Enhanced DC-bias stability and reliability in BaTiO₃ Ceramics via B-site Ca doping induced long-range order disruption

Sample preparation

The Ba_100-xCa_xTiO₃ (BCT) and BaTi_100-xCa_xO₃ (BTC) (x = 2, 4, 6) ceramics were fabricated by a conventional solid-state reaction method and were named as BCxT and BTCx, respectively. Pure BT ceramic was also prepared for comparison. The raw materials, BaCO₃ (99.8%, Aladdin), TiO₂ (99.0%, Aladdin), and CaCO₃ (99.99%, Aladdin) were weighed according to the design stoichiometric composition and ball-milled with zirconia balls and ethanol for 6 h. The powders were dried and then calcined at 1,100 °C (BCT) and 1,200 °C (BTC) in air for 2 h [Supplementary Figure 1], followed by a second ball-milling process for 6 h in ethanol. After drying, 6 wt% PVA was added as a binder, and the powders were granulated and then uniaxially pressed into 13 mm pellets at 200 MPa. All samples were sintered at 1,325-1,375 °C for 2 h in either air or N₂/H₂ atmosphere. The N₂/H₂ atmosphere sintered samples were fabricated using wet processing sintering to achieve enhanced densification and homogeneous microstructure. The pellets were then polished to a 0.3-0.6 mm thickness, and Ag electrodes were coated on both sides of the ceramic for electrical measurements.

Structural characterization

Crystalline phase formation was identified via X-ray powder diffraction (XRD; D8 Advance, Bruker) with a Cu Kα source at room temperature. High-resolution synchrotron powder XRD and synchrotron X-ray pair distribution function (PDF) patterns were collected at BL44B2 beamline of SPring-8 (Hyogo, Japan) at room temperature, employing a focused monochromatic beam at 50.00 keV [λ = 0.490030(1) Å], which was precisely calibrated through Le Bail refinement of LaB₆ standard data. Synchrotron diffraction data were corrected for anomalous scattering effects before structural analysis, and Rietveld refinements were performed using the JANA2006 crystallographic software suite. The X-ray absorption spectra (XAS), including X-ray absorption near-edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) at Ca K-edge, were collected at the Singapore Synchrotron Light Source center. The Ba K-edge EXAFS data were measured at room temperature in transmission mode using Beamline NW10A of Photon Factory Advanced Ring (PF-AR), High Energy Accelerator Research Organization (KEK). X-rays were varied using the fixed-exit Si (111) double-crystal monochromator, with higher-order harmonic X-rays removed using a rhodium-coated harmonic-rejection mirror. A bent cylindrical mirror was used to focus the incident light. All the XANES spectra were measured in the transmission mode. All the spectra were normalized using the Athena software^[19]. Thermal etching was performed on the cross-section of ceramic samples for grain size analysis using scanning electron microscopy (SEM; SU8220, Hitachi). Transmission electron microscope (TEM) samples were prepared using focused ion beam (FIB) milling (Helios Nanolab G3 UC, FEI) for microstructure observation. Atomic-resolution high-angle annular dark-field scanning transmission electron microscopy (HADDF-STEM) images were obtained using a 300 kV CS-corrected transmission electron microscope (HF5000, Hitachi). Polarization vector, polarization magnitude, and polarization angle were calculated and extracted using customized MATLAB scripts. Raman spectra were collected with the Raman microscope (InVia, Renishaw) using the 514 nm argon laser excitation. Electron paramagnetic resonance (EPR; JES-FA200, JEOL) was carried out on powders from 100 K to 400 K. X-ray photoelectron spectroscopy (XPS, ESCAlab250, Thermo Fisher Scientific) was used to analyze the valence states of the elements in the ceramics, with all binding energies calibrated to the C 1s peak at 284.8 eV.

