can be used for thin films devices, among which Pb(Zr, Ti), O 3 (PZT), SrBi 2 Ta 2 O 9 (SBT), BaTiO 3 , BFO, etc. However, nonartificial materials that have both ferroelectric and ferromagnetic properties are rarer. Among these materials, BFO is the only ferroelectric and antiferromagnetic properties that coexist at room temperature multiferroic materials, and the BFO Curie temperature (1123 K) and Neil temperature (653 K) are higher than other ferroelectric materials [8][9][10]. However, BFO film usually has a high leakage-current density due to the oxygen vacancy and the state of iron ions (Fe 3+ to Fe 2+ state) resulting from various oxygenations. This is a critical barrier hindering the development of practical application. Therefore, many efforts have been made to reduce the leakage-current density. Recently, the performance of BFO films could be improved by optimizing the process parameters and ion doping technique [11][12][13][14][15][16][17]. Compared with the process technology, ion doping has some advantages such as convenient operation, easy to realize the microstructure and characteristics of the film. Therefore, it has been widely used in the synthesis of high-quality BFO-based films. On the basis of current results chemical substitution is one of the most useful methods. Among them, the most popular substitution ions are the rare earth elements [18][19][20][21].
In this study, a Sol-Gel method was applied to grow BFO-doped Mg films on flexible stainless steel (FSS) substrate. The microstructure, ferroelectric, leakage current and dielectric properties in different bending conditions of BMFO flexible nanocrystalline films with different magnesium doping amounts were discussed.

Materials and Methods
The popular chemical formulas of the precursor solutions of Bi  3 , Alfa, 99.9% + purity) were used as source materials. Propionic acid and 2-methoxyethanol was used as solvents. A stock solution of~0.1-M concentration was obtained by a sol-gel method. Use an inductively coupled plasma mass spectrometry (ICP-MS) instrument to confirm that the deviation from stoichiometry was within ± 1%.
The BMFO solution was directly spin-coated onto FSS substrate at a spin rate of 2500 rpm for 30 s. After each coating step, the gel films were pyrolyzed on a hot plate at 300 • C for 2 min before final annealing. After multilayer coating, the BMFO films were annealed at 450 • C, 500 • C, 550 • C and 600 • C by rapid thermal annealing (RTA) in the ambient atmosphere at a heating rate of 100 • C/min for 2 min. In this study, the BMFO films annealed at 500 • C have the best ferroelectric properties and lowest leakage-current properties. Hereafter the analysis will be focused on the BMFO films (thickness 300 nm) annealed at 500 • C.
The crystallization and microstructures of all BMFO films were determined by X-ray diffraction (XRD) patterns using a Rigaku PC-2200 X-ray diffractometer with CuKα radiation, which was operated at an accelerating voltage of 40 kV and an emission current of 20 mA. The XRD data were recorded at room temperature in the 2θ range from 20 • to 60 • with a stepping width of 0.01 • and a scanning speed of 0.5 • /min. The top silver electrodes with an area of 7.85 × 10 −3 cm 2 were prepared by thermal evaporator. The measurements of dielectric constant and loss tangent values were performed by using an Agilent 4284A impedance analyzer. Measurements of the ferroelectric hysteresis loops were carried out in a Sawyer-Tower circuit in a metal-ferroelectric-metal (MFM) configuration. The leakage-current density was measured using Keithley 2400 source meter with voltages varying from 0 to 5 V in a MFM configuration. Figure 1 presents the XRD patterns measured from the BMFO (x = 0, 0.02, 0.04, 0.06 and 0.08) films. The positions of these XRD peaks are quite similar to those of the standard diffraction pattern data of BFO collected in the JCPDS card. The pure BFO thin film shows a polycrystalline rhombohedral perovskite structure with the space group R3c. No obvious second phase was observed for all the samples, indicating that the Mg-substitution has a benefit for stabilizing the perovskite structure. The (110) and (104) diffraction peaks in the 2θ ranges of 31 • to 33 • for the BFO films have a tendency to become a single peak by substituting Bi ions with Mg-doping. Close inspection of the (110) and (104) diffraction indicates an asymmetrical character of the reflection it means that at least two peaks may be resolved during fitting. The slight change in the angle may suggest for enhanced distortion of Symmetry 2020, 12, 1173 3 of 10 the octahedron for the doped samples [22]. Meanwhile, when the amount of Mg-doping is too large, x = 0.08, it will cause a serious lattice structure distortion of the film.

