Energy density and storage capacity of La³⁺ and Sc³⁺ co-substituted Pb(Zr_0.53Ti_0.47)O₃ thin films

The room temperature XRD patterns of highly oriented PL10x thin films were grown on MgO (100) substrates by employing PLD technique and are shown in figure 1(a). We observed a single-phase perovskite structure of thin films with preferred (100) coincide with MgO (100) orientation. We observed diffraction peaks for PL0 film at 2θ ∼ 21.76, 44.36 and 68.82 correspond to (100), (200), and (300) planes and a slight distortion in doped films (lanthanum and scandium) films. As per the XRD patterns, these films are highly oriented along the (100) plane with a large amount of tetragonality (JCPDS files 33-0784). Various studies have demonstrated the dominance of tetragonal structure for such PZT composition with La³⁺ doping [25, 26]. Reitveld refinement of XRD data carried out by Noheda et al reported as tetragonal symmetry for Pb(Zr_0.52Ti_0.48)O₃ system [27]. In addition, the PZT system at MPB revealed a higher tetragonal symmetry over rhombohedral phase [28]. This is due to smaller ionic radius of La³⁺ than that of Pb²⁺ which induces lattice distortion and shrinkage in volume accompanied with reduction in a-axis and c-axis [25, 29]_. However, it has also been reported that PZT over morphotropic phase boundary (MPB) region the tetragonal and rhombohedral phases with space group P4mm and R3c coexists at the room temperature for [30].

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We used XRD data to analyze the peak broadening in terms of the crystalline size and lattice strain due to dislocation. The instrumental broadening (β) was corrected, corresponding to each diffraction peak of thin films using the relation [31]:

$$\begin{eqnarray}&&\beta =\sqrt{{(\beta )}_{{\rm{measured}}}^{2}+{(\beta )}_{{\rm{instrumental}}}^{2}}\end{eqnarray} \tag{ 2 }$$

The average nanocrystalline size was calculated using Debye–Scherrer formula: The average nanocrystalline size of thin films sample is calculated using Debye–Scherrer equation

$$\begin{eqnarray}&&D=\displaystyle \frac{K\lambda }{\beta \,\cos \,\theta }\end{eqnarray} \tag{ 3 }$$

where D = crystalline size in nanometer, K = Scherrer constant (0.9), and λ = wavelength of the Cu Kα radiation (1.5406 Å) and β is the peak width at half-maximum intensity. The strain-induced (L_s) in thin films due to crystal imperfection and distortion was calculated using the formula:

$$\begin{eqnarray}&&{L}_{s}=\displaystyle \frac{\beta }{\tan \,\theta }\end{eqnarray} \tag{ 4 }$$

From this equation and the Scherrer equation, it is clear that the peak width from crystallite size varies as 1/cosθ, whereas the strain varies as tanθ. Williamson and Hall (W–H) proposed a method of deconvoluting size and strain broadening by looking at the peak width as a function of the diffracting angle 2θ and obtained the mathematical equation [32, 33].

$$\begin{eqnarray}&&\beta ={L}_{s}4\,\tan \,\theta +\displaystyle \frac{K\lambda }{D}\end{eqnarray} \tag{ 5 }$$

It can be rearranged as,

$$\begin{eqnarray}&&\beta \,\cos \,\theta ={L}_{s}4\,\sin \,\theta +\displaystyle \frac{K\lambda }{D}\end{eqnarray} \tag{ 6 }$$

The lattice planes corresponding to peaks (1 0 0), (2 0 0), (3 0 0) for the respective thin films were deconvoluted with the Gaussian model to calculate β and θ. The linear fitting of βcosθ (radian) along y-axis and sinθ (radian) along x-axis is shown in figure 1(b) and the fitted parameters are shown in table 2. We calculated the D from the y-intercept and obtained 35.28 nm for PL0 (viz; PZT) sample consequently decreases on doped (La³⁺ & Sc³⁺) PZT thin films. In addition, the highest incorporation of lanthanum (PL8) exhibits the lowest crystal size (22.39 nm). It suggests that peak broadening occurs on the doping samples and the highest peak broadening observed for PL8, might be due to higher atomic radii of lanthanum compared to scandium. Melo et al reported D ∼ 30 nm for ∼300 nm in (Pb_0.91La_0.09)(Zr_0.65Ti_0.35)_0.977O₃ thin films [34]. The calculated parameters D and L_s for all compositions are provided in table 2.