Electrical properties characterization

Temperature-dependent dielectric properties were measured using an impedance analyzer (E4990a, Keysight) with a temperature-controlling system (DMS-2000, Partulab) over the temperature range of -55-200 °C. Impedance as a function of frequency was tested from 20 Hz to 2 MHz using precision LCR meters [Inductance(I), Capacitance (C), and Resistance (R)] (E4980A, Agilent). The DC-bias stability was measured using a dielectric tunability test system (DSP0200, Tongguo Technology) at 1 kHz. To quantize the bias-field stability of the dielectric constant, the DC-bias stability coefficient (α) is defined as^[15,20]:

where ε_r(0) and ε_r(E) are the dielectric constant under zero bias field and applied bias field E, respectively. Polarization electric field (P-E) loops were measured at 1 kHz using a ferroelectric tester (TF Analyzer 2000E, aixACCT). The DC breakdown voltage was tested using a high-voltage breakdown tester (BDJC-100kV, Beiguang Jingyi Instrument).

Electrical performance of BTC ceramics

The effect of Ca doping on the temperature-dependent phase transition behavior of BT strongly depends on the substitution site [Figure 2A and B, Supplementary Figure 2]. For BCT ceramics, the T_c increases slightly from 129 °C (BT) to 134 °C as the Ca concentration increases, while the T_c of BTC ceramics decreases sharply to 60 °C (BTC4), accompanied by a significant broadening of the Curie peak^[8]. The room-temperature dielectric constant of BTC4 is 2200 at 1 kHz. Additionally, the dielectric loss peaks associated with the tetragonal-orthorhombic and cubic-tetragonal phase transitions disappear. The T_c of BTC6 increases slightly to 63 °C, likely due to exceeding the solid solution limit of substitution for the B-site [Figure 3A], causing partial A-site substitution by Ca^[21,22]. Figure 2C presents the complex impedance spectra of BT, BC4T, and BTC4 ceramics, where BTC4 exhibits substantially higher impedance than BT and BC4T. The calculated activation energy of BTC4 (1.23 eV) is also higher than that of BT (1.0 eV) and BC4T (1.1 eV), which is related to the movement of oxygen vacancies [Supplementary Figure 3]^[4,8]. The oxygen vacancies are more localized in BTC4 ceramics [Supplementary Figure 4]. In Figure 2D, BTC4 shows the most superior DC-bias stability compared with BT and BC4T, with the absolute value of α decreasing from 60% (BT) to 15% (BTC4) under an electric field of 30 kV/cm. At low electric field strengths, BT and BC4T ceramics exhibit an apparent positive value of α, while BTC4 does not. This behavior is primarily attributed to the ferroelectric domain wall motion under the applied field^[23,24]. In Figure 2E, BTC4 exhibits a narrower P-E loop with reduced remnant polarization and higher breakdown strength (243.5 kV/cm, Supplementary Figure 5), whereas BT and BC4T display conventional ferroelectric characteristics. The corresponding I-E curves for BTC4 reveal two sets of current peaks, indicative of antiferroelectric-like behavior, while BT and BC4T ceramics only show a single pair of peaks [Figure 2F]. The emergence of double hysteresis loops can be attributed to randomly oriented defect dipoles or strong aging in ferroelectrics^[25,26]. In this study, no intentional aging treatment was performed on the BTC4 samples; therefore, the observed double hysteresis loops are most likely attributed to the presence of defect dipoles.

Figure 2. Temperature dependence of (A) dielectric constant and (B) dielectric loss of BTC ceramics measured at 1 kHz; (C) Complex impedance spectra of BT, BC4T, and BTC4 ceramics measured at 200 °C; (D) The bias-field-dependent DC-bias stability coefficient (α) of BT, BC4T, and BTC4 ceramics; (E) P-E hysteresis loops and (F) corresponding I-E curves for BT, BC4T, and BTC4 ceramics. BTC: BaTi_100-xCa_xO₃; BT: BaTiO₃.