Results and Discussions
Symmetry 2020, 12, x FOR PEER REVIEW 3 of 11 amount of Mg-doping is too large, x = 0.08, it will cause a serious lattice structure distortion of the film. The average grain sizes of BMFO films from the XRD peaks were calculated by using Debye-Scherrer′s formula [23]: D = kλ/βcosθ, where D is the average grain size, k is a Scherrer constant (0.94), λ is wavelength of the X-ray radiation (1.54 Å), β is the full width at half maximum, and θ is the Bragg diffraction angle. The average grain sizes of BMFO films are found to be about 31.93, 22.97, 21.57, 19.55 and 19.62 nm, for x = 0, 0.02, 0.04, 0.06 and 0.08, respectively. It is generally known that the ion radius of Mg 2+ (0.72 Å) is much smaller than the Bi 3+ (1.03 Å). With an appropriate increase of the Mg-doping amount, the lattice structure of the film changes, which results in greater resistance to the film grain boundary migration. As a result, the grain growth rate is reduced, and the grain size of the film is gradually smaller. The change of surface morphology of the film has a relative impact on the change of crystal grain size caused by Mg-doping [24].
The ferroelectric hysteresis loops measured for the BMFO films at different applied electric fields and at frequency 10 kHz are shown in Figure 2. The residues remnant polarization (2 Pr) and the coercive field (2 Ec) of BMFO films for x = 0, 0.02, 0.04, 0.06 and 0.08 are 120, 124, 130, 140, 90 μC/cm 2 and 48, 40, 39.3, 38, 24 kV/cm 2 , respectively. Enhanced 2 Pr and 2 Ec values of 140 μC/cm 2 and 38 kV/cm 2 were obtained for the BMFO film with x = 0.06, which shows the optimal amount of spontaneous polarization for all the samples. The remanent polarization of Mg properly doped in BFO films are found to be increases remarkably. It is proposed that doping with Mg ion led to improve the oxygen ion stability in the lattice site of BFO and hence improve the fatigue resistance [25]. Due to some Bi 3+ ions in the pseudo-perovskite layers containing Fe-O octahedral are substituted by Mg 2+ ions. Moreover, the substitution of Bi 3+ ions by Mg 2+ having smaller ionic radius than bismuth, maintain a significant structural distortion of the perovskite structure of BFO, and improves the ferroelectric properties resulting enhanced 2 Pr value [26]. The average grain sizes of BMFO films from the XRD peaks were calculated by using Debye-Scherrer s formula [23]: D = kλ/βcosθ, where D is the average grain size, k is a Scherrer constant (0.94), λ is wavelength of the X-ray radiation (1.54 Å), β is the full width at half maximum, and θ is the Bragg diffraction angle. The average grain sizes of BMFO films are found to be about 31.93, 22.97, 21.57, 19.55 and 19.62 nm, for x = 0, 0.02, 0.04, 0.06 and 0.08, respectively. It is generally known that the ion radius of Mg 2+ (0.72 Å) is much smaller than the Bi 3+ (1.03 Å). With an appropriate increase of the Mg-doping amount, the lattice structure of the film changes, which results in greater resistance to the film grain boundary migration. As a result, the grain growth rate is reduced, and the grain size of the film is gradually smaller. The change of surface morphology of the film has a relative impact on the change of crystal grain size caused by Mg-doping [24].