Figures 2(a)–(e) shows AFM micrographs of thin films which exhibited smooth surface topography with an average roughness (R_a) of ∼1.81, 2.21, 3.47, 4.49, 8.69 nm for PL0, PL2, PL4, PL6, and PL8 respectively. Thin films without doping i.e., PL0 has low R_a that increased on lanthanum doping contents yielding roughness of ∼8.69 nm for PL8 thin film, and it may be due to higher ionic radius of lanthanum (1.061 Å) to scandium (ionic radii 0.745 Å). We observed XRD peak broadening due to La³⁺ and Sc³⁺ in PZT thin films, and higher incorporation of La³⁺ concentration resulted in higher roughness as evident from AFM images. A decrease in crystal size causes higher peak broadening which consequently increases the surface roughness of thin films [34, 35]. One can notice distinct surface roughness of respective films in 3D images as shown in the inset of figures 2(a)–(e).

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The frequency (f) dependence of the real component of relative dielectric permittivity (ε') at various temperatures from 100–650 K for all compositions of thin films are shown in figures 3(a)–(e) and their respective dielectric loss tangent (tanδ) in right y-axis. We observed stable ε' with high value and low tanδ in a wide range of frequencies in good agreement as reported in ferroelectric thin films of PbZr_0.52Ti_0.48O₃ [36]. We obtained room temperature (300 K) the value of ε' = 1064, 567, 820, 2016 and 556 for PL0, PL2, PL4, PL6, and PL8 respectively recorded at 1 kHz frequency. Thus, a suitable proportion of La³⁺ and Sc³⁺ can tailor dielectric properties.

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A comparison of temperature-dependence of the relative permittivity (ε' versus temperature) measured at frequency 1 kHz is shown in figures 4(a), (b). One can notice that PL0, PL6, and PL8 have dielectric maxima at ε_m' ∼ 575 K, 525 K, and 450 K respectively denoted as T_m. It is expected that such a peak for PL2 and PL4 existed above 650 K, out limiting temperature for measurements. Furthermore, we observed ε' as diffused over a wide range of temperatures on PL6 and PL8 which is in agreement with the earlier research on Lanthanum doped lead zirconate titanate thin films [37]. In ferroelectric materials, such type of behavior is pronounced as diffused phase transition (DPT) [38], known as disordered ferroelectric materials [39].

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The ferroelectric behavior with the DPT phenomenon of the dielectric materials can be explained by Curie-Weiss law above T_m [40]. The relationship for ε' with the temperature above T_m is given by equation (7).

$$\begin{eqnarray}&&\displaystyle \frac{1}{\varepsilon ^{\prime} }=\displaystyle \frac{T-{T}_{0}}{C}\,(T\gt {T}_{c})\end{eqnarray} \tag{ 7 }$$

Where; C is Curie-Weiss constant and T₀ is Curie-Weiss temperature (T_c) for second-order phase transition and less than T_m for the first-order phase transition [41].

Figures 5(a)–(c) show the reciprocal of ε' with temperature for PL0, PL6 and PL8 thin films. As we fitted using equation (2), we observed T₀ is above T_m for all thin films. We noticed the value of T₀ is reduced for the higher doping on lanthanum. We observed a degree of deviation, ${{\rm{\Delta }}}_{cw}={T}_{CW}-{T}_{m}$ = 15, 50, and 70 for PL0, PL6 and PL8 respectively due to compositional induced diffuse phase transition behavior [21]. Where T_cw represents the temperature from which ε' begins to deviate. Some of the parameters calculated are shown in table 3.