Figure 3. (A) XRD patterns of BTC ceramics, with enlarged views of (111), (002), and (200) diffraction peaks; (B) Raman spectra of BT, BC4T, and BTC4 ceramics measured at room temperature. Synchrotron powder XRD patterns of (C) BT, (D) BC4T, and (E) BTC4 ceramics, with accompanying Rietveld refinement results. A blue trace in the residual plot highlights the deviations between the measured and computed values. The positions of Bragg peaks are marked by vertical green and orange indicators, serving as reference points for crystallographic analysis. The primary diffraction peaks of all samples align well with theoretical Bragg positions (vertical ticks), confirming phase integrity. The refined profiles exhibit excellent agreement with peak positions and relative intensities, with high reliability factors. The illustration in Figure 3C shows the variation of the c/a ratio with Ca doping content for the BCT and BTC ceramics, as calculated from Rietveld refinement results. For the BTC ceramics, the c/a ratio was obtained by averaging the c/a values of the tetragonal and cubic phases. BTC: BaTi_100-xCa_xO₃; XRD: X-ray powder diffraction; BT: BaTiO₃; BCT: Ba_100-xCa_xTiO₃.

The polarization behavior of BTC4 ceramic

To understand the coexistence of a high dielectric constant and superior DC-bias stability in BTC4 ceramic, it is essential to investigate the impact of B-site Ca substitution on the microstructure and clarify its influence on polarization mechanisms. In the BTC system, increasing Ca content leads to a gradual shift of the (111) diffraction peak to lower angles and the merging of the (200) and (002) peaks, as shown in Figure 3A. These changes indicate a progressive expansion of the unit cell and a reduction in tetragonality, reflecting a transition toward a pseudo-cubic structure. This structural evolution is primarily attributed to the substitution of Ti⁴⁺ (0.60 Å) by larger Ca²⁺ ions (0.99 Å)^[6-9], which introduces significant local lattice distortion due to the large size mismatch. Such a high mismatch limits the solid solubility of Ca²⁺ at B-sites (x~0.04), and excess doping leads to the formation of the hexagonal BT phase in BTC6^[8]. In contrast, in the BCT system, where Ca²⁺ substitutes at the A-site (Ba²⁺: 1.61 Å vs. Ca²⁺: 1.34 Å), leading to unit cell shrinkage and enhanced tetragonal stability^[1,8]. This is evidenced by the shift of the (111) peak to higher angles and the persistent splitting of (200)/(002) peaks, as illustrated in Supplementary Figure 6. These structural evolutions are further validated by Raman spectra [Figure 3B]. The disappearance of the 167 cm^-1 and 470 cm^-1 modes, as well as the broadening and red-shifting of the 266 cm^-1 and 720 cm^-1 modes, indicate a reduction in tetragonality in BTC4 ceramics^[27,28]. Moreover, the activation of A_1g mode (832 cm^-1) provides evidence that B-site Ca substitution disrupts octahedral symmetry^[29,30]. Synchrotron radiation powder XRD combined with Rietveld refinement reveals a coexistence of tetragonal (P4mm) and cubic (Pm-3m) phases in BTC4, while BT and BC4T retain a single tetragonal phase [Figure 3C-E and Supplementary Figure 7]. In the inset in Figure 3C, the c/a ratio of BCT ceramics increases with increasing Ca doping content, whereas that of BTC ceramics shows a decreasing trend. This indicates that the tetragonality of BTC ceramics decreases with Ca doping, which is consistent with the XRD and Raman analysis results. PDF analysis further confirms that BTC4 is predominantly composed of the P4mm phase [Supplementary Figure 8], but with a significantly reduced c/a ratio of 1.0046. In contrast, BC4T and BT ceramics exhibit higher c/a ratios of 1.0113 and 1.0107, respectively. This contrast directly demonstrates that B-site Ca substitution enhances electron-phonon coupling, facilitating cubic phase nucleation. The significant decrease in tetragonality of BTC4 directly contributes to the marked reduction in T_c^[1]. The dielectric nonlinearity in BT-based ceramics originates from the constrained anharmonic interaction of Ti⁴⁺, as well as the limited ferroelectric domain switching and domain wall motion^[12,15]. The reduced c/a ratio and partial cubic phase presence in BTC4 contribute to enhanced DC-bias stability, while the preserved tetragonal phase maintains a high dielectric constant.

