Compared with traditional lithium-ion batteries, electrochemical capacitors, and polymer media, ceramic-based dielectric capacitors offer high power densities and are attractive for meeting the growing demand for energy storage devices^[1-5], and many studies have attempted to develop these systems^[6-10]. Ceramic-based dielectric capacitors have attracted much attention because of their high power densities, fast charge-discharge abilities, broad operating-temperature ranges, long cyclic times, and excellent thermal stabilities in pulse-power devices^[11-16]. These characteristics make ceramic dielectric capacitors promising for energy storage applications such as pulse-power supplies, electric vehicles, and electromagnetic pulse devices^[17-19].

Dielectric materials can be classified into four categories: linear dielectrics, normal ferroelectrics, antiferroelectrics (AFEs), and relaxor ferroelectrics^[20-23]. Among them, AFEs show unique double polarization-electric field (P-E) hysteresis loops in an external electric field, experience a transition from an AFE phase to a ferroelectric (FE) phase with an increasing electric field, and demonstrate a transition from an FE to AFE phase in a decreasing electric field. Because of the antiparallel arrangement of adjacent dipoles, the remnant polarization of AFEs is near zero, and the polarization and dielectric constant sharply increase when the electric field reaches the transition field. These features improve the discharged energy storage density and charge-discharge performance of AFEs in terms of increasing the integrated area of the upper branch of P-E hysteresis loop with respect to the polarization axis^[24-27]. The total energy storage density (W_tot), recoverable energy storage density (W_rec), and energy storage efficiency (η) of dielectric ceramic capacitors can be defined as follows^[28,29]:

(1) $$ W_{t o t}=\int_{0}^{P_{m}} E d P $$

(2) $$ W_{r e c}=\int_{P_{r}}^{P_{m}} E d P $$

(3) $$ \eta=\frac{W_{r e c}}{W_{t o t}} \times 100 \% $$

where E, P_m, and P_r denote the applied electric field, maximum polarization, and remnant polarization, respectively.

Therefore, improving the polarization, AFE-FE transition field, and dielectric breakdown strength (DBS) of AFE materials can enhance the energy storage performance of dielectric capacitors. The stability of the AFE phase can be evaluated using the Goldschmidt tolerance factor for the ABO₃ perovskite structure:

(4) $$ t=\frac{R_{A}+R_{O}}{\sqrt{2}\left(R_{B}+R_{O}\right)} $$

where R_A, R_B, and R_O denote the radii of A-site, B-site, and oxygen ions, respectively. When ionic doping decreases t, the stability of the AFE phase increases, thus increasing the phase transition field E_AFE-FE. For linear ferroelectrics, the polarization is usually proportional to the dielectric constant multiplied by the electric field, and it therefore increases with increasing electric field intensity. The DBS can be increased either intrinsically by increasing the bandgap through doping or extrinsically by refining the grain-size distribution to reduce defect concentration and interfacial flaws^[30-32]. Liu et al.^[32,33] investigated (Pb_0.925La_0.05)(Zr_0.995Ti_0.005)O₃ ceramics and obtained W_rec = 12.3 J/cm³ and η = 84% under an electric field of 420 kV/cm by refining the grain size distribution and enhancing the bandgap ($$ E_{B} \propto e^{\sqrt{E_{g}}} $$), where E_B is the DBS and E_g is the bandgap). Liu et al.^[31] also prepared a multilayer ceramic capacitor (Pb_0.94La_0.02Ca_0.04)(Zr_0.7Sn_0.3)_0.995O₃ via grain refinement and strengthened cation-O bonding, obtaining W_rec = 14.3 J/cm³ and η = 86.1% at 530 kV/cm. In addition, Li et al.^[34] investigated (Pb_0.92Gd_0.02Sr_0.05)(Zr_0.87Sn_0.12Ti_0.01)O₃ ceramics and achieved W_rec = 14.5 J/cm³ and η = 81% at 717 kV/cm using a phase tailoring strategy via chemical modification.