The ferroelectric hysteresis loops measured for the BMFO films at different applied electric fields and at frequency 10 kHz are shown in Figure 2. The residues remnant polarization (2 Pr) and the coercive field (2 Ec) of BMFO films for x = 0, 0.02, 0.04, 0.06 and 0.08 are 120, 124, 130, 140, 90 µC/cm 2 and 48, 40, 39.3, 38, 24 kV/cm 2 , respectively. Enhanced 2 Pr and 2 Ec values of 140 µC/cm 2 and 38 kV/cm 2 were obtained for the BMFO film with x = 0.06, which shows the optimal amount of spontaneous polarization for all the samples. The remanent polarization of Mg properly doped in BFO films are found to be increases remarkably. It is proposed that doping with Mg ion led to improve the oxygen ion stability in the lattice site of BFO and hence improve the fatigue resistance [25]. Due to some Bi 3+ ions in the pseudo-perovskite layers containing Fe-O octahedral are substituted by Mg 2+ ions. Moreover, the substitution of Bi 3+ ions by Mg 2+ having smaller ionic radius than bismuth, maintain a significant structural distortion of the perovskite structure of BFO, and improves the ferroelectric properties resulting enhanced 2 Pr value [26]. Figure 3 is showing the leakage-current density (J) as a function of the electric field (E) for the BMFO films. For the case of BMFO films, the leakage current increases with the increasing electric field. Evidently, doping of Mg can reduce the leakage-current density of BMFO films. Among all samples, BMFO (x = 0.06) film shows the lowest leakage-current density (3.73 × 10 −7 A/cm 2 ), which demonstrates a big improvement. A more than three orders reduction of leakage current compared to that of BFO film (5.86 × 10 −4 A/cm 2 ) was observed at applied field 50 kV/cm. The doping of Mg effectively stabilizes the electrons hopping of Fe 3+ and Fe 2+ , reduces the generation of oxygen vacancies, and effectively improves the problem of high leakage current in BFO film. However, when the amount of Mg-doping increases to x = 0.08, the film leakage-current density will increase. This phenomenon is due to the amount of Mg-doping that causes the distortion of the Fe-O octahedron in BMFO film to Symmetry 2020, 12, 1173 4 of 10 a critical point and cause leakage current to increase. Based on the results of surface morphologies analysis for BMFO films compared to the undoped ones, we found that the smaller grain size should be one of the main causes responsible for the lower leakage currents in the high-electric-field region. , which demonstrates a big improvement. A more than three orders reduction of leakage current compared to that of BFO film (5.86 × 10 −4 A/cm 2 ) was observed at applied field 50 kV/cm. The doping of Mg effectively stabilizes the electrons hopping of Fe 3+ and Fe 2+ , reduces the generation of oxygen vacancies, and effectively improves the problem of high leakage current in BFO film. However, when the amount of Mg-doping increases to x = 0.08, the film leakage-current density will increase. This phenomenon is due to the amount of Mg-doping that causes the distortion of the Fe-O octahedron in BMFO film to a critical point and cause leakage current to increase. Based on the results of surface morphologies analysis for BMFO films compared to the undoped ones, we found that the smaller grain size should be one of the main causes responsible for the lower leakage currents in the high-electric-field region.  In this work, the dielectric constant (εr) began to appear stable when the frequency was higher than 510 kHz of the BMFO films. The εr at 510 kHz for the BMFO (x = 0.06) film (55.29) was larger than that of BFO film (22.2). Throughout the test frequency, the dielectric constant of BMFO films was always greater than that of pure BFO film. This increase in dielectric constant value may be attributed to the decrease in the lone pair activity of the Bi 3+ after the gradual addition of higher amounts of Mg 2+ ions to BFO which is responsible for the ferroelectric distortion and dipolar polarization those contribute towards enhancing the dielectric constant. Meanwhile, the enhancement in the dielectric constant for BMFO films may be due to the suppression of impurity phases and microstructure oxygen vacancies (VO 2+ ) by the doping of Mg 2+ ions for volatile Bi 3+ . The dielectric loss (tan δ) at 510 kHz for the BMFO films (0.051) was smaller than that of the pure BFO film (0.139). All BMFO films with frequencies