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In addition, the modified Curie-Weiss law can also explain the DPT behavior of the relaxor materials related by equation (8) [42]. Where, γ provides DPT behavior and C' is Curie-Weiss like constant.

$$\begin{eqnarray}&&\displaystyle \frac{1}{\varepsilon ^{\prime} }-\displaystyle \frac{1}{{\varepsilon }_{m}^{{\prime} }}=\displaystyle \frac{{(T-{T}_{m})}^{\gamma }}{{C}^{^{\prime} }}\,\left(1\leqslant \gamma \leqslant 2\right)\end{eqnarray} \tag{ 8 }$$

For γ = 1, a normal Curie-Weiss law is obtained, and γ = 2 describes a complete diffuse phase transition. The value of γ lies between 1 and 2 representing incomplete diffuse phase transition of the materials [41]. γ = 1 denotes normal ferroelectric material whereas 2 represents complete phase transition behavior of relaxor materials.

The fitting with an equation (8) is shown in figures 5(a)–(c) inset, at 1 kHz frequency for PL0, PL6 and PL8 thin films. We obtained γ as 1.19 ± 0.05, 1.69 ± 0.05 and 1.95 ± 0.16 indicating that PL6 and PL8 thin films exhibit incomplete diffuse phase transition. Thus, on increasing Lanthanum concentration such behavior is dominant than undoped or lower doped of lanthanum. It also indicates that dopants with La³⁺ ≥ Sc³⁺ increase the DPT of the materials.

As we observed the DPT of PL6 and PL8 thin films, where ε'_m decreases and T_m shifts towards higher temperature with increasing frequency. Furthermore, we analyzed the frequency dependency of T_m by using the Vogel-Fulcher relation given in equation (9) [43].

$$\begin{eqnarray}&&f={f}_{0}\exp \left[\displaystyle \frac{-{E}_{a}}{{k}_{B}\left({T}_{m}-{T}_{VF}\right)}\right]\end{eqnarray} \tag{ 9 }$$

Where; f₀ is the pre-exponential factor, T_VF is the characteristic Vogel-Fulcher freezing temperature, E_a is the activation energy and k_B is Boltzmann's constant [44, 45].

The reasonably well fitted non-linear curve shown in figure 6, yielded f₀ ∼ 10⁶ Hz, T_VF = 477 K and 411 K and factor, E_a = 0.031 eV and 0.054 eV respectively and are physically acceptable values [46]. These are in good agreement with the earlier reports on Pb(Zr_0.53Ti_0.47)_0.60(Fe_0.5Ta_0.5)_0.40O₃ [47]. The earlier report on Pb(Zr_0.53Ti_0.47)_0.90Sc_0.10O₃ had shown E_a = 0.037 eV and f₀ = 1.538 × 10⁶ Hz [16]. Thus, analysis of Vogel-Fulcher relation, further supports PL6 and PL8 thin films behave disorder ferroelectric, typically called relaxor ferroelectric materials. In addition, one can notice a comparatively slim polarization electric field (P-E) hysteresis loop of those thin films which suggest higher content of lanthanum on PZT strengthen the spontaneous polarization.

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Figures 7(a)–(e) show the Cole-Cole plots of the temperature-dependent dielectric permittivity of the real (ε') and imaginary (ε'') part of PL10x thin films at frequency range 10²–10⁶ Hz. We observed some characteristics of ε' versus ε'' response for PL10x thin films in the temperature ranges 100–650 K. (i) The ε' radius of the semicircular arc shows high variation with temperature, (ii) With increasing temperature the bulk permittivity contribution (ε' radius, when ε'' = 0) in the Cole-Cole plot increases, since the intercept of the semicircular arc gives an estimation of sample resistance, this indicates that the resistance increases from PL0 to PL6 and again decreases for PL8. The incorporation of the La³⁺ and Sc³⁺ ions could be responsible for change in its conduction properties [36, 48]. These dopants are mainly of two types: La³⁺ is a donor dopant that produces a soft PZT and Sc³⁺ is an acceptor dopant that produces a hard PZT. In addition, the decrease in the resistance for PL8 is due to higher doping of Lanthanum compared to scandium may facilitate the domain wall motion [49, 50]. (iii) the samples exhibit multi-dispersive relaxation time on increasing the temperature. Two intercepts between the real axis ε' and the circular arc, assign for the static dielectric constant, ε_s (largest value ε' radius, when ε'' = 0) and the optical dielectric constant, ε_∞ (smallest value ε' radius, when ε'' = 0) were observed in all samples which increased on doping compounds, this large increase is due to the variation of the domain wall motion that affects the resistance of the compound. These observed changes in the shape of Cole-Cole plots of dopant films could be due to different strains, that are produced by the different sizes of the doping ions that produce a variation of the dielectric and conductivity properties of the materials [51, 52],.