Since the atomic-scale Energy-dispersive X-ray spectroscopy (EDS) results [Supplementary Figure 9] could not determine the substitution sites of Ca atoms in the BTC4 sample, XANES, EXAFS, and XPS analyses were conducted to comprehensively clarify the local structure. As shown in Figure 4A, the Ca K-edge absorption edge in BTC4 shifts to lower energy with a decrease in white line intensity compared to BC4T. This indicates that B-site Ca substitution induces hybridization between Ca 3d and O 2p orbitals via the pseudo-Jahn-Teller effect (PJTE)^[31,32], as white line intensity typically correlates with the density of unoccupied states. In Figure 4B, the Ca 2p orbital in BTC4 shifts toward lower binding energy, confirming partial electron transfer from O 2p to Ca 3d. In Figure 4C, the EXAFS spectrum of BC4T exhibits features similar to those of BT, with the first three peaks corresponding to Ca-O (~1.9 Å), Ca-Ti (~2.8 Å), and Ca-Ba (~3.6 Å) bonds. In contrast, BTC4 ceramic shows three split peaks of the Ca-O bond, indicating that Ca not only replaces the B-site but also undergoes displacement along the [001] direction. The PJTE effect typically leads to displacements along the [111]^[31,32], but Coulomb interactions caused by oxygen vacancies dominate and surpass the PJTE effect, resulting in Ca displacement along the [001] in BTC4 ceramic. This local structural distortion explains the presence of the P4mm phase in BTC4. It is well known that the ferroelectric phase of BT originates from the correlated alignment of local polar Ti displacements^[33]. The presence of B-site Ca substitution and oxygen vacancies disrupts the -Ti-O-Ti- chain, weakening local Ti displacement correlations and promoting pseudo-cubic phase formation^[8]. In Figure 4D, the Ba-Ba bond length increases while the Ba-Ti bond length decreases as the Ca doping content increases in BTC ceramics. This trend is attributed to the substitution of Ca for Ti, which leads to an increase in the lattice parameter a and a decrease in c. Furthermore, the reduction in both Ba-O and Ba-Ba bonds with increasing Ca content is consistent with the decreased unit cell volume caused by the substitution of Ca for Ba in BCT ceramics [Figure 4E]^[4]. These observations align well with the fitted lattice parameters presented in Supplementary Table 1, supporting the structural evolution induced by Ca doping.

Figure 4. (A) XANES spectra of the Ca K-edge in BC4T and BTC4 ceramics; (B) XPS spectra of Ca 2p in BC4T and BTC4 ceramics, which were obtained by subtracting the XPS intensity of BT from those of BC4T and BTC4, respectively; (C) Fourier transform (FT) of k-space EXAFS spectra for Ba in BT ceramic, and Ca in BC4T and BTC4 ceramics; FT of k-space EXAFS spectra for the Ba element in (D) BTC ceramics and (E) BCT ceramics. XANES: X-ray absorption near-edge structure; XPS: X-ray photoelectron spectroscopy; BT: BaTiO₃; EXAFS: extended X-ray absorption fine structure; BTC: BaTi_100-xCa_xO₃; BCT: Ba_100-xCa_xTiO₃.