These previous studies found that although these materials demonstrate high energy-storage densities, their energy storage efficiencies remain relatively low. By contrast, the energy storage efficiency of (PbLa)(ZrSnTi)O₃ (PLZST) ceramics is related to the hysteresis of the AFE-FE and FE-AFE phase transitions. Previous investigations have shown that the electric hysteresis in the P-E loop can be reduced by doping Sr²⁺ ions at A-sites, and a relaxor AFE with a diffuse phase transition can be constructed to form a slim P-E hysteresis loop, thereby effectively improving the energy storage efficiency of this system^[11,35]. Moreover, the doping of Ba²⁺ ions at A-sites has been shown to increase the dielectric constant and correspondingly decrease the phase transition temperature^[36,37]. Therefore, this study investigated Ba²⁺ and Sr²⁺ co-doped PLZST AFE bulk ceramics. In addition, doped PLZST thick-film ceramics were fabricated using a tape-casting process to further improve the DBS and energy storage performance^[38]. The effect of film thickness on DBS and polarization was evaluated, and the influence of the ceramic thickness on the energy storage density was statistically determined.

Figure 1A shows the XRD patterns of the PLSBZST1-4 AFE ceramics at room temperature. All ceramics demonstrate pure perovskite structures, and no diffraction peaks from the impurity phase are detected. In the magnified patterns near 2θ = 44°, the intensity of the (200) peak is approximately twice that of the (002) peak, indicating that the PLSBZST ceramics may have an orthorhombic structure^[30,39,40]. According to the Bragg equation,

(5) $$ 2 d sin \theta=n \lambda $$

where d is the distance between the two close crystalline planes, θ is the angle of incidence or the angle of reflection, n is the whole number, and λ is the wavelength of X-ray. The lattice shrinks and the lattice constant decreases as Sr²⁺ (1.19 Å) has a smaller ionic radius than Pb²⁺ (1.49 Å). Therefore, the diffraction peaks shift toward higher diffraction angles.

Rietveld refinements were used to confirm the exact phase structures and detailed lattice parameters of all samples. Figure 1B-E demonstrates the Rietveld refinement results of the PLSBZST thick-film ceramics, which show that all thick-film ceramics adopt an orthorhombic phase structure (Pbam space group). Table 1 summarizes the lattice parameters and reasonable agreement indices (R_p, R_wp, and χ²).

To further characterize the microstructures of PLSBZST ceramics, the sample with x = 0.06 was analyzed using transmission electron microscopy (TEM). In Figure 2A, typical nanosized stripe electric domains (e.g., ~200-300 nm in size) can be observed in the bright-field image. An HRTEM image covering an electric domain area with tens of nanometers in size is also shown in the inset of Figure 2A. The reduction in the size of the ordered regions is attributed to the disruption of long-range order caused by compositional and structural fluctuations. These nanosized domains, also called polar nanoregions (PNRs), result in slim P-E hysteresis loops and other typical relaxor AFE behaviors, such as diffuse phase transitions^[11,35]. Moreover, the relaxor AFE diffuseness parameter is > 1 and close to 1.6 (see Figure 2A)^[41,42]. Figure 2B shows the SAED pattern obtained along the [$$ 0\bar{1}1 $$] zone axis. In addition to the main reflection spots, 1/2{ooo}-type superlattice diffraction patterns (F-spots) are observed and indicated by the red boxes in Figure 2B. These reflections arise from the tilting of the oxygen octahedra within the crystalline structure. In Figure 2C and 2D, the diffraction spots indicated by the hollow triangles are adjacent to the main diffraction spots, which may result from the incommensurate modulation structure (IMS) caused by the antiparallel displacement of cations^[43,44]. As shown in Figure 2C, the IMS is formed along the $$ <\bar{1}0\bar{1}> $$ direction. The plane spacing ($$ d_{\bar{1}0\bar{1}} $$) results from an irrational number multiplied by the modulation wavelength in the diffraction spacing (λ) (i.e., $$ d_{\bar{1}0\bar{1}} $$ = nλ, where n = 4.91)^[43]. Figure 2D shows the SAED patterns obtained in the [010] direction near the 90° domain wall. The satellite patterns caused by the IMS are highlighted by the green and yellow hollow triangles, and these reflection patterns are arranged vertically along the <101> and $$ <\bar{1}01 $$ directions^[44]. The existence of the IMS can produce a relatively slimmer hysteresis loop. For the relaxor AFE with an IMS structure, the shape of the hysteresis loop is slimmer and more inclined, which improves the energy storage density and efficiency of this system.