higher than 510 kHz show a significant increase in tan δ, which may be attributed to the switches of dipoles in the films that cannot follow the change of In this work, the dielectric constant (ε r ) began to appear stable when the frequency was higher than 510 kHz of the BMFO films. The ε r at 510 kHz for the BMFO (x = 0.06) film (55.29) was larger than that of BFO film (22.2). Throughout the test frequency, the dielectric constant of BMFO films was always greater than that of pure BFO film. This increase in dielectric constant value may be attributed to the decrease in the lone pair activity of the Bi 3+ after the gradual addition of higher amounts of Mg 2+ ions to BFO which is responsible for the ferroelectric distortion and dipolar polarization those contribute towards enhancing the dielectric constant. Meanwhile, the enhancement in the dielectric constant for BMFO films may be due to the suppression of impurity phases and microstructure oxygen for the BMFO films (0.051) was smaller than that of the pure BFO film (0.139). All BMFO films with frequencies higher than 510 kHz show a significant increase in tan δ, which may be attributed to the switches of dipoles in the films that cannot follow the change of the applied electric field at high frequency [27]. In this study, detailed data values of dielectric constant, dielectric loss, residual remnant polarization, coercive electric field and leakage-current density of the BMFO films are listed in Table 1, respectively. From these research results, it is clearly found that the BMFO film can greatly optimize the dielectric, ferroelectric and electrical properties of the sample under the appropriate Mg (x = 0.06) doping amount. The leakage-current behaviors of BFMO (x = 0.06) film was investigated further on the relationship between the leakage-current density (J) and electric field (E), for example the ln J vs. E 1/2 plots, as shown in Figure 4. From the curves, we found that the leakage-current density is linearly related to the square root of the applied electric field. The linear variations of the current were usually corresponded either to the Schottky emission [28,29] or Poole-Frenkel emission [28,30]. The current resulting from Schottky-Richardson emission was controlled by the electrons flowing across the potential energy barrier via field-assisted lowering at a metal-insulator interface. The current density (J) in the Schottky emission can be expressed by the following equation [29]: where β s = (e 3 /4πε 0 ε) 1 2 , e is the electron charge, ε 0 is the dielectric constant of free space, A* is the effective Richardson constant, T is the absolute temperature, E is the applied electric field, ϕ s is the contact potential barrier, and k B is the Boltzmann constant. Poole-Frenkel emission was due to field-enhanced thermal excitation of trapped electrons from the valence band into the conduction band. The current density can be given by [30] where J 0 = σ 0 E is the low-field current density, β PF = (e 3 /πε 0 ε) 1/2 , σ 0 is the low-field conductivity, ϕ PF is the height of trap potential well. where J0 = σ0E is the low-field current density,  In this work, the dielectric constant of the BMFO (x = 0.06) film is 55. 29. Various values of βPF and βs can be calculated according to Equations (1) and (2), respectively, and the results are shown in Table 2. The βexp values of the experiment can be calculated from the slope (= β/kBT) of the curve lnJ-E 1/2 straight line portion in Figure 4. In the low-electric-field region (0-20 kV/cm), the βexp (1.72 × 10 −23 ) is closer to βPF (1.63 × 10 −23 ) than βs (8.16 × 10 −24 ). By increasing the external field greater than 20 kV/cm, the βexp (8.36 × 10 −24 ) is closer to βs (8.16 × 10 −24 ) than βPF (1.63 × 10 −23 ), which means that the current conduction will be affected by another mechanism. These results indicate that in the low-electric-field region (0-20 kV/cm), carriers are transported through the BFMO (x = 0.06) film of FSS substrate by the field-enhanced Poole-Frenkel mechanism. In addition, the mechanism can be explained by the Schottky emission from the FSS substrate in the high-electric-field region (20-80 kV/cm). In this work, the dielectric constant of the BMFO (x = 0.06) film is 55. 