**1. Introduction**

At present, the energy crisis and environmental pollution have aroused widespread concern. In order to solve these problems, it is necessary to develop and utilize clean and sustainable energy sources and energy storage devices [1–4]. At present, advanced energy storage techniques include batteries, superconducting magnetic energy storage systems and electrochemical/dielectric capacitors [5,6]. Among them, dielectric capacitors are attracting immense research interest in pulsed power systems due to their unique features of high-power density (up to 108 W kg−1) and short charge−discharge time (10<sup>−</sup>3–10−<sup>6</sup> s) [7–12].

For dielectric capacitors, the energy storage capability (recoverable energy storage density *W*rec, energy storage efficiency *η*) can be calculated by [13,14]:

$$\mathcal{W}\_{\text{rec}} = \int\_{P\_{\text{r}}}^{P\_{\text{m}}} E \, dP \tag{1}$$

$$\mathcal{W} = \int\_0^{P\_{\rm m}} E \, dP \tag{2}$$

$$\eta = \frac{W\_{\text{rec}}}{W} \times 100\% = \frac{W\_{\text{rec}}}{W\_{\text{rec}} + W\_{\text{loss}}} \times 100\% \tag{3}$$

**Citation:** Wang, W.; Qian, J.; Geng, C.; Fan, M.; Yang, C.; Lu, L.; Cheng, Z. Flexible Lead-Free Ba0.5Sr0.5TiO3/ 0.4BiFeO3-0.6SrTiO3 Dielectric Film Capacitor with High Energy Storage Performance. *Nanomaterials* **2021**, *11*, 3065. https://doi.org/10.3390/ nano11113065

Academic Editor: Sergio Brutti

Received: 11 October 2021 Accepted: 8 November 2021 Published: 14 November 2021

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where *W*, *W*loss, *E*, *P*<sup>m</sup> and *P*<sup>r</sup> represent the total energy storage density, the energy loss density, applied electric field, the maximum polarization and the remanent polarization during the discharge process, respectively. Therefore, *W*rec can be improved by increasing the difference between *P*<sup>m</sup> and *P*<sup>r</sup> and enhancing the electric breakdown strength (*E*b).

Currently, commercial biaxially oriented polypropylene (BOPP) has been widely employed in power inverter capacitor systems. The bottleneck problems faced by BOPP are its limited *W*rec of (<2 J cm−3) and poor thermal stability (<80 ◦C), which inevitably burden the weight of the device, increase the difficulty of structure design and narrow the working temperature window [15–17]. In recent years, inorganic dielectric capacitors using oxide thin films as functional elements have been widely studied due to their relatively high *W*rec compared with organic dielectrics. Recent investigations into the energy storage characteristics of several representative dielectric capacitors have been summarized and listed in Table 1. Obviously, energy storage properties such as *W*rec and *η* have been studied in film capacitors containing BiFeO3(BFO)/BaTiO3(BTO)/SrTiO3(STO). For example, Huang et al. reported that introducing Sr in BTO can effectively reduce the coercive field (*E*c) and *P*r, leading to an enhanced *W*rec and *η* [18]. Pan et al. demonstrated that a giant *W*rec of ~70 J cm<sup>−</sup>3, together with a high *η*, can be achieved in lead-free 0.4BFO-0.6STO films through domain engineering [6]. They also designed a 0.25BFO-0.3BTO-0.45STO ternary solid solution system, in which a high *W*rec of up to 112 J cm−<sup>3</sup> and an *η* of ~80% were obtained coexistence of the rhombohedral and tetragonal nanodomains in a cubic matrix [19]. Moreover, in Bi doped STO, ferroelectric relaxation behavior is observed, which plays a decisive role in the high energy storage property, especially the ultra-high *η* [20–23].

**Table 1.** Comparison of energy storage performance of different types of materials.


Poly(vinylidene fluoride-trifluoroethylene-chlorofluoroethylene) (P(VDF-TrFE-CTFE), vinylidene fluoride/Poly(vinylidene fluoride) (VDF/PVDF), Poly(vinylidene fluoride- chlorofluoroethylene) (P(VDF-CTFE), poly(diaminodiphenylmethane-diphenylmethane diisocyanate) (P(MDA/MDI), 0.1BiFeO3-0.9Bi0.2Sr0.7TiO3 (BST-BF), (Sr0.85Bi0.1)Ti0.99Mn0.01O3 (SBTMO), 0.4BiFeO3-0.6SrTiO3 (BFO-STO), BaZr0.15Ti0.85O3/BaZr0.35Ti0.65O3 (BZT/BZT), Pb0.8Ba0.2ZrO3 (PBZ), Pb0.97La0.02Zr0.66Sn0.23Ti0.11O3 (PLZST), Hf0.3Zr0.7O2 (HZO), Si-Hf0.5Zr0.5O2 (Si-HZO), BaBi4Ti4O15 (BBTO), 0.94(Bi0.5Na0.5)0.94TiO3-0.06BaTiO3/BiFeO3 (NBT-BT/BFO), 0.97(0.93Na0.5Bi0.5TiO3- 0.07BaTiO3)-0.03BiFeO3 (Mn:NBT-BT-BFO), Pb0.91La0.09(Zr0.65Ti0.35)0.9775O3 (PLZT), Ba(Zr0.35Ti0.65)O3 (BZT), Ba0.5Sr0.5TiO3/0.4BiFeO3- 0.6SrTiO3 (BST/0.4BFO-0.6STO).

With the rapid development of electronic devices leaning toward miniaturization and integration, flexible electronics have been an active research topic in various areas due to their distinctive advantages of being portable, lightweight, foldable, stretchable and even wearable [39–44]. Flexible and microscale dielectric capacitors as energy storage components are indispensable especially in next-generation micro-electrical power systems. Nevertheless, most inorganic dielectric films are grown on rigid substrates due to the lack of suitable flexible substrates. Common flexible polymer substrates, such as polyimide (PI) or polyethylene naphthalate (PEN), have very excellent mechanical compliance but they cannot withstand the high crystallization temperature of inorganic films due to their low melting point (PI ~ 520 °C, PEN ~ 270 °C). Fortunately, the emergence of MICAtronics provides a new idea to realize flexibility in oxide functional films with two-dimensional mica as the substrate. This is due to the fact mica possesses ultrahigh melting point (1000 °C–1100 °C) and atomically flat surface, making it more compatible with the inorganic thin film preparation process.[45–47]. However, a flexible dielectric film capacitor consisting of BFO, BTO, and STO elements has rarely been reported.

Considering that 0.4BiFeO3-0.6SrTiO3 (0.4BFO-0.6STO) is a relaxor ferroelectric with an attractive relaxor feature and Ba0.5Sr0.5TiO3 (BST) is paraelectric with low dielectric loss and high breakdown strength [6,48,49], a multilayer structure of BST/0.4BFO-0.6STO is envisaged in this work based on the two potential energy storage elements. A series of systematic studies about the energy storage capability are undertaken on the designed film, which is deposited on flexible mica substrate using a sol-gel method. The capacitor shows a high *W*rec of ~62 J cm−<sup>3</sup> and an *η* of ~74% simultaneously due to its relatively high *E*<sup>b</sup> of 3000 kV cm−<sup>1</sup> and strong relaxor behavior. Satisfyingly, prominent mechanical-bending resistance is also realized in the flexible BST/0.4BFO-0.6STO film, in which the *W*rec and *η* have no obvious deterioration under various bending radii (*r* = 12–2 mm) and even after 10<sup>4</sup> bending cycles at *r* = 4 mm.
