**3. Results**

Figure 1a shows the XRD pattern of BST/0.4BFO-0.6STO film grown on Pt/mica substrate. Visually, the film possesses a single perovskite phase with no detectable secondary phase, suggesting that the film can be well crystallized. Figure 1b shows the surface AFM image of BST/0.4BFO-0.6STO film. The average surface roughness (*R*a) and root mean square roughness (*R*rms) of the film are determined to be 2.54 nm and 2.06 nm, respectively, which may be attributed to the atomic flatness of mica substrate and high crystallinity of the film. The obtained roughness is at the same level of the reported inorganic films [36,47]. The grain size distribution of the film is analyzed using the Nano Measurer software by randomly selecting 100 grains. In addition, the average grain size value estimated from the AFM image is 53.26 nm. Figure 1c shows the cross-sectional image of multilayer film. From it, the film's thickness can be determined to be ~350 nm. Furthermore, the thickness of the bottom Pt electrode is about 20 nm. The ultimate film composition of the BST/0.4BFO-0.6STO film is determined via EDS spectrum, as displayed in Figure 1d. The atomic percentages (atom%) of O, Ti, Sr, Ba, Fe and Bi are 59.80, 16.44, 10.91, 5.14, 4.13 and 3.68, respectively, confirming a near perfect BST/0.4BFO-0.6STO stoichiometry.

The bipolar *P-E* loops for the BST/0.4BFO-0.6STO film in Figure 2a are measured from a low electric field to 3000 kV cm−<sup>1</sup> at room temperature, at a frequency of 10 kHz. Figure 2b presents the corresponding energy storage parameters of the *W*, *W*rec, *W*loss and *η* at various electric fields determined by *P-E* loops. The *W*rec and *η* extrapolated from a bipolar *P*-*E* loop under *E*<sup>b</sup> (3000 kV/cm) are 62 J cm−<sup>3</sup> and ~74%, respectively, which is a relatively high level among the flexible dielectric films [37,50]. It can be seen that the *P*<sup>m</sup> and *P*<sup>r</sup> are 63.52 μC cm−<sup>2</sup> and 6.73 μC cm−2, respectively, which contributed a great Δ*P* = 56.79 μC cm<sup>−</sup>2, and the result is beneficial for energy storage performance. This small *P*<sup>r</sup> can be due to the fact that BiFeO3-SrTiO3 is a relaxor ferroelectric and BST is paraelectric.

**Figure 1.** (**a**) X-ray diffraction pattern in the 2*θ* range of 20–60◦, (**b**) AFM, (**c**) Cross-sectional SEM images and (**d**) EDS spectrum of BST/0.4BFO-0.6STO thin film.

**Figure 2.** (**a**) The *P-E* loops for BST/0.4BFO-0.6STO under various applied electric fields. (**b**) The calculated *W*, *W*rec, *W*loss and *η* values as functions of the electric field. (**c**) Two-parameter Weibull analysis of dielectric breakdown strength. (**d**) Temperature-dependent *ε*<sup>r</sup> and tan*δ* under the frequency range of 1 kHz–100 kHz and the temperature range from −50 to 250 ◦C. (**e**) ln(1/*ε*r−1/*ε*m) as a function of ln(*T*−*T*m).

The Weibull distribution of *E*<sup>b</sup> can be obtained through the following formula:

