Enhanced Energy Storage Properties in Paraelectrics via Entropy Engineering

Electrostatic energy storage capacitors based on dielectrics have attracted much attention due to their wide applications in advanced electrical technology and electronic devices. Generally, high energy density is achieved at a high electric field, while conduction loss becomes nonnegligible, which harms practical applications. Here distinctly suppressed leakage current in BaZr0.5Ti0.5O3‐based films by entropy engineering is realized. With increased entropy, the leakage current density decreases by two orders of magnitude at the electric field of 3 MV cm−1, leading to a markedly improved energy efficiency of 87% at an ultrahigh breakdown strength of 8 MV cm−1 in high‐entropy films. Thereby, a high energy density of 51.9 J cm−3 is achieved. This work demonstrates the effectiveness of entropy engineering in improving the breakdown strength of dielectric films and shows great potential in enhancing the energy storage performance of capacitors.


Introduction
Energy storage capacitors with ultrahigh charging/discharging speed and power density are fundamental components of advanced electrical systems and electronic devices. [1]However, the low energy density of capacitors hinders further application in next-generation electrical and electronic technology.Massive efforts have been focused on improving the energy density of DOI: 10.1002/apxr.202300006dielectrics. [2]Nevertheless, improved energy density is often accompanied by a high electric field, which means the sacrifice of energy efficiency results from the increasing conduction loss.
Considering the simplest parallel plate capacitors, energy storage and release in dielectrics are achieved through the evolution of polarization P with applied electric field E. The discharge energy density U e can be calculated by U e = ∫ P m P r EdP (Figure S1, Supporting Information), where P m is the maximum polarization and P r is the remnant polarization, respectively.For ideal linear dielectrics, we can rewrite the equation as U e = 1 2  0  r E 2 , where the  0 and  r are vacuum permittivity and relative permittivity, respectively. [3]Thus, increasing the breakdown strength E b is highly desired to realize a high U e .However, the actual linear dielectrics with defects (vacancies, dislocations, interface, etc.) show distinct loss which is positively correlated to E. [4] Part of the stored energy is dissipated as the energy loss (U loss ), which reduces the energy efficiency  [defined as U e /(U e + U loss )].Commonly, the main origin of energy loss is the conduction loss (for ferroelectrics, the hysteresis may dominate loss [5] ).Suppressing charge transport and increasing insulation resistance, seems to be a promising strategy, which also improves E b .
At present, multiple strategies, such as alloying with wide band gap materials, [6] controlling growth oxygen pressure, [7] adopting multilayer structure, [8] forming vertical grain boundaries, [9] and introducing artificial dead layer, [10] have been put forward to improve the insulation properties of dielectrics.However, the low efficiency at the electric field near E b , which means the increased fraction of energy dissipation, still limits the practical use. [11]Recently, high entropy dielectrics designed from the configurational entropy S config have been explored. [12]The configurational entropy is defined as where R is the mole gas constant and x i is the mole fraction of the ith element in the equivalent lattice position. [13]High entropy Bi 2 Ti 2 O 7based linear dielectric films [14] and KNN-H ceramics [15] show enhanced E b and thus improved U e and maintained relatively high .However, comparison from low-entropy (S config ≤ 1.0 R) to medium-entropy (1.0 R ≤ S config ≤ 1.5 R) and then to highentropy (S config ≥ 1.5 R) [16] dielectrics with the same structure is lacking.Here we investigated the effect of entropy engineering on insulation properties and energy storage performance in the entropy-modulated Ba(Zr, Ti)O 3 -based films, which is a promising and widely researched material. [17]The chemical formulas of low-entropy (LE), medium-entropy (ME), and high-entropy (HE) films are Ba(Zr, Ti)O 3 , Ba(Zr, Ti, Hf)O 3 , and Ba(Zr, Ti, Hf, Sn, Ce)O 3 , respectively (Figure S2, Supporting Information).Various B-site elements are equimolar for each composition.Because room temperature is far above the T m (the temperature corresponding to the maximum  r ) of it, [18] the LE component BaZr 0.5 Ti 0.5 O 3 shows high relaxor characteristics (even near linear behavior) so we could study the effect of S config on energy storage performance without the ferroelectricity evolution.It is found that the leakage current density of the sample at the same electric field is negatively correlated with their entropy value.In addition, emission conductive mechanisms at the high electric field were suppressed.Moreover, with improved insulate properties, high energy density and efficiency were achieved simultaneously in HE films.