Figure 3A-D presents the surface SEM images of the four PLSBZST thick-film ceramics and their grain size distributions. All ceramic samples show dense microstructures, clear grain boundaries, closely packed grains, and small pores at multigrain junctions. The inset of each panel shows the grain size distribution histogram obtained using ImageJ software. The grain sizes are mainly distributed between 1 and 3 μm. These fine grain sizes improve the DBS of the ceramics via the relation $$ E_B\propto G^{-a} $$, where E_B is the DBS, G is the average grain size, and a is a constant^[45]. As shown in Figure 3E, the cross-sectional SEM image indicates that the thickness of the PLSBZST1 thick-film ceramic is 8.32 ± 0.67 μm, and the thicknesses of the other three samples (PLSBZST2, PLSBZST3, and PLSBZST4) are 7.00 ± 0.20, 7.26 ± 0.07, and 8.59 ± 0.15 m, respectively. The distribution of elements is another important factor affecting the DBS of the dielectric ceramics. An uneven elemental distribution can lead to local dielectric breakdown and eventually failure of the entire ceramic, which is not conducive to improving energy storage performance^[46]. Figure 3F shows the surface morphology and EDS mappings of all elements in the PLSBZST1 thick-film ceramic in the selected area (inside the red box). The elemental maps show that Pb, La, Sr, Ba, Zr, Sn, Ti, and O are evenly distributed throughout the analyzed area, with no obvious elemental aggregation observed, which helps enhance the energy storage performance of these ceramics.

Figure 4A-D shows the temperature-dependent relative dielectric constant (ε_r) and loss tangent (tanθ) for PLSBZST ceramics at frequencies of 1, 5, 10, and 50 kHz in the temperature range of 30-320 °C. At a constant temperature, the slight decrease in the dielectric constant with increasing measurement frequency is attributed to the reduced ability of dipoles to follow the alternating field at high frequencies^[43]. The maximum dielectric constant (ε_m) gradually decreases with increasing Sr²⁺ content, and the peak temperature (T_m) corresponding to ε_m also decreases. Due to the influence of the thermodynamic instability of PbSnO₃, all the samples underwent a stage in which the dielectric constant showed little variation and resulted in a flat, broad peak. This behavior is attributed to the occurrence of a multicell cubic (MCC) phase^[47], which exhibits dielectric characteristics similar to those of the relaxor AFEs. To further examine the relaxor AFE characteristics of PLSBZST thick-film ceramics, the modified Curie-Weiss law was used^[33]

(6) $$ \frac{1}{\varepsilon_{r}}-\frac{1}{\varepsilon_{m}}=\frac{\left(T-T_{m}\right)^{\gamma}}{c} $$

where T is the temperature above T_m, ε_r is the relative dielectric constant at T, ε_m is the maximum dielectric constant, C is the Curie constant, and γ is the diffuseness parameter. As shown in Figure 4E, γ increases with increasing x from 1.16 (x = 0.04) to 1.61 (x = 0.10). This indicates that the relaxor AFE characteristics of PLSBZST thick-film ceramics are gradually enhanced under these conditions.

In Figure 4F, 1000/ε_r as a function of temperature, based on the dielectric constant versus temperature plot, clearly shows the degree of diffuseness. T_B is the Burns temperature, defined as the formation of polar nano regions in relaxor ferroelectrics, at which ε_r begins to deviate from the Curie-Weiss law. The results show that T_B-T_m and the degree of diffuseness increase with increasing Sr²⁺ content. The increase in the diffuse degree and relaxor AFE character is beneficial for refining the P-E hysteresis loop, thus obtaining higher W_rec and η values^{[31,32,48,49]}.

Figure 5A and B shows the P-E and current - electric field (I-E) hysteresis loops for the PLSBZST1-4 thick-film ceramics at room temperature. All PLSBZST ceramic samples show typical AFE hysteresis loops and bimodal current curves. With increasing Sr²⁺ content, the P-E hysteresis loop exhibits stronger relaxor AFE characteristics, the I-E current peaks broaden, and the peaks shift towards high electric fields, which indicates that the AFE-FE phase transition electric field increases with x^[11].