$$X\_{\mathbf{i}} = Ln(E\_{\mathbf{i}}) \tag{4}$$

$$Y\_1 = Ln\left(-Ln\left(1 - \frac{i}{n+1}\right)\right) \tag{5}$$

where *Ei*, *i* and n signify the breakdown electric field, the serial number of tested specimens and the total number of tested specimens, respectively. Based on the Weibull distribution function, there exists a linear relationship between Xi and Yi. The mean *E*<sup>b</sup> for thin film can be extracted from the intersect points of the fitting lines and the horizontal axis at *Y*<sup>i</sup> = 0. The solid fitting straight line shown in Figure 2c is the Weibull analysis result of ten data gathered from our thin film. It can be observed that the slope parameter *β* is 9.32, which indicates both the good composition uniformity and high dielectric reliability of BST/0.4BFO-0.6STO [47]. The average *E*<sup>b</sup> extracted by the horizontal intercept is about 3010 kV cm−1. The temperature-dependent dielectric permittivity (*ε*r) and loss (tan *δ*) of the BST/0.4BFO-0.6STO film exhibit nearly flat permittivity peaks and frequency dispersion over the range of −50 to 250 ◦C, as shown in Figure 2d, indicating the relaxor characteristic. Notably, a broad and smeared peak of maximum *ε*<sup>r</sup> appears, especially near 150 ◦C. With increasing frequency, the maximum dielectric permittivity (*ε*m) at *T*<sup>m</sup> decreases and *T*m shifts to a higher temperature, which are important signatures of relaxor behavior [48]. To evaluate the relaxor dispersion degree, a modified Curie–Weiss equation of 1/*ε*<sup>r</sup> −1/*ε*<sup>m</sup> = (*T* − *T*m) <sup>γ</sup>/C can be used to estimate the relaxor dispersion degree, where *ε*<sup>m</sup> represents the maximum dielectric constant at *T*m, C is the Curie constant and *γ* is the relaxor diffuseness factor. Generally, *γ* = 1 represents a normal ferroelectric, 1 ≤ *γ* ≤ 2 represents the relaxor ferroelectric behavior and *γ* = 2 is valid for a classical ferroelectric relaxor [49]. After calculation, the *γ* for the film is 1.81 in Figure 2e, further evidencing the relaxor feature.

The temperature and frequency stability, as well as the antifatigue property for the sample, are evaluated, as shown in Figure 3. Firstly, the *P-E* hysteresis loops are measured at 10 kHz under 2286 kV cm−<sup>1</sup> in the temperature range of −50 to 200 ◦C. As illustrated in Figure 3a, the *P-E* loops almost preserve their pinched shape, and the *P*<sup>m</sup> and *P*<sup>r</sup> values have tiny changes. Correspondingly, the *W*rec and *η* of BST/0.4BFO-0.6STO films fluctuate slightly by 11% and 5% as shown in Figure 3b, which indicates the excellent thermal stability of the energy performance of the film. In practical application, it is necessary to meet the working temperature range of capacitors; for example, when in use in the fields of hybrid electric vehicles (~140 ◦C), drilling operations (150–200 ◦C), or in outer space and high-altitude aircraft (~−50 ◦C) [1,51–53]. The obtained temperature range in our film can basically fulfil the requirement. Furthermore, as more attention is paid to electronics technology, the requirement of reliability under high/low frequencies is highlighted. The room temperature frequency dependent *P-E* loops are displayed in Figure 3c. When the measured frequency rises from 500 Hz to 20 kHz, the changes of the *W*rec and *η* values are only 9% and 2%, respectively, as shown in Figure 3d. Furthermore, the energy storage performance of the capacitor in long-term working conditions is also a key requirement for practical application. To evaluate its long-term charging–discharging stability, the fatigue endurance of BST/0.4BFO-0.6STO film is evaluated under 10 kHz at room temperature. The *P-E* loops of samples over 10<sup>8</sup> charge–discharge cycles are exhibited in Figure 3e. It can be seen that there is no obvious change in the hysteresis loop. The corresponding *W*rec and *η* present a negligible degradation of 6% and 2%, respectively, as shown in Figure 3f. The weak dependence of the energy storage performance on the temperature, frequency and fatigue cycles makes the BST/0.4BFO-0.6STO thin film more competent to work in different complex environments.

It is generally believed that the bending strain *S* can be calculated using the equation *S* = (*t*<sup>f</sup> + *t*s)/2*r* [54,55], where *t*<sup>f</sup> is the film thicknesses, *t*<sup>s</sup> is the substrate thicknesses and *r* is the bending radius of the sample. The *t*<sup>f</sup> and *t*<sup>s</sup> for the BST/0.4BFO-0.6STO sample are ~350 nm and ~10 μm, respectively. Due to the limitations of stripping mica technology, the minimum bent radius of mica is 2 mm. In this curved state, the calculated *S* (~0.25%) is much less than the strain limit that the oxide film can withstand [56]. The mechanical stability of the BST/0.4BFO-0.6STO film is further evaluated under flex-in (compressive strain) and flex-out (tensile strain) modes at 2286 kV cm−<sup>1</sup> and 10 kHz with different bending radii (from 12 mm to 2 mm), as depicted in Figure 4a,b. Then, home-made molds with different required bending radii are used to test mechanical stability. It can be seen that the *P-E* loops keep its slim feature without obvious deterioration regardless of what compressive strain or tensile strain it is under. As plotted in Figure 4c, when the bending radius decreases from 12 mm to 2 mm, the corresponding *W*rec and *η* variations are both within 1%, indicating that the film possesses excellent bendability. The discharge energy density–time plots under various compressive and tensile radii are shown in Figure 4d,e. Obviously, all curves are very similar. Figure 4f shows the bending radius dependence of the discharged energy density and the discharge speed *t*0.9. The BST/0.4BFO-0.6STO film possesses a high discharged energy density (*W*dis) of ~32 J cm−3. Further, it can deliver the energy in ~40 μs without significant differences with the change of bending radius, exhibiting a fast charge–discharge rate and mechanical bending endurance.