Results and Discussion
Figure 1a shows the theta-2theta pattern of films, only (00l) peaks of film and substrate are observed, demonstrating that there is no detectable amorphous phase by macroscopic means.The magnified pattern of 40-50°shows a peak shift to a lower angle with increasing entropy, corresponding to the increase of lattice parame-ter c.The ionic radii of Zr 4+ , Ti 4+ , Hf 4+ , Sn 4+ , Ce 4+ in sixfold coordination are 0.72, 0.61, 0.71, 0.69, and 0.87 Å, respectively. [19]As a result, the mean ionic radius has a positive correlation to the entropy value in our design and the lattice should be expanded.The consistency between structure testing and calculated results suggests all elements are sitting on the lattice.Phi scans about {011} peaks reveal that the films have the same four-fold rotational symmetry together with the NSTO substrate (Figure 1b).Direct observation of microstructures was obtained by FE-SEM and TEM.The cross-section FE-SEM image in Figure 1c exhibits a uniform and dense film with a thickness of about 230 nm, which is favorable for dielectric energy storage performance.High-resolution TEM image of HE sample in Figure 1d shows various atomic arrangements under observation direction, which indicates a polycrystalline structure along the in-plane direction.The inset image of Figure 1d, which is its corresponding fast Fourier transformation (FFT) result, shows multiple diffraction patterns, which illustrates the existence of polycrystals with different orientations.There is no broad diffraction ring in the inset image, which reflects the complete crystallization of films.Both indirect diffraction characterization and direct microscope observation demonstrate that the films are crystalline, highly textured along the outof-plane direction, dense and uniform.
The contradiction between XRD and TEM may be due to the difference in the two test dimensions.To clarify the grain directions of the films, we carried out the electron backscattered diffraction (EBSD) measurement of a cross-section sample (Figure 2a,b).The maps show that the film is columnar crystal and has no secondary phase.The three colors in the Euler map represent mixed grain orientations, which confirm the polycrystalline structure of the film.Besides, the main out-plane orientation of the film is (001), which is same as the result of the XRD pattern.A film with partial grains of (00l) orientation may also show only {00l} reflections in its 2 scan, [20] so our measurements are reasonable.Moreover, the grains that contact the substrate are all (001) oriented, which indicates that the film is also subjected to the orientation of the substrate during spin coating.This effect is not the chemical bond cooperation during physical deposition, but may be the induction effect given by the surface hanging bond, which has been reported in other works. [21]ecause of the chemical distribution heterogeneity attributed to the multiple elements in B-site, the atomic-resolved energydispersive X-ray spectroscopy (EDS) based on STEM was adopted in the HE film (Figure 2c).Most elements in the B site (Zr, Ti, Hf, Sn) show uniform and periodic distributions, indicating a disordered coexistence in the equivalent lattice sites.Partial of the Ce element has spread to the A site, which may be attributed to the similar ionic radius between Ce 3+ (1.02 Å) and Ba 2+ (1.23 Å), resulting in a different S config with the design value (1.61 R).Although the proportion of diffused Ce is hard to estimate, the practice S config of HE film is still above 1.5 R.Moreover, all elements in the B site exhibit the same uniform distribution in the nanoscale (Figure S3, Supporting Information), and the electron probe microanalyzer (EPMA) images show similar uniformity on a larger scale (Figure S4, Supporting Information).The chemical homogeneity proposes a disordered distribution of the multiple elements in the B-site, which intensifies the local chemical disorder and lattice distortion.The surface fluctuation of the sample plays an important role in electric breakdown process.Because the breakdown paths may preferentially start from the defects in the electrode-dielectric interface, it brings the unpredictable breakdown of dielectrics.The surface micromorphology images of the films measured by AFM were shown in Figure S5 (Supporting Information) and a quantitative comparison of the roughness was also given.The results demonstrate that all the films are flat as their surfaces are smooth and crack-free, which excludes the effects of surface roughness on the difference of insulation.