The AFE-FE and FE-AFE phase transition electric fields and hysteresis width for the four ceramics (ΔE = E_AFE-FE - E_FE-AFE) are shown in Figure 5C. It can be seen that E_AFE-FE and E_FE-AFE increase from 306.08 and 260.45 kV/cm for PLSBZST1 to 328.68 kV/cm and 287.99 kV/cm for PLSBZST4, and ΔE decreases from 45.63 kV/cm for x = 0.04 to 34.59 kV/cm for x = 0.06, then increases with increasing x (x = 0.08, 0.10). Doping the A sites with elements of smaller ionic radii enhances the stability of the AFE phase and increases the AFE-FE transition field^[38]. The increase in E_AFE-FE and E_FE-AFE increases the area between the up branch of the P-E loop and the polarization axis, thus increasing the discharged energy density W_rec. A decrease in ΔE results in a higher energy storage efficiency η. As shown in Figure 5C, the maximum polarization (P_max) gradually decreases with increasing Sr²⁺ content. On the one hand, the decrease in P_max results from the Pb²⁺ ions being replaced by Sr²⁺ ions with smaller ionic radii, which leads to the shrinking of the unit cells and hinders the relative displacement and movement space of the ions at the A sites, thereby decreasing the polarization^[35]. This also affects the AFE-FE phase transition. With increasing Sr²⁺ content, the stability of AFE and the interaction between the two adjacent antiparallel dipoles in the AFE domain increase. Consequently, dipole switching within the AFE unit cells becomes more difficult, fewer dipoles align with the electric field, and the AFE-FE transition shifts to a higher electric field^[50]. A similar phenomenon has also been reported for Sr²⁺-doped PbZrO₃-based AFE ceramics^[11,30].

Figure 5D shows the Weibull distribution results used to obtain the DBS. The slopes (βs) of all the Weibull distributions are > 14, indicating that all the specimens have better qualities (e.g., DBS, consistency, narrow distribution of the DBS, etc.). The Weibull distribution results show that the PLSBZST2 (x = 0.06) sample demonstrated the highest DBS among the four thick-film ceramics, and it was approximately 7.00 ± 0.20 μm thick. These results indicate that a fine and uniform grain-size distribution, dense microstructure, and small ceramic thickness can effectively improve DBS.

The W_rec and η values for the PLSBZST ceramics are shown in Figure 5E to further investigate the energy storage performance of the PLSBZST ceramics. The PLSBZST2 (x = 0.06) ceramic sample demonstrates the highest W_rec and η values among all specimens, at 20.09 J/cm³ and 91.34%, respectively. With increasing Sr²⁺ content, P_max gradually decreases. However, the W_rec values of the PLSBZST3 (x = 0.08) and PLSBZST4 (x = 0.10) ceramic samples are larger than those of PLSBZST1 (x = 0.04) due to the increase in the relaxor AFE characteristics. Finally, as shown in Figure 5F, the W_rec and η values for PLSBZST2 are compared with those recently published for AFE ceramics^{[11,29,30,34,35,50-59]}. The enhanced W_rec and η will be favorable for the larger discharged energy density and higher energy efficiency of the pulse power capacitors.

The analysis of the P-E hysteresis loops indicated that the PLSBZST2 ceramic sample exhibits the highest W_rec among all PLSBZST AFE ceramics. In addition, the stability of W_rec with respect to temperature and frequency is an important parameter for evaluating the energy-storage performance of dielectric capacitors^[60]. Figure 6A shows the P-E hysteresis loops of the PLSBZST2 ceramic at 940 kV/cm and 10 Hz over the temperature range of 30-110 °C. The E_AFE-FE, E_FE-AFE, ΔE, and P_max values as a function of temperature for PLSBZST2 ceramics are shown in Figure 6B. As temperature increases, the hysteresis loop slightly widens, which can be attributed to the continuous increase in the loss tangent. Moreover, P_max decreases almost linearly from 41.13 to 36.86 μC/cm² at 940 kV/cm with increasing temperature, which is probably due to the diffuse phase transition from an orthorhombic phase to a MCC phase^[31], whereas ΔE increases from 14.87 to 39.89 kV/cm. The W_rec and η values as a function of temperature for the PLSBZST2 ceramics are shown in Figure 6C. With increasing temperature, W_rec gradually decreases from 13.39 to 11.65 J/cm³, corresponding to a variation of less than 15%. By contrast, η is initially constant with increasing temperature and then slightly decreases but remains above 86%. Because temperature does not significantly affect the shape of the P-E hysteresis loop, W_rec and η values show very small variations with increasing temperature, demonstrating excellent temperature stability. Figure 6D shows the P-E hysteresis loops for the PLSBZST2 ceramics at 880 kV/cm and room temperature over the frequency range of 0.2-100 Hz. The corresponding E_AFE-FE, E_FE-AFE, ΔE, and P_max values are shown in Figure 6E as a function of frequency. With increasing measurement frequency, P_max slightly decreases from 40.8 to 39.60 μC/cm² at 880 kV/cm, corresponding to a variation of less than 3%, which is due to the small variation in the shape of the P-E hysteresis loop with increasing frequency. E_AFE-FE and ΔE monotonically increase with increasing frequency, and E_FE-AFE slightly decreases, resulting in a slowly increasing energy storage density and efficiency for PLSBZST2 [Figure 6F]. At a low frequency of 0.2 Hz, W_tot is the largest among the tested frequencies while W_rec is the smallest because of the wide loop, and η is only 85.31%. However, at other frequencies from 1 to 100 Hz, W_rec increases from 12.44 to 12.86 J/cm³, corresponding to a variation of less than 3.4%, while η remains above 91%. Overall, the PLSBZST2 ceramics exhibit excellent temperature and frequency stabilities over the measured ranges, indicating their potential for use in pulse power capacitor applications.