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The energy storage performance of ferroelectric materials is one of the key indicators for evaluating materials engineering applications. It can be estimated using unipolar P-E loops under the external applied electric field. According to the definition of energy-storage density using P-E hysteresis loops, the stored energy per unit volume (U_st) and the recovered energy per unit volume (U_re) are given by [53]

$$\begin{eqnarray}&&{U}_{st}=\displaystyle {\int }_{{P}_{0}}^{{P}_{m}}EdP\end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray}&&{U}_{re}=\displaystyle {\int }_{{P}_{\max }}^{{P}_{r}}EdP\end{eqnarray} \tag{ 11 }$$

Where; E is the applied electric field, P is the displacement charge density for ferroelectric materials, and P_r is the remnant polarization, P_m is the maximum polarization. Evidently, based on equations (10) and (11), the value of U_st and U_re can be easily obtained by numerical integration of the area between the polarization axis and the curves of the P-E loops. To estimate these values, we analyzed the positive branch of P-E curve and calculated the energy storage efficiency (η) as

$$\begin{eqnarray}&&\eta =\displaystyle \frac{{U}_{re}}{{U}_{st}}\times 100 \% \end{eqnarray} \tag{ 12 }$$

Figures 8(a)–(e) shows temperature-dependent (100–500 K) P-E hysteresis loops of PL10x thin film measured under an applied electric field of 0.67 MV cm⁻¹ electric field at 1 kHz frequency. Reproducible and stable ferroelectric loops with slight changes in polarization and coercive field were observed for all thin films. From the comparative graph of PL10x thin films as shown in figure 8(f), we observed typical ferroelectric loops with enhanced polarization and reduced coercive field for PL2 and PL4 thin films. Furthermore, PL6 and PL8 show slim loop hysteresis with high ΔP (P_m–P_r). These changes in parameters of the hysteresis loop were due to the substitution of scandium and lanthanum in PbZr_0.53Ti_O.47 (PZT). We estimated the energy storage capacity at 300 K for the same applied electric field (0.67 MV cm⁻¹) for PL10x thin films, achieving enhanced U_re, U_st and η due to doping elements. The estimated U_re value estimated was the greatest ∼12.24 with η = 53.4% for PL6. But we had better η = 66.67% with U_re = 4.82 J cm⁻³ for PL8 thin films. All the calculated parameters are summarized in table 4. Considering energy storage capacity and efficiency, we further, analyzed the positive branch of P-E loop for possible energy storage applications. Figures 9(a), (b) show the room temperature unipolar P-E hysteresis loops of PL6 and PL8 thin films measured under various applied electric fields at 2 kHz of frequency. The slim loop of these thin-film capacitors revealed relaxor ferroelectric behavior in PL6 and PL8 in line with dielectric results. We observed slight asymmetries at positive and negative branches in the hysteresis loop of PL6 and PL8 films that could be due to different work functions of top (Pt) and bottom (LSMO) electrodes [54, 55]. In addition to the layer interface effect which acts as pinning centered, defect-related oxygen vacancy and impurities might be also responsible for the observed asymmetry hysteresis loop [56, 57].

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Table 4. Summary of ferroelectric and energy storage parameter of PL10x thin films under 20V (0.67 MV cm⁻¹) at 2 kHz frequency.

Parameter:	Pr (μC cm−2)	Pm (μC cm−2)	EC (kV cm−1)	Ure (J cm−3)	Ust (J cm−3)	η (%)
Sample
PL0	24.4	35.3	187	1.26	14.37	8.76
PL2	35.3	65.1	103	6.27	19.39	32.01
PL4	26.4	61.1	50	6.38	15.99	39.89
PL6	9.6	71.9	152	12.24	22.92	53.4
PL8	3.6	19.2	50	3.82	5.73	66.67