Figure 3a gives the results of the dielectric spectrum of films, including relative permittivity and loss tangent.All films show steady relative permittivity over a frequency range of 1 kHz to 1 MHz With the entropy increasing, the relative permittivity reduces slightly from 26.8 (LE) to 20.5 (HE).The high loss tangent in low frequencies may be attributed to the noise of the external circuit, where the relative permittivity also shows instability.18b] Adding other elements further weakens the ferroelectricity.Therefore, all the P-E loops of the films in Figure 3b are like straight lines, and the difference between calculated (by the equation P =  0  r E) and measured polarization decreased with the increased entropy (Table S1, Supporting Information).Based on the almost disappeared ferroelectricity, these films could be classified into near linear dielectrics, so that the next discussion of loss focused on the conduction loss instead of hysteresis loss.
To comprehensively evaluate the energy storage performance of films with different entropy values, the two-parameter Weibull distribution analysis was carried out to obtain the E b values (Figure 3c).The related equation is depicted as: [22] P where E i is the measured breakdown electric field, P(E i ) is the cumulative breakdown probability at E i , E b equals to the E i at which P(E i ) equals to 63.2%, and  is the Weibull modulus that evaluates the distribution of E i .From 5.6 MV cm −1 (LE) to 7.6 MV cm −1 (ME) then to 8.0 MV cm −1 (HE), the calculated E b values of the films increase along with the entropy value.The  also increases from 9.4 (LE) to 20.4 (ME) and 14.5 (HE), indicating enhanced stability and reproducibility.The improved E b should be ascribed to the significantly suppressed leakage current density at the same electric field (Figure 3d).It's worth noting that the suppression effect becomes more distinct at a higher electric field.For example, the difference is about one order of magnitude at 2 MV cm −1 , from 1.7 × 10 −6 A cm −2 (LE) to 1.8 × 10 −7 A cm −2 (HE), and two orders of magnitude at 3 MV cm −1 , from 8.8 × 10 −5 A cm −2 (LE) to 4.0 × 10 −7 A cm −2 (HE).
To further understand the effects of entropy on the insulation property of the films, correlated conduction mechanism models were used to fit the leakage data (Figure S6, Supporting Information and Note S1, Supporting Information).In our opinion, with the electric field increasing, the dominant conduction  [14,24] b) The evolution of maximum polarization as a function of the applied electric field.c) The calculated energy density and efficiency of films that correspond to the applied electric field up to the breakdown electric field.d) Normalized breakdown strength, normalized energy density, and efficiency at 5.25 MV cm −1 as functions of the configuration entropy.
1b,2a,23] Manifest delay of the electric field at which emission mechanisms in ME and HE films emerge demonstrates higher energy barriers in electrode-dielectric interfaces and deeper trap energy levels, which illustrates that increased entropy can help to scatter the electrical carriers. [14]ompared with other recent works on improving the breakdown strength in dielectric films, our work achieves one of the highest E b values of 8 MV cm −1 (Figure 4a).Furthermore, a high E b with a low leakage current is momentous to the practice applications of energy storage capacitors, because the enhanced insulation properties can reduce the unexpected breakdown probability under the working electric field and ensure high reliability for devices.The entropy design shows great promise in achieving high energy storage performance.Following the measured P-E loops of films (Figure S7, Supporting Information), we extracted and plotted the evolution of P m with the E in Figure 4b.Consistent with the evolution of the P-E loops, the P m curves of ME and HE films deviated upward from the linear trend at electric fields higher than 6 MV cm −1 , implying a considerably increased conduction loss which damages the .
The energy storage performance of the films was calculated by their P-E loops.Both U e and  of the films are shown in Fig- ure 4c.Compared with the moderate U e of 29.9 J cm −3 in LE films, the ME and HE films achieve higher U e of 46.1 J cm −3 and 51.9 J cm −3 , respectively, despite the relative permittivity and polarization at the same field decreased.In addition, the HE films exhibit distinctly improved efficiency in contrast with the ME films at electric fields higher than 6 MV cm −1 , which means the superior high field insulation behavior due to high entropy.The improved  at the high electric field provides a broader voltage range for the practice applications of energy storage capacitors, together with higher long-time working reliability and less loss.To directly display the effects of entropy design in our films, the normalized E b and U e are plotted as functions of the S config in Fig- ure 4d, with the comparison of energy efficiency of various S config values at the same electric field of 5.25 MV cm −1 .Compared with the primary LE films, the E b and U e of the HE films improve by 48% and 73%, respectively.The slight enhancement of  may be attributed to the reduced polar clusters and suppressed leakage current, which is, however, hard to accurately analyze due to the poor ferroelectricity of the system.