Moreover, it was observed that the thickness of the ceramic was closely related to the energy storage density. For example, an energy storage density W_rec of 20.09 J/cm³ was obtained at 1,440 kV/cm for a PLSBZST2 ceramic with a thickness of 7.00 ± 0.20 μm. In our previous studies, W_rec was 12.9 J/cm³ at 570 kV/cm for a (PbBaSrLa)(ZrSn)O₃ ceramic with a thickness of 32 μm^[54], 9.84 J/cm³ at 440 kV/cm for a (PbLa)(ZrSn)O₃ ceramic with a thickness of 50 μm^[61], and 5.72 J/cm³ at 280 kV/cm for (PbLa)(ZrSnHf)O₃ ceramic with a thickness of 50-70 μm^[62]. The energy storage density increases with decreasing thickness in thick-film ceramics. The thickness dependence of the energy storage density reminds us of the general relationship of energy storage density as a function of thickness. Especially whether or not we can figure out a mathematical relation to describe this kind of relation. Furthermore, the thickness dependences of polarization, especially the maximum polarization and DBS, might also be figured out. In fact, the DBS may be related to the thickness via the Gerson-Marshall relation^[63]:

(7) $$ E_{D B S}=27.2 t^{-0.39} $$

where t is in cm and E_DBS is in kV/cm.

In general, E_DBS can be written as

(8) $$ E_{D B S} \sim t^{s 1} $$

where s1 is a constant, -0.39. Because the polarization is proportional to the electric field, P = ε_rε₀E for linear ferroelectrics (ε₀ is the vacuum dielectric constant) and P~E² for nonlinear ferroelectrics (i.e., via the Rayleigh relation and even higher powers^[64]), the polarization remains an exponential function:

(9) $$ E_{D B S} \sim t^{s 1} $$

where s2 is also a constant. The recoverable energy storage density is defined as Equation (2) i.e., $$ W_{rec}=\int EdP $$. Here, because energy storage density is the product of electric field times the polarization, while both the electric field and the polarization have an exponential relationship with the thickness, thereby the energy storage density has an exponential relationship with the thickness, no matter the ferroelectric is a linear ferroelectric (P vs. E), or a nonlinear ferroelectric [P vs. E² for Rayleigh relationship, or P vs. Eⁿ (n > 2)]^[28]. Therefore, the recoverable energy storage density exhibits an exponential relationship with the thickness via

(10) $$ W_{r e c} \sim t^{s 0} $$

where s0 is still a constant. Because W_rec is the product of the polarization and the electric field, there exists the following relationship among s0, s1, and s2:

(11) $$ s 0=s 1+s 2 $$

We compared the data obtained with this study with DBS (a)^[65-69], P_max (b)^[70-74], and W_rec (c)^[75-79] data obtained in previous studies as a function of thickness^[80-84] for bulk ceramics, thick film ceramics, and thin films (see Supplementary Table 1)^{[11,31,33-35,41-43,55,56,85-93]}. The data were then fitted using Equations (8)-(10), and the results are shown in Figure 7A-C. We obtained s1, s2, and s0 values of -0.39 ± 0.03, -0.13 ± 0.03, and -0.43 ± 0.04, respectively. Here, s0 is notably less than the sum of s1 and s2, which likely resulted from the small polarization and electric field used to measure the recoverable energy storage density, because usually the applied electric field used for measuring the recoverable energy storage density is smaller than the DBS, and the polarization obtained at an electric field less than the DBS is smaller than the maximum polarization, and the larger the electric field, the larger the maximum polarization, the DBS and the recoverable energy storage density. Therefore, the absolute value of s0 will be less than the absolute sum of s1 + s2. For example, if less than 10% of each parameter is used, then a 20% error will be generated. Therefore, an s0 value of -0.42 will be obtained, which is similar to the actual s0 value of -0.43. In addition, it should be noted that the s1 value obtained here (-0.39) is the same as that obtained using Equation (7)^[63].