29. Various values of β PF and β s can be calculated according to Equations (1) and (2), respectively, and the results are shown in Table 2. The β exp values of the experiment can be calculated from the slope (=β/k B T) of the curve ln J-E 1/2 straight line portion in Figure 4. In the low-electric-field region (0-20 kV/cm), the β exp (1.72 × 10 −23 ) is closer to β PF (1.63 × 10 −23 ) than β s (8.16 × 10 −24 ). By increasing the external field greater than 20 kV/cm, the β exp (8.36 × 10 −24 ) is closer to β s (8.16 × 10 −24 ) than β PF (1.63 × 10 −23 ), which means that the current conduction will be affected by another mechanism. These results indicate that in the low-electric-field region (0-20 kV/cm), carriers are transported through the BFMO (x = 0.06) film of FSS substrate by the field-enhanced Poole-Frenkel mechanism. In addition, the mechanism can be explained by the Schottky emission from the FSS substrate in the high-electric-field region (20-80 kV/cm).  To further evaluate the ferroelectric and electrical properties of Ag/BMFO/FSS structure under different bending states, we adhered this structure to the molds with different fixed radii (r), as shown in Figure 5a. In this study, we used with the best ferroelectric, dielectric and leakage-current properties BMFO (x = 0.06) film as the test sample under different bending conditions. Subsequent measurements of various properties of the samples will be performed using different bending radii (r) of original unbent state r→∞ (flat), 12 mm, 10 mm and 6 mm. Since the film will deform on the curved surface, the resistance of small radius curvature is very important for the practicality of electronic and storage devices. Figure 5b shows the ferroelectric hysteresis loops of the flexible BMFO (x = 0.06) film in various bending states (flat, r = 12 mm, 10 mm and 6 mm). It shows that the residual polarization and coercive electric field were almost unchanged under various bending states from flat to r = 6 mm, which means that there is no effect on ferroelectric properties under bending. Just like flexible lead-free BaTiO 3 ferroelectric elements also have similar results [31]. electronic and storage devices. Figure 5b shows the ferroelectric hysteresis loops of the flexible BMFO (x = 0.06) film in various bending states (flat, r = 12 mm, 10 mm and 6 mm). It shows that the residual polarization and coercive electric field were almost unchanged under various bending states from flat to r = 6 mm, which means that there is no effect on ferroelectric properties under bending. Just like flexible lead-free BaTiO3 ferroelectric elements also have similar results [31]. For enhanced the practicability, BMFO (x = 0.06) film was prepared in the flexible equipment system. At different bending radius and applied electric fields, the leakage-current density was measured, as shown in Figure 6. From the measurement results, the BMFO (x = 0.06) film under different bending conditions flat, r = 12 mm, 10 mm and 6 mm can obtain the leakage-current density at 50 kV/cm of 3.73 × 10 −7 , 3.91 × 10 −7 , 4.08 × 10 −7 , 4.27 × 10 −7 A/cm 2 , respectively. From the inset in Figure 6, the leakage-current density of all samples is approximately 4.0 × 10 −7 A/cm 2 at 50 kV/cm, which shows the insulating property nearly remains unchanged. These results show that the effect of physical bending on the leakage-current behavior of the film is negligible [32]. For enhanced the practicability, BMFO (x = 0.06) film was prepared in the flexible equipment system. At different bending radius and applied electric fields, the leakage-current density was measured, as shown in Figure 6. From the measurement results, the BMFO (x = 0.06) film under different bending conditions flat, r = 12 mm, 10 mm and 6 mm can obtain the leakage-current density at 50 kV/cm of 3.73 × 10 −7 , 3.91 × 10 −7 , 4.08 × 10 −7 , 4.27 × 10 −7 A/cm 2 , respectively. From the inset in Figure 6, the leakage-current density of all samples is approximately 4.0 × 10 −7 A/cm 2 at 50 kV/cm, which shows the insulating property nearly remains unchanged. These results show that the effect of physical bending on the leakage-current behavior of the film is negligible [32]. The long-term working reliability of materials is a very important factor for the practicality of microelectronic and storage memory devices. As shown in Figure 7, the residual polarization (2 Pr) and leakage-current density (J) dependence on retention time were observed at the BMFO (x = 0.06) film with different bending conditions. From the measurement results, we clearly