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Near the breakdown electric field (∼2.67 MV cm⁻¹) at 2 kHz frequency, the enhanced polarization P_r ∼ 46.6 μC cm⁻² and P_m = 125.4 μC cm⁻², consequently yielded ${\rm{\Delta }}{P}_{m}=\tfrac{{P}_{m}}{{P}_{r}}=2.69,$ and reduced E_c ∼205 kV cm⁻¹ were obtained for PL6 films. In the similar applied electric field, for PL8 films E_c was further reduced to 12 kV cm⁻¹ and P_r ∼ 8.4 μC cm⁻² and P_m ∼ 39.2 μC cm⁻², achieved ΔP_m = 4.66, which resulted in slimmer P-E loop strengthening η. Thinner P-E loops were achieved in our films than undoped PbZr_0.53Ti_0.47O₃ (PZT) [58], PbZr_0.40Ti_0.60O₃ [59] films which were expected. It is obvious that higher ΔP_m would better to achieve enhanced η.

We estimated U_re, U_st and η for PL6 and PL8 films from their respective P-E loops. It turns out to be U_re = 51.15 J cm⁻³ U_st = 107.95 and η = 47.38% at an applied electric field of 2.67 MV cm⁻¹ and frequency 2 kHz for PL6 thin films which is in good agreement with ${U}_{st}={\varepsilon }_{0}\varepsilon ^{\prime} \tfrac{{E}_{BD}^{2}}{2},$ where E_BD is electric breakdown strength PL6 possesses higher ε' and high breakdown strength. The obtained values of PL6 are comparable with slightly less η as reported in Pb_0.91La_0.09(Zr _0.35Ti_0.65)O₃ thin films, U_re ∼ 28.7 J cm⁻³ with η ∼ 57% [60]. We thus achieved enhanced energy values than the studies on oriented Pb(Zr_0.52Ti_0.48)O₃) thin films, that had shown U_re ∼ 8 J cm⁻³ and η ∼79.6% under an applied electric field of 0.8 MV cm⁻¹, synthesized by chemical solution method [61]. On the other hand, Nguyen et al had reported [62] η ∼ 13.7 J cm⁻³ and a η ∼ 88.2% at 1 kV cm⁻¹ in 10% La-doped epitaxial PLZT thin films grown on SRO/STO/Si substrates using pulsed laser deposition. By comparing with this result, we have achieved higher U_re = 26.54 J cm⁻³ but with slightly less η = 65.88% for PL8 thin films under an applied electric field 2.67 MV cm⁻¹ and frequency of 2 kHz. The energy storage performance of our thin films showed higher breakdown strength and better U_re as compared to BaZr_0.20Ti_0.80O₃ (BZT) thin films showing U_re = 21.28 J cm⁻³ and η = 83.51% [63], however, these films have shown enhanced and better energy storage capacity for multilayer Pb(Zr_0.4Ti_0.6)O₃/BaZr_0.2Ti_0.8O₃/Pb(Zr_0.4Ti_0.6)O₃ (PZT/BZT/PZT), thus these materials might be useful for making sandwich structure to achieve high energy density capacitors. We observed U_re and U_st of PL6 and PL8 thin films are directly proportional to the applied electric field. However, η is slightly decreased with an increase in an electric field is expected as reported by 0.942[Na_0.535K_0.48NbO₃]−0.058LiNbO₃ (KNNLN) films [64]. The summary of the estimated value of ferroelectric functionalized parameters of PL6 and PL8 thin films is given in table 5.

Table 5. Summary of calculated values of energy storage parameters of PL6 and PL8 thin films measured under various electric fields at 2 kHz frequency.

Sample:	E (MV cm−1)	.67	1	1.33	1.67	2	2.33	2.67
PL6	Ure (J cm−3)	12.24	17.64	23.1	29.15	36.02	43.21	51.15
	Ust (J cm−3)	22.92	34.27	46.73	60.73	75.22	92.12	107.95
	η	53.4	51.48	49.43	47.99	47.88	47.38	47.38
PL8	Ure (J cm−3)	3.82	6.67	9.94	13.67	17.84	22.22	26.54
	Ust (J cm−3)	5.73	9.98	14.79	20.59	26.52	33.48	40.28
	η	66.67	66.83	67.21	66.73	67.26	66.36	65.88