The nominal energy density can be calculated by integrating the electric field with respect to the polarization for the P-E hysteresis loop. Therefore, the actual charging and discharging performance of ceramics can be evaluated using the resistor-inductor-capacitor (R-L-C) circuit^[30,94,95]. According to the different circuit parameters, the circuit can be divided into an underdamped circuit and an overdamped circuit depending on the load. In an underdamped circuit, the pulse capacitor can release a higher current and thus a higher power density. In an overdamped circuit, the energy stored in the ceramic capacitor can be fully released^[43], which is beneficial for analyzing the actual discharge performance of the ceramics. Figure 8A shows the discharged current as a function of time for the PLSBZST2 thick-film ceramic obtained under different electric fields in the overdamped circuit. The peak current gradually increases with increasing electric field. The discharged energy density (W_dis) may be defined as a function of time for different electric fields during charging, as shown in Figure 8B. In general, W_dis can be calculated via^[96]

(12) $$ W_{d i s}=\frac{R \int i(t)^{2} d t}{v} $$

where R is the total resistance in the overdamped circuit (here, R = 100 Ω), i(t) is the discharged current, and v is the effective volume of the sample under test. Therefore, W_dis increases with increasing electric field. When the electric field approaches 312 kV/cm near the transition field E_AFE-FE, W_dis rapidly increases, and the maximum W_dis value of 6.79 J/cm³ is obtained at 500 kV/cm. The discharge time (t_0.9) is defined as the time required to reach 90% of the discharged energy density W_dis^[97]. At an electric field of 500 kV/cm, the PLSBZST2 ceramics can release 90% of W_dis in 95 ns, demonstrating rapid discharge. Figure 8C shows the discharged current as a function of time for the PLSBZST2 ceramic under different electric fields in an underdamped state. Here, the peak current (I_max) increases with increasing electric field. The oscillatory pulse current can be evaluated in terms of the discharged current density (C_D) and power density (P_D)^[98]:

(13) $$ C_{D}=\frac{I_{ {max }}}{S} $$

(14) $$ P_{D}=\frac{E I_{{max }} }{2 S} $$

where I_max is the peak value of the first pulse current, E is the charging electric field, and S is the electrode area of the sample. I_max, C_D, and P_D are shown as functions of the electric field in Figure 8D. Here, I_max, C_D, and P_D monotonically increase with increasing electric field, and a pronounced increase occurs near the AFE-FE transition field. The maximum C_D and P_D values of 687.73 A/cm² and 128.95 MW/cm³, respectively, are obtained under an electric field of 375 kV/cm. These results demonstrate that the PLSBZST2 ceramic exhibits a high discharged energy density, high discharged current, high power density, and short discharge time, indicating its potential for application in pulse-power devices.

In this study, (Pb_0.92-xLa_0.04Sr_xBa_0.02)(Zr_0.64Sn_0.35Ti_0.01)O₃ (PLSBZST; x = 0.04, 0.06, 0.08 and 0.10) freestanding thick-film ceramics were successfully fabricated using the tape-casting process. The results show that the forward AFE-FE switching field and relaxor degree increase with increasing Sr²⁺ content, while a fine grain size and dense microstructure are beneficial for improving the DBS. In particular, the PLSBZST2 thick-film ceramic demonstrated a maximum W_rec of 20.09 J/cm³ with an η of 91.34% at 1,440 kV/cm, together with excellent frequency and temperature stabilities and an excellent discharging performance. In addition, under a load of 100 Ω, the PLSBZST2 ceramic exhibited a maximum W_dis value of 6.79 J/cm³ at 500 kV/cm and released 90% of this W_dis value within 95 ns. Moreover, maximum C_D and P_D values of 687.73 A/cm² and 128.95 MW/cm³ were obtained. These findings indicate the potential of PLSBZST thick-film ceramics for use in pulse-power devices. Moreover, reciprocal exponential relationships of the maximum polarization, DBS, and W_rec as a function of the sample thickness were obtained. The s2, s1, and s0 exponents associated with these relationships were -0.13 ± 0.03, -0.39 ± 0.03, and -0.43 ± 0.04, respectively. Here, the value of exponent s1 is the same as that obtained using the Gerson-Marshall equation, and s0 is almost equal to (s1 + s2) 80%, which results from using 10% less than the maximum polarization and a lower electric field than that used for the DBS due to the lower electric field that was employed during measurement. The thickness dependence of the recoverable energy storage density directly indicates that the reduction on the thickness of the ceramic layer will be one of the important approaches to enhance the energy storage density for the pulse power capacitors.