TEM analysis was performed to investigate the polar structure of BTC4 ceramics. As shown in Figure 5A, no obvious macro-domains are observed, but an incommensurate superlattice is detected by the diffraction pattern and the local strain field images shown in Figure 5B and C, likely induced by regular local lattice distortions associated with Ca substitution^[34]. HADDF-STEM was acquired along the [001] zone axis, and the results revealed the presence of PNRs in BTC4. The regions in Figure 5D where polarization vectors are aligned along the {001} crystal plane family exhibit tetragonal symmetry. The relatively high polarization intensity in these regions, as shown in Figure 5E, further confirms the presence of a locally tetragonal structure. In contrast, areas with minimal polarization displacement can be attributed to a pseudo-cubic phase. The substitution of Ti by Ca disrupts the long-range order of Ti displacements, preventing the formation of ferroelectric domains and instead leading to the development of PNRs. Grain refinement also benefits the production of PNRs, ensuring the high dielectric constant in BTC4 [Supplementary Figure 10]. PNRs exhibit short-range order with random orientations, resulting in a weak polarization response under an electric field, which contributes to excellent DC-bias stability in BTC4. The c/a ratio mapping [Figure 5F] further reveals that highly polarized PNRs are not isolated but embedded and interconnected within the non-polar matrix. The bridging between PNRs can facilitate polarization rotation and reduce domain-switching barriers, which leads to low hysteresis loss, slim P-E loops in BTC4^[35-37]. As a result, BTC4 ceramic is allowed to achieve both a superior dielectric constant and enhanced DC-bias stability simultaneously. This diffuse polar structure accounts for the broadened dielectric peak observed in BTC4. This observation aligns with the coexistence of tetragonal and cubic phases and provides further insight into their microscopic configurations in BTC4.

Figure 5. (A) TEM image of BTC4 ceramic; (B) Enlarged view of (A), with the inset showing the corresponding diffraction pattern; (C) Localized strain field images of (B) calculated by the Geometric phase analysis (GPA) method. The two-dimensional strain field is characterized by normal strain components e_xx and e_yy, which describe lattice elongation or compression along the X and Y directions, respectively. The shear strain component e_xy represents in-plane lattice distortion due to shear deformation, while the rotation component R_xy quantifies local rigid-body lattice rotation. High-angle annular dark-field scanning transmission electron microscopy (HADDF-STEM) images of BTC4 ceramics; (D) the polarization vector, (E) the polarization strength of the B site, and (F) the c/a ratio. Polarization vectors were defined as the displacement between the B-site cations and the center of the four nearest neighboring A-site cations, with polarization strength corresponding to the absolute magnitude of these vectors. TEM: Transmission electron microscope; BTC: BaTi_100-xCa_xO₃.

The enhanced insulation in BTC4 ceramic

The high impedance, high activation energy, high breakdown strength, and extended lifetime [Supplementary Figure 11] of BTC4 ceramics underscore its reliability as a dielectric material. The underlying mechanisms driving these enhanced electrical properties require further investigation. Carriers and their migration behavior play a critical role in determining electrical performance. The defect reaction equations for Ca substituting at the Ba site and Ti site are as follows:

While Ca substitution at the Ba site is isovalent, Ca substituting for the Ti atom is aliovalent, leading to the formation of oxygen vacancies to preserve charge neutrality. This is corroborated by XPS analysis, which reveals a higher oxygen vacancy concentration in BTC4 ceramics [Supplementary Figure 12]. However, the higher activation energy [Supplementary Figure 3] and the mismatch between Z” and M” [Supplementary Figure 4] suggest that oxygen vacancies are localized. The EPR spectroscopy was employed to probe the defect structures. Figure 6A shows that all the BT, BC4T, and BTC4 ceramics exhibit a distinct EPR signal near g = 2.004, which is assigned to titanium vacancies (V_Ti) with unpaired electron spin (e.g., $$ V_{T i}^{\prime} $$ and $$ V_{T i}^{\prime \prime \prime} $$)^[38]. Compared to BT and BC4T ceramics, the intensity and symmetry of this signal are significantly reduced in BTC4, due to the lower concentration of V_Ti caused by Ca substitution at the Ti site and the reduction in orbital degeneracy resulting from octahedral distortion. The g-value of the titanium vacancy signal of BTC4 ceramic decreases slightly as the temperature increases, which can be linked to the enhancement of crystal field symmetry as the temperature rises [Figure 6B]^[39]. Since cation vacancies ($$ C a_{T i}^{\prime \prime} $$ and $$ V_{T i}^{\prime \prime \prime \prime} $$) remain immobile and oxygen vacancies are randomly distributed in the bulk material, the latter can be trapped by cation vacancies^[9,40,41], as illustrated in Figure 6C. The formation of $$ C a_{T i}^{\prime \prime}-V_{o}^{..} $$ and $$ V_{o}^{..}-V_{T i}^{\prime \prime \prime \prime}-V_{o}^{..} $$ result in the localization of oxygen vacancies. This mechanism accounts for the two distinct sets of current peaks observed in the I-E curves in BTC4 [Figure 2F]^[26,42], further supporting the role of defect dipoles in stabilizing oxygen vacancies and enhancing the dielectric stability of BTC4 ceramic.