Conclusion
In this work, we demonstrate the effectiveness of high-entropy design for dielectric energy storage capacitors by significantly enhancing the insulation properties, which reflects in the suppressed leakage current density and improved energy efficiency at the electric field higher than 6 MV cm −1 .Noteworthy improvements in breakdown strength and energy density of the high entropy films are achieved by 48% and 73%, respectively.Besides, the comprehensive comparison of low-entropy, medium-entropy, and high-entropy dielectric films illustrates the continuous evolution of dielectric properties, thereby providing a feasible approach to high-performance energy storage capacitors.

Experimental Section
Sample Fabrication: The entropy engineering films were prepared by a chemical solution deposition (CSD) method.High-purity raw materials, including barium acetate (Alfa Aesar, 99.999%), tetrabutyl titanate (Sinopharm, 98%), zirconium n-propoxide (Aladdin, 70%), hafnium acetylacetonate (Alfa Aesar, 97%), zinnacetat (Alfa Aesar, 98.5%) and cerous acetate (Alfa Aesar, 99.995%), were used to prepare precursors.The solvent is propionic acid (Meryer Shanghai, 99.5%), and the precursor solution concentration was adjusted to 0.2 m.The solutions were heated at 60 °C for 10 min, then stirred at room temperature for 6 h, and finally aged for 2 days.The (001)-oriented 0.7 wt% Nb-doped SrTiO 3 (NSTO) single crystal substrates were used in the spin coating processes, with a speed of 6000 rpm for 20 s.After each spin process, the obtained films were baked at 200 °C for 2 min and then pyrolyzed at 400 °C for 10 min.The above steps were repeated 13 times to obtain films of a certain thickness.Finally, the films were annealed at 600 °C for 30 min in the rapid thermal processor.The thickness of the final film was controlled to about 230 nm.
Characterization: The cross-section images of the films were obtained by a field-emission scanning electron microscope (FE-SEM, MERLIN VP Compact, ZEISS), which is used to measure the thickness and observe the micromorphology.The crystal structures of films were characterized by a high-resolution X-ray diffractometer (XRD) with Cu K radiation (Rigaku, Smartlab).The surface micromorphology was characterized by atomic force microscopy (AFM, Asylum Research, MFP 3D Infinity).Highresolution atomic images were obtained by transmission electron microscope (TEM, JEOL, JEM-2100F).The TEM sample of HE film was prepared by focused ion beams (FIB) along the c-axis.To measure the dielectric properties, circular Au top electrodes were sputtered by a DC sputter.The real electrode size was slightly larger with the mask (150 m) due to the diffusion during sputtering and calibrated by the optical microscope.The dielectric spectrums were measured by a precision impedance analyzer (Agilent, 4294A).Ferroelectricity and leakage measurements were measured on the Precision Multiferroic II platform (Radiant Technology).All ferroelectric hysteresis loops (P-E loops) were tested by bipolar triangular voltage with a frequency of 5 kHz.The leakage measurements were given by a DC voltage increased in a ladder shape, of which the soak time and measure time are both 200 ms.
Scanning Transmission Electron Microscope (STEM) and EBSD: Sample for EBSD characterization and STEM characterization of a thickness about 30-40 nm was prepared by using focused ion beam (FIB) milling (FEI Helios 600i).Cross-sectional lamellas were thinned down to about 100 nm at an accelerating voltage of 30 kV with a decreasing current from the maximum 2.5 nA, followed by fine polish at an accelerating voltage of 8 kV with a draught of 21 pA.EBSD data were collected in a detector (Holiba) equipped on the Zeiss microscope.HAADF-STEM and EDS images were acquired on the spherical aberration (Cs) corrected JEOL JEM-ARM200F NEOARM (operated at 200 kV).ADF-STEM images were acquired at collection semi-angles of 90-370 mrad.

Figure 1 .
Figure 1.Structure characterization of films.a) Theta-2theta patterns of all films.Left is a wide scan form 10°to 50°and right is a magnified pattern for 40°to 50°.b) Phi scans about {011} peaks of the films and substrate.c) Typical cross-section FE-SEM morphlogy of HE film.d) High-resolution TEM image of HE film.The inset is the corresponding FFT result of the image.

Figure 2 .
Figure 2. Collection of a) cross-section image and b) its corresponding band contrast map (top panel), phase map (middle panel), and Euler map (bottom panel).The different colors in Euler map represent different grain orientations.The purple, pink, and green stand for [001], [5 −4 −2], and [−1 −2 2], respectively.c) HAADF STEM image of the HE film and corresponding atomic EDS mappings of Ba, Zr, Ti, Hf, Sn, Ce, and O elements.Scale bar: 1 nm.

Figure 3 .
Figure 3. a) The dielectric spectrum of films, including relative permittivity and loss tangent.b) The P-E loops of films under the electric field of 3 MV cm −1 at 5 kHz.c) Two-parameter Weibull distribution analysis of the breakdown strength of the films.d) The leakage current density of the films as a function of the DC bias electric field.The measured leakage current densities under low electric field fluctuate as the corresponding currents approach the limitation of the instrument (≈1 × 10 −11 A).

Figure 4 .
Figure 4. a) The comparison of the breakdown strength of the HE films with recent works.[14,24]b) The evolution of maximum polarization as a function of the applied electric field.c) The calculated energy density and efficiency of films that correspond to the applied electric field up to the breakdown electric field.d) Normalized breakdown strength, normalized energy density, and efficiency at 5.25 MV cm −1 as functions of the configuration entropy.