**Figure 3.** (**a**) The *P-E* curves and (**b**) the corresponding *W*rec and *η* measured from −50 to 200 ◦C at 2286 kV cm−1. (**c**) The *P-E* curves and (**d**) the corresponding *W*rec and *η* with various frequencies measured under 2286 kV cm<sup>−</sup>1. (**e**) The *P-E* curves and (**f**) the corresponding *W*rec and *η* during the 10<sup>8</sup> fatigue cycles at 2286 kV cm<sup>−</sup>1. The measurements are realized at about 76% of *E*b.

Figure 5a,b presents the *P-E* loops of the BST/0.4BFO-0.6STO sample in the flat and reflatted after experiencing repeated bending at *r* = 4 mm. Over the course of 10<sup>4</sup> cycles, nearly unchanged *P-E* hysteresis shapes are observed, guaranteeing high mechanical stability of the energy storage performances. As demonstrated in Figure 5c, the variations of the *W*rec and *η* are negligible, further ascertaining its bending–endurance property. Finally, the influences of the ferroelectric fatigue endurance are investigated with *r* = 4 mm (Figure 5d,e). The energy storage performance is apparently undamaged even after 108 switching cycles at a radius as small as of 4 mm.

**Figure 4.** *P-E* loops measured at various (**a**) compressive radii and (**b**) tensile radii. The inset is the photographs of the BST/0.4BFO-0.6STO film under different bending states. (**c**) *W*rec and *η* as functions of the bending radius. The energy discharge behaviors at various (**d**) compressive radii and (**e**) tensile radii. (**f**) Discharged energy density and discharge speed as functions of bending radius. (The lines in Figure 4a,b,d,e from black to purple represent the measurements of the bending radius of BST/0.4BFO-0.6STO film from ∞ to 2 mm, respectively.)

**Figure 5.** (**a**,**b**) *P*-*E* loops of BST/0.4BFO-0.6STO film under various bending cycles under the compressive and tensile states. (**c**) *W*rec and *η* as functions of bending number. (**d**,**e**) *W*rec and *η* as functions of switching cycle during 108 fatigue cycles under compressive and tensile bending states with *r* = 4 mm. The insets are the corresponding *P-E* loops. (The lines in Figure 5a,b from black to green represent the measurements of the bending cycles of BST/0.4BFO-0.6STO film from 100 to 104, respectively.)

Finally, the core parameters of *E*b, *W*rec and *η* for energy storage properties are compared with some previously reported representative dielectrics (Figure 6). As depicted

in Figure 6a, the BST/0.4BFO-0.6STO film exhibits relatively high *W*rec of 62 J cm−<sup>3</sup> at a moderate *E* of 3000 kV cm−1, which is much higher than HZO (46 J cm−3), BST-BF (48.5 J cm<sup>−</sup>3) and NBT-BT/BFO (31.96 J cm<sup>−</sup>3) [28,32,35], but slightly inferior to Mn: NBT-BT-BFO (81.9 J cm<sup>−</sup>3) and BFO-STO (70.3 J cm−3) [6,36]. In Figure 6b, it can be seen that the obtained *η* of 74% in this work is lower than the reported dielectrics on rigid substrate, such as SBTMO (87%), BBTO (87.1%) and PLZST (84%) [20,31,34] but reaches a relatively high level among all the currently reported bendable inorganic dielectric film capacitors. In view of the aforesaid observations, there is still much room for improvement of the *η* in the flexible film capacitors, and it needs further research.

**Figure 6.** A comparison of the (**a**) *W*rec and (**b**) *η* of the flexible BST/0.4BFO-0.6STO film capacitor reported in this study and a number of film capacitors reported previously.