Figure 6. EPR spectra of (A) BT, BC4T, and BTC4 ceramics measured at 100 K, and (B) BTC4 ceramic measured at different temperatures; (C)The model of trapping effect by $$ C a_{T i}^{\prime \prime} $$ and $$ V_{T i}^{\prime \prime \prime \prime} $$. EPR: electron paramagnetic resonance.

The non-reducibility in BTC4 ceramic

Non-reducibility is a crucial property of dielectric materials for MLCCs. Experimental results show that the BTC4 ceramics sintered in N₂/H₂ atmosphere (N₂-BTC4) exhibit outstanding resistance to reduction. As shown in Figure 7A, the temperature-dependent dielectric properties of N₂-BTC4 closely resemble those of BTC4, with the T_c shifting to approximately 50 °C and no significant dielectric loss peak. Notably, N₂-BTC4 exhibits an impedance several orders of magnitude higher than that of N₂-BT and N₂-BC4T ceramics, indicating its superior insulation performance [Supplementary Figure 13]. Although N₂-BTC4 theoretically has a higher oxygen vacancy concentration than BTC4, its calculated activation energy (1.27 eV) is higher than that of BTC4 [Figure 7B]. This suggests that oxygen vacancies are more strongly localized in N₂-BTC4, likely forming a greater number of $$ C a_{T i}^{\prime \prime}-V_{o}^{..} $$ and $$ V_{o}^{..}-V_{T i}^{\prime \prime \prime \prime}-V_{o}^{..} $$ defect dipoles, which contribute to the enhanced electrical insulation of the sample under reducing conditions. The strong pinning effect induced by these defect dipoles also leads to a higher coercive field (5 kV/cm, Figure 7C). Under the applied bias field, reorientation of the defect dipoles can occur, resulting in a temporary increase in dielectric constant and a more pronounced increase in α. Additionally, the absolute value of α of N₂-BTC4 (28% at 30 kV/cm) is higher than that of BTC4. This behavior is attributed to the higher concentration of defect dipoles in N₂-BTC4, which may facilitate the formation of PNRs. These defect dipoles generate an internal electric field that opposes the applied bias. Upon removal of the external field, this internal field facilitates the recovery of the initial PNR configuration. Such a reversible switching process provides a restoring force under DC bias, thereby reducing the remanent polarization and leading to the characteristic pinched P-E hysteresis loop accompanied by two pairs of well-defined current peaks in the I-E curves^[26,42,43], as shown in Figure 7D. Specifically, the remanent polarization of N₂-BTC4 decreases from 2.3 μC/cm² to 0.6 μC/cm² compared to BTC4. Furthermore, the pinning effect of defect dipoles also leads to a reduction in maximum polarization, from 15.6 μC/cm² (BTC4) to 14.8 μC/cm² (N₂-BTC4). These features are indicative of strong coupling between defect dipoles and PNRs, further substantiating the proposed mechanism.

Figure 7. (A) Temperature dependence of dielectric constant and dielectric loss at 1 kHz for N₂-BTC4 ceramic; (B) Complex impedance spectra of N₂-BTC4 ceramic, with the inset showing the Arrhenius plot of ln(f) versus 1000/T; (C) Dielectric constant and DC-bias stability coefficient as a function of the bias-field for N₂-BTC4 ceramic; (D) P-E hysteresis loops and the corresponding I-E curves measured at 60 kV/cm for N₂-BTC4 ceramic.