found that the sample under the different bending conditions of flat and r = 6 mm, the 2 Pr and J values remained almost unchanged at retention time to 10 6 s. It is worth noting from these results that the flat and bending BMFO film has excellent charge retention ability at room temperature, and the retention time can reach 10 6 s. The curve between bending state and flat holding time almost overlaps, no significant attenuation of polarization and leakage-current properties are found, indicating the ability to maintain bending stability of BMFO flexible film [33]. In order to optimize the practicality of the samples, we have developed novel BMFO films. A series of studies on the ferroelectric and electrical properties of these multiferroic films under flat and different bending conditions were The long-term working reliability of materials is a very important factor for the practicality of microelectronic and storage memory devices. As shown in Figure 7, the residual polarization (2 Pr) and leakage-current density (J) dependence on retention time were observed at the BMFO (x = 0.06) film with different bending conditions. From the measurement results, we clearly found that the sample under the different bending conditions of flat and r = 6 mm, the 2 Pr and J values remained almost unchanged at retention time to 10 6 s. It is worth noting from these results that the flat and bending BMFO film has excellent charge retention ability at room temperature, and the retention time can reach 10 6 s. The curve between bending state and flat holding time almost overlaps, no Symmetry 2020, 12, 1173 8 of 10 significant attenuation of polarization and leakage-current properties are found, indicating the ability to maintain bending stability of BMFO flexible film [33]. In order to optimize the practicality of the samples, we have developed novel BMFO films. A series of studies on the ferroelectric and electrical properties of these multiferroic films under flat and different bending conditions were carried out and practical-grade results were obtained.

Conclusions
High-quality BMFO films without bottom electrode processes were fabricated on FSS substrates. The effects of Mg-doping of BMFO films on ferroelectric, electrical and retention properties under unbent and different bending conditions were investigated in this research. The BMFO (x = 0.06) flat film had the best residual polarization value 140 μC/cm 2 , a high dielectric constant 55.29 and the lowest leakage-current density of 3.73 × 10 −7 A/cm 2 . Proper doping of Mg will decrease the lone pair activity of Bi 3+ ions and cause ferroelectric distortion, which will increase the residual polarization of the corresponding doped film. The leakage-current mechanisms of BMFO films obtained in the study were controlled by the Poole-Frenkel emission in the low-electric-field region, and the Schottky emission in the high-electric-field region. In addition, the excellent ferroelectric, leakage current, and retention characteristics of the BMFO films could be well maintained under different bending conditions. These findings prove that the flexible BMFO multi-ferroelectric films on FSS substrate have great potential for microelectronic device applications.

Conclusions
High-quality BMFO films without bottom electrode processes were fabricated on FSS substrates. The effects of Mg-doping of BMFO films on ferroelectric, electrical and retention properties under unbent and different bending conditions were investigated in this research. The BMFO (x = 0.06) flat film had the best residual polarization value 140 µC/cm 2 , a high dielectric constant 55.29 and the lowest leakage-current density of 3.73 × 10 −7 A/cm 2 . Proper doping of Mg will decrease the lone pair activity of Bi 3+ ions and cause ferroelectric distortion, which will increase the residual polarization of the corresponding doped film. The leakage-current mechanisms of BMFO films obtained in the study were controlled by the Poole-Frenkel emission in the low-electric-field region, and the Schottky emission in the high-electric-field region. In addition, the excellent ferroelectric, leakage current, and retention characteristics of the BMFO films could be well maintained under different bending conditions. These findings prove that the flexible BMFO multi-ferroelectric films on FSS substrate have great potential for microelectronic device applications.